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London. Edinburgh Glasgow New York 
Toronto Melbourne Capetown Bombay 
Calcutta Madras 



Reprinted photographically in Great Britain in 1943 
from corrected sheets of the second impression 







‘These times tti«he ancient times, when the world is 
ancient, and not tn^e which we account ancient, ordine 
retrogradOf by a computation backwards from ourselves.’ 

Francis Bacon. 

‘The whole succession of men through the ages should 
be considered as one man, ever living and always learn- 
ing.’ — Pascal. 



This book seeks to present, in simple form, j the development of 
the conception of a rational and interconnected material world. 
It considers, therefore, both physical and biological, but not psy- 
chological, social, or abstract mathematical problems. A natural 
pause is reached with the acceptance, in the nineteenth century, 
of that classical body of scientific doctrine which is the normal 
fomidation of modern scientific discipline. 

/So elementary a work can indicate only a very few out of many 
Knes of thought, especially for the period since the Revival of 
I^eaming. In dealing with these later centuries I have had recourse 
to a type-system. Persons, movements, advances, and inventions 
are selected as illustrative examples. No two writers would make 
the same choice ; mine has been determined largely with an eye 
to continuity in the narrative and, specifically, to the emergence 
of the doctrines of Energy, of Atomism, and of Evolution. 

It is impossible to complete even the simplest account of any 
human activity extending over two and a half millennia without 
a sense of inadequacy. Many reasons make this peculiarly true 
for science. In constructing this book I have felt, in particular, 
the lack of accepted precedents as to method. There are few com- 
prehensive histories of science ; all are comparatively modern, and 
there is no consensus as to the lines on which such a work should 
be constructed. My own attempt is, I am aware, of an experi- 
mental nature. 

I have been occupied upon this little book for far more years 
than the result may justify. Through all this time my wife and 
I have been engaged on complementary tasks and the work of 
each has made that of the other possible. Dr. Douglas McKie has 
been of assistance on many special points and has saved me from 
at least some errors. Moreover, for Chapter VIII, he has written 
most of Section 4 and some part of Section 5. Had he not done 
so the book would have been delayed yet longer. To him I express 
my grateful thanks. 

I would like this volume to go as a greeting to two transatlantic 
colleagues, George Sarton and Henry Sigerist. With the former 
I have been in fraternal relations for half a lifetime ; with the latter 



for a time shorter only because he has had the advantage of having 
been bom later. I owe much to the work and personality of both. 

A word of advice to the reader. The argument is, at times, 
necessarily somewhat intricate and it tends to become more so 
as it proceeds. It can be more easily followed if the pattern of the 
narrative is held clearly in view. This can only be done by con- 
stant reference to the rather elaborate Table of Contents. 

C. S. 

April 1941 


I HAVE been able to make some corrections in this reprint. For 
indicating errors I am especially indebted to Prof. E. N. da C. 
Andrade, Dr. Julian Huxley, Dr. D. McKie, and Dr. F. J. North. 

C. S. 

March 1943 



INTRODUCTION. Nature of the Scientific Process 

1 . What is Science ? ..... i 

2. Origins of the Scientific Tradition , . .2 

I. RISE OF MENTAL COHERENCE. The Foundations (about 600- 
400 B.c.).* Ionia, Magna Graecia, Athens 

1 . Beginnings of Ionian Science and the Eastern School . 6 

2 . The Pythagoreans and the Western School . .17 

3. Fathers of Athenian Science . . . .26 

II. THE GREAT ADVENTURE. Unitary Systems of Thought: 
Athens, 400-300 B.c. 

1. Plato and the Academy . . . . .32 

2. Aristotle . . . . . .39 

3. Peripatetics, Stoics, and Epicureans . . .50 

III. THE FAILURE OF NERVE. Divorce of Science and Philo- 
sophy (300 B.c.-A.D. 200): Alexandria 

1. Early Alexandrian Period (300-200 b.c.) . . . 56 

2. Archimedes. Rise of Mechanics . . . .63 

3. Middle Alexandrian Period (200-0 b.c.) . . , 69 

4. Late Alexandrian Period to a.d. 200 . . .80 

of Practice (50 b.c.-a.d. 400): Imperial Rome 

1. Development of the Roman Attitude to Nature . . 94 

2. Geography and Imperialism . . . .99 

3. Imperial Organization of Medicine, Hygiene, and Public 

Health ...... 105 

4. Roman Mathematical, Physical, and Calendarial Science . iii 

5. Roman Astronomy and Astrology . . .116 

6. The Passage from Pagan to Christian Thought . .121 

V. THE FAILURE OF KNOWLEDGE. The Middle Ages (about a.d. 

400-X400): Theology, Queen of the Sciences 

1. The Dark Age (400-1000) . . . .126 

2. Science in the Orient (750-1200) .... 129 

3. Oriental Penetration of Occident (1000-1300) . . 14 ^ 

4. Scholasticism and Science (1200-1400) . . 

5. Main Personalities of Scholastic Science (Thirteenth 

century) . . . . . *155 



VI. THE REVIVAL OF LEARNING. The Rise of Humanism 

(1250-1600), The Attempted Return to Antiquity 

1. Humanism ...... 162 

2. Recovery of Ancient Scientific Classics . . .167 

3. Scientific Atmosphere of the Early Renaissance . .170 

4. Revival of Direct Study of Nature . . .175 

5. Astronomical Observation and Hypothesis in i6th Century 179 
VII. THE INSURGENT CENTURY (1600-1700). Downfall of 

Aristotle. New Attempts at Synthesis 

1. Doctrine of the Infinite Universe . . .185 

2. Mathematics becomes the Instrument of Physical In- 

vestigation . . . . . .189 

3. Physico-Mathematical Synthesis . . . .195 

4. The Re-Formation of the Heavens . . . 200 

5. Implications of the Galilean Revolution . . .212 

6. Prophets of Science . . . . .221 

7. Character and Conduct of Matter . . . 230 

8. Mechanization of Physiology .... 236 

Enthronement of Determinism (1700-igth Century) 

1. The Newtonian Key to the Mathematics of the Heavens 248 

2. Morphology of the Universe 

(i) Observational Astronomy .... 257 

(ii) Dynamical Astronomy . . . .264 

(iii) Astrophysics ..... 269 

3. The Terrestrial Globe 

(i) Measurement of the Earth . . . .271 

(ii) Cartography . . . . *273 

’.-^iii) Wind and Water . . . . *275 

(iv) Terrestrial Magnetism .... 276 

(v) Early Views of Earth History . . . 278 

(vi) Stratigraphy . . . . .280 

4. Transformations of Matter 

(i) Rise of Quantitative Method . . . .283 

(ii) Intensive Study of Chemical Reaction . .285 

(iii) Gases . . . . . .287 

(iv) The Elements . . . . .288 

(v) Atomism ...... 290 

(vi) Molecular Theory ..... 294 

5. Transformations of Forces 

(i) The Imponderables ..... 297 

(ii) Temperature Measurement .... 298 

(iii) Heat a Mode of Motion .... 299 



(iv) Static Electricity ..... 302 

(v) First Study of Current Electricity . . . 305 

(vi) Electromagnetism ..... 307 

(vii) The Dynamo . . . . .310 

(viii) Undulatory Theory . . . .316 

(ix) Doctrine of Energy .... 323 

6. Multiplicity of Organic Forms 

(i) Early Classificatory Systems . . *327 

(ii) Main Subdivisions of Biological Study . -330 

(iii) N atuYphilosophie ..... 332 

(iv) Correlation of Parts . . . -336 

(v) Biological Exploration .... 339 

(vi) Distribution of Living Things . . .342 

7. Physical Interpretation of the Living Organism 

(i) Beginnings of Modern Physiology . . .347 

(ii) Foundations of Bionomics . . . -350 

(iii) Cell Theory ..... 355 

(iv) Protoplasm. ..... 358 

(v) Physiological Synthesis . . . .361 

(vi) Supremacy of Nervous System . . .364 

(vii) Mind as Condition of Life . . . -369 

8. Evolution 

(i) The Word . . . . . .371 

(ii) Eighteenth-Century Evolutionists . . .374 

(iii) "Transformism* ..... 377 

(iv) 'The Origin of Species .... 379 

(v) Doctrine of Descent of Man . . *383 

(vi) Reception of the Doctrine of Evolution . .384 

ENVOI . . . . . . .388 

INDEX ..... .393 



I, Magdalenian drawings of bison with arrows embedded in the 
heart, from the cavern of Manx on the Ari^ge, S. France 

2. Map of Western Asia Minor ...... 7 

3. Special case of squares on s^es of right-angled triangle . . 9 

4. Thales' method of measuring distance to ship at sea . .10 

5. Egyptian map of gold-mines. New Kingdom . . .11 

6. The World as conceived by Hecataeus, c. 500 b.c. . . 13 

7. The World as known to Herodotus, c. 450 b.c. . . .16 

8. Western Greek Colonies . . . . . *17 

9. Triangular and square numbers . . . . ,20 

10. The Pythagorean presentation of the equation 

(^+y)^ = . . .21 

11. The five Platonic bodies. From F. W. Westaway, The Endless 

Quest (Blackie & Son, Ltd.) . . . . .22 

12. The 'magic pentagram'. ...... 23 

13. Paintings of fish on plates from Magna Graecia of fourth century 

B.c. ......... 24 

14. The vascular system as described by Diogenes of Apollonia about 

400 B.c. ........ 25 

15. The Four Elements and Four Qualities of Empedocles . -25 

16. Lune of Hippocrates of Chios . . . . .30 

17. Types of curve obtained by section of cones by planes . . 38 

18. Aristotle's Ladder of Nature . . . . .41 

19. Generative and excretory systems of a mammal as described by 
Aristotle ........ 

20. The universe of Aristotle as conceived by a medieval writer . 47 

21. Break-up of Alexander's'Empire . . . . *56 

22. Aristarchus measures relative distances of sun and moon from 

earth ........ 59 

23. Screw of Archimedes ....... 64 

24. The three orders of lever ...... 66 

25. Doctrine of limits ....... 68 

26. Circle as special case of ellipse, shown by series of sections 

through a cylinder . . . . . . ‘71 

27. Eratosthenes measures the earth . . . * 72 

28. The world according to Eratosthenes c. 250 b.c. . . . 74 

29. The Sieve of Eratosthenes ...... 75 

30. The astronomical elements ...... 76 

31. To illustrate epicyclic motion . . . . * 78 


List oj Text-Figures 

32. Adonis aestivilis ('Pheasant’s eye’) as represented by Crateuas. 

Juliana Anicia MS. at Vienna . . . *79 

33. Hero’s magic jug . . . . . . .80 

34. Hero’s steam-engine . . . . .80 

35. Hero’s mechanical repertoire . . . . .81 

36. Hero’s 'Dioptra’ for taking angles. From Schone’s Hero Alexan- 

drinus (Teubner, Leipzig) . . . .82 

37. Refraction of ray by atmosphere makes the apparent position of a 

star nearer the zenith than the real position . . .84 

38. A simple form of Astrolabe ...... 85 

39. Measuring Parallax of Moon ...... 86 

40. Ptolemaic world-^system. From F. W. Westaway, op. cit. . 87 

41. Ptolemy’s Map of the World showing his scheme of projection. 

From R. E. Dickinson and O. J. R. Howarth, The Making of 
Geography (Clarendon Press) . . . . .88 

42. The British Isles according to Ptolemy. After the drawing by 

the late Dr. Henry Bradley in Archaeologia, vol. xlviii, pt. 2. 89 

43. Galen's Physiology . . . . . . .91 

44. The world according to Pomponius Mela c. a.d. 50 . . 103 

45. Conventional medieval OT map, as in Isidore of Seville . 104 

46. Map of Western Europe from descriptions of Tacitus. From 

Tacitus, vol. i, translated by W. Peterson (William Heinemann, 

Ltd.) ......... 105 

47. Mechanism of Roman double-action pump . . .110 

48. Essentials of the Roman abacus. . . . . .112 

49. The Groma . . . . . . . .113 

50. Babylonian boundary stone, showing a seated deity, above whose 

head are the heavenly bodies . . . . .118 

51. The recession of Islam in Spain . . . . .145 

52. Italy in the first half of the thirteenth century . . ^ .146 

53 and 54. Roger Bacon’s view of optical action of burning-glass 

and lens ....... 157 

55. Copemican world-system. From F. W. Westaway, op. cit. . 181 

56. Tycho’s world-system. Ibid. . . . . .183 

57. Stevin’s proof of conditions of equilibrium on inclined planes . 190 

58. The circle as special case of the ellipse . . , . . 191 

59. Snell’s law. Rays of light, passing from air into a denser medium, 

are bent toward the vertical to a definite amount . .194 

60. Galileo’s method of tracing path of projectile . . . 199 

61. From Kepler’s Mysterium Cosmographicum (Tubingen 1596), 

illustrating supposed relationships between the five Platonic 
bodies and the number and distances of the planets . . 202 


List of Text-Figures 

62. Planets sweep out equal areas in equal times. From F. W. 

Westaway, op. cit. ....... 205 

63. The Moon as seen by Galileo in 1609 .... 207 

64. Galileo’s thermometer ...... 232 

65. Diagram to illustrate Harvey’s theory of the circulation of the 

blood ......... 238 

66. To illustrate bodily action as mechanism. Modified from Borelli 240 

67. Spermatozoa as seen in the seventeenth century . . *244 

68. Illustrating orbit of moon as compounded of tangential and 

centripetal movements . . . . . *253 

69. Parabola and elongated ellipse become indistinguishable from 

each other as they approach their common focus . .261 

70. Path of Halley’s Comet ...... 262 

71. Precession and nutation ...... 263 

72. Section of the universe according to Herschel’s lens-theory. 

From Hutchinson’s Splendour of the Heavens . . .264 

73. Illustrating the path of a point moving in a varying ellipse . 265 

74. Diagram of Watt’s model illustrating condensing principle for 

steam-engine, 1765 ...... 300 

75. Coulomb’s torsion balance ...... 304 

76. Galvani’s experiments on effects of metallic contacts on nerves 

and muscles of frogs’ legs, 1765. From A. Galvani, On Electric 
Forces, 1792 . . . . < . . . . 305 

77. Volta’s Pile and Crown of Cups. From his article On the 

Electricity excited by the mere Contact of Substances of different 
kinds, 1800 ........ 306 

78. Oersted’s experiment on the effect of an electric current on a 

magnetic needle ....... 308 

79. Arago’s experiment of rotating a copper disk below a magnetic 

needle ........ 309 

80. The simplest form of galvanometer or apparatus for measuring 

electric current ....... 309 

81. Faraday’s apparatus for demonstrating how an electric current 

can be disposed so as to produce a continuous rotational 
movement ........ 310 

82. Faraday’s ring . . . . . . .311 

83. Production of momentary electric current by magnetic ’make’ 

and ‘break’ ........ 312 

84. Lines of force due to current in a straight conductor . • 313 

85. Field due to currents in the same direction . . *314 

86. Field due to currents in the opposite direction . . *314 

87. Huygens’s conception of ‘ wave-fronts ’ . . . -317 

88. Explanation of refraction in terms of wave theory . • 3^^ 


List of Text-Figures 

89. To illustrate the principle of interference . 

90. To illustrate bending of light 

91. Polarization of light .... 

92. Fresnel’s interference experiment . 

93* Illustrating interference in light waves 
94. Zoogeographical regions 









Nature of the Scientific Process 
I. What is Science? 

* What is meant by science ? * is the question that will naturally be 
asked on opening this book. Yet this question, if answered at all, 
can hardly be answered at the outset. In a sense the book is itself 
an answer. 

Science is often conceived as a lody of knowledge. Reflection, 
however, will lead to the conclusion that this cannot be its true 
nature. History has repeatedly shown that a body of scientific 
knowledge that ceases to develop soon ceases to be science at all. 
The science of one age has often become the nonsense of the next. 
Consider, for example, astrology ; or, again, the idea that certain 
numbers are lucky or unlucky. With their history unknown, who 
would see in these superstitions the remnants of far-reaching 
scientific doctrines that once attracted clear-thinking minds seek- 
ing rational explanations of the working of the world? Yet such, 
in fact, is their origin. So, too, we smile at the explanation of 
fossils as the early and clumsier attempts of an All-powerful 
Creator to produce the more perfect beings that we know ourselves 
to be. Yet such conceptions were legitimate stages in the develop- 
ment of modem geological theory, just as the scientific views of our 
own time are but stages in an agelong process that is leading to 
wider and more comprehensive conceptions of the nature of our 

It therefore behoves the historian of science to be very chari- 
table, very forbearing, very humble, in his judgements and pre- 
sentations of those who have gone before him. He needs to 
remember that he is dealing with the work of erring and imperfect 
human beings, each of whom had, like himself, at best but a 
partial view of truth, but many of whom had a sweep of genius 
far beyond his own. 

There is an unquenchable and irresistible thirst of the soul that 
demands an explanation of the world in which it finds itself. One 
expression of that eternal yearning is the formulation of religious 





systems. Akin to such aspiration is that of the historian, who also 
seeks law and order in the universe. History, like science, like 
religion, is a constant search for such law, which yet always just 
eludes the grasp. And if the historian hopes to be judged at all 
by posterity, he can but echo the epitaph: 

Reader, thou that passest by. 

As thou art so once was I ; 

As I am so shalt thou be ; 

Wherefore, reader, pray for me. 

Time, still, like an ever-rolling stream, bears all its sons away. It 
is the stream itself and the spirit that dwells therein that we shall 
seek to study. 

Science, then, is no static body of knowledge but rather an active 
process that can be followed through the ages. The sheer validity 
and success of the process in our' own age has given rise to a good 
deal of misunderstanding of its nature and not a little misapplica- 
tion of such terms as 'science* and 'scientific*. We hear of the 
scientific methods of some prize-fighter, and a book has been 
published on the Science of the Sacraments. There is nothing in 
the laws of this or any other country which forbids its citizens 
from giving to the words of their language such significance as they 
may choose, but science and scientific as employed in these con- 
nexions have no relation to the great progressive acquisition of 
knowledge with which we have here to deal. The very form of the 
adjective 'scientific* might give pause to those who would force 
the word to cover such topics as the skill of the boxer, or a know- 
ledge of the theory and practice of the sacraments. By derivation 
scientific means knowledge making, and no body of doctrine which 
is not growing, which is not actually being made, can long retain 
the attributes of science. 

2. Origins of the Scientific Tradition, 

Science, then, is a process. But when did the process begin ? It 
is as hard to answer this as to answer the question, When does a 
man begin to grow old? 'Before that I to be begun, I did begin 
to be undone. * Anthropologists perceive germs of the scientific 
process in the rudest races of mankind. When a child fitst begins 
to observe, he marks the differences of dress and manner in those 


Nature oj the Scientijic Process 

about him. The savage sees the action of living beings in the sway 
of the trees or the stir of the waters. Both generalize from imper- 
fect experience. The baby calls every woman ‘ mummy ’ and every 
man ‘daddy’. Both make imperfect attempts to deduce general 
rules or laws. The attempts of both, in their kind and in their 
degree, partake of the nature of science. 

Man of the Old Stone Age lived on the flesh of the creatures he 
could slay. His dependence on the chase led him to observe the 
habits and the forms of the animals that he hunted. The magic in 
which he believed suggested to him that the mere representation 

Fig. I. Magdalenian drawings of bison with arrows embedded in the 
heart, from the cavern of Manx on the Ari^ge, S. France. 

of these animals, in the act of being slain, might result in their 
falling within his power (Fig. i). The accuracy and beauty of his 
paintings rouse the wonder and admiration of those who explore 
his caves. The exactness of the observations of the palaeolithic 
artist and the care exerted in the representation of the form, 
movements, and even the anatomy of animals certainly betray 
elements akin to the scientific process. 

When man attained the agricultural stage, he felt the need of 
some means of fixing the time of onset of the seasons. In the 
tropics, where man first became human, the days do not lengthen 
and shorten with the change in relation of earth and sun. There 
the most natural and obvious means of calculating time is by 
changes of the moon. Her recurring appearances are still recalled 
in our calendars. Our months are but mooneths altered to fit our 
newer reckoning of time. Our weeks are but quarters of the 28-day 
cycle of the moon and recall her changes (‘ week compare German 



As man spread beyond the seasonless tropical forest he came to 
inhabit regions where agriculture arose. There was now need for a 
calendar that should tell him when to sow and when to reap. The 
movements of the stars were found to bear a fixed relation to that 
of the sun and therefore of the seasons. Observations of a very 
early date that bear on their relationship have come down to us 
from the civilization that developed in the valley of the Euphrates 
and Tigris. Thus the demands of agriculture, the first occupation, 
after hunting, for which man became organized, led to the accumu- 
lation of knowledge and to processes of generalization. These, 
on their level, are certainly scientific. 

A settled agricultural civilization demands tools. Technology 
developed. The age of stone passed into the age of metals. The 
treatment of ores and the working of metals called for a class with 
special knowledge. The development of rights in land demanded 
some sort of surveying. Greek tradition has it that the inundation 
of the Nile, by obliterating all landmarks, forced on the Egyptians 
an annual remeasurement of their fields. Thus geo-metry (literally 
earth-measurement) was born. The craft of the butcher, as well as 
the practice of sacrifice and the examination of the entrails of the 
victims for purposes of divination, led to some knowledge of the 
structure of the body. In these processes we may see the practical 
sources of sciences that we now call metallurgy, mathematics, 

As society became more complex, commerce developed. A 
system of numerical notation was now evolved. The ancient world 
presents us numerous such instances of invention fathered by 
necessity and mothered by experience. All have a like dnim to be 
included in a history of science. Ultimately a work will be written 
which will include them all. 

The older civilizations, which advanced thus far along scientific 
lines, all developed cultural and religious bonds which united 
their members into tribal and ultimately into imperial units. 
Looking back on the past and viewing it from the vantage point 
of our own civilization, we are struck with the failure of these 
ancient cultures to stress human individuality. In the earlier 
Biblical record the punishment or reward of a people for the short- 
comings or virtues of a single member passes without remark. 


Nature of the Scientific Process 

Of none of the great primary discoveries which made social life 
possible has the name of the discoverer come down to us. The 
inventors and the successive improvers of the means by which 
fire can be made, of pottery, of the wheel, of the cutting-edge, of 
the bow, of the metals and their preparation, advanced mankind 
along the path which led to science. Yet their names, their dates, 
even their tribal affinities are utterly lost. So with the early 
thinkers. While we have ample record of the religious and ethical 
outlook of the peoples of the ancient world, we have none of that 
peculiarly individual product of the human intellect that in its 
later development we call philosophy, a product of which science is 
a part. We have no knowledge of those who first set out on the 
prime task of the philosopher, the individual endeavour to under- 
stand and to explain himself and his world. Even when prophet 
or priest seeks to deliver a message, he is always insistent that it 
is not his but another’s ; and not seldom that other is beyond our 
ken, for he is the Dweller above the Firmament. 

Thus it happens that while we may discern science in these more 
ancient civilizations, no one has yet been able to give a continuous 
account of the development among them of scientific ideas ; still 
less has it been possible to show how science influenced the modes 
of thinking of the ancient peoples. For a clearer view we must 
turn to another and later culture. In our survey of the history of 
science we therefore disregard the broken lights that are all that 
can be distinguished of the scientific elements in the once brilliant 
civilizations of the Empires of the ancient East. We open with 
the Greeks. It is not that the first men of science were Greeks — 
for they were not. But it is true that the first men of whom we 
have a record, who were conscious of science as a distinct process 
and who were conscious, too, that the process might be indefinitely 
extended, spoke a dialect of Greek and numbered themselves 
aniong the Hellenes. 


Fig. 2. Western Asia Minor. 


The Foundations {about 600-400 B.C.): Ionia, Magna 
Graecia, Athens 

I. Beginnings of Ionian Science and the Eastern School, 

In writing history it is commonly necessary to rely upon written 
documents. Without such records, the narrative is always im- 
perfect and often incoherent. The earliest scientific documents 
that we possess that are in any degree complete are in the Greek 
language. They were composed about 500 b.c. Our story starts 
about a century before that date. 

It is certain that Greek science in its origin was dependent on 
traditions that came from more ancient civilizations, notably from 
Egypt and Mesopotamia. On this the Greeks themselves insisted. 
They have been confirmed by modern discoveries. Documents of 
Egyptian and Mesopotamian origin have been brought to light 
which take back the scientific disciplines of medicine and mathe- 
matics at least a thousand years behind the earliest Greek records 
of these studies. 

The Greeks were themselves immigrants. They first invaded the 
eastern shores of the Mediterranean as a mixed host about 1400 b.c. 
The main impact of invasion fell on continental Greece. Tribal 
streams passed also eastward to the sea coasts and islands of 
Asia Minor and westward to Sicily and Southern Italy. Chief 
among the Asiatic Greeks were the lonians, who colonized the 
shores of the Aegean from Ephesus in the north to Halicarnassus 
in the south. Yet farther south settled the Dorians (Fig. 2). South 
Italy and Sicily were colonized secondarily both from Greece and 
Asia Minor (Fig. 8). It was among the lonians that the first great 
scientific movement arose. Dorian elements, however, crept into 
it at an early date. 

The lonians were very favourably placed for the reception of 
foreign ideas. Eastward they were in relations with the ancient 
Mesopotamian culture. This was invaded in the sixth century by 
a people from yet farther East, the Persians, who left a permanent 
mark on all contemporary civilizations. Their influence is to be 
discerned in the New Testament where we read of the Magi 


Rise oj Mental Coherence 

[Authorized Version 'wise men', Matthew ii. i), a Persian word 
that has given us our term magic. Persia was the most vigorous 
power of the age and brought new contacts to the lonians. 
Further, the lonians were a maritime and trading people. Through 
their regular sea.traffic suggestions came to them from Egypt, the 
most ancient and settled of all civilizations. lonians traded, too, 
with Phoenicia and reached as far as India whence some of their 
ideas were derived. 

It was,* in general, a time of travel, of movement, of the break- 
down of old and of the rise of new civilizations. Such was the stage, 
such the atmosphere of change in which science became first 
clearly distinguished. We see science emerging into the light of 
historic day in the person of the Ionian Greek Thales. 

Though the son of a Phoenician mother, thales [c. 624-565 b.c.) 
was a citizen of the Ionian city of Miletus. Tradition tells that he 
was a man of great sagacity, exhibited no less in politics and 
commerce than in science. He suggested a federal system for the 
cities of Ionia and made a fortune as a merchant. 

In the course of his business Thales visited Mesopotamia and 
Egypt. In the former country he learned of the ' Saronic cycle ', 
that is to say the interval of eighteen years and eleven days, a 
multiple of which the observations of ages by temple star-gazers 
had shown to be usual between eclipses of the sun.* Knowledge 
of this enabled the shrewd traveller to make a lucky forecast of 
the eclipse visible at Miletus in 585 b.c. His prediction drew much 
attention. It may well be that the impression thus created directed 
the attention of the Greeks to the advantages that might accrue 
from systematic observation of nature. At any rate, they always 
reputed Thales to be the father of that study. 

Further achievements of Thales were chiefly of a geometrical 
nature. Now it is important here to recall that the Greeks did not 
invent geometry. They could and did gather some knowledge of the 
subject from their neighbours in the Nile Valley. The Egyptians, 
however, had hardly reached beyond an empirical usage of certain 

* Saros from a Babylonian word savu (Greek saros) for the number 3,600, 
i.e. (60)* and hence for a period of 3,600 years. The application of the word 
to the cycle of 223 lunations (18 years ii days) is a modern misunderstand- 
ing. The word is, however, now firmly fixed in scientific nomenclature. 


The Foundations: Ionia, Magna Graecia, Athens 

special relations of figures, and especially of triangles and rect- 
angles, of pyramids and spheres. Thus, for instance, the Egyptians 
knew that the square on the longest side of a right-angled triangle 
is equal to the sum of the squares on the other two sides ; but they 
knew it only for such special cases as that in which the sides are 
in the ratio 3 , 4 , and 5 ; thus 5X5 = 3X3+4X4 (Fig. 3 ) • Again, 

Fig. 3. Special case of squares on sides of right-angled triangle. 

they could estimate the cubic contents of a pyramid, but only of 
a pyramid of a certain definite type with a certain definite number 
of sides sloped at a certain definite angle.* Thales succeeded in 
generalizing such special cases. He thus discovered that the angles 
at the base of an isosceles triangle are equal; that when two 
straight lines cut one another the opposite angles are equal ; that 
the angle on the circumference of a circle subtended by the dia- 
meter is always a right angle; that the sum of the angles of a 
triangle is equal to two right angles ; that the sides of triangles 
with equal angles are proportional. 

* The question as to how far the Egyptians generalized mathematical 
conceptions is still under discussion. 


Rise of Mental Coherence 

Thales, moreover, succeeded in applying such knowledge. He 
was able, for example, by a simple application of the principle of 
similar triangles, to determine the distance from the shore to a 
ship at sea (Fig. 4), and to measure the height of a pyramid by 
comparing the length of its shadow with that cast by an object 
of known height. Such problems had been tackled before his 
time. But Thales not only sought to enunciate them clearly and 
to solve them demonstrably but also to widen and generalize them 
so as to lay bare their essential nature. 

Fig. 4. Thales measures distance to ship at sea. Triangle EHP similar 
to triangle EBS. Therefore EH is to HP as EB is to J5S. Since EH, HP, 
and EB are all measurable BS can be calculated. 

As with every Ionian thinker, the ultimate object of the 
thought of Thales was to find a formula for all things. He thus 
set himself th'e task of discerning constancy amidst the diversity 
and variety of nature. This is but to say that his science was a 
part of his philosophy. To the general question ‘ Of what is the 
world made?' he would answer ‘Water', meaning thereby some 
mobile essence, changing, flowing, without distinctive shape or 
colour, yet presenting a cycle of existence passing from sky and 
air to earth, thence to the bodies of plants and animals, and back 
to air and sky again. But his real place in the history of science is 
better brought out by the more concrete statement that in his 
mathematical work we have the first enunciation, as distinct from 
implicit acceptance, of natural laws. 


The Foundations: lonia^ Magna Graecia, Athens 

Following on Thales, a long line of Asiatic Greeks, mostly of 
Miletus, contributed to the extension of the conception of natural 
law. Thus ANAXIMANDER (611-547 B.C.), a Miletan pupil of Thales, 
took much interest in geography. He was the first among the 
Greeks to represent the details of the surface of the earth by maps. 
The idea of map-making was known in Egypt, where plans of 

Fig. 5. Egyptian map of gold mines. New Kingdom. 

particular districts or objects as mines, houses, and temples were 
being drawn up as early as 1400 B.c. (Fig. 5). Anaximander, 
however, sought to convey a concrete picture of the surface of the 
earth as a whole. The suggestion doubtless came from Meso- 
potamia, where simple diagrams of this sort were being made in 
his time. From Babylon also he introduced the sun-dial. It 
consisted in essence of a gnomon, a fixed upright rod, the direc- 
tion and length of the shadow of which can be measured hour by 
hour. The records of these make it possible to determine the move- 
ments of the sun as well as the dates of the two solstices (the shortest 


Rise of Mental Coherence 

and longest days) and of the equinoxes (the two annual occasions 
when day and night are equal). Anaximander was thus led to deve- 
lop his own astronomical conceptions. He was the first to speculate 
on the size and distance of the heavenly bodies. The earth was for 
him a fiat disk in the centre of all things. Sun, moon, and stars 
are enclosed in opaque rings, rotating with the earth as centre. We 
see them only through vents in these rings. 

ANAXIMENES (bom c, 570 B.C.), another Miletan, extended 
Anaximander’s ideas, especially in astronomy. 

The ultimate essence of all things he regarded as ‘air’ rather 
than the ‘water’ of Thales. This air was linked up with that 
essence which is essential to life. He called it pneuma — literally 
breath — and held that in a sense the universe itself was alive : ‘As 
our soul, being air, sustains us, so pneuma and air pervade the 
whole World'. 

At about the same date cleostratus of Tenedos, who lived 
rather outside the Ionian zone, made two important contributions 
to astronomy. One was an improvement in the calendar, involving 
a better measure of the solar year. The other was the knowledge 
of the signs of the zodiac which he introduced from Mesopotamia. 
Zodiacal signs are frequently encountered upon Mesopotamian 
boundary stones and indicate the time of year at which the stones 
were erected (Fig. 50). 

Among the Greeks of Asia Minor towards the end of the sixth 
century b.c. there was not only considerable speculative activity, 
but also the sum of positive knowledge was being systematically 
increased. The process was encouraged by the roving character 
of the Asiatic Greeks. Active and daring seamen, they brought 
back to their homes accounts of many of their adventures by 
land and sea. 

Of these early explorers, the most distinguished was hecataeus, 
also of Miletus (bom c. 540 b.c.). He visited Egypt, the provinces 
of the Persian Empire, Thrace and Lydia. He penetrated the 
Dardanelles and explored the coasts of the Black Sea. About 
500 B.c. he adventured westward to the Gulf of Genoa and as far 
as Spain, reaching Gibraltar. There he had been preceded by the 
Phoenicians, who set up to their god Melkarth a great column on 


The Foundations: lonia^ Magna Graecia^ Athens 

either side of the Strait. Later writers identified Melkarth with 
Hercules, and the gateway of the Mediterranean came to be called 
the Tillars of Hercules*. Hecataeus collected his experiences into 
a geographical handbook (Fig. 6). He is memorable for that 

Fig. 6. The World as conceived by Hecataeus, c. 500 b.c. 

scepticism of the marvellous which is a hall-mark of the man of 
science and a condition for scientific progress. He detested 
mythology. ‘The stories of the Greeks*, says Hecataeus, ‘are in 
my opinion no less absurd than numerous.* 

About the turn of the sixth into the fifth century, the character 
of Ionian thought was modified by closer contact with Persia. 
That power, under its great Emperor Darius I (522-486 B.c.), was 
^advancing steadily westward. The weak and quarrelsome little 


Rise of Mental Coherence 

Asiatic Greek States were coming under its shadow. The Persian 
service attracted many of their citizens, who brought back to their 
native homes further knowledge of the world. Among the more 
typical of these venturers was the physician democedes of 
Cnidus (born c, 540 b.c.). The peninsula of Cnidus was the seat of 
the most ancient medical school of which we have any record. 

After travelling widely in Greek lands, Democedes became the 
medical attendant of the Persian monarch. Later he was employed 
as a spy to explore the coasts of Greece. He escaped from this 
service, however, and settled in the Greek colony of Croton, in the 
instep of Italy. Here he devoted himself to writing a treatise on 
medicine, the first Greek work on that subject of which we have 
tidings. Croton became an important scientific centre. 

Thus, as time wore on, Ionian thinkers came more closely into 
contact with other civilizations. Their work becomes increasingly 
sophisticated. Philosophy is no longer the product of the leisure 
hours of business men, of sailors, or of physicians. Thinking has 
become a profession. 

Amongst the great lonians who concerned themselves ex- 
clusively with philosophy was heracleitus of Ephesus (c, 540-475 
B.C.). He is specially remembered for his view that ‘every- 
thing is in a state of flux*. Change is the only reality. ‘ There *s 
nothing is and nothing was, but everything’s becoming.’ Fire, 
the most changeful of elements, is the origin and image of all things. 
Living creatures are formed of a mixture of the changeful essences 
of which fire and air are types. Nothing is bom and nothing dies. 
The illusions that we call birth and death are but a rearrangement 
of these unresting elements.^ 

Very different from the point of view of Heracleitus was that of 
his younger contemporary, the Miletan Leucippus (flourished 
c, 475 B.C.), founder of the atomic doctrine of matter. That theory 
has had a wide influence in both ancient and modem times. It has 
been associated with the attitude towards the world known some- 
times as ‘philosophic materialism*. 

* The thought of Heracleitus bears a certain resemblance to that 
ascribed to the founder of Buddhism who was his contemporary. Whether 
one derived from the other or both from a common source is a matter which 
future research may decide. 


The Foundations: Ionia, Magna Graecia, Athens 

Leucippus — of whom we know little — is overshadowed by his 
pupil, DEMOCRITUS (c. 47 o~c. 400 B.c.) who was perhaps also of 
Miletus. This Democritus was a contemporary of Socrates 
(470-399 B.c. ; p. 31), though the outlook of the two men is in the 
strongest possible contrast. For Democritus, very different to 
Heracleitus, all things were made up of solid concrete atoms, 
together with the space or void between them. We should note 
that this void has as much claim to be regarded as a primary 
reality as the atoms themselves. The atoms are eternal, invisibly 
small, and cannot be divided. (The word atom means * indivis- 
ible*.) They are incompressible and homogeneous. They differ 
from one another only in form, arrangement, and size, that is to 
say only quantitatively, not qualitatively. The qualities that we 
distinguish in things are produced by movement or rearrangement 
of these atoms. Just as atoms are eternal and uncaused, so also is 
motion, which must, of its nature, originate in preceding motion. 
As everything is made up of these unchangeable and eternal atoms, 
it follows that coming into being and passing away ar^ but a 
seeming, a mere rearrangement of the atoms. The beings that you 
and I think we are, are but temporary aggregations of atoms that 
will soon separate to ehter into the substance of other beings. 
And yet, in ages of time, perhaps, we shall be re-formed, when it 
may so fall out that our atoms come together again. Thus history 
may repeat herself endlessly. 

At first sight the positive teaching of Democritus and the con- 
crete character of his atoms suggest a ‘ common-sense ' philosophy 
that might be set against the Heracleitan vagueness. It must be 
remembered, however, that the atoms of Democritus were in no 
sense the product of experimental investigation. His atoms, like 
their motion and like the void in which they moved, were alike 
hypotheses and based on no sort of exact knowledge or experience. 
His teaching has obvious parallels with more modem scientific 
doctrines concerning the 'indestmctibility of matter* and the 
* conservation of energy *, but the parallels are more apparent than 
real. Despite the positive trend of the thought of Democritus, his 
followers — known as ' Epicureans ' after his most distinguished 
adherent, epicurus of Samos (342-270 b.c.)— showed little ten- 
dency to extend the range of scientific ideas. 


Rise oj Mental Coherence 

Much of the spirit of Ionia is summed up in the life and writings 
of HERODOTUS of Halicamassus {c. 484-425 b.c.). The native 
town of this remarkable man was within the limits of the Persian 
Empire at the time of his birth, and he remained a Persian subject 
till he was well into his thirties. From an early date his inquiring 
spirit led him to travel. He explored Greece and Asia Minor 
thoroughly, visiting many of the islands of the Greek Archipelago. 

He made the long and difficult journey from Sardis in Lydia, near 
the modem Smyrna, to Susa, the Persian capital (Fig. 7). He 
travelled next to Babylon ; then he explored the coast of the Black 
Sea and penetrated into Scythia and Thrace. His journeys were 
extended westward, and he visited Italy and Sicily. Southward 
from his home he passed jnto Syria, sojourned at Tyre, saw some- 
thing of Palestine, and made a long stay in Egypt. Wherever he 
heard of anything Qurious or interesting, he stayed for a while and 
noted what he saw. Finally he joined a Greek colonizing party 
that settled in Italy. He spent the rest of his life preparing his 
delightful History, 

Herodotus does not concern himself with the world as a whole, 
but he gives an excellent idea of the geographical knowledge of his 
day. His careful observations on the nature and habits of different 

The Foundations: lonia^ Magna Graecia^ Athens 

peoples entitle his work to be regarded as the first treatise on 
the science of man. He is thus the father of anthropology, as 
he is also the father of history. Many of his allusions to the 
beliefs and practices of the time help us to check the early records 
of the history of science.^ 

2. The Pythagoreans and the Western School. 

From a very early date Greeks had penetrated westward and 

had established colonies in Southern Italy and Sicily, Magna 
Graecia as the area came to be called (Fig. 8). The intellectual 
activity of these western colonies played an important part in 
the development of Greek science. The most influential of the 
western scientific movements was that of the ' Pythagoreans 

The founder of this school or sect, Pythagoras (bom c. 582 b.c.), 
was by birth an Ionian of Samos. He travelled widely. About 
530 he settled at Croton, where a Dorian colony had been estab- 

* Herodotus is especially responsible for the view that Greek institutions 
were derived from Egypt. 

30IZ Q 

Rise oj Mental Coherence 

lished. There he founded his brotherhood or sect, which persisted 
long after him. He left nothing in writing, and the veil of mystery 
which his followers drew over themselves often prevents us from 
ascribing the scientific advances which they made to their actual 

From the hazy philosophical outlook of the Pythagoreans there 
emerge certain ideas which have exerted a profound influence. 
Foremost is their peculiar teaching on the subject of numbers. 
These were held to have a real and separate existence outside our 
minds. The use by the Greeks, as by the Hebrews, of letters to 
express numbers gave an especial currency to this conception, 
which was capable of, and received, all sorts of mystical and magical 
application. An example will readily come to the mind in con- 
nexion with 666 ' the number of the beast ' in the book of Revela- 
tion (xiii. i8). There was a similar Pythagorean tendency to 
ascribe an objective independence to the divisions of time. Again 
a Biblical illustration is to hand: 

'Job cursed the day. 

Let that day perish wherein I was born. 

Let it not be joined unto the days of the year.* 

{Job iii. 1-6.) 

The word mathematics itself — ^which means simply * learning ' — 
was given its special relationship to numbers by the Pythagoreans.^ 
Aristotle tells us in his Metaphysics that 

'the Pythagoreans devoted themselves to mathematics. They 
thought that its principles were the bases of all things. In numbers 
they saw many resemblances to the things that exist and are coming 
into being — one modification of number being Justice, another 
Reason, another Opportunity — almost all things being numerically 
expressible. Again they regarded the attributes and ratios of the 
musical scale as expressible in number. They therefore regarded 
numbers as the elements of all things, and the whole heaven as a 
musical and numerical scale. The very arrangement of the heavens 
they collected and fitted into their scheme. Thus, as lo was thought 
to be perfect and to comprise in itself the whole nature of numbers, 

X Qrgek mathesis 'learning*, mathetes 'disciple*, so used in New Testa- 
ment, mathematikos ' fond of learning ’, so used by Plato and Aristotle. The 
word mathematics did not enter the English language till the late sixteenth 
century. The curious plural form is an elliptical expression for 'mathe- 
matic sciences ’ and has no foundation in Greek. 


The Foundations: Ionia ^ Magna Graecia^ Athens 

they said that the bodies which move through the heavens were 
ten in number ; but since the visible heavenly bodies are but nine, 
they invented a counter-earth/ (See Philolaus, p. 21.) 

The conception seems very fanciful to us now. Nevertheless 
fancies of this type have been repeatedly of value in the history 
of science. The human mind, it must be supposed, is somehow 
attuned to the processes of nature. We live in a world that is 
susceptible of mathematical expression. Thus the theoretical 
investigations of mathematicians correspond in some degree to the 
findings of the physicists and astronomers. Such is the nature of 
things, though why this should be so is a mystery. Perhaps it is 
not even the business of science to discuss this mystery. But 
consciousness of a correspondence between the workings of our 
minds and the workings of nature is illustrated by this doctrine of 
the Pythagoreans. Their conception of the 'harmony of the 
spheres ' — on which Aristotle touches in the above passage — was 
related to an interest in music. It proceeded from the observation 
that the pitch of musical notes depends on a simple numerical 
ratio in the length of the chords struck. This numerical ratio, it 
was held, corresponded to the distances of the heavenly bodies 
from the centre of the world. 

The beautiful conception of a world bound together in a har- 
mony has captivated the imagination of poets in every age. 
There was a time 

When the morning stars sang together 
And all the sons of God shouted for joy. 

{Job xxxviii. 7.) 

It is the dullness of the ear of flesh, so the Middle Ages would have 
had us believe, that prevents us from hearing still these glorious 
notes. The Christianity, which set off body against spirit, at times 
would claim to catch the heavenly tones ; 

soft stillness and the night 
Become the touches of sweet harmony. 

There 's not the smallest orb which thou behold’st 
But in his motion like an angel sings. 

Still quiring to^the young-eyed cherubins; 

Such harmony is in immortal souls ; 


Rise oj Mental Coherence 

But, whilst this muddy vesture of decay 
Doth grossly close it in, we cannot hear it. 

(Merchant of Venice, Act V, Sc. i, 11. 56-65.) 

The Pythagorean habit of giving character and qualities to 
numbers becomes more intelligible to us if we remember that for 
the Greeks mathematics was, in effect, geometry. Thus, to take 

• •• ••• •••• 

Fig. 9. Triangular and square numbers. 

a prominent example, the Pythagoreans distinguished the series 
1+2, i+ 2 + 3 i 1+2+3+4, I+2+3+4+5 • • • 
as triangular numbers, and they exhibited geometrically the 
interesting fact that the sum of any two consecutive triangular 
numbers is a square number (Fig. 9) . 

The so-called ‘ Pythagorean theorem ’, that is that the square on 
the hypotenuse of a right-angled triangle is equal to the sum of the 
squares on the othertwo sides (Fig. 3), was referred by the ancients 
to Pythagoras himself. The Pythagoreans erected a system of plane 
geometry in which were formulated the principal theorems which 
concern parallels, triangles, quadrilateral and regular polygonal 
figures and angles. They discerned many important properties of 
prime numbers and progressions. In particular they worked out 
a theory of proportion which involved both commensurables and 
incommensurables. This was of great importance as providing 

The Foundations: Ionia , Magna Graecia, Athens 

the link between arithmetic and geometry. They recognized at 
least four types of proportion. Thus: — 

arithmetical proportion a—h — h—c 
geometrical proportion a:b :\h\ c 
harmonic proportion a~b : b—c : \ a \ c 

. , 2ab a+b , 

musical proportion a : r : : — ^ : b 

a-\~b 2 

The most striking mathematical achievement of the Pytha- 
gorean thinkers is perhaps their attainment of a conception of the 
nature of irrational quantities ^ 
such, that is, as are not expressible 
by ordinary nurhbers. With the 
imperfect mathematical notation 
of the time, however, great alge- 
braical advance was impossible, 
and irrational numbers could not 
be algebraically represented (com- 
pare p. 189). Greek mathematics 
was thus forced to preserve its 
geometrical bias. The Greeks, in 
fact, constantly resorted to geo- 
metric methods when we should 
prefer algebraic. A very simple 
example will suffice. The equa- 
tion (x+y)^ = x'^-\- 2 xy-{-y’^v 7 dJS geometrically proved by reference 
to such a figure as the adjoining (Fig. 10). 

Led by their mystical view that the sphere is the perfect figure, 
just as 10 is the perfect number, the Pythagoreans introduced the 
conception that the earth and the heavenly bodies are spheres. 
This important advance is among the many in the history of 
science in which the formation of general ideas on theoretical 
grounds has preceded and not followed practical observation. 

An interesting astronomical hypothesis was put forward by 
the Pythagorean philolaus of Tarentum (c. 480-400 b.c.). He 
abandoned the theory that the Earth is the mid-point of the 
universe, and supposed that it is similar to the other planets in its 
movements, and that all revolve round a central fire. This fire, 
he held, is invisible to us, since the part of the earth which we 

Fig. 10. The Pythagorean 
presentation of the equation 


Rise of Mental Coherence 

inhabit is ever turned away from it. To balance his system he 
invented a counter-earth, bringing his spheres of the movable 
heavenly bodies up to the sacred number lo, that is to say, Sun, 
Moon, Earth, five planets. Counter-earth, and sphere of the stars. 
Philolaus was the first to publish a book on Pythagorean doctrine. 
It was used by Plato in the composition of the Timaeus (p. 34). 
The conception by Philolaus of a moving earth and central fire 
influenced Copernicus (p. 180). 

Another Pythagorean development was destined to influence 
thinkers in after ages in a very curious way. Manipulating equilateral 
triangles and squares in three dimensions, the Pythagoreans dis- 

46 8 12 20 sides 

Fig. II. The five Platonic bodies. 

cerned four 'regular solids', that is figures with all their sides and 
angles equal. These four were the regular 4-sided pyramid [tetra- 
hedron), the 6-sided cube, the 8-sided octahedron, and the 20-sided 
icosahedron. They were taken to represent the four elements of 
the physical world, earth, air, fire, and water. Later was dis- 
covered the geometrical mode of constructing regular pentagons 
or 5-sided plane figures. One of the Pythagoreans found that these 
could be built into a fifth regular solid, the 12-sided dodecahedron. 
In the absence of a fifth element this was taken to represent the 
universe. The five possible regular solids became later known as 
the 'Platonic bodies'. They played a large part in subsequent 
philosophical and mathematical development, much of it very 
fanciful. Kepler's thought about the Platonic bodies in the six- 
teenth century suggested the first modern unitary theory of the 
universe (p. 200-6) (Figs, ii and 61). 

From the regular pentagon it was easy to pass to the 5-pointed 
star or pentagram, formed by an endless line joining alteriiate 
angles of a pentagon. The Pythagoreans used the pentagram as 
a secret sign of recognition. It thus started on its career of 


The Foundations: lonia^ Magna Graecia^ Athens 

mystery, passing into magic and humbug. For Pythagoreans and 
Platonists it expressed completeness, health, well-being. Among 
lesser souls it degenerated into the commonest and most banal 
of charms. No evil could pass it! Faust has a pentagram on the 
threshold of his study which prevents Mephistopheles from leaving 
it. The history of the pentagram provides a type of the degrada- 
tion that science has repeatedly suffered (Fig. 12). 

Fig, 12. The ‘magic pentagram*,, a continuous line or ‘endless knot’ 
formed by producing the sides of a regular pentagon both ways or by joining 
its alternate angles. 

It was not only in cosmical and mathematical speculation that 
the western colonies exhibited their intellectual activity. During 
the fifth century b.c. there developed among the Greeks in Italy 
and Sicily a remarkable naturalistic art. Painters closely observed 
and represented the parts and structures of animals (Fig. 13). 
This naturalistic tendency is reflected by the Italo-Greek scientific 
thinkers. Among them, alcmae 6 n of Croton (c. 500 a pupil 
of Pythagoras, extended the scientific field to living things. He 
began the practice of scientific dissection. He discovered the 
nerves that proceed from the brain to the eyes. He described 
those passages connecting mouth and ear, through which, if the 
nose be pinched and the cheeks blown out, air is driven into the 
ear-drums. These tubes were next investigated by the anatomist 
Eustachi, after whom they are now called Eustachian tubes. 
Eustachi lived in Italy more than twenty-two centuries after 


Rise oj Mental Coherence 

Alcmaeon! Alcmaeon believed that these tubes carried the 
pneuma (see Anaximenes, p. 12). 

An important Western thinker, upon whom Pythagoras had 
influence, was empedocles of Agrigentum in Sicily {c. ^oo-c. 
430 B.C.). He held that the blood is the seat of the mysterious 
innate heat, an idea taken from folk belief that ' the blood is the 
life' {Deuteronomy xii. 23). This innate heat he closely identified 
with the soul. He held the heart to be the centre of the system 
of blood-vessels through which the innate heat, or essential factor 
of life, is distributed to the bodily parts. Thus for the followers of 
Empedocles the heart was the special seat of life. This idea 
passed to Aristotle (p. 44). 

Sargus vulgaris 



Fig. 13. Paintings of fish on plates from Magna Graecia of fourth 
century b.c. They are very exactly drawn and the species can be identifiod. 

The teaching of Empedocles led to curiosity as to the distribu- 
tion of the blood-vessels. Our first coherent account of these is the 
work of DIOGENES of Apollonia in Crete (c. 430 b.c.), who was 
greatly influenced by the thought of Empedocles and his school 

(Fig- ^4). . , ^ 

Empedocles supposed that Love and Strife alternately held 
sway over all things. Everywhere there was opposition and 
affinity. In matter itself the so-called four elements could be dis- 
tinguished as exhibiting these relationships. All matter was held 
by him to be made up of the four essential elements — earth, air, 
fire, and water. These were in opposition or alliance to one another. 


The Foundations: lonia^ Magna Graecia^ Athens 

Thus water was opposed to fire, but allied to earth. Each of the 
elements was, moreover, in its turn compounded of a pair of 

Fig. 14. The vascular system as described by Diogenes of Apollonia 
about 400 B.c. He described a system of vessels penetrating the whole body, 
proceeding from great medial trunks, and he distinguished arteries from 
veins as regards form, function, and distribution. 



Fig. 15. The Four Elements and Four Qualities of Empedocles. 

the four 'primary qualities', heat and cold, moisture and dryness 
(Fig. 15). These qualities exhibit affinity and opposition as do the 

It must not be imagined that such philosophers as Empedocles 


Rise of Mental Coherence 

thought that the 'elements' were the substances that we know by 
the names of earth, water, air, and fire on our earthly sphere. 
Here we find the elements only in combination. Thus the sub- 
stance we know as water contains, according to the theory, a pre- 
ponderance of elemental water, but contains also small amounts of 
the other three elements. The element water forms only the 
essence of water, an essence that we human beings can never 

This doctrine has left its mark on our language. We still speak 
of a storm as 'the raging of the elements'; we wear coats 'to 
protect ourselves from the elements'; and we think of 'elemental 
forces'. We still read the passage in Galatians in which St. Paul 
adjures us not to ' turn again to the weak and beggarly elements ' 
(Galatians iv. 9) ; nor have we difficulty in understanding refer- 
ences to a ' fiery nature ' or to an ' aerial spirit '. These things come 
to us from Empedocles, and they come through Aristotle (p. 48) 
and the Athenian Schooh 

3. Fathers of Athenian Science. 

By the middle of the fifth century B.c. both the Eastern and the 
Western schools of Greek thought were overshadowed by Athens, 
now the intellectual centre of the Greek world. An important 
factor in this concentration was the Ionian anaxagoras (488- 
428 B.c.) of Clazomenae. He came to Athens (464 b.c.) burning 
with scientific zeal, and attracted the attention and friendship 
of the statesman Pericles (490-429 b.c.) and of the poet Euripides 
(480-406 B.C.), both of 'whom he inspired with his own love of 
science. From Socrates (p. 31) he differed profoundly. Much of the 
course of thought in later ages may be traced to this divergence, 
for Plato was the philosophic heir of Socrates while Aristotle took 
much from Anaxagoras. 

Anaxagoras developed an obscure and difficult philosophic 
system which involved rational theories concerning many celestial 
phenomena. He gave scientific accounts of eclipses, meteors, and 
rainbows. The sun was a vast mass of incandescent metal, the 
light of the moon was reflected from it, and other heavenly bodies 
were stones rendered white hot by rotation. Such interpretation 
outraged the religious opinion of the day, and he was prosecuted for 

The "Foundations: lonia^ Magna Graecia^ Athens 

impiety. Defended by Pericles and acquitted, he yet found it 
prudent to withdraw to his native Asia Minor. Thus early began 
the persecution of scientific doctrine opposed to current religion. 

The intellectual conditions in the Athenian metropolis were very 
different from those in the colonies of Ionia and Magna Graecia. 
In Athens the greater complexity of life was making itself felt. 
The systematic accumulation of knowledge was beginning to 
render a little old-fashioned those who ' took all knowledge to be 
their province*. The eloquence of the popular educators known 
as 'sophists* entertained and attracted the volatile Greeks beyond 
anything else. But many of the sophists were little but professional 
talkers, and few or none had any direct acquaintance with scientific 
matters, which were left to another class. Thus something in the 
nature of scientific specialization began to appear. The movement 
affected especially two departments, medicine and mathematics. 
By a curious chance, the two typical exponents of these disciplines 
bore the same name and came from neighbouring and similarly 
named islands. They were the physician, Hippocrates of Cos, and 
the mathematician, Hippocrates of Chios. 

HIPPOCRATES THE PHYSICIAN was bpm about 460 B.c. on the 
island of Cos just inside the Dorian Zone. He came of a family of 
physicians. Both on his own island and on the opposite peninsula 
of Cnidus (p. 7) medical schools had long been established. It was 
their destiny to transform the tradition that had developed there 
into a scientific procedure. The change afterwards became tradi- 
tionally associated with the name of Hippocrates. 

Hippocrates led a wandering life, following his profession in 
Thrace, in the neighbourhood of the sea of Marmora, on the island 
of Thasos, at Athens, and elsewhere. He had many pupils, among 
whom* were his sons and sons-in-law. He is said to have died in his 
hundredth year, an appropriate age for a great physician ! This is 
almost all we know of his personal history. Yet it is impossible to 
exaggerate the influence on medicine of the picture that was early 
formed of him. Learned, observant, humane, with a profound 
reverence for the claims of his patients, but possessed of an over- 
mastering desire that his experience should benefit others ; orderly 
and calm; anxious to record his knowledge for the use of his 
brother physicians*and for the relief of suffering ; grave, thoughtful, 


Rise of Mental Coherence 

and reticent ; pure of mind and master of his passions ; such is the 
image of the father of medicine as it appeared to his successors. 

While the philosophers developed the conception of a rational 
world, it was the physicians, typified by Hippocrates, who first put 
the rational conception to the test of experience. It was they who 
first consciously adopted the scientific procedure which, in its 
relation to medicine, is sometimes called the ‘Hippocratic Method 

The method of the Hippocratic writers is that now known as 
‘inductive'. Without the vast scientific heritage that is ours to- 
day ; with but a small number of recorded observations and those 
from scattered and little organized experiences ; surrounded by all 
manner of bizarre religious cults which recognized no adequate 
relation of cause and effect ; above all, constantly urged by the 
exuberant genius for speculation of their own people whose 
intellectual temptations they shared, the Hippocratic physicians 
remained, nevertheless, patient observers of fact, sceptical of the 
marvellous and the unverifiable, hesitating to theorize beyond the 
facts, yet eager to generalize from actual experience. There are 
few types of mental activity known to us that cannot be paralleled 
among the Greek writings. Careful and repeated return to verifica- 
tion from experience, expressed in a record of actual observations,, 
has been rare at all times in history. It is wonderful that so many 
Greek works have come down to us expressing this attitude. A 
large proportion of these are by Hippocratic authors. 

It is true that the Greeks had scientific forebears (p. 7) . It is 
probable that they borrowed, more frequently than we know, 
from other civilizations. But the ‘Religion of Science' of these 
early physicians, the belief in the constant and universal sequence 
of cause and effect in the material world, was theirs before all 
other men. The first prophet of that religion was Thales. The 
first writings on that religion bear the name of Hippocrates. 
The first great exponent of that religion whose works are still 
substantially intact is Aristotle (p. 39). 

The Hippocratic writings, important for the history of medicine, 
are even more significant for the conception that they contain of the 
nature of science itself. This conception is beautifully expounded 
in a treatise on the falling sickness y or epilepsy. In those days the 
affliction was regarded as a divine visitation, a ‘sacred disease'. 


The Foundations: lonia^ Magna Graecia^ Athens 

A Hippocratic writer composed a book on it, in which he sets forth 
the proper attitude of the scientific man towards such claims. It 
is a monument of the rational spirit, and is perhaps the first book 
in which there is clear opposition between the claims of science 
and of religious tradition. 

In our own time natural events are not always treated, even by 
educated men, in the spirit of the Hippocratic writers. Both leases 
and insurance certificates have still sometimes a clause as to the 
type of accident to which the lawyers refer as an 'act of God'. The 
type of these acts of God has altered in the course of ages. They 
used to include, for instance, infectious disease. Our word ' plague ' 
is from a Latin word meaning a blow or stroke which comes to us 
from the days when the 'plague-stricken' were held to be stricken 
by God himself. The legal term 'act of God' still includes the 
action of tempest and of lightning. Yet the attitude of the 
Hippocratic work called the Sacred Disease, written more than 
400 years before the birth of Christ, is very different : 

'As for this disease called divine, surely it has its nature and 
causes, as have other diseases. It arises — like them — from things 
which enter and quit the body, such as cold, the sun and the 
winds, things ever . changing and never ^t rest. Such things are 
divine or not — as you will, for the distinction matters not — and 
there is no need to make such division anywhere in nature, for all 
are alike divine or all are alike human. All have their antecedent 
causes which can be found by those who seek them.' [Slightly 

We have spoken of the belief in the constant sequence of cause 
and effect as a 'religion' (p. 28), since it was — and perhaps still 
is — essentially a matter of faith. In Hippocratic times there was 
as yet no large body of exact observations by which the operations 
of nature could be exactly forecasted, save only the astronomical 
record. Thus the regularity of the astronomical sequences was, 
by an act of faith, set forth as the type to which all nature should 
accord. The heavenly bodies herald those regularly recurring 
changes of season which determine the lives of men. It is but 
a step to regard them as the causes of those changes and thus to 
treat them as gods. The step was often taken and the planets still 
bear the names of deities. 


Rise of Mental Coherence 

HIPPOCRATES OF CHIOS, the mathematician (c. 430 b.c.), was the 
first to compile a work on the Elements of Geometry. This title 
has made a household word of his successor, Euclid (p. 57). 
Hippocrates of Chios is the first known mathematical 'specialist'. 
He began life as a business man. Chance brought him to 
mathematics. He came on a law-suit to Athens. That city was 
rapidly becoming the centre of learning, and the provincial Hippo- 
crates had now an opportunity to consort with philosophers. His 

real abilities rapidly asserted them- 
selves, and he began to devote 
himself with ardour to mathemati- 
cal pursuits. 

The work of Hippocrates of Chios 
may be illustrated by one of his 
most acute investigations. It gives 
an idea of the standard to which 
mathematics had attained in Greece 
about 400 B.c. Hippocrates dis- 
covered that the lune bounded by 
an arc of 90°, and by a . semi- 
circle upon its chord, is equal in area to the triangle formed hy^ 
the corresponding chord with the centre as its apex (Fig. 16). 
The lune — a figure bounded by curves — being thus equated with 
a figure bounded by straight lines, its area can be ascertained. He 
discovered two other lunes of which the areas could be similarly 
expressed. Finally, he discovered a particular lune which, when 
added to a circle, enables the whole to be represented geometrically 
as a square. This lune by itself cannot, however, be squared, and 
so the method cannot be used for squaring the circle. These 
remarkable researches became misrepresented and tradition told 
tha Hippocrates had succeeded in the impossible geometrical 
task of squaring the circle! His proofs, in fact, imply great 
familiarity with advanced geometric methods. They are based on 
the theorem, which he himself proved, that circles are to one 
another as the squares of their diameters. 

Thus by the end of the fifth century not only had philosophical 
thought taken a scientific turn, but science itself had emerged as 
a preoccupation of men set aside from their fellows. Two depart- 


Fig. 16. Lune of Hippocrates 
of Chios. 

The Foundations: Ionia ^ Magna Graecia^ Athens 
ments, medicine and mathematics, had become well differentiated. 
Astronomy had been the special interest of such philosophers as 
Pythagoras (p. 17), Philolaus (p. 21), Empedocles (p. 24), and 
Anaxagoras (p. 26) . This earlier phase of Greek thought terminated 
in the fifth century with a thinker of a very individual type. 

The name of socrates (470-399 b.c.) is associated with a 
great intellectual revolution, perhaps the greatest that the world 
has seen. Hisoverwhelmingpreoccupation was with conduct. For 
him * Knowledge is Virtue'. The attitude of Socrates towards the 
sciences of his day has been set forth by his pupil Xenophon 
(430-350 B.C.), who tells that 

‘with regard to astronomy Socrates considered a knowledge of it 
desirable to the extent of determining the day of the year or of the 
month and the hour of the night ; but as for learning the courses of 
the stars, occupying oneself with the planets or inquiring about 
their distance from the earth or about their orbits or the causes of 
their movements, to all these he strongly objected as a waste of 
time. He dwelt on the contradictions and conflicting opinions of the 
physical philosophers . . . and, in fine, he held that speculators 
on the Universe and on the laws of the heavenly bodies were no 
better than madmen.* 

The triumph of the Socratic revolutjion depressed for a while 
both science and physical philosophy. But out of the conflict 
between the Socratics and the physical philosophers arose the 
main streams of later Greek thought. These two streams derive 
their titles and their tendencies from the two gigantic figures that 
occupy the stage during the fourth century, the age of Plato and 



Unitary Systems of Thought: Athens, 400-300 B.C. 

I. Plato and the Academy. 

The thought of plato (427-347 like that of his master 

Socrates, was dominated by the ethical motive. Convinced, like 
Socrates, that Truth and Good exist and that they are inseparable, 
he embarked on an inquiry which had as its object to expose, 
account for, and resolve into one comprehensive theory the 
discrepancies of ordinary thinking. During this process he 
developed a doctrine destined to be of great moment for the subse- 
quent relation of scientific thought with that which comes under 
the heading of religion and philosophy. It is the so-called Doctrine 
of Ideas. The nature of this doctrine and the manner in which 
Plato reached it have been briefly set forth by his pupil, Aristotle. 

'In his youth', says Aristotle, ‘Plato became familiar with the 
doctrine of certain philosophers that all things perceived by the 
senses are ever in a state of flux and there is no knowledge concern- 
ing them [see Heracleitus, p. 14]. To these views he held even in 
his later years, Socrates, however, busied himself about ethical 
matters, neglecting the world of nature, but seeking the universal 
in conduct. He it was who fixed thought for the first time on 
definitions. Plato accepted his teaching but held that the problem 
of what was to be defined apphed not to anything perceived by the 
senses but to something of another sort. His reason was that there 
could be no real definition of things perceived by the senses because 
they were always changing. Those things which could alone be 
defined he called Ideas, and things perceived by the senses, he said, 
were different from these Ideas and were all called after them.' 
(Aristotle's Metaphysics.) 

Thus concepts, things of the mind, became for Plato something 
more concrete, while our impressions of the material universe, 
percepts, became something more vague. It is as though the word 
'horse' were to suggest to the mind not Ned or Dobbin or even 
a cart-horse or a carriage-horse but a generalized being that is 
approximately expressed by the biologist's definition of the species 
hors^. Further this ' Idea ' of the species was more truly an entity 
than any individual horse. The Platonic "Idea' contained in it 


Unitary Systems of Thought: Athens^ 400-300 B,a, 

the conception of form, for only in the Idea was the form separated 
from matter. The conception is put epigrammatically by Plato 
in the phrase 'the Soul is the place of forms',* that is, of those 
forms which can be defined. 

Plato expresses a great admiration for mathematical principles, 
and he regards mathematics as exhibiting that type of certitude 
and exactness to which other studies should conform. Mathe- 
matics indeed relies for its material upon something of the nature 
of Plato's Ideas. It might be expected, therefore, that mathe- 
matics would appeal to him. Many of Plato's thoughts assume a 
mathematical gtiise. He exhibits at times a view which seerris to 
approach that of Pythagoras, who had attached a moral and 
spiritual value to numbers (p. 18). Plato thus tended to respect 
a science in the degree to which it had progressed in the mathe- 
matical stage of its development. The heavenly bodies evinced, 
in the opinion of those Pythagorean days, the exemplars of perfect 
geometric forms (p. 22) . For astronomy — especially on its theoretic 
as distinct from its observational side — Plato had therefore a high 
regard. Indeed, for many of his Greek followers mathematics 
became identified with astronomy. We think of astronomy as a 
field for the application, the Platonists rather for the exemplifica- 
tion of mathematics. 

The attitude of Plato was less favourable to those sciences, other 
than astronomy, to which we nowadays habitually apply our 
mathematics. On the non-mathematical sciences he smiled even 
less. He repudiated the theories of such thinkers as Democritus, 
who not only denied the existence of mind as a separate entity but 
also assumed the universe to be the result of accident (p. 15) . Such 
a universe was hardly susceptible of exact presentation. In ulti- 
mate analysis the position of Democritus was a denial of the 
validity of philosophy. On the other hand, Plato speaks with 
respect of Hippocrates the physician, the very type of the scienti- 
fic man in antiquity— -Hippocrates of whom a follower said 'he 
was the first who separated science from philosophy'.^ Plato's 
respect for Hippocrates, however, did not tempt him to follow in 

* The phrase is not found in the extant works of Plato but is quoted by 
Aristotle in the De anima, 

^ Celsus, De re medica, Introduction. 




The Great Adventure 

his footsteps. Nor is this surprising, for, firstly, Plato assigned a 
relatively unimportant place to phenomena and, secondly, his 
mind was too full of a greater vision to enable him to lend himself 
to the tedium of the pursuit of the inductive method. 

Nevertheless, the greatest of thinkers could not refrain from 
producing some general theory of the universe of phenomena. 
The work in which this appeared, the dark and difficult Timaeus, 
is under strong Pythagorean influence (p. 22). Its spokesman is 
a member of that sect. Its very darkness and difficulty provide 
an unintentional appeal for that patient, impartial objective pro- 
cess of observation arid record that is the very foimdation of 
science. The Timaeus demonstrates how knowledge can be de- 
graded, even by Plato, in the relentless endeavour to ascribe a 
meaning to all parts of the universe. The work displays the 
Platonic mood at its weakest. 

The trend of Platonism in general and of ancient Platonism in 
particular has normally been away from observational activity, 
even when friendly to mathematics. There are, however, many 
and evident exceptions and, moreover, Platonism has often 
been helpful to science in the presence of an entrenched and static 

It has been said that ' everyone is by nature a disciple either of 
Plato or of Aristotle ’. There is much truth in this. Aristotle him- 
self set forth the difference between the two attitudes, reduced 
to its simplest expression. In his great work, the Physics, Aristotle 
discusses the use of mathematical formulae. The objects studied 
in the physical sciences, he says, do present, of course, planes, 
lines, and points. Such planes, lines, and points are the subjects 
also of mathematical study. How, then, are we to distinguish the 
procedure of mathematics from that of the true physical sciences 
which often invoke mathematics ? 

To this, Aristotle answers that the mathematician does indeed 
study planes, lines, and points, but he studies them as mental 
abstractions and not as the 'limits of a physical body'. The 
objects of mathematics, though in fact inseparable from a physical, 
movable, and therefore changeable body, are studied in abstraction 
from that change to which all material things are subject. This 
process of abstraction necessarily involves error. The mistake 


Unitary Systems of Thought: Athens, 400-300 B.c. 

made by Plato’s theory of Ideas, says Aristotle, is that of attempt- 
ing to exclude from his consideration of matter those conceptions 
in which are involved the very nature of matter, though not that 
of mathematical objects. Thus odd and even, straight and curved, 
number, line, figure — all these can be studied wholly out of con- 
nexion with the change or movement inseparably connected with 
material things. They are subjects for the mathematician. Such 
things as flesh, bone, man, nay, even inorganic nature, minerals 
and earths, sounds and colours, heat and cold, cannot be so 
studied. They are subjects for the man of science. Change is 
indeed an essential part of nature, fundamental to real existence, 
as Thales, the father of science, had seen (p. 8) and Heracleitus 
with his 'being as becoming* had emphasized (p. 14). Yet change 
has to be ignored in pure mathematical investigation. This prin- 
ciple of change or movement prevents nature from ever really 
repeating herself, while in mathematical conceptions one unit is 
exactly like another. 

We may see the contrasted effects of the Platonic and the 
Aristotelian attitudes in the scientific works of the two great 
philosophers. So far as science is concerned, it is by their fruits 
that we must know them. Plato has shrouded his views in the 
Timaeus. From the deceptive shadows seen in the twilight of that 
work he has elevated into picture form, from an ‘ Idea *, a mechan- 
ism that never was on land or sea. On the other hand, in the great 
biological works of Aristotle we have a magnificent series of first- 
hand observations and positive studies to which, in each succeeding 
generation, naturalists still return with delight, with refreshment, 
and with respect. 

The importance of Plato, so far as the subsequent development 
of science is concerned, is thus to be sought chiefly in the depart • 
ment of mathematics. Plato was, in fact, an accomplished mathe- 
matician and had had Pythagorean teachers. The 'Platonic bodies’, 
the five regular solids which have equal sides and equal angles, 
were known to the Pythagoreans (p. 22). Plato describes them in 
the Timaeus, exhibiting full understanding of them. There are 
many other passages in his writings which show mathematical 
penetration, nor is it easy to overrate his influence upon later mathe- 
matical developments. We may consider it under four headings : 


The Great Adventure 

{a) It is through Plato that mathematics obtained, and retains, 
a place in education. In the abstractions of mathematics he saw 
an instrument for the training of logical thought. The study of 
mathematics was thus for him the portal to philosophy. 'Let 
none who has not learnt mathematics enter here' was inscribed 
over the entrance to his school, the Academy. 

[h) The hand of Plato may be traced in the actual course of 
mathematical development. To his logical teaching the body of 
mathematical knowledge owes the systematic structure and logical 
finish that have since distinguished it. This factor exhibited itself 
in his pupils and his spiritual descendants. Such a work as 
Euclid's Elements is in essence a product of Plato's thought and 
of Plato's school (p. 37). It is certainly no overstatement that, 
through Euclid (p. 57), every schoolboy is nowadays a student of 

[c) The inspiration of Plato can be traced very clearly also in the 
history of astronomy. He early came to regard the irregularities 
of planetary motion as inconsistent with his view of the essential 
perfection of the universe. These movements had, in his opinion, 
to be explained as somehow compounded of simple circular move- 
ments, a conception that he derived from his Pythagorean 
teachers (p. 21). Plato accordingly set his pupils to seek out rules 
by which the movements of the heavenly bodies could be reduced 
to a system of circles and spheres. This was the main task of 
astronomers from his time to Kepler (p. 200) — a stretch of two 
thousand years! During all those centuries the hand of Plato 
ruled astronomy. Here Aristotle (p. 39) is but a pupil of Plato as 
Plato is of Pythagoras. 

[d) Plato may be said to have made a positive contribution to 
science of first-class importance. It cannot be said that this is 
wholly his creation, since the germs of it are to be found among the 
Pythagoreans, but its formal introduction is Plato's work. It is 
the method of assuming that a problem is solved and working back 
from it until a statement is reached, the truth or falsehood of 
which is already known. Thus may be discerned whether the prob- 
lem is, in fact, soluble or not, and indications may be forthcoming 
as to the general direction of the solution and whether there are 
any limitations to it. The method is set forth in the Meno, 


Unitary Systems of Thought: Athens^ 400-300 B.c. 

Euclid often used this method and it is current in modern elemen- 
tary geometry. 

There is a curious Platonic conception that is perhaps a mere 
by-product of his thought but was yet fraught with consequences 
for after ages. The Pythagorean Timaeus, in Plato's dialogue of 
that name, pictures the universe as a living thing with a soul 
penetrating its body. The passage is well summarized by Aristotle : 

* Timaeus tries to give a physical account of how the soul moves 
its body. The soul is in movement and the body moves because it 
is interwoven with it. The Creator compounded the soul-substance 
out of the elements and divided it according to the harmonic num- 
bers (p. 18) that it might have an innate perception of harmony and 
that its motion might be with movements well attuned. He bent 
its straight line into a circle. This he divided into two circles united 
at two common points. One of these he divided into seven circles 
[that is the orbs of the seven planets] in such wise that the motions 
of the heavens are the motions of the soul.’ (De anima) 

^This view of the universe gave a framework for the Neoplatonic 
conception that the structure of the universe foreshadowed that 
of man. Thus arose the doctrine of the intimate relation of macro- 
cosm ('great world’) and microcosm (Tittle world’, that is, Man). 
This doctrine permeated medieval Christian thought (p. 123). 

Plato’s school, under the name of the Academy, persisted for 
many centuries, but was chiefly occupied with philosophical dis- 
cussion. One of his first disciples to dfstinguish himself in science 
was EUDOXUS (409-356 B.c.) of Cnidus, the founder of observational 
cosmology. Eudoxus had also studied with the Pythagoreans. 
Under the stimulus of Plato he made advances in mathematical 
theory, but occupied himself chiefly with examining the heavens. 
Among his achievements is his remarkably accurate estimate of 
the solar year as 365 days and 6 hours. His most influential 
contribution was his view that the heavenly bodies move on a 
series of concentric spheres, of which the centre is Earth, itself 
a sphere. Eudoxus had observed the irregularities in the move- 
ments of the planets. To explain these he supposed each planet to 
occupy its own sphere. The poles of each planetary sphere were 
supposed to be attached to a larger sphere rotating round other 
poles. The secondary spheres could be succeeded by tertiary or 


The Great Adventure 

quaternary spheres according to mathematical and observational 
needs. For Sun and Moon Eudoxus found three spheres each 
sufficient. In the explanation of the movements of the other 
planets, four spheres each were demanded. For the fixed stars 
one sphere sufficed. Thus twenty-seven spheres in all were 
demanded. These spheres — save that of the fixed stars — were 
treated by Eudoxus not as material but in the manner of mathe- 
matical constructions. 

CALLIPUS of Cyzicus, a pupil of Eudoxus and friend of Aristotle, 

observed movements of the heavenly bodies and irregularities 
unknown to his master. To explain these he added yet further 
spheres, making thirty-four in all. The Eudoxan theory thus 
modified was adopted by Aristotle (p. 47). 

HERACLEiDES of Pontus [c, 388-315 B.C.), a pupil of Plato, con- 
tributed to astronomy a suggestion that the Earth rotates on its 
own axis once in twenty-four hours, and that Mercury and Venus 
circle round the Sun like satellites. His teaching led on to that of 
Aristarchus (p. 59). 

Important for subsequent mathematical developments was 
MENAECHMUS, another pupil of Eudoxus. Menaechmus initiated 
the study of conic sections. He cut three kinds of cone, the 'right 
angled', the 'acute angled', and the 'obtuse angled', by planes at 
right angles to a side of each cone. Thus he obtained the three 
types of conic section which we now call by the names allotted to 
them by his Alexandrian successor Apollonius (p. 70) (Fig. 17). 


Unitary Systems of Thought: Athens^ 400-300 b.c. 

Many others of Plato's followers made contributions to pv^re 
mathematics, and, in the sense which we have discussed (p. 36), 
all subsequent mathematicians are Plato's spiritual heirs. There 
is also evidence of a certain amount of botanical activity in the 
Academy, and some physiological theories which became popular 
in later centuries may be traced to Plato. Platonism passed into 
Christianity early, mainly through St. Augustine, so that the 
Christian Middle Ages, until the twelfth century, were mainly 
Platonic. The later school of philosophy known as ‘ Neoplatonism ' 
also profoundly influenced Christianity (pp. 121-5). 

2. Aristotle. 

ARISTOTLE (384-322 B.C.) was bom at Stagira, a Greek colony a 
few miles from the northern limit of the present monastic settle- 
ment of Mount Athos. His father was physician to the monarch 
of Macedon. At seventeen Aristotle became a pupil of Plato at 
Athens. On his master's death in 347 he crossed the Aegean Sea 
to reside in Lesbos, an island off the coast of Asia Minor. In 342 
he became tutor to the young prince Alexander of Macedon. He 
remained in Macedon till 336 when Alexander started his career 
of conquest that was to alter the face of the world. Aristotle then 
returned as a public teacher to Athens. There he owned a garden 
known as the Lyceum, whence the word has derived its special 
significance. In it he established his famous school afterwards 
called the Peripatetic (Greek, ‘walking around'), for he had there 
his favourite Peripatos or cloister where he lectured. 

Aristotle's writings cover the whole area of knowledge. The 
earliest are biological. These were written, or at least drafted, 
during his residence in Asia Minor (347-342). Most of his other 
works were produced during his second period at Athens (335- 
323), in the twelve years that preceded his death. We must 
always remember that the whole of Aristotle's science, and indeed 
the whole cast of his mind, was deeply influenced by his biological 

Regarded from the modem scientific standpoint, Aristotle 
appears at his best as a naturalist. His first-hand observations 
are on living things, and his researches on them establish his claim 
to be regarded as a man of science in the modem sense. In his 


The Great Adventure 

gr^at work, On the Parts of Animals, he sets forth what he regards 
as the relation between 'physics' — which is for him a general 
description of the universe — and the study of living things. 

‘ Of things constituted by nature *, he says, * some are ungenerated, 
imperishable, eternal ; others subject to generation and decay. The 
former are excellent beyond compare and divine, but less accessible 
to knowledge. The evidence that might throw light on them, and 
on the problems which we long to solve respecting them, is furnished 
but scantily by our senses. On the other hand, we know much of 
the perishable plants and animals among which we dwell. We may 
collect information concerning all their various kinds, if we but 
take the pains. 

* Yet each department has its own peculiar charm. The excellence 
of celestial things causes our scanty conceptions of them to yield 
more pleasure than all our knowledge of the world in which we live ; 
just as a mere glimpse of those we love is more to us than the 
grandest vista. On the other side we may set the certitude and 
completeness of our knowledge of earthly things. Their nearness 
and their affinity to us may well balance the loftier interest of the 
things of heaven, that are the objects of high philosophy. 

' But of a truth every realm of nature is marvellous. It is told 
that strangers, visiting Heracleitus (p. 14) and finding him by the 
kitchen fire, hesitated to enter. ‘Xome in, come in*', he cried, ‘*the 
gods are here too.'’ So should we venture on the study of every 
kind of creature without horror, for each and all will reveal some- 
thing that is natural and therefore beautiful. Absence of haphazard 
and conduciveness of all things to an end are ever to be found in 
nature’s works, and her manner of generating and combining in 
ever-changing variety is of the highest form of the Beautiful.’ 
[Somewhat paraphrased.] 

Though it cannot be claimed that Aristotle was an evolutionist 
in the sense that he regarded the different kinds of living things as 
actually related by descent, yet there can be no doubt that he fully 
realized that the different kinds can be arranged in a series in 
which the gradations are easy. His scheme was a ‘Ladder of 
Nature' (Fig. 18) as it came to be called by later naturalists. 
Thus he writes in his History of Animals: 

' Nature proceeds by little and little from things lifeless to animal 
life, so that it is impossible to determine the exact line of demarca- 
tion, nor on which side thereof an intermediate form should lie. 
Thus, next after lifeless things in the upward scale, comes the plant. 


Unitary Systems of Thought: Athens, 400-300 b.c. 

Of plants one will differ from another as to its amount of apparent 
vitality. In a word, the whole plant kind, whilst devoid of life as 
compared with the animal, is yet endowed with life as compared 
with other corporeal entities. Indeed, there is observed in plants 
a continuous scale of ascent toward the animal.* 

The peculiar principle that Aristotle invoked to explain living 
phenomena we may call *sour, translating thereby his word 





Fig. 18.' Aristotle's Ladder of Nature. 

psyche. His teaching on that topic is to be found in his great work 
On the Soul usually cited by its Latinized title De anima. He 
thinks of things as either * with soul ' or ‘ without soul ' [empsychic 
or apsychic). His belief as to the relationship of this soul to the 
matter in which it is embodied is difficult and complicated, but 
he tells us that ' Matter is identical with potentiality, form with 
actuality, the soul being that which gives the form or actuality in 
living things '. Thus for Aristotle ‘ soul ' is not a separate existence. 
In this he differs from his master Plato and no less from early 
Christianity which, through St. Augustine (p. 123), borrowed 
much from Plato. Aristotle believes, too, that the soul works 
ever to an end, and that 

* As every instrument and every bodily member subserves some 
partial end, some special action, so the whole body must be destined 


The Great Adventure 

to minister to some fuller, some completer, some greater sphere of 
action. Thus an instrument such as the saw is made for sawing, 
since sawing is a function, and not sawing for the saw. So, too, the 
body must somehow be made for the soul and each part thereof for 
some separate function to which it is adapted.' [Parts of Animals, 
somewhat paraphrased.] 

Aristotle is thus a vitalist (Latin vita, 'life') and a teleologist 
(Greek telos, 'end', 'object'), that is to say, he believes that the 
presence of a certain peculiar principle is on the one hand essential 
for the exhibition of any of the phenomena of life, while on the 
other hand it serves to integrate all such phenomena towards the 
emergence of the perfect living individual. The Democritans, to 
whom Aristotle was opposed, believed that all the actions of 
living things were the result of the interaction of the atoms of 
which they were composed (p. 15). Thus life, for the Democritans, 
was capable of mechanical expression. They were mechanists. 
The division between vitalist and mechanist extends throughout 
the history of science and still separates students of living things. 

Living things are for Aristotle the type of existence, and exis- 
tence as a whole presents, according to him, evidence of design. 

* Everything that nature makes is a means to an end. For just as 
human creations are the products of art, so living objects are mani- 
festly the products of an analogous cause or principle. . . . That the 
heaven is maintained by such a cause, there is, therefore, even more 
reason to believe than that mortal animals so originated. For order 
and definiteness are even more manifest in the celestial bodies than 
in our own frame. . . . Thus Nature is marvellous in each and all her 
ways.' [Parts of Animals, greatly abbreviated.] 

Aristotle attempted to analyse the nature of generation, of 
heredity, of sex. His are the first presentations of many such 
topics which are to-day discussed by naturalists. There is an 
amazing variety and depth in his biological speculations. These 
have a permanent value* and are constantly cited by biologists 
of our own time, 

Aristotle's psychological studies are only partly within our 
purview. The psychological questions with which we are con- 
celmed come mostly into his discussion of the nature of life. ' Of 
natural bodies,' he says, ' some possess life and some do not ; where 
by life we mean the power of self-nourishment and of independent 


Unitary Systems oj Thought: Athens^ 400-300 b.c, 

growth and decay/ It should be noted that in the Aristotelian 
sense the egg or germ is not at first a living thing, for in its earliest 
stages and before fertilization it does not possess ‘ soul ' even in its 
most elementary form. 

In a famous passage from his work On the Soul Aristotle says : 

‘The term life is used in various senses. If life be present in but 
a single one of these senses, we speak of a thing as alive. Thus, there 
is intellect, sensation, motion from place to place and rest, the 
activity concerned with nutrition, and the processes of decay and 
growth. Plants have life, for they have within themselves a faculty 
whereby they grow and decay. They grow and live so long as they 
are capable of absorbing nutriment. In virtue of this principle 
[the vegetative soul] all living things live, whether animals or plants, 
but it is sensation which primarily constitutes the animal and 
justifies us in speaking of an animal souL For, provided they have 
sensation, creatures even if incapable of movement are called 
animals. As the nutritive faculty may exist, as in plants, without 
touch or any form of sensation, so also touch may exist apart from 
other senses/ 

Apart from these two lower forms of soul (a) the vegetative, or 
nutritive and reproductive, and (6) the animal, or motile and sensi- 
tive soul, stands (c) the rational or conscious and intellectual soul 
that is peculiar to man. 

The possession of one or more of the three types of soul, vegeta- 
tive, animal, and rational, provides in itself a basis for an elemen- 
tary form of arrangement of living things in an ascending scale. 
In fact the basis of Aristotle's * Ladder of Nature' (p. 40) is really 
psychological, depending on the character of soul or mind. It is 
characteristic of Aristotle's method that the various departments 
of investigation should thus interlock. 

In the closest possible association with Aristotle's biological 
views stand his innumerable and admirable observations. Among 
the more striking are the following: 

{a) A series of records of the life and especially the breeding 
habits of a large variety of animals. About 540 species are 

(6) Embryological investigations of the developing chick, which 
has ever since been the classic object for such investigations. 

Accounts of the habits and development of the octopuses and 


The Great Adventure 

squids which have, in some cases, been surpassed only in modern 

{d) Anatomical descriptions of the four-chambered stomach of 
the ruminants, of the complex relationships of the ducts and 
vessels in 'the mammalian generative system and of the mam- 
malian character of the porpoises and dolphins, all unsurpassed 
until the sixteenth century. 

(e) Accounts of exceptional modes of development of fish. 
Among them is one of a species of dogfish of which the young is 
linked to the womb by a navel cord and placenta, much in the 
manner of a mammal. Nothing has contributed more to Aristotle's 
scientific reputation in modem times than the rediscovery of 
this phenomenon. 

(/) As a result of his embryological investigations Aristotle 
attached very great importance to the heart and vascular system. 
He came to regard the heart as *the first to live and the last to 
die',^ a conception which passed to the Middle Ages and was 
current until the eighteenth century. 

(g) A lasting addition to the technique of scientific instruction was 
made by Aristotle in introducing diagrams to illustrate complex 
anatomical relations. Some of his diagrams can be restored from 
his descriptions (Fig. 19). 

Most of Aristotle’s biological work reads like that of a modern 
naturalist, for his methods are closely similar to those of our own 
time. But when we turn to examine Aristotle’s view of the universe 
we encounter not only a different method of work but a mode of 
thought so diverse from ours that we can neither understand nor 
sympathize with him without some special study. The intellectual 
revolution of the insurgent century (Ch. VII) resulted in com- 
plete destmction of the Aristotelian physical philosophy. Modem 
science is the product of that revolution, and it is difficult for us 
to go behind it in our thinking. 

We are all of us brought up from early years with the idea of 
the 'uniformity of nature’, that is that the same causes always 
and everywhere produce the same results. Thus, for instance, 
we think of astronomers exploring the heavens and discovering 

* This sentence is often given as a quotation from Aristotle. It occurs, 
however, nowhere in his writings, though the idea is to be found there. 


Unitary Systems oj Thought: Athens^ 400-300 B.a 

new facts about worlds other than our own. We assume, and 
we are justified in assuming, that in the starry spaces there 
rule the general physical laws which we have learned on our 

Ducts from Ducts from 
aorta (Renaf vein {Renal 

Fig. 19. Generative and excretory systems of a mammal as described 
by Aristotle. The part framed in a dotted rectangle restores a lost diagram 
prepared by Aristotle and described in his Historia animalium. The legends 
in brackets are the modern scientific terms, the others transliterations or 
translations of Aristotle’s terms. 

earth. On this principle astronomers deduce, for instance, the 
exact chemical constitution of many of the stars. Did we question 
ourselves on this matter, we might, perhaps, ask how, if the physical 


The Great Adventure 

laws that we know on earth did not prevail in the stars, could 
astronomers make discoveries at all ? But this law of uniformity 
that we take for granted was by no means obvious to Aristotle. 
To him heaven was not only different from earth, but its ways were 
incommensurate with the ways of earth. 

Aristotle knew nothing of the book of Isaiah. But his philo- 
sophical distinction between the rules of heaven and of earth 
made a special appeal to the Church fathers and to his medieval 
followers who had read that book. It was brought nearer to them 
by a superb and oft-quoted passage, 

*My thoughts are not your thoughts, neither are your ways my 
ways, saith the Lord. For as the heavens are higher than the earth, 
so are my ways higher than your ways, and my thoughts than your 
thoughts,* {Isaiah Iv. 8, 9.) 

Isaiah, like Socrates (p. 31), was thinking of the moral order in his 
contrast of heaven and earth. So, often, was Aristotle. But Aris- 
totle was thinking also of other kinds of order, and it is with the 
other kinds of order, and especially with the physical order, that 
our present work has to deal. We must remember, however, that 
for Aristotle all the kinds of order were related to each other. 

When Aristotle had completed his biological works he applied 
himself to set forth a general view of the universe which should 
link together its various aspects. The structure of the material 
universe was among these aspects. He revised his account over 
and over again, seeking to fit his earlier biological findings into his 
general scheme. We are only concerned with that scheme in so 
far as it concerns the material world. Aristotle's physical and 
astronomical conceptions, however, were unlike his biological con- 
ceptions in being untouched by profound personal knowledge and 
experience. Regarded scientifically they are far inferior to his 
biological conclusions. Nevertheless it was Aristotle's physical 
and astronomical conceptions that influenced the centuries which 
followed, while his biological works were neglected and ultimately 
forgotten, to be rediscovered in relatively modem times. 

Aristotle, like Plato, exhibits in his physical scheme some 
Pythagorean tendencies. Especially he emphasized the circle and 
the sphere as the most 'perfect' figures and therefore those on 
which the world is modelled. Thus he was led to regard the heavens 


Unitary Systems of Thought: Athens y 400-300 b,c, 

as a series of concentric spheres arranged round our earth as a 
central body (Fig. 20). These spheres he described, however, as 
crystalline, mechanizing them frofn the mathematical scheme of 
Eudoxus (p. 37). Around our earth was the sphere of the atmo- 
sphere and around that spheres of pure elemental nature, bdng, 
from within outward and in order of density, earth (or rather 

Fig. 20. The Universe of" Aristotle as conceived by a medieval writer. 

earthy exhalation) water, air, and fire. These spheres of pure 
elements are as inaccessible to us as the heavens themselves. Next, 
outward beyond the sphere of elemental fire, lies the region of a 
yet more mysterious substance, the ether (Greek ‘shining*) which 
enters into the composition of the heavenly bodies. Yet farther 
out are in succession the seven spheres, each of which carries a 
planet, while beyond is the eighth sphere which bears the fixed 
stars. Finally, beyond all others, is the sphere whose divine har- 
mony causes the circular revolution of the whole celestial system. 

Such was the basis of the system that was to control for two 
thousand years the view that men took of Nature. We may thus 
summarize the system, its history, and its fate : 

(a) Matter is continuous. 

In taking this view Aristotle opposed Democritus and sided 
with Socrates and Plato. The followers of Democritus and of his 
disciple Epicurus, who took an atomic view of matter (p. 14), were 


The Great Adventure 

associated with doctrines which were peculiarly abhorrent to the 
early and medieval Church. The atomic theory was the only 
alternative to Aristotle’s conception of matter. Thus criticism 
of Aristotle on this point drew theological odium on itself. The 
atomic theory, we shall therefore see, passed into the background 
for many centuries. 

(6) All mundane things are made up of four * elements \ earth, air, 
fire, and water, which, in their turn, contain the four ‘qualities*, 
heat, cold, dryness, and moisture, in binary combination (Fig. 15). 
This view of matter was taken from Empedocles (p. 24) and is 
probably of yet more ancient origin. It is the Aristotelian expres- 
sion of the Pythagorean conception of all things being in a state of 
love or hate — fire, for instance, being opposed to water but allied to 
air. The doctrine of the four elements was almost unquestioned 
until the seventeenth and lasted until the end of the eighteenth 
century. It fitted well with Christian and Moslem thought and 
became a part of orthodox medieval theology. 

(c) Stars and planets move with uniform circular velocity in crystal- 
line spheres, centred round the earth. Each sphere is subject to the 
influence of those outside it. 

This general conception is of Pythagorean origin (p. 21). 
Aristotle did little but borrow it from Eudoxus, mechanize it, and 
fit it into a general system of philosophy. His scheme, or some 
modification of it, held its ground tiU the time of Kepler in the 
seventeenth century (p. 200). 

[d) Circular movement is perfect since the circle is the perfect figure. 
Circular movement represents the changeless, eternal order of the 
heavens. It is contrasted with rectilinear movement which prevails 
on this our changing and imperfect earth. 

'Where imperfection ceaseth, heaven begins.’ 

Here again are Pythagorean influences. The basis of the con- 
ception is that while heavenly bodies appear to circle round us, 
bodies on earth tend to fall or rise. Newton at the end of the 
seventeenth century succeeded in expressing the movements of 
the heavenly bodies in known and experimentally demonstrated 

Unitary Systems oj Thought: Athens^ 400-300 b.c. 

terms. Until his time the differences between the behaviour of 
earthly and heavenly bodies remained a puzzle or paradox or both. 

(e) The Universe is limited in space in the sense that it is contained 
within an outer sphere. It is unlimited in time in the sense that it 
is subject neither to creation nor destruction as a whole. 

The finiteness of the Universe both in space and time became 
necessary to all the theological systems of the Middle Ages and 
notably to that of the Western Church. It was effectively unques- 
tioned till the time of Bruno (died 1600). Thus Aristotle himself 
could not be completely accepted. The philosophical return 
to the conception of a Universe infinite both in space and time 
is a landmark in the history of science (p. 186). 

It has been urged against Aristotle that he obstructed the 
progress of astronomy by divorcing terrestrial from celestial 
mechanics, for he adopted the principle that celestial motions were 
regulated by their own peculiar laws. He thus discouraged 
astronomical observation, placed the heavens beyond the possi- 
bility of experimental research, and at the same time impeded 
advance in the knowledge of mechanics by his assumption of a 
distinction between 'natural' and 'unnatural' motion. For two 
thousand years the general outline of the world as set forth by 
Aristotle remained the orthodox view. It was dangerous even to 
question it. How far was Aristotle responsible for this intellectual 
tyranny ? To this question there are many answers, of which we 
shall adduce but four, 

{a) It was not Aristotle who introduced the distinction between 
celestial and terrestrial physics. Such distinction had been taken 
for granted by his predecessors. The Pythagoreans, for example, 
had made much of them. In fact by his exposition of a positive 
and tangible scheme he gave a new interest to the study of nature. 

(6) It is unfair to bring his own greatness as a charge against 
Aristotle. All our conceptions of the material world — ‘scientific 
theories' as we call them— should be but temporary devices to be 
abandoned when occasion demands. This is a proposition which 
Aristotle himself puts forth. In expounding the motions of the 
planets he advises his readers to compare his views with those that 




The Great Adventure 

they themselves reach. That his scheme lasted for two thousand 
years without effective criticism is no fault of his. It is rather 
evidence that the men who followed him were dwarfs compared 
with 'the master of those who know*. 

(c) Some of Aristotle*s reasons against what we now regard as 
the form of our world are, in fact, valid. Thus he argues against 
the motion of the earth. Such movement, if it existed, should, he 
considered, produce apparent motion among the fixed stars. This 
is a just objection. It was only met in the nineteenth century 
by the demonstration of interstellar motion. The reason that 
this was not previously detected is that the vast distance of the 
heavenly bodies from us makes this apparent motion so small that 
excessively delicate instruments are needed. 

{d) We need to remember that the rigidity of the Aristotelian 
scheme lay not in itself but in the interpretation given to it' 
especially in the Middle Ages. By linking the theories of Aristotle 
with their own religious views, men of those times introduced a 
bitterness into the debate concerning the validity of the Aristotelian 
scheme that had nothing to do with its philosophical or scientific 

3. Peripatetics, Stoics, and Epicureans. 

It is improbable that his connexion with Alexander was of any 
service to Aristotle himself.* There can be no doubt, however, 
that the great conqueror was a friend of learning and that impor- 
tant investigations were initiated by him. Thus he made an 
attempt to survey his empire by employing a special force whose 
duty it was to maintain the condition of the main roads. The 
services of these men were available for scientific purposes, such 
as the collection of data bearing on the natural history of the 
districts where they were at work. Investigations were also made 
by certain of Alexander's commanders, notable by his admirals, 
NEARCHUS and ANDROSTHENES. Portions of their botanical and 
geographical works are preserved. 

Aristotle*s own work was continued by his school, the Peri- 
patetics, of whom the best-known was the long-lived theo- 

* A number of statements to the contrary can be found in writings of 
later classical antiquity. None, however, bears critical scrutiny. 


Unitary Systems oj Thought: Athens^ 400-300 b.c. 

PHRASTus (372-287 B.c.) of Ercsus in the island of Lesbos. Though 
a pupil of Aristotle he lived to be contemporary with the first 
generation of Alexandrian science (Ch. II). He made important 
botanical researches and continued Aristotle's work in Aristotle's 
spirit. It is interesting to observe that he exhibits the same 
'evolutionary' bias that characterizes the biological work of his 
master. In one of his great botanical treatises Theophrastus 
observes that 'where there is growth there is life. Wherefore we 
should observe these things not for what they are but for what they 
are becoming. And, moreover, though some be peculiar, yet the 
general plan can everywhere be traced and is never lost.' 

Ancient science suffered from lack of a scientific terminology. 
This defect Theophrastus attempted to remedy in his own chosen 
department of botany. For his technical terms he did not rely, 
as do we, on an ancient and classical language, but sought rather 
to give special meanings to words in current use. Among such 
words were carpoSy 'fruit', diXid pericarpion, 'seed vessel'. From 
Theophrastus are derived the modem botanical definitions of fruit 
and of pericarp. Many Theophrastan plant-names also survive in 
modern botany. 

The botanical works of Theophrastus are the best arranged 
biological treatises that have survived from antiquity. They 
contain many acute and accurate observations. Among these are 
his clear and exact distinction between monocotyledons and 
dicotyledons. Interesting, too, is his attempted distinction of sex 
in plants, an attempt which is only successful in the case of the 
palms. Of those plants, as Herodotus teUs us, the ancient Baby- 
lonians had the same idea. 

Another younger contemporary of Aristotle was autolycus of 
Pitane (c. 360-c. 300). He worked at his native town and at 
Sardis, and expounded the geometry of the sphere for astronomical 
and geographical purposes. A pupil of Aristotle who worked on 
somewhat the same lines was dicaearchus (c. 355*-c. 285). He 
employed himself on physical geography and wrote a description 
of the world accompanied by a map. He, too, worked on informa- 
tion derived from Alexander's officers and was the first to draw 
a parallel of latitude across a map. This was used merely as a 
convenient dividing line.* It extended from the Pillars of Hercules 


The Great Adventure 

(P- 13) due east along the Taurus and Tmaus’ (Himalaya) ranges 
to the Eastern Ocean. 

It is appropriate to mention here the explorer pytheas of 
Marseilles {c, 360-c. 290 b.c.) though he was not of the Peripatetic 
school. The itinerary of his remarkable voyage can be traced with 
some exactness. He left Marseilles about March 320 b.c. and 
made for Spain, followed the coast through the pillars of Hercules 
to Cadiz and then along the Atlantic seaboard as far as Cape 
Ortegal. From there he struck across the ocean to Ushant and 
on to Cornwall. He next sailed round Great Britain and, return- 
ing to Kent, crossed to the continental side of the English Channel 
and followed the North Sea coast to the mouth of the Elbe. From 
there he turned north following the Scandinavian coast as far as 
Trondhjem at about latitude 63. After having put forth thence 
into the open sea, he turned back along the way he had come and 
reached Marseilles towards the end of October of the same year. 

Pytheas was a good astronomer, and made a number of observa- 
tions of latitude, among others of his native place Marseilles, 
which he fixed with remarkable accuracy. He was the first of the 
Greeks who arrived at any correct notion of the tides, indicating 
their connexion with the moon and its phases. 

One of the best-known of the earlier Peripatetics was the 
Thracian, strato of Lampsacus {c. 300 b.c.). He reduced the 
formation of the world to the operation of natural forces. He 
recognized nothing beyond natural necessity and, while retaining 
opposition to atomism, he sought to explain all the functions of 
the soul as modes of motion. 

After the first generation the Peripatetic school devoted itself 
to preserving or to commenting upon the work of its founder. 
It exhibited no scientific originality, and from about 300 b.c. 
onward Athens ceased to be a great scientific centre. Two of the 
later Peripatetics are, however, of some importance for the history 
of science. One, andronicus of Rhodes, was about contemporary 
with Christ. He prepared a critical text of the works of Aristotle 
which was probably closely similar to that which we now possess. 
The other was the Cilician Alexander of Aphrodisias (c. a.d. 200). 
He was an industrious commentator whose writings, much used 
by the Neoplatonists (p. 122), were the foundation of the Arabian 


Unitary Systems oj Thought: Athens^ 400-300 B.c, 

commentaries (p. 129 et seq.) and through them of many of the 
Latin Aristotelian commentaries. Soon after Alexander's death 
the Peripatetic was merged into the Neoplatonic school (p. 122). 

Contemporary in origin with the Peripatetics was the philo- 
sophical school called Stoic, from a sioa or corridor of the market- 
place at Athens, where its members used first to meet. The Stoics 
stressed the operation of natural forces in the manner of Strato 
the Peripatetic (p. 52) . They differed from the Peripatetics, how- 
ever, in emphasizing the interaction of all different parts of the 
material world. Thus, while there are reasons for everything in 
nature, it is also true that everything in nature is among the 
reasons for the rest of nature. All existence is capable of acting 
or being acted upon so that 'force' the active and 'matter' the 
passive principle pervade each other. With this doctrine of 
' universal permeation ’ there is no real difference between matter 
and its cause. The conception of Deity becomes indistinct and 
blended with that of ' reason ' or ' law ' which is but an aspect of a 
pantheistic system. 

Important for the history of science was the Stoic cosmology. 
From 'primitive being' or pneuma ^here separated the four 
elements in succession, fire first, earth last. The remaining 
is the 'ether' (p, 47). From these five factors arose a universe 
on the Aristotelian model. In the world which has thus been 
formed we, who are parts of it, must obey the inevitable laws. 
But this world will again decay and dissolve into elements and 
finally into primitive being or pneuma. Our individual souls are 
part of the universal pneuma, temporarily separated therefrom. 
In the embryo the soul is still in the ' vegetative ' stage. It becomes 
successively 'animal' and 'rational' (p. 43) but joins, in the end, 
the universal pneuma. 

So far as human relations and human conduct go, the key to 
Stoicism is fate. The Stoic schooled himself to disregard the in- 
escapable, the nature of which came to be tested by astrology 
(p. 63). He devoted himself to the development of his own soul 
through duty, awaiting inevitable absorption into the world-soul. 

The Stoic school maintained itself in Athens, Rhodes, and 
Alexandria. It attained no great importance till Roman Imperial 
times, but then became the prevalent faith of the upper class 


The Great Adventure 


(p. 94). Among its exponents were the poet Clean thes of Assus 
{c, 250 B.C., p. 116), the meteorologist Aratus of Soli (c, 260 b.c., 
p. 116) and the Bithynian scholar Posidonius of Apamea (135- 
50 B.C.). The latter, as an exponent of Stoicism, was anxious to 
demonstrate the interrelations of different parts of the universe. 
He was thus attracted to the discussion of the influence of the 
Moon on the tides. He also made estimates of the size of the Sun 
in excess of those of any other ancient writer. Posidonius was a 
friend and admirer of Cicero (p. 118) and thus links Greek with 
Roman Stoicism. 

A rival sect to Peripatetics and Stoics was that of the Epicureans 
refounded in 307 B.c. by epicurus of Samos (342-270). The 
thought of Epicurus was based on the atomism of Democritus 
(p. 15) and to a less extent on Anaxagoras (p. 26). Epicurean 
philosophy was traditionally divided into the three branches of 
logic, physics, and ethics. Beyond a discussion of atomic doctrine, 
however, the school exhibited little interest in phenomena, and 
Epicurus himself deprecated scientific pursuits. 

Epicurean philosophy spread rapidly and widely in Asia and 
Egypt. About 150 B.c. it established itself at Rome where its 
ablest exponent was Lucretius {c. 95-55 b.c., p. 95). 

The warring of these sects — Peripatetic, Stoic, Epicurean — seems 
a trivial incident as against the great constructive thought of 
Plato and Aristotle. With Aristotle we have parted with the first 
and most active stage of ancient scientific thought. In estimating 
his place in the history of science we may say that 

(а) He represents the final stage of the 'Great Adventure', the 
attempt to represent the world as a whole and as a unitary 

(б) He provided a philosophic synthesis which, in more or less 
modified form, satisfied intellectual aspirations from his own 
time until the seventeenth century. 

In that philosophical system there remained two great breaks 
in continuity. One hiatus was between celestial and terrestrial 
physics. This first began to be filled by tthe workers of the 
'Insurgent Century' from Bruno (p. 185) to Newton (p. 248). 
The other gap was between the world of the living and of the 
not-living. The Epicurean philosophy attempted to fill the 


Unitary Systems of Thought: Athens^ 400-300 b.c. 

breach in ancient times by the introduction of a ‘mechanist 
system (p. 42). The Christian Church in medieval times, repudiat- 
ing with vigour the Epicurean solution, accepted the breach as 
part of the divine order of the world. The physiologists in modem 
times, beginning with van Helmont (p. 231), Descartes (p. 221), 
Borelli (p. 239), and Sylvius (p. 240) in the seventeenth century, 
have been seeking to resolve it ever since. 

In leaving the heroic age of Greek science we would again 
emphasize the 'universal' character of the philosophical attempt 
that we call the 'Great Adventure'. The scientific activity of the 
age partook of the nature of what we should now term 'philo- 
sophy '. The object of each investigator was to fit his observations 
and the laws that he deduced into some general scheme of the 
universe. From their day to ours philosophy has continued her 
attempt thus to storm the bastions of heaven. But with the new 
age that we have to discuss, there was a failure of nerve in that 
great frontal attack. Science, becoming gradually alienated from 
philosophy, begins to proceed by her own peculiar method of 
limited objectives. The first series of these attempts resulted 
in the ' Great Failure ', the story of which we shall trace through 
two thousand years (Chs. Ill, IV, V). 'Nerve fails first, as with 
the Alexandrian school (Ch. Ill), next Inspiration falters under 
the Roman Empire (Ch. IV), lastly Knowledge itself fades in the 
Middle Ages (Ch. V). At length there is a rebirth. The science 
of the Renaissance — in which we still live — began again to proceed 
by the method of limited objectives (Ch. V). How that method 
differed from that with which the Great Failure is associated is 
a matter which we shall have to discuss. 



Divorce of Science and Philosophy (500 b.c,-a.d. 200) : 

I. Early Alexandrian Period {300-200 B.C.), 

When Alexander died (323 b.c.), his Empire broke into fragments 
(Fig. 21) . Egypt was seized by one of his generals, named Ptolemy, 
and the Ptolemaic dynasty endured for three hundred years. Its 
members were mostly able and intelligent men and women. The 

first of the line established the tradition of learning. The second 
founded a library and museum at Alexandria. That city became 
the centre of the scientific world. Learned men flocked to it and 
were supported by funds provided by the Ptolemaic rulers. The 
school continued very active for a couple of centuries. By 100 b.c. , 
however, it was beginning to languish, and by a.d. 200 in rapid 
decay, though there was spasmodic scientific activity until 
about 400. 

The Alexandrian library in its earlier stages had many distin- 
guished. curators. Most were literary men, but some, such as 
Eratosthenes (p. 70) and Apollonius (p. 69), were also men of 
science. From 300 b.c. to a.d. 200 most eminent men of science 
were teachers at Alexandria. A few, notably Archimedes and 
Galen, were less intimately linked with the Egyptian metropolis. 
Yet even they were pupils of the school and corresponded with 


Divorce oj Science and Philosophy: Alexandria 
Alexandrian teachers. Greek science from about 300 b.c. onward 
is thus not inadequately described as 'Alexandrian science'. 

Alexandria was not, however, entirely without rivals as a seat 
of learning. The most prominent were the island of Rhodes and 
the city of Pergamum in western Asia Minor. Of the enmity 
between Alexandria and Pergamum there is an interesting re- 
minder in our language. The Alexandrian books were written on 
rolls prepared from papyrus reeds, whence our word paper. To 
prevent Pergamum from acquiring copies of their literary trea- 
sures, the jealous Ptolemies put an embargo on the export of 
papyrus. The Pergamene kings, cut off from a valued import, 
sought to improve the preparation of skins, the Asiatic medium 
for writing. Thus was developed the memhranum pergamentum 
which has reached our language as parchment. 

It is characteristic of Alexandrian science that it developed along 
the lines of 'specialities'. These came to lose their relation to 
general philosophic thought with which they had hitherto been 
linked. It is convenient to consider Alexandrian science in three 
chronological divisions ; an early period containing the first and 
second generations of the school to nearly 200 b.c., a middle period 
to about the birth of Christ, and a late period to the complete 
decline of the school. Archimedes (p. 63) demands individual 

The early Alexandrian period is noteworthy for the fact that 
mathematics at once assumed a prominent and independent posi- 
tion. Among the first to be called to the Alexandrian Academy 
was the illustrious mathematician euclid [c. 330-c. 260). He was 
trained at Athens, probably by a pupil of Plato. His most famous 
work, the Elements of Geometry, has determined all subsequent 
teaching. Perhaps no book save the Bible has been so much 
studied. For the next twenty-two centuries parts of the Elements, 
and especially the first six of its thirteen books, were the customary 
introduction to geometry. Even though the work has recently 
been superseded in the schools, the newer forms of geometrical 
teaching are based on their Alexandrian predecessor. 

To what extent was Euclid's work original ? Elementary works 
on geometry had already been written by other authors, notably by 
Hippocrates of Chios (p., 30), Before Euclid, it had been generally 


The Failure oj Nerve 

agreed to base geometry on the straight line and circle. The 
properties of the right-angled triangle and the doctrine of propor- 
tion for both commensurables and incommensurables (p. 20) had 
been investigated. Some properties of conic sections were known 
(p. 38). Philosophers were familiar with the five ' Platonic bodies ' 
(pp. 22, 35), The solution of such problems in solid geometry 
as the relation between the volume of a cone or pyramid and that 
of the cylinder or prism circumscribed around it had been attained. 
To all this mathematical activity Euclid certainly added advances 
in arrangement, in logical sequence, in form of presentation, and 
in completeness. His treatise displaced all that had gone before 
it, and rapidly assumed the position which it has since held. 

Although Euclid's great work is called the Elements of Geometry ^ 
its subject-matter extends far beyond what is now regarded as 
geometry. Thus three of its thirteen books are devoted to the 
theory of numbers. In particular they contain the proof that no 
limit can be set to the number of prime numbers. This is a matter 
of importance in view of the great attention focused on the prime 
numbers by previous mathematicians such as the Pythagoreans 
and Plato and by subsequent mathematicians, notably by Erato- 
sthenes (p. 70), Euler (p. 265), Lagrange (p. 266), and Gauss 
(p. 277). 

Euclid’s tenth book expounds the dominating concept of 
irrational quantities, thus opening up a thought-world of which 
the facts cannot be given tangible expression. The Pythagoreans 
(p. 21) had already broken into that world, and of it both Plato 
and Aristotle had had a Pisgah sight, but Euclid was the first to 
attempt any systematic exploration of it. It should be noted, 
however, that Euclid and his Greek successors distinguished 
sharply between irrational quantities and irrational numbers. In 
the theory of proportion as developed in Euclid's fifth book, 
the basis of the theory of irrational numbers is laid but is not 
developed. For its exposition the world had to wait until Des- 
cartes (p. 221) showed the deep unity of the long separated fields 
of number and form. 4 

Euclid was a voluminous writer. Many of his works are lost, 
others survive in Arabic translation or in interpolated or corrupted 
texts. Of those lost we should particularly like to have his work, 


Divorce oj Science and Philosophy: Alexandria 

On Fallacies, which dealt with the causes of error in geometrical 
research. Other of his works dealt with astronomy, optics (p. 8o) , 
and music. 

ARISTARCHUS of Samos (c. 310-230 B.c.) taught at Alexandria 
soon after Euclid. He was himself the pupil of a disciple of Strato 
(p. 52). The peculiar views of Aristarchus on the position of the 
Earth among the heavenly bodies have earned him the title of the 
* Copernicus of Antiquity’. He extended the view of an earlier 
philosopher that the Earth rotates about its own axis (p. 26) by 
maintaining that the Sun itself is at rest, and that not only 
Mercury and Venus but also all the other planets, of which the 


Fig. 22. Aristarchus measures relative distances of Sun and 

Moon from Earth. 

Earth is one, revolve in circles about the Sun. It is interesting to 
observe that this view of Aristarchus brought on him the same 
charge of impiety as had descended on the head of Anaxagoras 
(p. 27) two centuries earlier. 

We owe to Aristarchus the first scientific attempt to measure 
the distances of the Sun and Moon from the Earth, and their 
sizes relative to each other (Fig. 22). He knew that the light of the 
Moon is reflected from the Sun. \\dien the Moon is exactly at the 
half, the line of vision from the observer on the Earth to the centre 
of the Moon’s disk M must be at right angles to the line of light 
passing from the centre of the Sun’s disk S to the centre of the 
Moon’s disk M, Now the observer can measure the angle that 
the Sun and Moon form at his own eye 0 . With a knowledge of the 
two angles at M and 0 "the relative lengths of the sides OS and 


The Failure oj Nerve 

OM can be determined. This gives the relative distances of Sun 
and Moon from the observer. 

The difficulty lay in determining exactly the angle at 0 . A very 
small error here makes a very great difference in the result. 
Aristarchus estimated this angle as 87 degrees when the reality is 
89 degrees 52 minutes. In the resulting calculation he estimated 
the Sun as 18 times more distant than the Moon, instead of over 
346 times more distant 1 

If we have the relative distances of Sun and Moon from the 
observer, the relative sizes of these bodies can be estimated, 
provided that we know the relative sizes of their disks, as they 
appear to an observer on the Earth. On this basis Aristarchus 
calculated that the Sun was seven thousand times larger than the 
Moon. Here further observational errors were introduced, and the 
ratio is very far from the truth. Nevertheless Aristarchus per- 
ceived that while the Moon is smaller than the Earth, the Sun is 
enormously greater. This fundamental relationship may well have 
affected his thought, for it seems inherently improbable that an 
enormously large body would revolve round a relatively minute one. 

Contemporary with Aristarchus at Alexandria were other 
astronomers who recorded the positions of stars by measurements 
of their distances from fixed positions in the sky. Thus they 
defined the position of the more important stars in the signs of the 
zodiac, near to which all the planets in their orbits pass. They 
thereby facilitated accurate observations and record of the move- 
ments of the planets. Their observations were used by later 
astronomers, notably by Hipparchus (p. 76) . 

The philosophy which was the parent of science among the 
Greeks interested itself in three main aspects of the material 
world: [a) number and form and their relation to each other and 
to material objects, {h) the form and workings of the universe, and 
{c) the nature of man. In Alexandria, where science had freed 
itself from philosophy (p. 57), it was thus to be expected that the 
systematization of mathematics and astronomy would be accom- 
panied by a similar development in the basic studies by which 
alone medicine can continue its progressive scientific tradition. 

It was during the first generation at Alexandria that anatomy 
and physiology became recognized disciplines. The earliest im- 


Divorce oj Science and Philosophy: Alexandria 

portant medical teacher of the school was heropiiilus of Chalce- 
don (flourished c, 300 b.c.), contemporary with Euclid. He began 
the practice of dissecting the human body publicly. In describing 
the anatomy of man he compared it with that of animals. He 
recognized the brain as the centre of the nervous system, and he 
regarded it as the seat of the intelligence. The name of Herophilus 
is still attached to certain parts of the brain. One is called by 
modem anatomists the 'winepress of Herophilus’. It is the 
meeting-place of four great veins at the back of the head. 
Their arrangement reminded him of the handles of a press. 
Herophilus was the first to distinguish clearly between veins and 
arteries. He observed that arteries pulsate, in which respect, 
among others, they differ from the veins. Their movement, 
however, he did not ascribe to the heart’s action, but wrongly 
considered that it was natural to the arteries themselves. 

A little younger than the anatomist Herophilus was the physio- 
logist ERASISTRATUS of Chios (c. 28o B.C.), who also taught at 
Alexandria. He was an atomist and a follower of Democritus 
(p. 15), but his physiology was based on the idea that every organ 
is a complex of a threefold system of vessels — veins, arteries, and 
nerves — extending by ever more minute branching beyond the 
reach of vision. In those days, and for long afterwards, the nerves 
were regarded as hollow. Their imaginary cavities were thought to 
convey the hypothetical ‘nervous fluid’, much as the arteries and 
veins carry blood, 

Erasistratus, like Herophilus, paid particular attention to the 
brain. He distinguished between the main brain, or cerebrum, and 
the lesser brain, or cerebellum. He observed the convolutions in the 
brain of both man and animals, and associated their greater 
complexity in man with his higher intelligence. He made experi- 
ments on animals which led him to distinguish between the 
posterior nerve-roots of the spinal cord, which convey sensations 
from the surface of the body, and the anterior nerve-roots which 
convey the motor impulses. This discovery was forgotten or 
neglected till the time of Sir Charles Bell (1774-1842) in the 
nineteenth century (p. 365). 

Erasistratus also observed the lacteals, those lymphatic vessels 
that convey the white, milk-like fluid — the so-called ‘chyle’ — 


The Failure of Nerve 

derived from the food in the intestine, to the liver. The lacteals 
were seldom mentioned again until the Italian Gasparo Aselli 
(1581-1626) recorded them in the seventeenth century. They 
play a very important part in the animal economy. 

A word must be said as to the views of Erasistratus on the 
general working of the animal body. He supposed that air is taken 
in by the lungs and passes to the heart. Here, as he held, it enters 
the blood and is changed into a peculiar kind of pneuma or spirit — 
the 'vital spirit* — which is sent to the various parts of the body 
by the arteries. It is carried to the brain, among other parts, and 
is there further altered into a second kind of pneuma, the ' animal 
spirit'. This animal spirit reaches different parts of the body 
through the nerves, which he wrongly regarded as hollow. The 
physiological system of Erasistratus was further developed by 
Galen, who, however, advanced great objections to the views of 
his forerunner (p. 90). 

After the first generation anatomical enthusiasm at Alexandria 
waned. We may refer to three special points concerning it and 
concerning Alexandrian science in general: 

{a) The names of Herophilus and Erasistratus are linked with 
the terrible charge of having dissected living men. Historians who 
have investigated the charge are satisfied that it is false. 

(6) Erasistratus considered the pneuma that circulates in the 
body to be ultimately drawn from the air, or pneuma of the great 
world. This gave a physiological basis to the philosophical concep- 
tion of the spirit of man as part of the world-spirit. Such a con- 
ception is frequently encountered in later writings, as, for example, 
in the works of the Stoic school (2nd cent, a.d.) such as those of 
the Emperor Marcus Aurelius or in the so-called 'Hermetic' 
writings (3rd cent. a.d.). Physiology and philosophy thus reacted 
on each other. 

[c) In the third century b.c. Alexandria was an important Jewish 
centre. Parts of the Old Testament had been rendered from 
Hebrew into Greek by about 250 b.c. Greek contacts went far 
toward rationalizing the Hebrew view of nature. Thus, while 
earlier Biblical literature contains many references to divine 
intervention in the course of nature, the Wisdom Literature of 
Alexandrian date equates natural law with divine ordinance. In 

Divorce oj Science and Philosophy: Alexandria 

some passages the various types of Greek philosophy are set over 
against this Hebrew view. Among the Greeks various 'first 
principles' had been adopted. Thales had proposed 'water' 
(p. lo), Heracleitus 'fire' (p. 14), Pythagoras the ' circling stars ' 
(p. 18), Anaximenes 'air' (p. 12), yet other philosophers vague 
essences that may be rendered 'wind' or * pneuma* (p. 12). 
Finally the new astrological science coming in from Babylon 
suggested the complex mathematical order of the heavenly bodies, 
which signalled the seasons, as controlling the seasons and through 
them the lives of men. A Jewish work written in Alexandria.about 
100 B.c. inveighs against all these views: 

' Surely vain were all men in their natures, and without perception 
of God Who could not, from the good things that are seen, know 
Him that is ; Neither by giving heed to the works did they recognise 
the Workmaster, But either fire [Heracleitus] or wind or the swift 
air [Anaximenes] Or circling stars [Pythagoras] or raging water 
[Thales] or the lights of heaven [astrology] 

They deemed the gods that govern the world.* 

{Wisdom of Solomon xiii. 1-2.) 

The influence of Greek science can similarly be traced into the 
domain of Hebrew physiological conceptions. Thus, for instance, 
the seat of the understanding in the Wisdom Literature is 
usually placed in the heart. This is Aristotelian and contrary to 
Herophilus and Erasistratus, who placed the seat of intelligence 
in the brain. It is also opposed to the older Hebrew view (e.g. 
Psalm xvi. 7) which placed it in the liver. In several places, too, 
the Alexandrian "Wisdom Literature" as well as the New Testa- 
ment writings (e.g. 2 Peter hi. 10 .'Galatians iv. 8-9) set forth the 
Greek doctrine of the four elements. 

2. Archimedes, Rise of Mechanics. 

ARCHIMEDES (287-212 B.C.) of Syracuse in Sicily was the greatest 
mathematician of antiquity. His life was entirely devoted to 
scientific pursuits, and his work is so fundamental that it affects 
every department of science. He was himself the son of an astrono- 
mer and on intimate terms with King Hiero of Syracuse. He 
visited Alexandria, where he met successors of Euclid. His whole 
work is instinct with a human element. Moreover, despite his 
absorption in science, he was not above applying his knowledge 


The Failure of Nerve 

to practical matters. Thus his name is remembered in connexion 
with the Archimedean screw for raising water (Fig. 23). It is said 
that he invented it during a visit to Egypt, and it is still in wide 
use there. The use of the screw as a means of applying mechanical 
force was unknown before Archimedes and was probably suggested 
by his device. He also contrived war engines for the defence of 
his native city against the Romans. Accounts of these and of his 
other mechanical devices are extant, but he himself wrote no 
works on them. 

The writings of Archimedes show a generous appreciation of the 
mathematical achievements of others. He had friendly personal 
relationships with his younger contemporaries, notably Erato- 
sthenes (p. 70). His lofty intellect, his compelling lucidity, and his 
terseness of exposition, made a profound impression on his fellow 
mathematicians. His mechanical skill must have been of a high 
order, for we hear also of his 'planetarium', a sphere of the heavens 
with models of the Sun, Moon, Earth, and planets, whose move- 
ments were displayed with an elaboration of detail that showed 
even eclipses. 

A well-worn story tells of one application of the knowledge of 
Archimedes to practical affairs. The tyrant Hiero, on gaining 
power in Syracuse, vowed a golden crown to the gods. He con- 
tracted for its manufacture and weighed out the gold. The con- 
tractor duly delivered a crown of correct weight. But a charge 

Divorce of Science and Philosophy: Alexandria 

was made that some gold had been abstracted and an equivalent 
weight of silver substituted. Hiero invoked Archimedes to put the 
matter to the test. While it was on his mind, Archimedes happened 
to go to the bath. On getting in, he observed that the n^ore of his 
body was immersed, the more water ran over the top. This 
suggested the solution. Transported with joy he rushed home 
shouting ‘Eureka! Eureka!* (‘I have found it, I have found it!’) 
What he had found was, in effect, the conception of specific gravity. 

He made two masses of the same weight as the crown, one of 
gold, the other of silver. Next he filled a vessel to the brim and 
dropped in the mass of silver. Water ran out equal in bulk to the 
silver. The measure of this overflow gave the bulk of silver. The 
same was done with the gold. The smaller overflow corresponding 
to the gold was, of course, as much less as the gold was less in 
bulk than the silver, for gold is heavier than silver. The same 
operation was now done with the crown. More water ran over 
for the crown than for the bulk of gold of like weight, less than 
for the bulk of silver. Thus was revealed the admixture of silver 
with the gold. Archimedes had, in effect, obtained the relative 
specific weights of gold, silver, and of the mixture of the two, by 
comparing the relative amounts of water displaced by the same 
weight of the three. The scientific aspect of the subject is set forth 
in his work On Floating Bodies, This is the first record of the 
scientific employment of what we should call in modem parlance 
‘specific weights’, though, of course, long before Archimedes, men 
must have been well aware that some substances were relatively 
heavier than others. 

This question of the scientific use or development of a piece of 
common knowledge is important for the history of science. Dis- 
cussion of it throws some light on the nature of the scientific 
process. Thus to Archimedes the ancient world owed a general 
exposition of the doctrine of levers (Fig. 24). This must not be 
taken to mean that Archimedes invented the lever any more than 
that he had discovered some bodies to be heavier than others. 
Levers in various forms were used from remotest antiquity, and 
an intelligent ape will use a stick as a lever. But it is one thing to 
use or even to contrive a device, and another to lay bare its exact 
mathematical principles and to follow them to their theoretical 

3012 F 65 

The Failure oj Nerve 

applications and conclusions. Important in this connexion is the 
statement of Archimedes of the possibility of moving a weight, 
however large, by a force, however small — a valuable theoretical 
application of levers. His saying is often recalled, ' Give me but 
a place to stand, and I can move the world.' He demonstrated 
this with a compound lever by which, with only the slightest 
effort, he was able to move a laden ship. Archimedes no more 
invented levers than the Greeks invented science. But science 
owes to the Greeks its formal and conscious development as a 

Fig. 24. The three orders of lever. 

discipline and a method (p. 5), and the doctrine of levers owes 
to Archimedes its first formal and systematic exposition as 
susceptible of exact analysis. Formal and systematic exposition 
is a main task of science and without it knowledge cannot rise 
into the realm of science. 

Perhaps the earliest work of Archimedes that we have is that 
On Plane Equilibrium, In this some fundamental principles of 
mechanics are set forth as rigorous geometric propositions. The 
work opens with his famous 'postulate': 'Equal weights at equal 
distances are in equilibrium ; equal weights at unequal distances 
are pot in equilibrium but incline toward the weight at the greater 
distance.' This is, in effect, the principle of the steelyard. It led 
him in the end to the discovery of the centre of gravity in a variety 
of geometric figures. 

Among the mathematical achievements of Archimedes a very 


Divorce of Science and Philosophy: Alexandria 

high place must be given to his methods of measuring the areas 
of curved figures and surfaces. The simplest expression of this 
effort, 'squaring of the circle', had been broached by Hippocrates 
of Chios (p. 30). Eudoxus (p. 37), in estimating the volume of 
certain solid bodies, had propounded a method that involved in its 
essence the idea of ‘limits'. This idea had been used by Euclid 
for a particular proposition of his twelfth book. Archimedes, how- 
ever, employed limits systematically. This doctrine is of the ut- 
most practical and historical importance, since it has formed a 
main foundation of modern mathematical development. It is 
essential to the ‘calculus' as developed by Newton (p. 252) and 
Leibniz (p. 265) . The calculus in its turn has been the starting- 
point for the development of many types of mathematical research. 

The principle of the doctrine of limits can be expressed very 
simply. A square can be inscribed within a circle. Of such a 
figure two propositions are obvious: 

(a) The sum of the sides of the square is less than the circum- 
ference of the circle : 

(b) The area of the square is less than the area of the circle. 

It is quite easy to double the number of sides and make an 
eight-sided figure, still inscribed within the same circle. Proposi- 
tion (a) and (b) remain true but the difference is smaller in each 
case. We can go on doubling the number of sides to 16, 32, 64, 
128, 256 or to any higher number. The more we increase the 
number of sides the more nearly wiU the sum of the sides and the 
area of the inscribed figure approach the circle. ‘In the limit', 
when its sides are so small as to be no more than points, the poly- 
gon may be conceived as becoming the circle. Archimedes realized 
that this limit can never be reached but that it can be approached 
as nearly as we wish (Fig. 25). 

Archimedes proves that the area of a circle is equal to that of a 
triangle of base equal to the circumference of the circle and of 
height equal to the radius of the circle. To calculate this area it 
is necessary to find the ratio between circumference and diameter, 
In estimating this ratio Archimedes sought the limit approached 
by the sides of regular polygons both inscribed and circumscribed 
on the circle. The limits for their ratio to that of the diameter he 
foimd to he between 3^^ and 3|§. The latter has, since his day, 


The Failure of Nerve 

been generally accepted as a good approximate value of the 
quantity known as tt. 

In his Quadrature of the Parabola Archimedes relates that he 
had been led by the study of mechanics to the solution of the 
problem of finding the area of a segment of a parabola, and that 
he had then obtained geometric proof of the correctness of his solu- 
tion. His method resembles that which he adopted for the circle, 
namely to take both an inscribed and a circumscribed figure in 

relation to the curve under investigation. The two rectilinear 
figures are, as it were, compressed one from within and the other 
from without until they coincide with the curvilinear figure. 

This mode of procedure, as well as that of using mechanics for 
the solution of problems afterwards demonstrated by geometry, 
leads us to the consideration of an extremely interesting treatise 
by Archimedes, the nature of which is suggested by its title 
On Method, 

For the most part, Archimedes, like other Greek men of science, 
gives us only his final results. He gives us his proofs, but does not 
tell us how he reached them. In the Method, however, Archimedes, 
addressing Eratosthenes (p. 70), recalls the mathematical dis- 
coveries which he had sent on a former occasion and proceeds to 


Divorce oj Science and Philosophy: Alexandria 

inform him that he is now sending a description of the way in 
which he elicited them. 

In essence the ‘Method’ consists in the application of two 
principles. The first is that a plane figure may be regarded as an 
aggregate of an infinite number of parallel lines with certain 
common properties. The second is the consideration of the 
respective weights of the two plane figures as drawn on paper 
whose area has to be compared. The process is also applied to 
demonstrate relationship between the areas of solid figures con- 
sidered as aggregates of an infinite number of parallel planes. 
It amounts to a practical solution of problems of the relation 
between areas or volumes of two figures by analysis, mechanical 
or other, after which the philosopher returns to a synthetical 
mathematical process. He thus gains by experiment some insight 
into the solution before he seeks its mathematical demonstration. 

Finally we may mention the remarkable system used by 
Archimedes for expressing very large numbers. It is so efficient 
that it enables any number to be expressed, up to that which, in 
our notation, would require eighty thousand million million 
ciphers. Archimedes expressed the opinion that his system was 
adequate to express the number of grains of sand that it would 
take to fill the universe ! He therefore called his work the Sani 
Reckoner. From his calculation of the size of the universe, we 
get our idea of the cosmic conceptions of Archimedes. He knew 
the view of Aristarchus (p. 59) that the universe was heliocen- 
tric, the Earth revolving round the Sun in a comparatively un- 
important orbit. 

The sum of the contributions to knowledge by Archimedes is 
enormous. With his character, his humanity, his width of interest, 
his simplicity of exposition, and his unity of purpose, no mathe- 
matician of any age has commanded such general sympathy and 

3. Middle Alexandrian Period (200-0 B.C.). 

A worthy Alexandrian successor of Archimedes was Apollonius 
(fl. 220 B.c.) of Perga in Asia Minor (not to be confused with 
Pergamum) . He studied under successors of Euclid at Alexandria 
and also at Pergamum.* Apollonius is specially remembered for his 


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Conic Sections, a subject which he developed greatly and placed 
on a new footing. 

Apollonius built on the work of Menaechmus (p. 38). That 
writer had derived the three types of conic section from three types 
of right cone. Apollonius showed, however, that all the three 
types of conic section can be derived from the same cone, whether 
right or scalene (Fig. 17). He established the terms ellipse, para- 
bola, and hyperbola to denote the three types of section previously 
indicated by the angle of the cone of origin. The general geometric 
laws which give the properties of conic sections come to us, like 
the nomenclature of these figures, from Apollonius. 

Archimedes and Apollonius between them originated two of the 
great problems which have ever since occupied geometers. The 
first is the quadrature of figures outlined by curves. This gave 
rise in due course to the infinitesimal calculus. The second is the 
theory of conic sections. This gave rise in due course to the theory 
of geometrical curves of all degrees. 

The Ptolemies, in their zeal for learning, did not forget geo- 
graphy. Ptolemy III Euergetes (247-222 B.c.) rendered the 
greatest service to the science by his encouragement of Erato- 
sthenes (c. 276-c. 194 B.C.), the librarian at Alexandria, and the 
most learned man of antiquity. His most important investigation, 
the measurement of the globe of the Earth, was performed by an 
operation of beautiful simplicity. Eratosthenes started from the 
three propositions (Fig. 27) : 

(a) That at Syene on the Nile (the modern Aswan) at noon on 
midsummer day an upright rod casts no shadow ; 

(b) That Syene is 5,000 stadia from Alexandria; 

(c) That Syene is directly south of Alexandria. 

Now, it is clear that, if we consider the Earth as a sphere, then 
the ratio 

Angle at centre subtended by 5000 stadia 5000 stadia 

Four right angles ~ Circumference 

The problem is, therefore, to determine the angle at the centre 
subtended by 5,000 stadia. But if on midsummer day the shadow 
cast by an upright rod at Alexandria is measured, then we shall 
be able to estimate the angle which the Sun's ray makes with the 
rod. Since, however, the Sun is so vastly distant from the Earth, 


Fig. 26. The circle as special case of the ellipse, shown by series of sections 
through a cylinder. The cylinder of the diagram exactly contains a series 
of spheres ; the points of contact of these with the section planes are the 
foci. The left figure is pictorial while the curves on the right give the true 
shape of the sections. 

With a slightly more complex diagram the same relations may be shown 
in a series of sections through a cone, the cylinder being itself a special case 
of the cone (compare Fig. 58). 

The Failure oj Nerve 

the Sun's ray at Alexandria is in effect parallel to the Sun's 
ray at Syene. Therefore the angle that the Sun's ray makes with 
the rod is equal to the angle subtended by 5,000 stadia at the 
Earth's centre. There is thus but one unknown — the Earth's 

circumference — ^in our equation. The circumference of the Earth 
thus obtained is a very fair estimate. 

Having measured the Earth, Eratosthenes proceeded to con- 
sider the known parts of it. Here, in common with almost all 
ancient geographers, he fell into an error, or rather a self-imposed 
limitation. Eratosthenes regarded the habitable world as placed 
wholly within the northern hemisphere and forming only about 
a third of that. Again following his predecessors, Eratosthenes 
considered that the habitable world was longer than it was broad. 

Divorce oj Science and Philosophy: Alexandria 

He estimated that the distance from the Atlantic to the Eastern 
Ocean was 78,000 stadia (that is, about 7,800 geographical miles), 
and from the parallel of the Cinnamon Land (Taprobane or Ceylon) 
to the parallel of Thule was 38,000 stadia. As Eratosthenes 
estimated the circumference or equator of the Earth at 250,000 
stadia, he was able to estimate the circumference at the parallel 
of the Pillars of Hercules (p. 13), which he knew was also that of 
Rhodes (latitude 36°) (Fig. 28). 

This fundamental parallel passed, as he erroneously thought, 
through other important points — the westernmost point of Spain, 
for example, and the southern points of Italy and Greece and along 
the Taurus mountains. At this parallel the total circumference 
of the world he estimated at 200,000 stadia. The rest was sea, 
so that, as he observed, 'if it were not for the vast extent of the 
Atlantic one might sail from Spain to India along the same 
parallel* . This is the first suggestion for the circumnavigation of 
the globe. 

At right angles to the important parallel of Rhodes, Eratos- 
thenes determined a north-south line between Alexandria and 
Syene. This line, produced northward, he regarded as passing 
through Byzantium and, beyond, to the mouth of the river Borys- 
thenes (now called the Dnieper). Southward, he considered that 
it passed to Meroe, and then along the Nile to the Sembritae. 

Both these fundamental lines contain several errors of alloca- 
tion. Their determinations, together with those on other parallels 
of latitude and lines of longitude, are, however, sufficiently ac- 
curate for the construction of a map of the Mediterranean area 
recognizably similar to one based on modem knowledge (Fig. 28). 

Eratosthenes exhibited great ability as a mathematician. He 
advanced the knowledge of prime numbers, a subject to which 
Archimedes had paid much attention. The famous sieve of 
Eratosthenes is a device for eliciting these numbers. Write down 
all integers in their natural succession. Then strike out all the 
multiples of 2, then the remaining multiples of 3, then those of 5, 
&c., through the other prime numbers (Fig. 29). The properties 
of prime numbers have attracted mathematicians in all ages, and 
it is astonishing how some simple rules concerning them have not 
been rationally explained to this day. Thus it is now well over a 


R»ali9l oF 

Meridian Mendtan H^dfar? Mertd/an ’ Meridmn 

Pi f Jars of Carthage (^Akxandna oPfuphrates of Caspian of Indus 

Fig. 28. The World according to Eratosthenes. 

Divorce oj Science and Philosophy: Alexandria 

century since it was remarked that every even number is the sum 
of two primes. This has been verified up to 200,000,000, but no 
proof is yet forthcoming. 

Mathematical advance in Alexandrian times made possible a 
great development of astronomical theory. The discussion of the 

Fig. 29. The Sieve of Eratosthenes. 

supposed rotation of the celestial spheres and of the movements 
of the heavenly bodies gave rise to a nomenclature, parts of which 
have survived to our day, but parts of which have been modified 
by the Arabian and other authors through whose hands the Greek 
mathematical works have passed (p. 147). 

The astronomical observer regarded himself as being in the 
centre of the vast heavenly sphere bearing the fixed stars. He 
considered the Earth so small that his distance from its centre was 
as nothing to his distance from the celestial boundary. Of this 
celestial sphere he could only see half, for the other hemisphere 
was hidden from him by the opaque Earth. The limiting circle 
thus imposed on his vision was the horizon (from a Greek word 
meaning *to bound' or 'to limit'). This horizon formed a great 
circle on the heavenly sphere. He recognized, too, the celestial 
poles or points on the sphere pierced by the axis about which the 


The Failure of Nerve 

heavens seem to turn. On the sphere he marked out the meridian, 
which passes through the zenith (a word of Arabic origin) and 
the poles. The great circle at right angles to the line joining the 
poles was the equator • Starting from these elementary conceptions 
the Alexandrian observers worked out their whole astronomical 
system (Fig. 30). 

Besides measuring the size of the Earth Eratosthenes also made 

Fig. 30. The astronomical elements. 

a remarkably accurate measurement of the angle which the circle 
of zodiacal constellations makes with the celestial equator, in 
other words a measurement of the obliquity of the ecliptic. His 
estimate works out at 23 degrees 51 minutes. This is only seven 
minutes from the truth. 

The greatest astronomer of antiquity was hipparchus of Nicaea 
(c, 190-120 B.C.). He worked at Rhodes, where he erected an 
observatory and made most important researches. He developed 
trigonometry by which numerical calculations can be applied to 
figures drawn on either plane or spherical surfaces. The study is 
of great value to astronomy. 

Hipparchus made numerous accurate astronomical observa- 
tions. He also collected and collated the records of previous 


Divorce of Science and Philosophy: Alexandria 

observers to see if astronomical changes had taken place in the 
course of the ages. There were available to him records of his 
Alexandrian and earlier Greek predecessors, and also those of the 
yet more ancient Babylonian astronomers. As a result of these 
comparisons he gave to the world two brilliant astronomical con- 
ceptions. (a) One of these, the precession of the equinoxes, was of 
permanent value, (b) The other, his theory of the movements of 
the planets and notably of the Sun and Moon, was of value to 
subsequent generations for the calculation of eclipses. 

(a) Precession of the equinoxes. In 134 B.c. Hipparchus observed 
a new star in the constellation Scorpio. This suggested to him that 
he should prepare a catalogue of star positions. He therefore drew 
up a list of upwards of a thousand stars, each of which was given 
its celestial latitude and longitude. The constellations to which 
Hipparchus referred these stars are those which are to-day gener- 
ally accepted. He showed great foresight in recording a number 
of cases in which three or more stars were in a line, so that 
astronomers of subsequent ages might detect changes in their 
relative positions. 

Hipparchus proceeded to compare his observations with others 
of about 150 years earlier. He found that in this lapse of time there 
had been changes in the distance of the stars from certain fixed 
points in the heavens. The changes were of a kind that could only 
be explained by a rotation of the axis of the earth in the direction 
of the apparent daily motion of the stars. This causes the equi- 
noxes to fall a little earlier each year. The knowledge of this 
precession of the equinoxes and of the rate at which it takes place 
was necessary for the progress of accurate astronomical observa- 
tion. The complete cycle of precession takes 26,000 years. 

(b) Theory of motion of the planets. When Hipparchus came to 
examine the apparent movement of the planets he had before him 
two theories, namely, that of *epicyclic motion* and that of 
^excentric motion'. Certain of his predecessors — notably Apol- 
lonius of Perga (p. 69) — ^had suggested the epicyclic view (Fig. 
31). According to this each planet moves on a circle the centre of 
which moves on another circle, the centre of which is the centre 
of the Earth. Others of his predecessors had set forth the view 
of excentric motion. According to this the jplanet moves around 


The Failure of Nerve 

the Earth but in a circle whose centre is not at the centre of the 
Earth. This secondary centre may also be represented as moving 
on a circle. Hipparchus explained the behaviour of the sun by a 
fixed and the moon by a moving excentric. (The geometric 
results of moving excentric and epicycle are identical.) 

The epicyclic view finally prevailed through the mediation of 
the astronomer Ptoleniy (p. 83). The theory of the excentric 

space ) 

Fig. 31. To illustrate epicyclic motion. 

motion of the Moon and to a less extent of the Sun, as enunciated 
by Hipparchus, was, however, of great service in that calculations 
based on it accorded much more closely with actual observations 
than did calculations based on any older doctrine of their move- 
ments. From the time of Hipparchus onward eclipses of the Moon 
could be predicted within an hour or two. Eclipses of the Sun 
could be predicted less accurately. 

The Middle Alexandrian period, so brilliant in its development 
of the mathematical sciences, is disappointing when we come to 
consider its biological achievement. Of true scientific biology, 
apart from medicine, there was very little. The tradition almost 
died with Theophrastus (p. 51). With one exception the writings 
with biological bearing that have come down to us from the middle 
period are trivial. The exception is the herbalist crateuas 

Divorce of Science and Philosophy: Alexandria 
(c 8o B.C.), who had the merit of introducing the systematic 
representation of plants by figures rather than by description. 
This method, important still, was doubly valuable in the absence 
of a system of botanical nomenclature. The plants figured by 
Crateuas were all of medical application. Copies of his figures 

Fig. 32. 'Pheasant's eye’, Adonis aestivalis, as represented by Crateuas 
about 80 B.c. and preserved in a MS. derivative of about 500 a.d, 

have survived. They are of interest as the earliest specimens of 
scientific draughtsmanship (Fig. 32), and the tradition that they 
created can be traced through the ages to our own time. 

In more purely medical matters illustration is perhaps also the 
main contribution of the middle Alexandrian period. The medical 
writings of the time were mainly commentaries on the works of 
the Hippocratic collection. Copies of the sketches of operations 


The Failure of Nerve 

and bandaging by Apollonius of Citium (c. loo b.c.) have sur- 
vived, and give a good index of the conditions under which ancient 
medical practice was conducted. 

4. Late Alexandrian Period to 200 a.d. 

Eg5^t became a province of the Roman Empire in 50 b.c. 
Alexandria's achievement had now become an episode in her 
history. There remained little native power of initiative, but some 
scientific curiosity and considerable compilatory capacity. Creative 
efforts — as those of Strabo (p. 100), of Ptolemy (p. 83), and of 

Fig. 33. Hero’s magic jug. As the thumb is pressed on or released from 
the hole in the handle, the jug will pour or not. 

Fig. 34. Hero’s steam-engine. The globe is pivoted on tubes rising from 
the boiler. It revolves by the reaction of the issuing steam. 

Galen (p. 90) — ^were forthcoming only in response to definite 
imperial needs. 

An ingenious writer of the age was one hero of Alexandria 
(c. A.D. 100). He applied himself to entertaining contrivances 
and sometimes to practical devices rather than to high scientific 
themes. His Pneumatica describes many conjuring tricks. Thus 
the principle of the siphon is applied to a jug from which water 
pours or not at will (Fig. 33). Most famous of his toys was a globe 
which whirls by force of steam— the first suggestion of a steam- 
engine (Fig. 34). In his Mechanica he shows understanding of the 
cogwheel, of rack and pinion, of multiple pulleys, of transmission 
of force from a rotating screw to an axis at right angles to it, and 


Divorce oj Science and Philosophy: Alexandria 

to the combination of all these devices with levers (Fig. 35). 

Hero records advances in optics. The oldest treatise on the 
mathematical aspect of that subject is by Euclid (p. 57), who 
considered that light moves in straight lines and believed vision 
to be something that goes forth from the eye. Hero showed that 
when light is reflected from a surface, it is at an angle equal to the 
angle of incidence. One of his surve5dng instruments depended for 
its working on the equality of these angles. His Dioptra (Fig. 36) 

Fig. 35. Hero's mechanical repertoire. 

served many purposes for which the theodolite is now used. 
Hero was also particularly ingenious in his use of water-levels in 

Attempts were made to study refraction, that is, the behaviour 
of light in passing from one medium into another of different 
density, as from air into glass or water. The bent appearance of 
oars or rods dipped in water must have been observed very early, 
CLEOMEDES (first century a.d.) referred to the same principle the 
fact that an object, lying in an opaque basin and just obscured 
by the brim, could be rendered visible by pouring in water. He 
applied this principle to the atmosphere and suggested that the 
Sun, even when below the horizon, might be visible under certain 
circumstances (see Fig. 37) . It is remarkable that he failed to give a 
practical application to this view of atmospheric refraction, for he 




The Failure oj Nerve 

disbelieved statements of his predecessors that in certain lunar 
eclipses the Sun seems to be still above the horizon while the 
eclipsed Moon rises in the east. 

Fig. 36. Hero’s ‘Dioptra’ for taking angles as in levelling, estimating 
heights or distances between far-off points, etc. The circular graduated table 
has two sights, movable about its centre on a rigid arm. The table is 
supported by a column which can be rotated on its axis by a fixed screw 
working on a toothed disk. The table rests directly on a second toothed 
disk which can be rotated in a vertical plane by a second screw fixed to 
the column. 

That some beginning had already been made of the science 
which deals with the eye as an optical instrument we learn from 
a work by a medical writer, rufus of Ephesus (c. a.d. ioo). He 
had a fairly accurate conception of the structure of the eye. Some 
of the names which he applied to parts of this organ have survived 


Divorce oj Science and Philosophy: Alexandria 

in modem scientific nomenclature. Rufus is the first to describe 
the eye as possessing a lens\ he speaks of it as ‘lentil-shaped*. 

A late Alexandrian writer, diophantus (perhaps of about 
A.D. i8o), is important as the best ancient exponent of algebra. 
His work on that subject was commented on by hypatia of 
Alexandria, the only woman mathematician of antiquity. She 
was murdered by Christian fanatics in 415. The work of Dio- 
phantus is the first that employs signs systematically. He gives 
symbols for the unknown, for powers, for minus, for equality, and 
so forth. He solves equations of the first, second, and, in one 
instance, of the third degree. He sets forth a method for finding 
two or more square numbers the sum of which is a given number, 
while each of the two approximates to the same number. The 
device he adopts is a method of approximation to limits. Thus 
in dividing 13 into two square numbers each of which is to be 
greater than 6 he readies the result that the sides of the required 
2S8 2^7 

squares are and Diophantus solved other comparable 

Not only was Greek algebra far behind Greek geometry but it 
was also far less influential on later mathematical development. 
Thus the work of Diophantus did not appear in print until 1575 
and then only in a Latin translation. It was, therefore, without 
effect on the revival of mathematics in the sixteenth century. 
With Diophantus creative Greek mathematics comes to an 

PTOLEMY of Alexandria (flourished a.d. 170),' who provided the 
final astronomical and geographical s3mtheses of antiquity, con- 
tributed also to the knowledge of optics. He not only knew that 
luminous rays in passing from one m,edium to another are deflected, 
but he actually measured the angle of deflection. Applpng the 
known principle of the refraction of light, Ptolemy points out that 
the light of a star on entering the earthly atmosphere and on 
penetrating to the lower and denser parts must at each stage be 
gradually bent or refracted (Fig. 37). Thus it will appear to be 
nearer the zenith than is actually the case. 

The great work of Ptolemy known as the Almagest has proved 
* Not to be confused with the Ptolemies, kings of Egypt, 


The Failure of Nerve 

one of the most influential of all scientific writings. The very name 
has a history. The Greeks called the work the megale syntaxist 
i.e. ‘great composition'. The later translators from the Greek 
into Arabic, either from admiration or carelessness, converted the 
positive megale into the superlative megiste. Thus it became in 
Arabic Almagisti, whence Latin Almagestum and colloquial 

The Almagest, a work of utmost skill, was of the highest signifi- 

Fig. 37. Refraction of ray by atmosphere makes the apparent position 
of a star nearer the zenith than the real position . The atmosphere, following 
Ptolemy, is represented as ending abruptly. 

cance for mathematical development. It has provided the founda- 
tions of trigonometry, both plane and spherical. Its basic cosmic 
conceptions, however, Ptolemy certainly derived from his prede- 
cessors. Thus he invoked epicyles (p. 77) to explain the movements 
and behaviour of the planets, employing them to resolve some 
errors and inconsistencies of Hipparchus. He retained, however, 
excentrics (p. 78) to explain the movements of the Sun and Moon. 

Among the contents of the Almagest is an account of the con- 
struction of the astrolabe (Fig. 38), the qjiief astronomical instru- 
ment of ancient and medieval times. It was, in essence, a device 
for determining the angle of elevation of a heavenly body. Ptolemy 
used the instrument to obtain the distance of the Moon hy parallax. 
The method is substantially that still in use and is, in principle, 
very simple (Fig. 39) . If in one place Z, the Moon is at zenith, then 
a line passing from the Moon at that place passes also through the 
centre of the Earth C. If an observer 0 takes at the same time 
the elevation of the centre of the Moon M , then we know the angle 


Divorce oj Science and Philosophy: Alexandria 

at 0 of the triangle MOC. If we know the distance from 0 to Z 
we can calculate the angle at C. We thus know the three angles 
and therefore the relative lengths of the sides of the triangle MOC, 
Thus we can determine the ratio of CM to CO. Ptolemy thus 
estimates the Moon's distance to be 59 times the radius of the 

Fig. 38. A simple form of Astrolabe. It consists essentially of a sus- 
pended disk graduated in degrees around the centre of which turns a limb 
with a sight at each end. The adjustment of the sights on to a heavenly 
body gives its elevation. 

Earth, which is not very far from the truth. Working on an 
eclipse method of Hipparchus he estimates the Sun, however, to 
be only 1,210 Earth radii distant. This number is about one- 
twentieth of the true reckoning. He tells us that he has no 
means of estimating the distances of the lesser planets, but he 
follows tradition in accepting rapidity of motion as the main test of 


The Failure, of Nerve 

nearness. Thus from within outward his universe consists of Earth, 
Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. This scheme 
was passed on to the Middle Ages (Fig. 40). 

Ptolemy's other great work was his Geographical Outline, This 
was essentially a product of the knowledge brought by the expan- 


sion of the Roman Empire. He studied itineraries of Roman 
officials and merchants. Thus he may be said to have preserved 
for us a summary of Roman knowledge of the Earth's surface, 
presented, however, in a form quite beyond the capacity of any 
Latin geographical writer. Ptolemy may well have had access to 
the great map prepared by Vipsanius Agrippa at Rome (p. 102). 

Ptolemy developed his own manner of representing the curved 
surface of the Earth on a plane surface. In his scheme of * projec- 
tion' the parallels of latitude are arcs of concentric circles, the 
centres of which are at the North Pole. Chief among the parallels 
are the Equator and the circles passing through Thule, through 
Rhodes, and through Meroe. The meridians of longitude are 


Divorce of Science and Philosophy: Alexandria 

represented by straight lines which converge to the Pole* (Fig. 41). 
He delineates in this manner the whole of the then known world. 
Its boundaries are : on the north, the ocean which surrounds the 
British Isles, the northern parts of Europe, and the unknown land 
in the northern region of Asia ; on the south, the unknown land 

Fig. 40. The Ptolemaic World-System. 

which encloses the Indian Sea, and the unknown land to the south 
of Libya and Ethiopia; on the east, the unknown land which 
adjoins these eastern nations of Asia, the Sinae (Chinese) and the 
people of Serica, the silk-producing land ; on the west, the great 
Western Ocean and unknown parts of Libya. The portion of the 
Earth thus surveyed covers in length a hemisphere and in breadth 
between 63° north latitude and 16° south latitude. 

* He has another scheme of projection in which the meridians are also 


The Failure oj Nerve 

As originally written Ptolemy's geography was furnished with 
maps. These have long since disappeared, but as Ptolemy gives 
the latitude and longitude of the places that he mentions his charts 
can be reconstructed. A pecxiliar interest attaches to the map of 
Britain, which can thus be put together (Fig. 42) . Scotland is bent 
eastward with its axis at a right angle to that of England. This 

Fig. 41. Ptolemy's Map of the World showing his scheme of projection. 

is an unusual degree of error for Ptolemy. It is probable that he 
was here working not on the records of travellers, but on maps of 
the island, and that he had made the error of fitting the map of 
Scotland on to that of England on the wrong side ! 

Ptolemy exhibits the final' extension of scientific geography in 
the Empire. How far the average educated citizen of the Empire 
was able or willing to appreciate science in general and geography 
in particular is another matter. It was the attitude of the Romans 
and especially of the Roman ruling class to things of the mind that 
determined the fate of science and with it, perhaps, the fate of 
the Empire. To estimate the attitude of the Roman to science we 
must turn to geographical works in Latin (pp. 102-4). 

The Almagest of Ptolemy was translated into Latin in the later 
twelfth century and his Geography in the fifteenth. Thus they 
could not directly influence the earlier Middle Ages during which 


Divorce oj Science and Philosophy: Alexandria 

a simpler cosmic scheme based on Aristotle prevailed. In the 
later Middle Ages conflict between the views of Aristotle and those 
of Ptolemy became of considerable importance for the history of 

The picture presented by the exact sciences of the late Alexan- 

Fig. 42. The British Isles according to Ptolemy. 

drian period is that of a number of minor works followed by one 
great S5mthesis and then a steady decline. We have seen this for 
astronomy and geography. It is repeated for the biological and 
medical sciences. In those departments we need only note the 
figures of Dioscorides and Galen. 

PEDANius DIOSCORIDES of Anazarba in Asia Minor was an army 
surgeon who served in his own country under Nero. He wrote a 
work on drugs. It consists of short accounts of plants arranged, 
however, on a system that has hardly any reference to the nature 


The Failure of Nerve 

of the plants themselves. The descriptions given are often terse 
and striking, and sometimes include a few words on the habits and 
habitats of plants. This elaborate pharmacopoeia was early 
illustrated in the style of Crateuas (p. 78), and some fine copies 
of these figures have come down to us. 

The history of the work of Dioscorides reveals it as one of the 
most influential botanical treatises ever penned, despite the 
absence from it of anything like general scientific ideas. It pro- 
vided most of the little botanical knowledge that reached the 
Middle Ages. It furnished the chief stimulus to botanical research 
at the time of the Renaissance. It has decided the general form 
of every modern pharmacopoeia. It has determined a large part 
of modem plant nomenclature, both popular and scientific. 

The great biological and medical synthesis of antiquity was 
made by galen (a.d. 131-201) of Pergamum (p. 57). In his 
youth he visited Alexandria and other centres of learning, collect- 
ing all the knowledge of the day. Later he proceeded to Rome 
where almost all the rest of his very active life was passed. 

In Galen's time the dissection of the human body had fallen into 
desuetude. The knowledge of anatomy had therefore declined. 
He made, however, accurate anatomical and physiological studies 
on a number of animals. Among these was the Barbary ape, the 
structure of which is not very far removed from that of man. 
Galen also made numerous dissections and experiments on living 
animals. He was thus able to evolve a complete and very ingenious 
physiological system. This was generally accepted by later anti- 
quity and did not begin to be undermined until the work of Vesalius 
(P- 177) in the sixteenth century. 

The basic principle of life in the Galenic philosophy was a spirit, 
or pneuma, drawn from the world-spirit by the act of breathing 
(compare Erasistratus, p. 61). It entered the body through the 
wind-pipe and so passed to the lung and thence (through the ' vein- 
like artery ', which we 'now call the pulmonary vein) to the left 
ventricle, where it encountered the blood (Fig. 43). But what was 
the origin of the blood ? To this question his answer was most 
ingenious, and the errors that it involved remained till the time 
of Harvey. Galen believed that chyle, brought from the alimen- 
tary tract by the portal vessel, arrived at the liver. That organ, he 


Divorce of Science and Philosophy: Alexandria 

considered, had the power of elaborating the chyle into venous 
blood, and of imbuing it with a second spirit, or pneuma, innate 
in all living substance so long as it remains alive. This pneuma 
was called the natural spirit. Charged with natural spirit derived 

Fig. 43. Galen's Physiology. 

from the liver, and with nutritive material derived from the 
intestines, the venous blood, Galen believed, was distributed by 
the liver throughout the venous system which arises from it, 
ebbing and flowing in the veins. 

One great main branch of the venous system was the cavity that 
we now call the right ventricle of the heart. For the venous blood 
that entered this important branch, the right side of the heart, the 
Galenic scheme reserved two possible fates. The greater part 
remained awhile in the ventricle, parting with its impurities, which 
were carried off (by the 'artery-like vein* — ^now called the puU 
monary artery) to the lung, and there exhaled. These impurities 


The Failure of Nerve 

being discharged, the venous blood in the right ventricle ebbed 
back again into the general venous system. A small portion of this 
venous blood from the right side of the heart followed a different 
course. This small portion trickled through minute channels in 
the interventricular septum and entered the left ventricle drop by 
drop. There it encountered the pneuma brought thither from the 
outside world by the wind-pipe (through the Vein-like artery'). 
These drops of venous blood in contact with the air in the left 
ventricle became elaborated into a higher type of pneuma, the 
vital spirit. Charged with this, the dark venous blood became fully 
developed bright arterial blood which was distributed through the 
arteries to all parts of the body. 

Of the arteries, some went to the head, and thereby vital spirit 
was brought to the base of the brain. Here the arterial blood was 
minutely divided and became charged with yet a third pneuma, 
the animal spirit. This was distributed by the nerves, which were 
supposed to be hollow (Fig. 43). 

The whole knowledge possessed by the world in the department 
of physiology, nearly all the biological conceptions, most of the 
anatomy, much of the botany, and all the ideas of the physical 
structure of living things from the third to the sixteenth century 
were contained in a small number of works of Galen. The bio- 
logical works of Aristotle and Theophrastus lingered precariously 
in a few rare manuscripts in the monasteries of the East ; the out- 
put of hundreds of years of Alexandrian and Pergamene activities 
was utterly destroyed ; forgotten "vyere the Ionian biological works, 
of which fragments have marvellously survived; but the vast, 
windy, ill-arranged treatises of Galen lingered on. Translated into 
Latin, Syriac, Arabic, and Hebrew, they saturated the intellectual 
world of the Middle Ages. Commented on by later Greek writers, 
who were in turn translated into the same list of languages, they 
were yet again served up under the names of other Greek writers 
in the Middle Ages and later. 

What is the secret of the vitality of these Galenic biological 
conceptions ? The answer can be given in four words : Galen was 
a teleologist. He believed that everything is made by God to a 
particular and determinate end (telos = *end', aim'). Moreover, 
Galen's teleology is of a kind which happened to fit in with the 


Divorce oj Science and Philosophy: Alexandria 

prevailing theological attitude of the Middle Ages, whether Chris- 
tian, Moslem, or Jewish. According to Galen, everything which 
exists and displays activity in the human body is formed by an 
Intelligent Being on an intelligible plan, so that the organ in 
structure and function is the result of that plan. *It was the 
Creator’s infinite wisdom which selected the best means to attain 
his beneficent ends, and it is a proof of his omnipotence that he 
created every good thing according to his design, and thereby 
fulfilled his will.’ To know man you must therefore know God’s 
will. This attitude removes the foundation of scientific curiosity. 
After Galen there is a thousand years of darkness, and both 
medicine and biology almost cease to have a history. Men were 
interested rather in the will and purpose of God than in natural 

In leaving the Alexandrian period we may touch on one activity 
the influence of which has b^en peculiarly persistent. Antiquity 
had a very highly developed and exact technology, but the 
attempts to rationalize it are lost. That such there were can be 
inferred from the earliest traces of ‘ alchemy ’ that reach us from 
Alexandrian sources from about loo a.d. onward. Alexandrian 
alchemy is very sophisticated and clearly the result of a long 
evolution. The surviving texts are all in Greek and carry marks 
of Christian, Jewish, Neoplatonic, Gnostic, Greek, Egyptian, and 
perhaps Persian elements. Many names are associated with this 
strange literature, of which two are worth recording. One is mary 
THE JEWESS, who is Still remembered in the steam bath of our 
laboratories, the hain Marie of French chemists. The other is 
zosiMUS, the first alchemist who can be treated as an historic 
figure. He flourished about 300 a.d. These Alexandrian al- 
chemical texts contain ideas that persisted to the very dawn of 
modem chemistry. It is fairly certain that the early Arabic 
alchemists (pp. 132-4) had access to far more Alexandrian material 
than now exists. 



Science the Handmaid^/ Practice (50 b.c.-a.d. 400): 

Imperial Rome 

I. Development of the Roman Attitude to Nature. 

The scientific idea, the conception of a reasonable universe, came 
to the peoples of central Italy much later than to the Greeks of the 
eastern Mediterranean and of southern Italy. Moreover, science 
with the Romans always remained somewhat of an exotic. Rome 
established her protectorate throughout the eastern Mediterranean 
soon after 200 b.c. The influence of Greek ideas on Roman 
civilization thenceforth grew rapidly. All educated men came to 
learn Greek and were inevitably affected by Hellenic philosophy. 
Yet despite the stimulus of Alexandrian thought, the Latins 
produced no great creative men of science. 

The prevalent attitude towards nature among the Latin-speak- 
ing governing classes, whether Italian or provincial, was best 
expressed by the Stoic creed. The Epicurean philosophy gained 
fewer adherents among them. The Stoic system laid great stress 
on correct conduct and duty. It was based on a rigid conception of 
the interrelation of the different parts of the world. It provided 
little stimulus for the acquisition of new knowledge or for any- 
thing in the way of research (p. 53). Thus, in place of knowledge 
accumulating progressively on a basis of a wide and far-reaching 
theory, we get, under Stoicism, either a type of exact but intel- 
lectually motiveless observation, or a rejection of a}l knowledge 
not of practical importance. The dogmatism of Epicurean teach- 
ing was even less favourable to scientific research than was the 
Stoic outlook. 

There have been many attempts to explain why the Romans did 
not continue the scientific works of the Greeks. It has been said 
that the Roman mind could find no time from conquest and 
administration to attend to scientific matters. This wiU not 
explain the situation, for there were Romans who were able to 
answer the no less exacting claims of philosophy and literature. 
The matter, in fact, lies deep in the Roman character and tradition. 
It was related to the ethics of the favourite Roman philosophy, 


Science the Handmaid oj Practice: Imperial Rome 

Stoicism, and is not unconnected with the Roman passion for 
Rhetoric. In general we may say that Roman science appears at 
its strongest in the department of the general study of nature and 
at its weakest in pure mathematics. The success or failure of the 
Romans in any scientific field may be roughly gauged by its near- 
ness to one or other of these disciplines. But Roman culture is 
so large a source of our own civilization that it is desirable to 
consider the Roman influence on the course of science in greater 
detail than the direct Roman contribution would itself warrant. 

We have several works by Latins which deal with the implica- 
tions of science in general. None involves any expert knowledge of 
natural phenomena, and they are concerned rather with the 
philosophical relations of science than with science itself. Of such 
works the most striking and widely read is Lucretius (c. 95- 
55 B.C.), On the Nature of Things. The book is magnificent as 
literature and important as our best representation of Epicurean 
views (p. 54). It is, however, too much a work of propaganda to 
be of high scientific value. Moreover, it neither records first-hand 
observations nor does it even present a typically Roman attitude 
of mind. 

The attention of the scientific reader of Lucretius will naturally 
be drawn to his atomic views. Following his master Epicurus, 
Lucretius explains the origin of the entire world as due to the 
interaction of atoms. This interaction, he believes, is without the 
intervention of any creative intelligence. Even mental phenomena 
are of atomic origin and there is no reality save * atoms ' and * the 
void' {inane, p. 15). ‘Nothing is ever begotten of nothing by 
divine wiU.' Everything springs from determinate units {semina 
certa). The genesis of all things is typified by the generation of 
organic beings. The species of plants and animals give us models 
for all processes and natural laws. This conception of generation 
has its converse. ‘Things cannot then ever be turned to naught.' 
Such an attitude involves that indestructibility of matter ' which, 
despite modem changes in our conceptions, is the historical 
foundation on which our chemical and physical knowledge has 
been built (pp. 283-4). 

The resemblance of the Lucretian theory to modern atomic 
views is. however, more apparent than real. Not only are the 


The Failure oj Inspiration 

atoms of Lucretius of different sizes and shapes, but also he knows 
nothing of definite laws by which they hold together as molecules. 
He has no inkling of chemical combination. He is without that 
'doctrine of energy* that is so characteristic a feature in all 
modem physical theory. His work indeed had little direct 
influence on the development of the modern doctrine and probably 
was not widely read even in its own day. Epicurean thought was 
not favourable to scientific development. Moreover, the atomic 
view of matter was practically lost during the Middle Ages, and 
Aristotelian philosophy, which implied continuity of matter, was 
paramount for centuries. 

Some have seen in Lucretius the beginnings of a theory of 
evolution. He certainly exhibits a 'ladder of nature* (p. 41) not 
unlike that of Aristotle. The earth produces first plants and then 
animals of ever higher type. 'Even as down and hair and bristles 
are first formed on the limbs of beasts ... so the newborn earth 
raised up herbage and shrubs first, and thereafter the races of 
mortal things.* This idea of 'spontaneous generation* was in- 
evitable until the realm of minute microscopic life could be 
explored (p. 245). It is thus no wonder that Lucretius follows 
Aristotle and all antiquity in assuring us that 'even now many 
animals spring forth from the earth, formed by rains and the heat 
of the sun*. 

Did Lucretius take the matter further and did he have any 
conception of lower forms passing into higher forms? In a 
sense he did. Moreover, he invoked a process of 'survival of 
the fittest' for the formal exposition of which the world had to 
await the arrival of Darwin. But the Lucretian presentation of 
the manner in which the more perfect creatures reached their 
present state has no relation whatever to the historic geological 

When we turn to the phenomena which Lucretius has chosen 
for special description w'e note that they are drawn from the 
magnificent, dramatic, or cataclysmic. His temper is far from the 
impartial spirit of science and there is nothing of the quietly 
scrupulous careful observer about him. Thunder and lightning, 
water-spout, volcano and thunderbolt, suffocating vapours and 
devastating pestilences — these are the themes he selects. There 


Science the Handmaid of Practice: Imperial Rome 

is no reason to give to Lucretius an important place among those 
who have helped or inspired the study of nature. 

More characteristic of the Roman mind are the works of Varro 
(116-27 of Pliny the elder (a.d. 23-79), and of Seneca 

(3 B.C.-A.D. 65). 

VARRO, a country gentleman of the old Roman school, went to 
Athens and was influenced by Platonism, but developed definite 
Stoic leanings. He wrote an encyclopaedia of the sciences, and his 
works were the prototype of the numerous medieval treatises on 
the ‘liberal arts He distinguished nine such disciplines, namely, 
grammar, dialectic, rhetoric, geometry, arithmetic, astronomy, 
music, medicine, and architecture. Of these the last two were not 
recognized by the later Latin writers who handed down the tradi- 
tion to the Middle Ages. The number of liberal arts was thus 
reduced to seven (p. 127). 

Varro tried to collect Latin learning and set it over against the 
Greek. He was in a good position to do this for he possessed the 
old Roman tradition and he had also received a good Greek educa- 
tion. He was employed by Caesar to arrange the great stores of 
Greek and Latin literature for the vast library which he intended 
to found. His work On Farming {Res rusticae) was written in his 
eightieth year. In it he records his own rich experience, but he 
has collected his material mainly from the writings of others. He 
thus exhibits the derivative tendency which is so disastrous a 
feature of Latin writers on scientific topics. He uses every oppor- 
tunity to bring in etymology, rejoicing in artificial separations and 
divisions, so that the work gives much the impression conveyed by 
many treatises of medieval origin. 

In the elder pliny the Greek leaven has worked further than in 
Varro. Pliny had a literary education in Rome, where he took to 
studying plants. Coming under the influence of Seneca (p. 98) he 
turned to philosophy and rhetoric, and practised as an advocate. 
After military service in Germany, and having visited Gaul and 
Spain, he returned to Rome. There he completed his Natural 
History, dedicating it to the Emperor Titus. As prefect of the 
fleet he was stationed in the bay of Naples at the time of the 
eruption which overwhelmed Pompeii and Herculaneum in a.d. 79. 
He owed his death to his desire to observe that phenomenon more 




The Failure oj Inspiration 

closely. His education, career, opinions, and character are all 
typical of the Italian tradition of his day. 

The Natural History of Pliny was drawn from about 2,000 works 
— most of them now lost — by 146 Roman and 326 Greek authors. 
Its erudite, travelled, and industrious author exhibits an interest 
in natural phenomena that is quite uncontrolled by scientific or 
critical standards. The main thought that runs throqgh the book 
is that nature serves man. Natural objects are hardly described 
as such but only in relation to man. All things have their ‘uses'. 
‘Nature and the Earth', he says, ‘fill us with admiration ... as we 
contemplate the great variety of plants and find that they are 
created for the wants or enjoyments of mankind.' This world of 
wonder is, however, effectively without a God and works by rule — 
though it is a crazy rule which these disordered, credulous, wonder- 
loving volumes set before us. 

Many of the matters on which Pliny expresses a judgement 
would have been impressed on him in the manifold life of Imperial 
Rome. Many of the animals he discusses were brought to the 
capital for the arena or for the kitchen from the farthest ends of 
the Earth. So too with plants. He describes a botanic garden kept 
by a Roman for the purpose of ascertaining the medical and allied 
properties of herbs. In descriptions of living creatures Pliny goes 
back to Aristotle and Theophrastus, but there is no systematic 
building of the subject and he is scientifically far inferior to his 
sources. Medical plants are treated in greatest detail, and he holds 
that all plants have their own special medical powers. The thought 
that nature exists for man constantly recurs. His philosophy, 
which accords in general with the Stoic scheme, is largely drowned 
and lost in his love of detail, and is often submerged in rhetoric. 
He presents a confused cosmology. 

SENECA has gone over to the Greek more fully than either Varro 
or Pliny. A Spaniard by birth, he moved to Rome at an early age. 
There he came under Stoic influence and made his mark as an 
advocate and public servant. A member of one of the new pro- 
vincial families, a brilliant rhetorician with a passion for philo- 
sophy, of which he was an eloquent but unsystematic exponent, 
a man whose undoubted balance and judgement had been earned 
in affairs rather than in action, with an interest in nature rather 


Science the Handmaid of Practice: Imperial Rome 

in its cosmical than in its detailed aspects, Seneca provides an 
interesting contrast to his contemporary Pliny. 

Seneca’s work is more philosophical and far more critical than 
that of Pliny. Yet his Natural Questions, even more than the 
Natural History of Pliny, is borrowed material. He, too, is a StoiCj, 
but does not hesitate to criticize the opinions of that school. His 
subject is a general account of natural phenomena, but it is ill- 
arranged and imperfect. It deals chiefly with astronomy, meteoro- 
logy, and with physical geography. He exhibits, like Lucretius, 
a special interest in the convulsions of nature. Moreover, Seneca 
was absorbed, like many Romans, by ethics, a moralist first and 
physicist afterwards. Thus physics — which for him meant a 
general description of the Universe — led to a knowledge of man's 
destiny and through that to a consideration of man’s duty. 

Seneca repeatedly tells of the moral to be derived from the 
phenomena investigated. The relation is often of the most distant 
and strained character. Thus, terminating his discussion of the 
phenomena of light, he asks, ‘What were nature’s purposes in 
providing material capable of receiving and reflecting images ? ’ 
And he answers, ‘To show us the Sun with his glare dulled, for 
eyes are too weak to gaze at him direct. Secondly, that we might 
investigate eclipses reflected in basins. Thirdly, mirrors were dis- 
covered in order that man might know himself.' [Abbreviated.] 

Such a point of view appealed greatly to the medieval Church, 
by which Seneca was regarded as a Christian. He was included by 
St. Jerome among the ‘ecclesiastical writers’ and is frequently 
quoted by later Christian authors. But the ethical attitude to 
phenomena is inconsistent with the effective advancement of 
knowledge and has been one of the great enemies of science. In 
spite of the nobility of his sentiments, in spite of his lip-service 
to the advancement of learning, in spite of his faith in human 
destiny, Seneca could do nothing to stay the downfall of ancient 

2 . Geography and Imperialism, 

Just as the conquests of Alexander had opened up the East to 
science, so did the advance of Rome open up the West. Unfor- 
tunately the quality of 4he science had changed. 


The Failure of Inspiration 

A link between the Alexandrian and the Roman geographical 
standpoints is provided by the Arcadian polybius (204-122 b.c.), 
who had resided at Alexandria and later took service with the 
Roman army. He was present at the destruction of Carthage in 
146 B.C., and was employed by the younger Scipio (185-129) to 
explore the coasts of Africa. He also visited Gaul and Spain. His 
descriptions, particularly of Spain, are very accurate, and he even 
attempts an estimation of the length of the Tagus. He has much 
valuable information about the Alps, and his knowledge of the 
geography of Italy was superior to that of any of his predecessors. 
Though an historian rather than a geographer, Polybius under- 
stood the necessity of constructing a correct map, and therefore 
gives much attention to the determination of distances and 

During the second and first centuries b.c., improved accounts of 
the Red, Black, and Mediterranean Seas, and the countries bound- 
ing them, began to be available for students. Determinations, 
even of points in India, were attempted. Mention should be made 
of the navigator eudoxus of Cyzicus (not to be confused with 
Eudoxus of Cnidus, p. 37). After exploring the Red Sea Eudoxus 
made at least two voyages southward along the African coast and 
brought back considerable new information. 

The wars and military expeditions of the Romans yielded much 
further geographical knowledge. Thus strabo of Amasia in 
Pontus (bom c. 63 b.c.) had plenty of material when he began his 
general survey of the world. He was something of a traveller and 
had journeyed westward to the part of Etruria opposite Sardinia 
and southward from the Black Sea to the borders of Ethiopia. 
' Perhaps not one of those who have written geographies *, he says, 
'has visited more places than I within these limits.' He travelled 
right through Egypt and made a considerable stay at Alexandria. 
Working for long at Rome, he was in a good position to receive 
authentic information. His mathematical qualifications were, 
however, inadequate and inferior to those of Eratosthenes (p. 70) 
on whom his work is based, though his circumstances gave him a 
greater knowledge of detail, especially for Europe. 

Strabo opens by indicating the vast extension of knowledge as 
a result of the expansion of the Empire of Rome and that of her 


Science the Handmaid of Practice: Imperial Rome 

enemies on the east, the Parthians. Yet he is struck by the 
comparative smallness of the inhabited world. He makes the 
suggestion that there might be other continents still unknown. 
The length of the inhabited world from the Islands of the Blessed 
(that is the Canaries) to the Silk Land (that is China) was not more 
than about a third of the total circumference of the globe in the 
temperate zone. It was therefore possible that within the vacant 
space might be other lands inhabited by different races of men. 
In describing the inhabited world Strabo reduces its width from 
north to south to 30,000 stadia, an estimate below the 38,000 of 
Eratosthenes. The abbreviation is due to his scepticism as regards 
the northern regions. He rejects Thule, and disbelieves in any 
habitable land as far north as the Arctic Circle. Ireland, the most 
northerly of known territories, is ‘barely habitable on account of 
the cold*. Southward, he considers the habitable world extends 
about 3,000 stadia beyond Meroe. 

A feature of Strabo's work is his account of how a map of the 
world should be made. This, he points out, would not be difficult 
upon an actual globe, but such a globe would need to be very large 
for the insertion of details. He therefore considers the countries 
as though represented on a flat surface. Many of the distortions 
in Strabo's account are due to erroneous projection. His best 
accounts are of the countries bordering on the Mediterranean, 
where his map is distorted least. As he gets farther from the 
Mediterranean, his errors become greater. Even in the Mediter- 
ranean, however, he makes unexpected blunders. Thus the 
Pyrenees are represented as running north and south instead of 
east and west (cp. Fig. 46). With regard to the Caspian, Strabo 
shared the opinion of geographers since Herodotus that it was an 
inlet of the Northern Ocean (Figs. 28, 44) . The north of Asia and the 
region east of Sogdiaria was, he tells us, a mere blank to him. A 
vast chain of mountains extended, he thought, from east to west 
across Asia, bounding India on the north. From this range the 
Tigris and Euphrates took their rise in the west, the Indus and 
Ganges in the east. Thus the Himalayas are confused with the 
mountains of Asia Minor and with the Caucasus. 

Among the very few native Romans who had a true conception 
of the nature of scientific inquiry was julius caesar (102-44). 


The Failure of Inspiration 

He formulated the splendid scheme of a complete survey of the 
Empire. The government of the provinces, the demands of trade, 
and the distribution of the fleet all made the need evident. The 
death of Julius left the execution of this plan to his successor, 
Augustus. The survey was superintended by his son-in-law, 
viPSANius AGRIPPA (died 12 B.c.) and finally completed after 
nearly thirty years' work in 20 b.c. It was rendered possible by the 
fact that the Empire was well furnished with roads, marked with 
milestones.' There was a regular service of skilled surveyors, 
whose wprk, incorporated in the reports of provincial governors, 
was available at head-quarters. TTie vast chart prepared from 
these details was exhibited in a building especially erected for the 
purpose at Rome. In this map all other geographical elements 
were subordinated to indications for the marching of armies. 

Geography in the limited sense, as distinct from cosmography, 
was a topic that might be expected to appeal to the practical and 
imperialistically minded Roman. He was, however, hardly in an 
intellectual position to appreciate geography, save in the form of a 
road-book or rough strategic chart. To general geography the 
Roman paid little attention. The only important Latin writer on 
the subject is the Spaniard pomponius mela (c. a.d. 40), who refers 
to Britain as about to be more fuUy explored by an expedition then 
in progress. This was the visit of the Emperor Claudius in a.d. 43. 

Pomponius Mela clearly meant his work as an easy account of 
his subject. In his general description of the Earth he avoids 
mathematical topics in the true Roman manner, nor does he give 
distances or measurements. The world is a sphere, and the land 
upon it is surrounded on all sides by sea. Five zones may be 
distinguished. Of these the middle zone is as uninhabitable by 
reason of its heat as are the two extreme zones by reason of cold. 
We live in one of the two intermediate temperate zones while in 
the other dwell the 'Antichthones'. The land in our own hemi- 
sphere is completely surrounded by ocean, from which it receives 
four seas or gulfs, one at the north, the Caspian, two in the south, 
the Persian Gulf and the Red Sea, and the fourth to the west, the 
Mediterranean. The scheme is taken from Eratosthenes (p. 70), 
and it is clear that Pomponius Mela is a mere borrower from 
Greek sources (Fig. 44). 


Science the Handmaid of Practice: Imperial Pome 

Mela gives a general description of the three continents, Europe, 
Asia, and Africa. Between the three is the Mediterranean, which 
he speaks of as 'our sea'. He takes the river Tanis {Don), Lake 
Maeotis {Sea of Azov), and the Euxine Sea {Black Sea) as frontiers 
between Europe and Asia, while it is the Nile that divides Asia 
from Africa. Asia is as large as Europe and Africa together. These 
ideas were passed on to the earlier Middle Ages and are expressed 

in the world-maps of which the earliest is in a seventh-century 
codex of St. Isidore of Seville (560-636). The so-called OT map 
of the Middle Ages is well known (Fig. 45). 

The haziness of the geographical ideas even of an intelligent 
Roman of Imperial times may be gathered from tacitus {c. a.d. 
55-120). He tells how, under Agricola, the Roman fleet rounded 
Britain and proved it to be an island, discovering at the same time 
the Orcades {Orkney Islands) and coming in sight of Thule' 
(? Shetlands ) . Yet Tacitus, like Caesar and the elder Pliny, believes 
that Spain lies to the west of Britain (Fig. 46). Like Strabo he 
describes the Pyrenees as running north and south (p. loi). He 
goes on to explain the phenomenon of the Midnight Sun — which 
he brings as far south as the north of Scotland — by telling us that 
' the flat extremities of the Earth, casting a low shadow, do not 


The Failure of Inspiration 

throw the darkness up high, and the night does not reach to the 
sky and stars’. The statement implies the view that the Earth is a 
disk with flattened edges. This from a Roman gentleman who had 
access to the ideas of Aristotle, Hipparchus, Archimedes, and 

As antiquity passes into the Middle Ages, geography as a science 
becomes yet further degraded and is represented by mere route- 



Fig. 45. Conventional medieval OT map, as in Isidore of Seville. 

books. Of these the best are the earliest, for the deterioration is 
progressive. We have a fairly complete register of the roads of the 
whole Empire, put together in its present form about a.d. 300. 
Both principal and cross-roads are indicated by lists of the towns 
and stations upon them, the distance from place to place being 
given in Roman miles. Of more limited scope are the pilgrim 
books, which mostly give the itinerary to and from Jerusalem. 
The earliest of these Christian works is by a lady, sylvia of Aqui- 
taine (about 380) . Of a somewhat similar character is the work of 
RUTiLius NAMATiANUS of Toulouse, who wrote in 417 a versified 
account of a journey from Rome to Gaul. He was a pagan who 
fiercely attacked the monks — 'men who dread the evils without 
being able to support the blessings of the human condition His 
work naturally delighted the heart of Gibbon, and is of interest 
as still exhibiting the faith that Rome is immortal. Of special 
note, as marking the passage to the Middle Ages, is the work of 


Science the Handmaid of Practice: Imperial Rome 

an anonymous geographer of Ravenna put together in the seventh 
century. It contains valuable information concerning Roman 
roads and towns and is still using sources employed five centuries 
earlier by Ptolemy. 

3. Imperial Organization of Medicine, Hygiene, and Public Health, 

The original native Roman medical system was that of a people 
of the lower culture and devoid 
of scientific elements. Inter- 
woven with ideas that trespass 
on the domain of religion, it 
possessed that multitude of 
'specialist deities* characteris- 
tic of the Roman cults. Thus 
Fever had three temples in 
Rome, and was supplicated as 
the goddess Fehris and flatter- 
ingly addressed as ' Divine Fe- 
ver *, ' Holy Fever *, ' Great God- 
dess Fever*. Foul odours were 
invoked in thenameofM^^^^Ws, 
to whom a temple was erected 
at a place where asphyxiating 
fumes emerged from the earth. 

Lassitude was implored as Fes- 
'Sonia. Uterina guarded the 
womb. Lucina, with her as- 
sistant goddesses, had charge 
of childbirth. Over the entire 
pantheon of disease and physio- 
logical function presided the Dea Salus, 'Goddess Health*, who 
had a special temple on the Quirinal. She was the deity who 
took the public health under her supervision. 

The entire external aspect of Roman medicine was gradually 
transformed by the advent of Greek science. The change, however, 
hardly penetrated below the upper classes. Thus many references 
in the City of God of St. Augustine (334-430) show the ancient 
beliefs still current in the Italy of his day. After the fall of the 


The Failure of Inspiration 

Empire, they lingered among the barbaric peoples that entered 
into its heritage. Nor are they yet extinct. Prescriptions and 
practices of Pliny (p. io8) and of his even more gullible successors 
may still be traced in European and in American folk-customs and 

During the Republic, medical education had been a private 
matter. The direct relation of pupil and master exhibited by the 
Hippocratic oath was evidently that which prevailed 
under the early Empire. The initiate declared: 

' I will reckon him who taught me this Art as dear to me as those 
who bore me. I will look upon his offspring as my own brethren and 
will teach them this Art, if they would learn it, without fee or stipu- 
lation. By precept, lecture, and every other mode of instruction, I 
will impart a knowledge of this art to my own sons, and to those 
of my teacher, and to disciples bound by a stipulation and an oath, 
according to the Law of Medicine, but to none other.' (See p. 27.) 

Despite the ancient Greek dress in which this formula is cast, 
there is evidence that it is of Imperial date and of Roman rather 
than of Greek origin. The very form suggests the arrangements 
which were gradually made for medical instruction at Rome. 

The first important teacher there was the Greek asclepiades 
of Bithynia (died c. 40 b.c.), a contemporary of Lucretius and like 
him an Epicurean (p. 54 )- He influenced deeply the course of later 
medical thought, ridiculed, and perhaps we should add misunder- 
stood, the Hippocratic attitude of relying on the vis medicatrix 
naturae ^ ‘the healing power of nature', which he regarded as a 
mere ‘meditation on death', and urged that active measures were 
needed for the process of cure. He founded a regular school at 
Rome which continued after him. 

At first the school was the mere personal following of the physi- 
cian, who took his pupils and apprentices round with him on his 
visits. • Later, such groups met to discuss questions of their art. 
Towards the end of the reign of Augustus (died a.d. 14) these 
societies constructed for themselves a meeting-place with a regular 
organization. Finally the emperors built colleges for the teaching 
of medicine. At first the professors received only the fees of 
pupils, but before the end of the first century they were given a 


Science the Handmaid of Practice: Imperial Rome 

salary at the public expense. The systenoi was extended in the 
second and third centuries. Thus Rome became a centre of medi- 
cal instruction. Moreover, subsidiary centres were established in 
other Italian towns. These provincial schools were largely training 
places for army surgeons. 

A very weak point in the Roman medical curriculum was the 
absence of any practical study of anatomy. Considering the 
indifference to human life which the Romans exhibited, consi- 
dering their brutality to slaves and the opportunities offe'red by 
gladiatorial combats, considering the value — obvious to us — of 
anatomical knowledge for surgical practice, and considering the 
organization of the military medical service of the Empire, it is 
highly significant that the knowledge of antiquity was thus 
allowed to lapse. 

Had a great Roman military leader been questioned on this 
point he would probably have replied, 'Of course doctors want 
anatomy, but isn’t Galen’s anatomy good enough ? Cannot they 
read that ? ’ But he would have been wrong. It is not by 
reading that science is sustained. It is by contact with the 
object — by systematic observa!tion and experiment. From these 
the Roman army doctor was cut off, and we see the result 
of his deprivation in the poverty of Roman science. 

As regards the literature of medicine, the earliest scientific 
work in Latin bears the name of celsus and was prepared in 
Rome about a.d. 30. It is in many ways the most readable and 
well arranged of all ancient medical works. The ethical ton6 is 
high and the general line of treatment sensible and humane. The 
most interesting section is perhaps that on surgery, which gives an 
excellent account of what might be thought to be the modem 
operation for removing the tonsils. The dental practice includes 
the wiring of loose teeth and the use of the dental mirror. In view 
of the attractive character of the work it is disappointing to find 
that it is but a compilation from Greek sources. This fact also 
is significant of the status of science in Rome» 

The remaining Latin medical writings of Imperial times are not 
of high scientific value. In this connexion we must recall Pliny 
(p. 97). A large section of his Natural History is devoted to medical 


The Failure of Inspiration 

matters. Yet he scorned medical science and the Greeks who 
practised it. 

'Medicine, in spite of its lucrativeness/ he says, *is the one Greek 
art that the serious Roman has so far refused to cultivate. Few of 
our fellow-citizens have been willing even to touch it, and if they 
do so they desert at once to the Greeks. . . . Unfortunately there is 
no law to punish ignorant physicians, nor is the capital punishment 
inflicted upon them. Yet they learn by our suffering, and experi- 
ment by putting us to death!' 

The collection of Pliny that was to displace the works of the 
despised Greeks is a vast series of remedies chosen on the sup- 
posedly firm ground of ‘experience'. Their selection is based on 
no theory, supported by no doctrine, founded on no experiment. 
Yet this drug book is the prototype of the medical output of the 
next fifteen hundred years. The cry of Pliny for ‘ experience ' as 
against ‘theory' has been plaintively echoed by the ‘practical' 
man down the ages. Y et there are subjects and there are conditions 
in which the man without a theory may be the most unpractical 
of all. Medicine is such a subject ; disease is such a condition. 

When ‘experience' is invoked by Pliny and by later writers, 
especially of the Middle Ages, we must beware against confusing 
it with the ‘ experience ' of science. In scientific matters the essence 
of experience is that it be under control. Such experience is 
normally capable of repetition at will, as a chemical reaction, for 
instance, may be repeated. All true scientific experience, in fact, 
approaches the character of ‘ experiment '. Scientific experience 
is thus the result of a series of observations provoquees} 

A single example from Pliny will suffice to illustrate this distinc- 
tion. ‘The herb dittany', he says, ‘has power to extract arrows. 
This was proved [note the word ; it really means tested] by stags 
who had been struck by these missiles, which were loosened when 
they fed on this plant.' Had Pliny exhibited any desire to verify 
such a statement? Could he have verified it eyen if he had 
desired? The answer is not difficult. He had, in fact, taken his 

* There are scientific experiences in which the mind comes to rest with 
conviction, even when not repeated. Thus an astronomical prediction, 
involving exact and detailed calculation, if confirmed in an exact and 
detailed way, may carry conviction as to the soundness of its principle even 
though verified by but a single observation. 


Science the Handmaid of Practice: Imperial Rome 
experience ' from an interpolated and spurious passage of a work 
t>y Theophrastus (p. 51) and he omits to mention his source! 
Prepossession with the idea of the value of such experience led 
Pliny and the ages which followed him — as it leads men to this 
day — into innumerable absurdities. ' General experience ’ whether 
first hand or second hand is no substitute for exact scientific 

If in medicine itself the Roman achieved but little, in organiza- 
tion of medical service, and especially in the department of public 
health, his position is far more honourable. Several Roman 
writers on architecture give much attention to the orientation, 
position, and drainage of buildings, and from an early date 
sanitation and public health drew the attention of statesmen. 
Considering the dread of the neighbourhood of marshes on the 
part of these practical sanitarians and in view of modem know- 
ledge of the mosquito-borne character of malaria, it is entertaining 
to find the use of the mosquito net (conopeum) ridiculed as effemi- 
nate by poets such as Horace and Juvenal. 

Sanitation was a feature of Roman life. Rome was already 
provided with cloacae or subterranean sewers in the age of the 
Tarquins (6th cent. b.c.). The first construction of the Cloaca 
maxima, the main drain of Rome, parts of which are in use to this 
day, is referrable to that period. 

The growth of hygienic ideas is seen in an interdict of as early as 
450 B.c. against burial in the city. There is in this edict no refer- 
ence to any physician. The same absence of professional interven- 
tion may be noted in the instructions issued to the city officers 
for cleansing the streets and for the distribution of water. Nor is 
any medical help or opinion invoked by the ancient law, attributed 
to Numa the first king of Rome, which directed the opening of the 
body of a woman who had died pregnant in the hope of extracting 
a live child. This, is the so-called Caesarian section by which Caesar 
himself is said to have been brought into the world. The expres- 
sion stiU has a surgical meaning. 

The finest monument to the Roman care for the public health 
stands yet for all to see in the fourteen great aqueducts which 
supplied the city with 300,000,000 gallons of potable water daily. 


The Failure oj Inspiration 

Few modem cities are better equipped. The distribution of water 
to individual houses was also well organized, and excellent speci- 
mens of Roman plumbing have survived (Fig. 47). 

Under the early Empire a definite public medical service was 
constituted. Public physicians were appointed to the various 
towns and institutions. A statute of the Emperor Antoninus of 
about the year a.d. 160 regulates the appointment of these 

Fig. 47. Mechanism of Roman double-action pump. 

physicians, whose main duty was to attend the needs of the poor. 
In the code of the great law-giving Emperor Justinian (a.d. 533) 
there is an article urging such men to give this service cheerfully 
and to prefer it to the more subservient attendance on the wealthy. 
Their salaries were fixed but they were encouraged to undertake 
the training of pupils. 

Linked with the public medical service is the hospital system. 
It arose out of the Roman genius for organization and is connected 
with the Roman military system. Among the Greeks private 
surgeries were well known. Larger institutions were connected 
with the temples to Aesculapius, the god of healing, but there is 
no evidence of scientific medical treatment in these places. Such 
a temple had been established on an island of the Tiber in Repub- 
lican times. On this island of Aesculapius writes the historian 
Suetonius [c. a.d. 120) ‘certain men exposed their sick and worn- 


Science the Handmaid of Practice: Imperial Rome 

out slaves because of the trouble of treating them. The Emperor 
Claudius (41-54), however, decreed that such slaves were free, 
and that, if they recovered, they should not return to the control 
of their masters'. Thus the island became a place of refuge for 
the sick poor. It was an early form of public hospital. The example 
was imitated, the facilities improved, and the service extended 
to free men. 

The development of public hospitals naturally early affected 
military life. As the Roman frontiers spread ever wider, military 
hospitals were founded at important strategic points. Later there 
were constructed similar institutions for the numerous imperial 
officials and their families in the provincial towns. Motives of 
benevolence, too, gradually acquired weight, and finally public 
hospitals were founded in many localities. The idea naturally 
passed on to Christian times, and the pious foqndation of hospitals 
for the sick and outcast in the Middle Ages is to be traced back to 
these Roman institutions. 

The first charitable institution of this kind concerning the 
foundation of which we have clear information was established 
at Rome in the fourth century by a Christian lady named fabiola 
of whom we learn from St. Jerome. The plan of such a hospital 
projected at St. Gall in the early days of the ninth century has 
survived. It reminds us in many respects of the early Roman 
military hospitals. These medieval hospitals for the sick must 
naturally be distinguished from the even more numerous *spitals' 
for travellers and pilgrims, the idea of which may perhaps be 
traced back to the rest-houses along the strategic roads of the 

4. Roman Mathematical, Physical, and Calendarial Science. 

As with all peoples, the first system of numeration adopted by 
the Romans was finger counting. From it developed methods 
of mechanical reckoning. The simplest was a board covered with 
sand, divided into columns by the finger, counters being used in 
calculation. Such counters had graven upon them figures of the 
hand in various positions to represent different numbers. These 
S3mibols are identical with those which remained in vogue till late 
medieval times. 


The Failure oj Inspiration 

A more complicated apparatus was the true abacus. This began 
as a board with a series of grooves in which pebbles or calculi 
would be moved up and down, hence the verb calculo and the 
modem use of ' calculate *. In its more developed form the abacus 
consisted of an upper row of short rods and a longer row of long 
rods (Fig. 48). Each short rod had a single perforated bead 
running on it ; each of the longer ones four such beads. The first 
rod on the right was marked for units, the next on its left for tens. 

t t T 1 

0^60660 6 66 ^ 

ipOQOOOIOaOOO 10,000 1.000 100 10 l 6OQOOO 40,000 1, 000 700 90 2 

Fig. 48. Essentials of the Roman abacus, consisting of beads running 
on wires. On the left it is set for reckoning. On the right a total of 641,792 
is represented. Without an abacal representation and in Roman figures this 
would need twenty-one elements, namely CCCCCCXLIMVIICLXXXXII. 

and so on up to a million. The mode of application of the abacus 
was more comphcated than might be imagined. 

The whole mathematical system of antiquity was handicapped 
by its inadequate notation. The system with which we are nowa- 
days familiar, with nine separate integers and a zero, each of 
which has a local value, did not reach Europe until the Middle 
Ages. The Greeks used mostly geometrical methods where we 
should invoke the aid of algebra (p. 21), and their mathematical 
developments made little impression on the Romans. How slight 
was the mathematical knowledge absorbed by Latin scientific 
authors may be gathered from the Geometrica and the Arithmetica 
bearing the name of boethius (a.d. 480-524). Those elementary 
works ascribed to ' the last of the ancients ' represent the mathe- 
matical legacy of antiquity to the earlier Middle Ages. It is 
interesting to note that Boethius divides mathematics into four 
sections, Arithmetic, Music, Geometry, and Astronomy, and that 

Science the Handmaid oj Practice: Imperial Pome * 

he is the first to describe these four disciplines as the quadrivium 
(* four pathways ') . Even when Rome had world dominion, Cicero 
bemoaned that 'Greek mathematicians lead the field in pure 
geometry while we limit ourselves to reckoning and measuring 
The Romans held that the art of surveying was at least as old 
as their city, and had been practised from the first by the priests. 

In Imperial times a regular school for surveyors was established. 
The chief instrument in general use was known as the groma 
(Fig. 49). It consisted of two sets of plumb-lines fixed at right 
angles and arranged to turn about a vertical pivot. One set was 
used for sighting and the other to determine the direction at right 
angles to the first. As both agricultural and town-planning were 
mainly on rectangular lines this instrument was of wide applica- 
tion. A dioptra (p. 82) was in use and also a very clumsy water- 

Compasses and other instruments employed in mensuration 
recovered from Pompeii are well made, and the excellence 
of Roman masonry is' a household word. Thus the inaccuracy 



The Failure oj Inspiration 

of some Roman measurements is strange. For instance, 3^^ is 
given as the value of tt by Vitruvius {c. a.d. 10), a competent 
architect who must often have had occasion to examine the drums 
of columns. A better result might have been expected from any 
schoolboy provided with a compass and a tape-measure, and 3^ 
had already been suggested as an approximation by Archimedes. 

Vitruvius gives a method of estimating the distance from an 
observer of an inaccessible point on the same level as himself, 
e.g. on the opposite bank of a river. A line is traced along the 
near bank, and is measured by rolling along it a hodometer, an 
instrument consisting of a wheel the length of the circumference 
of which is known and whose revolutions can be counted. This 
is in principle a 'taxicab*. From each end of the measured line 
a sight is taken by means of the dioptra (p. 82). Angles and 
base being thus available a triangle congruent 40 that formed 
by joining the point on the far bank to the extremities of the 
measured line, can be constructed on the near bank. The vertical 
height of this triangle as measured by the hodometer gives the 
breadth of the river. 

Mechanical knowledge among the Romans always had a practi- 
cal direction. Among the few devices of native Roman origin is 
perhaps the steelyard. This instrument is a device of considerable 
antiquity and may be traced back at least as far as the third 
century b.c. The principle of the pulley, too, was well known. An 
elaborate system of pulleys was adapted to cranes and to engines 
of war. 

The inadequate theoretical basis of the physical conceptions of 
Latin writers is shown in various directions. Thus Pliny recounts 
a fable of the Remora, a fish of the Mediterranean which has a 
sucker on its head. 'This tiny fish can restrain all the forces of 
ocean. Winds may rage and storms may roar, yet the fish with- 
stands their might and holds ships still by simply adhering to 
them!* Three centuries before, Archimedes had demanded 'a 
fixed place on which to stand that he might move the world* 
(p. 65). The full understanding of the works of Archimedes 
failed for the next millennium and a half. Yet his simpler practical 
devices, such as the water-screw, were familiar^ enough to the 

Science the Handmaid of Practice: Imperial Rome 

Applied mathematics underwent some development in early 
Imperial times, julius caesar (102-44) himself was an astrono- 
mical author and wished to improve the Roman calendar which 
had fallen into great confusion. 

The early history of the Roman calendar is obscure. At an 
early date there emerged a lunar year of 355 days, which is almost 
exactly twelve lunations. Of this calendar Martins (the month of 
Mars) was the first month, Aprilis (probably for aperilis from 
aperire, 'to open*), Maius (perhaps related to major), and Junius 
(which may be related to junior and juvenis) were named in 
connexion with the opening, growth, and ripening of vegetation. 
The following six months, Quinctilis, Sextilis, September, October, 
November, and December were given merely the numerical 
names from fifth to tenth which the last four still bear. Januarius 
was named from the god Janus, and Februarius, the last month, 
was the season of ritual purification (februare, 'to purify* or 
'expiate *). 

To obtain some relation of this lunar reckoning to the solar year 
a cycle of four years had been invented of which the first year 
contained 355 days, the second 377, the third 355, and the fourth 
378. The cycle thus covered 1,465 days, and the average year was 

of 5 ^= 366 i days. So variable a year had little value for agri- 
cultural purposes. The farmer had thus still to rely on the rising 
and setting of certain constellations for timing his operations. The 
year was variously modified at different periods, but until the 
reforms of Julius Caesar no adequate correspondence to solar 
events was attained. 

In place of this system Julius Caesar, acting upon the advice 
of an Alexandrian mathematician, substituted a solar year of 
365 days and abandoned any attempt to adapt the years or months 
to the lengths of the lunations. In every fourth year one day was 
interpolated, thus introducing the system of leap years. This 
reform was probably a reproduction of an Alexandrian calendar 
enacted in 238 b.c. and had perhaps been designed at a yet 
earlier date by the Greek astronomer Eudoxus (p. 37) . In 44 b.c., 
the second year of the Julian Calendar, one of the months, 
Quinctilis, was named lulius — our July — ^in honour of its founder. 


T/ie Failure of Inspiration 

In 8 B.c. another month, Sextilis, was called Augustus after his 
successor. The Julian Calendar, the year of which began in the 
month of March, remained in general use until reformed by Pope 
Gregory XIII in 1582. 

5. Roman Astronomy and Astrology, 

The Romans did not deal with astronomical matters until late, 
and then only for practical purposes such as the calendar, seaman- 
ship, or agriculture. Popular astronomy is represented in Latin 
by certain metrical writings bearing the name of avienus [c, a.d. 
380). These, which were popular in the early Middle Ages, are 
adapted from various Greek works. To one of the Greek sources 
of Avienus, namely aratus of Soli (271-213 b.c.), peculiar interest 
is attached. St. Jerome tells us that when, in Acts, St. Paul says 
* In Him we live, and move, and have our being ; as certain even 
of your own poets have said. For we are also his offspring' [Acts 
xvii. 28), he is quoting the Phaenomena of Aratus. The words 
' for we are also his offspring ' are in fact to be found in the opening 
invocation to Zeus in Aratus, and in a slightly different form in a 
work of the poet Cleanthes [c, 250 b.c., p. 54) and in an expanded 
form in Avienus. Aratus was a native of Cilicia, St. Paul 's native 
province. Both Aratus and Cleanthes were claimed by the Stoics, 
who, with the Epicureans, were opposing the apostle at Athens 
(Acts xvii. 18). 

Though backward in astronomy, the Romans had early de- 
veloped a good knowledge of such elementary developments 
as the sundial, which was known to them in the third century 
B.C., and the results of which were early applied to calendarial 
reckoning. Full directions for the construction of sundials are 
given by the architect vitruvius [c, a.d. 10, p. 114) who tells of a 
number of different forms in use in his time. Some of these, he 
says, were invented by various Greeks, of whom Aristarchus (p. 59) 
and Eudoxus (p. 37) are the best known. The construction of 
these various forms implies command of considerable mechanical 
skill and some efficiency in the making and recording of elementary 
astronomical observations. Sundials suitable for use by travellers 
were also not uncommon. Vitruvius describes also a water-clock 
of an extremely simple and effective type. 


Science the Handmaid of Practice: Imperial Rome 

The difference in the length of day in different latitudes was 
well known to the Romans. From the fact that the longest day 
in Alexandria was 14 hours, in Italy 15, and in Britain 17, Pliny 
deduces that lands close to the Pole must have a 24-hours' day 
in the summer and a 24-hours' night in winter. 

Many passages in Pliny reflect a contest concerning the form of 
the Earth, reminding us of earlier disputes of the same order 
(pp. 21, 103). He opens his work with a description of the 
general structure of the universe and discusses the spherical 
form of the Earth: 

* Science and the opinion of the mob says Pliny, ' are in direct 
opposition. According to the former the whole sphere of the Earth 
is inhabited by men whose feet point towards each other while all 
have the heavens above their heads. But the mob ask how men on 
the antipodes do not fall off ; as though that did not present the 
opposite query why they should not wonder at our not falling off. 
Usually, however, the crowd objects if one urges that water also 
tends to be spherical. Yet nothing is more obvious, since hanging 
drops always form little spheres,* 

To the Moon and fixed stars the Romans had already, in Pliny's 
time, begun to attribute an influence on human affairs. ‘ Who does 
not know', he asks, 'that when the Dog Star rises it exercises 
influence on the widest stretch of Earth ? ’ The influence of the 
Dog Star is an idea that may be traced back in Greek literature at 
least as far as Hesiod (8th cent, b.c.) and has given us our modem 
superstition of the 'dog days'. The Moon's influence on tides was 
recognized, and it was thought that besides influencing the outer 
world, the macrocosm, the Moon had influence also on the body of 
man, the microcosm (p. 37). With the waxing of the Moon it was 
believed that the muscles became bigger and blood increased. 
This theory gave rise to the practice of periodical blood-letting 
which took so prominent a place in early monastic life. 

The supposed influence of the heavenly bodies on the Earth 
and on the life of man is a topic that leads to judicial astrology 
(p. I5i)« A knowledge of that subject became under the Empire a 
professional possession, illegal and prohibited, but often tolerated 
and invoked even by emperors. Astrology was beginning to spread 
in Rome in the first century of the Christian era. 

The Failure of Inspiration 

‘There are those', Pliny tells us, ‘who assign [all human events] 
to the influence of the stars, and to the laws of their nativity. They 
suppose that God, once for all, issues his decrees and never after 

intervenes. This opinion begins 

to gain ground, and both the 
learned and the vulgar are ac- 
cepting it.* 

The art was of foreign origin. 
The credit of its invention is 
always ascribed to Xhaldeans', 
but the main channel of trans- 
mission was Greek. 

‘As for the branch of astro- 
nomy which concerns the influ- 
ences of the twelve signs of the 
zodiac, the five Planets, and the 
Sun and Moon on man's life', 
says Vitruvius, ‘we must leave 
it to the calculations of the Chal- 
deans to whom belongs the art 
of casting nativities, which en- 
ables them to declare the past 
and future.' 

The original meaning of the 
zodiacal figures is disputed, but 
they were certainly in very an- 
cient use in Mesopotamia (Fig. 

Fig. 50. Babylonian boundary 
stone showing a seated deity above 
whose head are the heavenly bodies. 
The Zodiacal sign of the Scorpion is 
exhibited. The inscription records a 
donation to the temple of Marduk 
in Babylon. Second millennium b.c. 

50) whence came the methods of 
dividing time and the divisions 
of the heavenly sphere based on 
them. Against these Chaldeans 
Cicero directed his dialogue On 
Divination. He misunderstood 

the basis of astrology and marshalled ancient and fallacious 
arguments against it. Yet even Cicero accepted some astrological 
doctrine, and in his Dream ofScipio he spoke of the planet Jupiter 

as helpful and Mars as harmful. To the early Christian writers 
astrology was even more abhorrent, for it seemed to them to be 
the negation of that doctrine of free will that was so dear to 


Science the Handmaid oj Practice: Imperial Pome 

them. The fathers TertuUian {c, 155-c. 222), Lactantius (c. 260- 
c, 340), and Augustine (354-430) all inveigh against it. With the 
spread of Christianity in the West and the disappearance of the 
Stoic philosophy, astrology passed into the background, to return 
with the Arabian revival and the rise of the Universities. 

At an early date there arose a large literature on the subject. 
Nevertheless, astrology seems on the whole to have been rather 
less cultivated in Rome itself than the general state of society and 
the wide spread of the Stoic philosophy might perhaps suggest. 
Lovers sought to learn of astrologers a lucky day for a wedding, 
travellers inquired what was the best day for starting on a journey, 
and builders asked the correct date for laying a foundation stone. 
All these may easily be paralleled by instances among the empty- 
headed in our own time and country. But Galen (130--200)., who 
practised among the well-to-do and educated, assures us that they 
only bothered about astrology for forecasting legacies — and again 
a parallel might be drawn. 

But astrology must not be considered only as a superstition and 
an occupation for empty heads and idle hands. The astrological 
system of antiquity was, in essence, a formal presentation of those 
beliefs concerning the nature and working of our mundane sphere 
which had been fostered by a scientific astronomy and cosmology. 
Faith in it was part of the Stoic creed. In the mechanism of the 
world there was no room for those anthropomorphic gods, the belief 
in whom was still encouraged by the priests and held by the multi- 
tude. The spread of belief in that mechanism had led at last to 
a complete breach between the official faith and the opinions of the 
educated classes. The idea of the interdependence of all parts of 
the universe produced in time a new form of religion. The world 
itself must be divine. 'Deity,* says Pliny, 'only means nature.* 
From such a view to the monotheism of Virgil, in which the world 
as a whole is regarded as the artistic product of an external god, 
is perhaps no great step. Roman Stoicism, however, failed to take 
that step, and assumed among later Latin writers a fatalistic and 
pessimistic mood. ' God, if God there be, is outside the world and 
could not be expected to care for it*, says Pliny. The idea 
of immortality seems to him but the 'childish babble* of those 
who are possessed by the fear of death, as Lucretius had once 


The Failure of Inspiration 

maintained. After death, so Pliny would have us believe, man is 
as he was before he was born — and this he tells us as he plunges 
into his magic-ridden pages ! 

Once and once only in these Latin scientific writings have we 
a clear note of real hope. It is significant that that note is sounded 
in connexion with a statement of a belief in the progress of know- 
ledge, an echo of the Greek thought of the fifth and fourth cen- 
turies B.c. It is significant, too, that the note is sounded by one 
who approached, nearer perhaps than any other pagan Latin 
philosopher, to the idea of the divine immanence. In his natural 
questions Seneca wrote : 

* How many heavenly bodies revolve unseen by human eye ! . . . 
How many discoveries are reserved for the ages to come when our 
memory shall be no more, for this world of ours contains matter 
for investigation for all generations. . . . God hath not revealed all 
things to man and hath entrusted us with but a fragment of His 
mighty work. But He who directeth all things, who hath estab- 
lished the foundation of the world, and clothed Himself with 
Creation, is greater and better than that which He hath wrought. 
Hidden from our eyes, He can only be reached by the spirit. ... On 
entering a temple we assume all signs of reverence. How much 
more reverent then should we be before the heavenly bodies, the 
stars, the very nature of God ! ' 

But the science of antiquity as exhibited elsewhere in Latin 
writings contains very little of this belief in man's destiny, this 
hope for human knowledge. The world in which the Imperial 
Roman lived was a finite world bound by the firmament and 
limited by a flaming rampart. His fathers had thought that great 
space peopled by numina, 'divinities', that needed to be pro- 
pitiated. The new scientific dispensation — the lex naturae of 
the world that had so many parallels with the jus gentium of 
the Empire — had now taken the place of those awesome beings. 

In the inevitableness of the action of that law Lucretius the 
Epicurean might find comfort from the unknown terror. Yet for 
the Stoic it must have remained a limited, fixed, rigid, and cruel 
law. His vision, we must remember, was very different from that 
given by the spacious claim of modern science which explores into 
ever wider and wider regions of space and time and thought. It 
was an iron, nerveless, tyrannical universe which science had 


Science the Handmaid of Practice: Imperial Rome 

raised and in which the Roman thinker must have felt himself 
fettered, imprisoned, crushed. The Roman had forsaken his early 
gods, that crowd of strangely vague yet personal beings whose 
ceremonial propitiation in every event and circumstance had filled 
his fathers* lives. He had had before him an alternative of the 
oriental cults whose gods were but mad magicians — a religion un- 
worthy of a philosopher — and the new religion of science whose 
god, he now saw, worked by a mechanical rule. He had aban- 
doned the faith of his fathers, had flung himself into the arms 
of what he believed to be a lovelier goddess, and lo! he found 
himself embracing a machine ! His soul recoiled and he fled into 
Christianity. A determinate yiew of the world induced that 
essential pessimism which clouds much of the thought of later 
antiquity. It was reaction against this pessimism which led to 
the great spiritual changes in the midst of which antiquity went 
up in flames and smoke. 

6. The Passage from Pagan to Christian Thought, 

We have gained a general view of the course of ancient thought 
in relation to science. Fotit stages may be distinguished: 

(a) During the rise of Greek thought, philosophy is based on 
natural science. It neglects ethics and ignores popular religion 
(Chapter I). Here was the emergence of Mental Coherence. 

(b) Plato and Aristotle seek to adjust the rival claims of ethics 
and science, while giving preference to the former. Popular 
religion is repudiated (Chapter II). This is the Great Adventure. 

(c) Alexandrian thought develops separate departments for 
science, ethics, and religion. The age of the ‘ specialist * has begun. 
The Alexandrian period terminates with definite scientific de- 
terioration (Chapter III). Intellectual Nerve is failing. 

{d) Under the Empire the prevalent schools of thought, Stoicism 
and Epicureanism, are indifferent to science, which deteriorates 
further (Chapter IV). Great emphasis is laid on Ethics. Scientific 
inspiration has waned to nothing. 

We must now consider somewhat more deeply certain aspects 
in this final stage of ancient thought in so far as it is related to the 
material world. Stoicism, in the first two Christian centuries 
divided the thinking wjorld with Epicureanism and certain less 


The Failure oj Inspiration 

important philosophical sects. The Stoic philosophy assumed that 
man’s life in all its details is controlled by an interplay of forces. 
Both the nature and the behaviour of these were, in theory, com- 
pletely knowable. The same assumptions were made by Epicurean- 
ism, save that different forces were held to control man’s fate. 
The Stoic invoked the action of the spheres and astrology. The 
Epicurean invoked the play of atoms. Both schemes were deter- 
minate. In this they differed from the new and rising school of 
Neoplatonism, the indeterminacy of which fitted better the doc- 
trine of free will on which Christianity came to insist. Atomism 
being opposed by the authority of both Aristotle and Plato and 
by Stoicism and Neoplatonism alike, Epicureanism fell into the 
background. All philosophical sects became ultimately absorbed 
into Neoplatonism, the history of which it is necessary to trace. 

Alexandria of the third century of the Christian era presented 
an extraordinary mixture of religions, philosophies, and sects. 
The old scientific school was in decay. Christian, Jewish, and 
pagan elements jostled each other. The cults of ancient Egypt, 
of Greece, of Rome, and of the Orient appealed to the devout and 
the superstitious. The decayed schools of Aristotle and Plato had 
still conservative followers. There were also those who called 
themselves Stoics and Epicureans. A common factor among these 
various elements was contempt for science. 

It must be remembered that the science of those days differed 
from that of ours in that it had introduced no obvious and exten- 
sive amelioration of man’s earthly lot. Nature had not been 
harnessed as we have harnessed her. Science was a way of looking 
at the world rather than a way of dealing with the world. And as 
a way of looking at the world — a way of life — positive knowledge 
that is, science was a failure. The world was a thing that men could 
neither enjoy nor master nor study. A new light was sought and 
found. In its glare the old wisdom became foolishness and the old 
foolishness wisdom. Weary of questioning, men embraced at last 
and gladly the promises of faith. The faith that was immediately 
most successful was that which included within itself the experi- 
ences of the largest number of educated men. This was the 
syncretic system known as Neoplatonism. 

The S3mcretic tendency exhibited itself very early in Alexandria. 


Science the Handmaid of Practice: Imperial Rome 

Philo, who was about twenty years older than Christ, developed 
a system that used the Jewish scriptures in the light provided by 
Plato and Aristotle, and with some admixture of mysticism. He 
introduced the doctrine of the logos, and his tendency is away 
from observational science. Following Philo in the first, second, 
and third centuries were writers of ‘Neopythagorean' and 
' Hermetic ' leanings whose views and tenets were as syncretic as 
Philo's. They need not delay us. It would be possible to consider 
the earliest Christian writers as members of this syncretic group. 

Early in the third century there arose in Alexandria one 
AMMONius SACCAS — that is the 'sack-carrier' or 'porter' — (died 
245), whose personal influence was destined to be fatal for science. 
Bom a Christian he apostatized and opened a school of philo- 
sophy which became known as the Neoplatonic. The teaching of 
his school was secret, after the Pythagorean model (p. 17). His 
pupils, however, were not averse to writing ; and the greatest of 
them, PLOTINUS (204-70), himself a Roman, carried Neoplatonism 
to Rome and thence to the pagan world at large. 

We are not here concerned with any general consideration of 
Neoplatonism and but little with a further discussion of its 
numerous sources. These included Aristotle and Plato and their 
successors and various religious cults, together with the philo- 
sophical sects such as Stoicism. There is, however, a certain 
doctrine of great historic importance which demands some notice 
here. It is a doctrine shared by Neoplatonism and Stoicism. Both 
philosophies set off the Universe, the great world, the macrocosm, 
against Man, the little world, the microcosm (p. 117). The one was 
a reflection of the other. Broadly speaking, the Neoplatonist would 
have said that the Universe had been made for Man who is the 
essential reality; the Stoic that Man has been made for the 
Universe. The Neoplatonic view was victorious. The view of 
the macrocosm and microcosm as elaborated by Neoplatonism 
was not unacceptable to Christianity. 

Neoplatonism developed a characteristic metaphysic derived 
mainly from Plato but in part also from Stoicism whence it drew 
its ethics. The Platonic ' Idea ' was greatly emphasized and almost 
personified. The Idea, as expressed by form, governs matter just 
as the soul governs the body. But matter may at times break 


The Failure of Inspiration 

away from the Idea and then the world of matter becomes a world 
of strife and discord. Idea is in the end identifiable with form. 
Matter, destitute of form or idea, is evil ; with form it is at best 
neutral. It must be the soul's aspiration to free itself from such 
dangers. Then and then only it can hope for ecstatic union with 
the Divine. 

During the fourth century Neoplatonism flourished. Associat- 
ing itself with the theologies of various sects, it was a serious rival 
to Christianity. Its hopes rose high when Julian the Apostate 
became Emperor (361-3), but they fell again even before the end 
of his short reign to sink still lower with the victory of Christianity 
in the age of Valentinian (364-75) and Theodosius (379-95). 
Christianity in its spread absorbed, with the masses, their super- 
stitions, their magic, and their theurgy. Neoplatonism, on the 
other hand, at first saturated with these elements, became at last 
purged of them, though passing thereby out of touch with the 
spirit of the age. Towards the end of the fourth century the head 
of the Neoplatonist school at Alexandria was Hypatia (379-415). 
Her murder ended the effectiveness of the Neoplatonic school 
as such. She influenced Christian thought directly through her 
pupils, the most famous of whom, Synesius of Cyrene (373-414), 
became a very free-thinking bishop. 

The passage of Neoplatonic doctrine into Christianity was in 
the main the work of ST. Augustine (354-430). After a youth and 
young manhood spent in devotion to Manichean studies he turned, 
at last, to study the exact sciences. In 383 he came to Rome 
whence he moved in 384 to Milan. There he became acquainted 
with Neoplatonic teachers. In 386 he became* converted to 
Christianity. His great literary activity, begun in 393, ended only 
with his life. 

We have it from Augustine himself that his debt to Neo- 
platonism was very great. In all his cardinal doctrines — God, 
matter, the relation of God to the world, freedom, and evil — 
Augustine borrowed freely from Neoplatonism. Through him we 
may regard Neoplatonism, itself the final stage of Greek thought, 
as passing in its final stage into Christianity. Through St. 
Augustine, above all men, early Christianity acquired its distaste 
for a consideration of phenomena. ‘Go not out of doors', said 

Science the Handmaid of Practice: Imperial Rome 

the great Father of the Church. ‘Return into thyself. In the 
inner man dwells truth.* For a thousand years men responsible 
for the thought of the Western world did not go out of doors. 

It was through St. Augustine that certain Neoplatonic doctrines, 
notably that of the macrocosm and microcosm, passed to the 
Latin West, where they awaited the Arabist revival (p. 150) 
for their fuller development. In a somewhat similar way such 
traditions lingered for centuries in the Byzantine East until, with 
the great outburst of Islam, they were caught up and elaborated 
by the Arabic culture (pp. 139-41). Stamped with specific Islamic 
characters the same doctrines were sent forth a second time to 
Christian Europe in the process of translation from the Arabic 
(pp. 150-3). 



The Middle Ages [about a.d, 400-1400): Theology, Queen 
of the Sciences 

I. The Dark Age (400--1000). 

We now enter the last and longest phase of the Great Failure. 
With the decline and fall of the Empire the decay of philosophy 
was as pronounced as the decline of science. Neoplatonism gives 
place to the great philosophical and religious movement known 
as Christianity. The standpoint of its early champions, the Church 
Fathers, TertuUian (155-222), Lactantius (260-340), and, above 
all, St. Jerome (340-420) and St. Augustine (354-430), is outside 
the department with which we deal, but it was assuredly not 
conducive to the exact study and record of phenomena. Never- 
theless, the Middle Ages, under the influence of the Church, de- 
veloped a characteristic attitude towards nature. 

For our purposes we may place the limits of the medieval period 
between about the years 400 and 1400. This millennium is divided 
unequally by an event of the highest importance for the history 
of the human intellect. From about 900 to 1200 there was a 
remarkable development of intellectual activity in Islam. The 
movement reacted with great effect on Latin Europe through 
works which reached it, chiefly in the twelfth and thirteenth cen- 
turies, in Latin translations from the Arabic. This intellectual 
event divides the medieval peijod in the Latin West into two parts, 
an earlier Dark Age which terminates in the twelfth century, and 
a later Age of Arabian Influence which expressed itself charac- 
teristically in Scholasticism. As we pass from one period to the 
other, the general outline of beliefs as fo the nature of the external 
world changes relatively little, but their presentation is vastly 
altered and the whole doctrinal scheme of the material world 
assumes a formal rationality. 

During the closing centuries of the classical decline, the body 
of literature destined to pass down to subsequent ages had been 
delimited and translated into Latin, the only language common 

The Middle Ages. Theology: Queen oj the Sciences 

to the learned West. We must briefly discuss this legacy that 
antiquity passed on to the Dark Age. 

Of the works of Plato, the Timaeus fitted well the views of the 
Neoplatonic thinkers of the late Empire and fitted not ill to 
Christian belief. A Latin commentary on the Timaeus, prepared 
in the third century, presents a doctrine held throughout the 
entire Middle Ages as to the nature of the universe and of man. 
This book became one of the most influential of all the works of 
antiquity, and especially it conveyed the central dogma of medie- 
val science, the doctrine of the macrocosm and microcosm. This 
conception, that the nature and structure of the universe fore- 
shadows the nature and structure of man, is basic for the under- 
standing of medieval science. 

Of the writings of Aristotle there survived only the logical 
works translated in the sixth century by boethius (480-524). 
These determined the main extra-theological interest for many 
centuries. Boethius had purposed to translate all of Aristotle and 
it is a world-misfortune that he did not live to prepare versions 
of those works that display Aristotle's powers of observation. 
Had a translation of his biological treatises reached the earlier, 
Middle Ages, the whole history of thought might have been 
different. Boethius repaired the omission, to some small extent 
by compiling elementary mathematical treatises based on Greek 
sources. Thanks to them we can at least say that during the long 
degradation of the human intellect, mathematics, the science last 
to sink with the fall of Greek thought, did not come quite so low 
as the other departments of knowledge. 

A somewhat similar service to that of Boethius was rendered by 
MACROBius (395-423) and by martianus capella (c. 500). The 
latter, especially, provided the Dark Age with a complete though 
very elementary encyclopaedia of the seven Tiberal arts', namely 
the ‘trivium', grammar, dialectic, rhetoric, and the ‘quadrivium* 
(p. 1 12) geometry, arithmetic, astronomy, and music. This classi- 
fication of studies dates back to Varro (p^ 97) and was retained 
throughout the Middle Ages. The section on Astronomy has 
a short passage containing a suggestion that Mars and Venus may 
circle the sun, perhaps derived from Aristarchus (p. 59). The 
passage, however, is without relation to the text as a whole, and 


The Failure oj Knowledge 

the cosmology of Capella and of Macrobius is similar to that of 
the Timaeus. It may be described as Neoplatonic. 

In addition to the little cosmography, mathematics, and astro- 
nomy that could be gleaned from such writings as these, the Dark 
Age inherited a group of scientific and medical works from the 
period of classical decline. By far the most widely read was the 
Natural History of Pliny (p. 98). Very curious and characteristic 
is a group of medical pseudepigrapha bearing such names as 
Dioscorides, Hippocrates, Apuleius, and others. These extremely 
popular works were translated into Latin between the fourth and 
sixth centuries. They provided much of the medical equipment 
of the Dark Age. 

Such material, then, was the basis of the medieval scientific 
heritage. Traces of it are encountered in works of cassiodorus 
(490-585), perhaps the earliest general writer who bears the 
authentic medieval stamp. The scientific heritage is, however, 
much more fully displayed by Bishop Isidore of Seville (560-636) 
who produced a cyclopaedia of all the sciences in the form of an 
* Etymology ' or explanation of the terms proper to each. For many 
centuries this was very widely read. The works of the series of 
writers, the Spaniard Isidore (560-636), the Englishmen bede 
(673-735) and ALCUIN (735-804), and the German rabanus 
MAURUS (776-856), who borrow successively each from his prede- 
cessor and all from Pliny, contain between them almost the entire 
corpus of the natural knowledge of the Dark Age. 

It must be remembered that the Dark Age presented no 
coherent philosophical system, and men were capable of hold- 
ing beliefs inconsistent with each other. The world was but 
God's footstool, and all its phenomena were far less worthy of 
study than were the things of religion. In the view of many 
patristic writers, the study of the stars was likely to lead to 
indifference to Him that sitteth above the heavens. This is the 
general attitude of the fourth and fifth centuries, set forth for 
instance by St. Augustine, who speaks of * those imposters the 
mathematicians (i.e. astrologers) . . . who use no sacrifice, nor 
pray to any spirit for their divinations, which arts Christian and 
true piety consistently rejects and condemns'. 

By the sixth and seventh centuries the Church had come to 

The Middle Ages: Theology, Queen oj the Sciences 

some sort of terms with astrology. Thus St. Isidore regards 
astrology as, in part at least, a legitimate science. He distin- 
guishes, however, between natural and superstitious astrology. 
The latter is 'the science practised by the mathematici who read 
prophecies in the heavens, and place the twelve constellations 
(of the Zodiac) as rulers over the members of man's body and soul, 
and predict the nativities and dispositions of men by the courses 
of the stars'. Nevertheless, St. Isidore accepts many of the con- 
clusions of astrology. He advises physicians to study it, and 
he ascribes to the moon an influence over plant and animal life 
and control over the humours of man, while he accepts without 
question the influence of the Dog Star and of the comets. He is 
followed by the other Dark Age writers on natural knowledge, 
who accept successively more and more astrological doctrine. 

A certain 'revival of learning' under Charlemagne, centred 
round about the year 800, is very important for its literary 
activity and certainly did much to preserve such few scientific 
texts as were available. This movement is greatly emphasized by 
general historians, but it cannot be considered in the light of 
a scientific awakening. Perhaps only one figure in the Dark Age 
is worth our attention here. It is that of gerbert who became 
Pope as Sylvester II (died 1003). His merit is to have introduced 
the abacus (p. 112) which had disappeared with the Roman 
decline. Its use lingered among the Byzantines whence it reached 
Arabic-speaking Spain in Gerbert's time. Gerbert had studied in 
Spain and there, perhaps, learnt of it. He also visited the court 
of Otto I (913-73) in Southern Italy (970). From wheresoever 
he derived his abacus there can be no doubt that the details 
of his arithmetic, like the numerals that he used, he drew from the 
works of Boethius (p. 127). The immediate future of learning lay 
not in the West but in the East. 

2. Science in the Orient (750-1200). 

During the Dark Age the intellectual level of the Greek world 
stood higher than that of the Latin. Science, it is true, was as 
dead in the one as in the other, but in the Byzantine Empire there 
was still some activity in the preservation and multiplication of 
copies of the works of antiquity. The classical dialect was not 




The Failure oj Knowledge 

wholly unknown to the educated class. Despite intense theological 
preoccupation, classical learning was still occasionally cultivated. 
A few scholars still glossed the works of Aristotle and Plato. 

The Byzantine Empire included many Syriac-speaking subjects. 
The Syriac language had, from the third century, replaced Greek 
in Western Asia. There in the fifth century the heretical Nestor- 
ian Church had been established. The Nestorians, bitterly perse- 
cuted by the Byzantines, emigrated to Mesopotamia. Yet later, 
they moved to south-west Persia where, from the sixth century 
onward, they long exhibited great activity especially at their 
capital Gondisapur. Literature in Syriac became very extensive. 
It included translations of the works of Aristotle, Plato, Euclid, 
Archimedes, Hero, Ptolemy, Galen, and Hippocrates. 

It was in the seventh century that the Arabs first entered into 
the heritage of the ancient civilizations of Byzantium and Persia. 
From their desert home they brought no intellectual contributions 
save their religion, their music, and their language. Moreover, in 
the Byzantine and Persian Empires, Greek science was at a low ebb 
save among the Syriac-speaking Nestorians. Thus the Nestorian 
metropolis, Gondisapur, became the scientific centre of the new 
Islamic Empire. From Gondisapur during the Umayyad period 
(661-749), learned men and especially physicians came to Damas- 
cus, the capital. They were mostly Nestorian Christians, or Jews 
bearing Arabic names. 

The rise of the Abbaside Caliphs (750) inaugurated the epoch 
of greatest power, splendour, and prosperity of Islamic rule, but 
Islamic thought was still in the absorptive period. The most 
important agents in the transmission of Greek learning through 
S3n:iac into Arabic were members of the great family of Nestorian 
scholars that bore the name of bukht-yishu ('Jesus hath de- 
livered'). This family produced no less than- seven generations 
of distinguished scholars, the last of whom lived into the second 
half of the eleventh century. It was the skill of the physicians of 
this family that instigated the Caliphs to propagate Greek medical 
knowledge in their realm. 

During the century 750-850 the old Syriac versions were 
revised and others added. The translators, mostly Nestorians of 
the Bukht-Yishu family or their pupils, had a command of the 


The Middle Ages: Theology^ Queen oj the Sciences 

Greek, Syriac, and Arabic languages and often also of Persian. 
Most of them wrote first in S5n:iac. The venerable Yuhanna Ibn 
Masawiah, the John mesue of the Latins (d. 857), one of the 
Bukht Yishu, and medical adviser to Harun ar-Rashid, the fifth 
Abbaside Caliph, produced, however, many works in Arabic. As 
time went on Arabic began to replace Syriac for scientific and 
medical works. Just as 750 to 850 was the century of translation 
into Syriac, so 850 to 950 was the century of translation into Arabic. 

The seventh Abbaside Caliph, Al-Mamun (813-33), created in 
Bagdad a regular school for translation. It was equipped with a 
library, honain ibn ishaq (809-77), a particularly gifted philoso- 
phical and erudite Nestorian, was the dominating figure of this 
school. He passed his life in Bagdad, serving nine caliphs and 
exhibiting phenomenal intellectual activity. He translated into 
Arabic almost the whole immense corpus of Galenic writings. His 
predilection for the scholastic turn in Galen’s theories contributed 
much to give Galen his supreme position in the Middle Ages in the 
Orient, and indirectly also in the Occident. He began the transla- 
tion of Ptolemy’s Almagest and of works of Aristotle. Honain 
and his pupils rendered also a number of astronomical and mathe- 
matical works into Arabic as well aa the Hippocratic writings. 
Many of these translations passed ultimately into medieval Latin. 

Bagdad now rapidly replaced Gondisapur as the centre ol 
learning. The Caliphs and their grandees furnished the necessary 
means to allow the Christian scholars to travel in search of Greek 
manuscripts and to bring them to Bagdad for translation. It was 
at Bagdad that most of the Aristotelian writings were first made 
accessible in Arabic, together with works on botany, mineralogy, 
and mechanics, as well as many Greek alchemical works. There 
was also an active intake of ideas and of texts from Indian and 
Persian sources. It seems likely that many alchemical methods 
were of Persian origin, while there was a strong mathematica] 
influence, expressed especially in the system of numeration, exer- 
cised by Indian civilization. 

The general course of thought may be considered separately 
for Eastern and Western Islam. Of these the East is more impor- 
tant for the positive sciences, which we can consider under the 
headings (i) Alchemy, ‘(ii) Medicine (p. 133) (iii) Mathematics am 


The Failure of Knowledge 

Astronomy (p. 134), and (iv) Physics (p. 135).' For Western 
Islam see pp. 138-40. 

(i) Alchemy in Eastern Islam. 

Of original scientific writers using the Arabic language one of 
the earliest was geber [c. 850), ^ a pagan Syrian. Geber was the 
father of Arabic alchemy and through it of modem chemistry. 
In discussing his work we must rid ourselves of the conception of 
alchemy as a bundle of fantastic superstitions. The word ‘ alchemy' 
is usually said to be derived from the Egyptian kem-ity * the black 
or from the Greek chyma (molten metal), but in any event it comes 
to us through Arabic. The fundamental premises of alchemy are 
of Alexandrian origin (p. 93) and may be set forth thus : 

{a) All matter consists of the same ingredients, the four elements, 
in various mixtures. 

[h) Gold is the 'noblest' and 'purest' of all metals, silver next 
to it. 

(c) Transmutation of one metal into another is possible, by an 
alteration in the admixture of the elements. 

{d) Transmutation of 'base' into 'noble' metal can be achieved 
by rneans of a certain precious substance often called the 
fifth element, or quintessence. (The earliest alchemical docu- 
ments call the process 'tincturing' the base metal, and in 
fact describe an alloy.) 

These conceptions, absurd though they seem to us, are no more 
so than those of many eminent chemists of as late as the eighteenth 
century. In fact they had the great merit of provoking experi- 
ment. It is a misfortune that at Alexandria, where alchemy 
specially flourished, mystical tendencies, largely of Neoplatonic 
origin, overlaid the experimental factor. Alchemy, which for 
Geber was a matter of experimental research, thus tended with 
his successors to superstitious practice, passing into fraudulent 

On the practical side, Geber described improved methods for 

* There was also considerable geographical activity. As, however, it 
contributed little to the general current of Western science, we omit its 

* The date of Geber is much in dispute. Recent evidence points to the 
ninth century. 


The Middle Ages: Theology ^ Queen oj the Sciences 

evaporation, filtration, sublimation, melting, distillation, and 
crystallization. He prepared many chemical substances, e.g. cin- 
nabar (sulphide of mercury), arsenious oxide, and others. He 
knew how to obtain nearly pure vitriols, alums, alkalis, sal- 
ammoniac, and saltpetre, and how to produce so-called diver' 
and ‘milk' of sulphur by heating sulphur with an alkali. He 
prepared fairly pure mercury oxide and sublimate, as well as 
acetates of lead and other metals, sometimes crystallized. He 
understood the preparation of crude sulphuric and nitric acids 
and of the mixture of acids called ‘aqua regia’ and of the solu- 
bility of gold and silver in it. Several technical terms have 
passed from Geber's Arabic writings through Latin into the 
European languages (see p. 147). 

After Geber there is a great number of alchemical writers, 
many of whose works found their way into Latin. Except for 
Rhazes (see below), the quality of their work is commonly much 
below that of the great original and is frequently cursed by that 
wilful obscurity that sometimes usurps the name of ‘mysticism’. 

(ii) Medicine in Eastern Islam. 

The first original Arabic writer ori medicine was the Persian 
known to the Latin West as rhazes (865-925). He was undoubt- 
edly one of the great physicians of all time. He studied in Bagdad 
under a disciple of Honain (p. 131) who was acquainted with 
Greek, Persian, and Indian medicine. His erudition was all- 
embracing, and his scientific output remarkable, amounting to 
more than two hundred works, half of which were medical. In 
his youth Rhazes practised as an alchemist but later, when his 
reputation attracted pupils and patients from all parts of western 
Asia, he devoted himself to medicine. 

The greatest medical work of Rhazes, and one of the most 
extensive ever written, is his ‘Comprehensive Book' known to 
medieval Europe as the Liber continens (p. 149). It gathers into 
one huge corpus the whole of Greek, Syriac, and early Arabic 
medical knowledge and incorporates also the life experience ol 
Rhazes himself. Rhazes was the first to describe small-pox and 
measles adequately. ,His account of them is a medical classic. 

Besides medicine, l^azes left writings on theology, philosophy, 


The Failure oj Knowledge 

mathematics, astronomy, and alchemy. His great Book of the Art 
[of Alchemy) is dependent partly on his predecessor Geber. Rhazes 
excels Geber in his exact classification of substances, and in his 
clear descriptions of chemical processes and apparatus. These 
are always devoid of 'mystical* elements. While Geber and the 
other Arabian alchemists divide mineral substances into ‘ bodies * 
(gold, silver, &c.), 'souls* (sulphur, arsenic, &c.), and 'spirits* 
(mercury and sal-ammoniac), Rhazes classified alchemical sub- 
stances as animal, vegetable, or mineral, a conception which 
passed from him into a commonplace of modern speech. 

A prominent contemporary of Rhazes was the writer known 
to the Latins as Isaac judaeus (855-955). This Egyptian Jew 
became physician to the Fatimid rulers of Kairouan in Tunisia. 
His works were among the first to be translated from Arabic into 
Latin (p. 143). That On Fevers was one of the best medical works 
available in the Middle Ages. 

AVICENNA (980-1037) of Bokhara was one of the greatest thinkers 
of the Islamic world. He was less remarkable as a physician than 
as a philosopher, but his influence on medieval Europe was chiefly 
through his gigantic Canon of Medicine. It is the culmination 
and masterpiece of Arabic systematization and has been perhaps 
more studied than any medical wort ever written. The classifica- 
tion adopted in it is excessively complex, and is in part respon- 
sible for the mania for subdivision which afflicted Western 
Scholasticism. Avicenna wrote also on alchemy. The early Arabic 
literature of medicine is very extensive. 

(hi) Mathematics and Astronomy in Eastern Islam. 

Of aU the peoples of antiquity there was none except the Greeks 
that attained so high a standard in mathematics as the Hindus. 
Just as the Greeks developed geometry, the Hindus developed 
arithmetic and algebra. It is extremely difficult to fix the dates 
or even the chronological sequence of the Indian mathematical 
works. The Arabs, however, had much commerce with India and 
there can be no doubt that by the ninth century Hindu science 
was available in Arabic. Thus Arabic algebra and arithmetic are 
essentially Indian. 

The most influential mathematical work produced in Arabic 


The Middle Ages: Theology, Queen oj the Sciences 

was the Arithmetic of the Persian al-kwarizmi (c. 830). In it is 
used our so-called ‘Arabic’ numerical notation, in which the 
digits depend on their position for their value. The method is, in 
fact, of Indian origin. The Algebra of Al-Kwarizmi is the first 
work in which that word appears in the mathematical sense. 
‘Algebra’ means ‘restoration’, that is to say the transposing of 
negative terms of an equation to the opposite side. The word is 
used also in Arabic surgery for treatment of fractures, the word 
there meaning ‘ restoration’ of a broken bone to its correct position. 
Al-Kwarizmi also prepared astronomical tables. 

The mathematics of Al-Kwarizmi shows little originality, and 
in general the achievement of the Arabs in the department of 
pure mathematics is below the Greeks in geometry and below the 
Hindus in algebra. On the other hand, they exhibited great skill 
in applying their mathematics to physical and to a less extent to 
astronomical problems. 

Astronomy and astrology were constant preoccupations of the 
Arabic-speaking world. Very early works on the subject were th'fe 
compendia by the Bagdad Jewish writer, messahala (770-820), 
whose name means ‘What God will’. 

The Caliph Al-Mamun (813-33) built a fine observatory at 
Bagdad (829) where observations were long recorded. The greatest 
of all the Arabic astronomers al-battani, Albategnius of the 
Latins (d. 929), observed chiefly at his home Raqqa (Aracte) in 
Asia Minor, but also at Bagdad. He worked over the observa- 
tions of Ptolemj' in a searching and exact manner. He thus 
obtained more accurate values for the obliquity of the ecliptic and 
the precession of the equinoxes (pp. 76-77). His improved tables 
of the sun and the moon contained his great discovery that the 
direction of the sun’s excentric (p. 78), as recorder! by Ptolemy, 
was changing. Expressed in the terms of more modem astro- 
nomical conceptions, this is to say that the earth is moving in a 
varying ellipse (p. 265). Al-Battani drew up his observations ii 
tabular form. 

A popular elementary writer on astronomy was alfargan; 
of Transoxiana (d. c. 850). He worked at Bagdad and served the 
Caliph Al-Mamun and his followers. His work deeply influencec 
the Latin West. 


The Failure oj Knowledge 

(iv) Physics in Eastern Islam. 

Among the Arabic writers on Physics alkindi (813-80) of Basra 
and Bagdad was the earliest. No less than 265 works have been 
ascribed to this ‘first philosopher of the Arabs’. Of these at least 
fifteen are on meteorology, several are on specific weight, and 
others on tides. His best work is on optics, and deals with the 
reflection of light. 

In the ninth century the technical arts were rapidly developing 
in Mesopotamia and Egypt, where irrigation works and canals 
for water-supply and communications were created. Theoretical 
mechanics roused much interest, and many books were written on 
such topics as raising water, on water-wheels, on balances, and 
on water-clocks. The earliest appeared about 860 as the Book of 
Artifices by the brother mathematicians Muhammed, Ahmed, and 
Hasan, sons of Musa ben Shakir, who were themselves patrons of 
translators. They describe one hundred technical devices, of which 
some twenty are of practical value, among them being vessels for 
warm and cold water, wells with a fixed level, and water-clocks. 
Most, however, are mere scientific toys like those of Hero (p. 81) . 

The tenth and early eleventh centuries were the golden age of 
Arabic literature. It was also remarkable for its wealth of techni- 
cal knowledge. Optics especially was developed to its highest 
degree, alhazen (965-1038) of Basra was the greatest exponent 
of this science. He entered the service of the Fatimid Caliph al- 
Hakim (996-1020) at Cairo. In his main work, the Treasury of 
Optics, Alhazen opposes the theory of Euclid and Ptolemy and 
others among the ancients that the eye sends out visual rays to 
the object of vision. It is, he thinks, rather the form of the per- 
ceived object that passes into the eye and is transmuted by its 
'transparent body’, that is the lens. He discusses the propagation 
of light and colours, optic illusions and reflection, with experi- 
ments for testing the angles of reflection and of incidence. His 
name is still associated with the so-called ' Alhazen ’s problem’. 
‘In a convex mirror, spherical, conical, or cylindrical, to find the 
point at which a ray coming from one given position will be reflec- 
ted to another given position. * It leads to an equation of the fourth 
degree which Alhazen solved by the use of an hyperbola. Alhazen 


The Middle Ages: Theology^ Queen oj the Sciences 

examines also the refraction of light-rays through transparent 
media (air, water). In detailing his experiments with spherical 
segments he comes very near to the theoretical exposition of 
magnifying lenses which was made centuries later (p. 195). 

Alhazen regards light as a kind of fire that is reflected at the 
spheric limit of the atmosphere. His calculation of the height of 
this atmosphere gives about ten English miles. He treats also of 
the rainbow, the halo, and the reflection from spherical and para- 
bolic mirrors. He constructed such mirrors of metal on the basis 
of most elaborate calculations. His fundamental study On the 
Burningysphere represents real scientific advance, and exhibits a 
profound and accurate conception of the nature of focusing, 
magnifying, and inversion of the image, and of formation of rings 
and colours by experiments. The work is far beyond anything 
of its kind produced by the Greeks. Alhazen records in it the 
semi-lunar shape of the image of the sun during eclipses on a wall 
opposite a fine hole made in the window-shutters. This is the first 
mention of the camera obscura. 

Among the most characteristic products of Arabic thought is a 
group of writings on what we may call scientific theory and classi- 
fication. An early exponent of these was the Turkish philosopher 
ALFARABi (d. c. 95i)i the authpr of the most important oriental 
work on the theory of music. His treatise on the classification of 
the sciences was very influential. 

The Persian albiruni (973-1048), physician, astronomer, 
mathematician, physicist, geographer, and historian, is perhaps 
the most prominent figure in the phalanx of the versatile scholars 
of the Golden Age. His Chronology of Ancient Nations is an 
important historical document. Most of his mathematical work 
and many others of his writings await publication. In physics 
his greatest achievement is the very exact determination of the 
specific weight of eighteen precious stones and metals. His method 
was, in effect, that of the bath of Archimedes (p. 65). 

In the tenth and eleventh centuries several secret or at least 
esoteric sects professing the atomic nature of matter established 
themselves in Mesopotamia. Certain of them professed an Epi- 
curean attitude to the world and to Creation which was opposed 
to the orthodox Aristotelianism of Moslem theologians. A struggle 


The Failure of Knowledge 

ensued comparable to that of later date in Europe. In the end 
the unorthodox atomists were vanquished. 

Among the secret societies mention may be made of the breth- 
ren OF PURITY, a philosophical sect founded in Mesopotamia 
about 980. They combined to produce an encyclopaedia of fifty- 
two treatises, seventeen of which deal with natural science, 
mainly on Greek lines. They contain discussions on the formation 
of minerals, on earthquakes, tides, meteorological phenomena, 
and on the elements, all brought into relation with the celestial 
spheres and bodies. The work of the Brethren, although burnt 
as heretical by the orthodox in Bagdad, spread as far as Spain 
where it influenced philosophic and scientific thought. 

In Western Islam the scientific tradition was established later 
than in the East. It first appears in Spain, during the glorious 
reigns of the Caliphs Abd Ar- Rahman III and Al-Hakam II of 
Cordova, in the person of hasdai ben shaprut (d. c. 990), a Jew 
who was at once minister, court physician, and patron of science. 
He translated into Arabic, with the help of a Byzantine monk, a 
splendid manuscript of Dioscorides (p. 89) sent, as a diplomatic 
present, to his sovereign from Constantine VI of Byzantium. The 
Moslem known to the Latins as abulcasis (d. c, 1013) was likewise 
court physician in Cordova. His name is associated with a great 
medical handbook in thirty sections, the last of which deals with 
surgery, an art which had till then been neglected by Islamic 

A library and academy was founded at Cordova in 970, and 
similar establishments sprang up at Toledo and elsewhere. As- 
tronomy was specially studied. The chief astronomer of the 
Moslem Spain was known to the Latins as arzachel. He was a 
Cordovan but worked at Toledo. He drew up so-called Toledan 
tables which attained a high degree of accuracy (1080). One of 
the last significant men of science of Moslem Spain was Al-Bitrugi 
of Seville, known to the Latins as alpetragius. He wrote a 
popular text-book of astronomy (c. 1180). The work contains an 
attempt to replace the Ptolemaic by a strictly concentric plane- 
tary system and is important for having provided suggestions tc 
Copernicus (p. 179). 


The Middle Ages: Theology^ Queen oj the Sciences 

In the twelfth century a great change came over Islamic thought. 
Under the influence of the religious teacher Al-Ghazzali (d. iiii), 
tolerance gave place to persecution of studies thought to ' lead to 
loss of belief in the origin of the world and in the Creator'. 
Outstanding and independent works become rarer. Among the 
scientific writers an increasing proportion of Jews is to be observed, 
because they were relatively free from the restraints of orthodox 
Islam. Of these the most eminent was the court physician, philo- 
sopher, and religious teacher, maimonides (1135-1204). Bom in 
Spain, he spent most of his active life in Cairo under the great 
Saladin and his sons. In his medical works he even ventured to 
criticize the opinions of Galen. As a court official he wrote 
hygienic treatises for the Sultan which are good typical specimens 
of the medical literatilre of Islam. His cosmological views are of 
great importance and influenced St. Thomas Aquinas and through 
him the whole thought of Catholic Europe. His Guide for the Per- 
plexed is perhaps the most readable treatise on general philosophy 
produced by the Middle Ages, whether Arabic, Byzantine, or Latin. 
It has the crowning merit, most unusual for the period, of relative 

The latest and the greatest exponent of Islamic philosophy was 
the Spaniard averroes (1126-98). He was born at Cordova, 
son and grandson of a legal officer. He himself held the office of 
judge, but also studied and practised medicine. His very volu- 
minous philosophical writings earned the enmity of orthodox 
Moslem theologians, some of whom regarded him as having 
become a Jew. In fact, no writer exerted greater influence than 
Averroes on later medieval Jewish thought. His writings were 
burned by royal decree, and most of the latter part of his life was 
passed in disgrace. 

Averroes has certainly been one of the most influential of all I 
thinkers. He placed his thought in the form of a long series of* 
commentaries on the works of Aristotle, whom he exalted above 
all other men. Nevertheless, his teaching was basically, though 
unconsciously, modified by Neoplatonism, notably in his concep- 
tion of the human soul as part of the Divine world soul. His most 
discussed doctrine was that the world is eternal. This some of his 
interpreters represented as a denial of creation. Nevertheless, 


The Failure of Knowledge 

Averroes did accept the idea of creation, though not of an entire 
universe out of nothing as demanded by the current theology of 
Islam, Christianity, and Judaism alike. 

Averroes believed, not in a single act of creation, but in a con- 
tinuous creation, renewed every instant in a constantly changing 
world, always taking its new form from that which has existed 
previously. This is true philosophic evolutionism. For Averroes 
the world, though eternal, is subject to a Mover constantly produc- 
ing it and, like it, eternal. This Mover can be realized by observa- 
tion of the eternal celestial bodies whose perfected existence is 
conditioned by their movement. Thereby may be distinguished 
two forms of eternity, that with cause and that without cause. 
Only the Prime Mover is eternal and without cause. All the rest 
of the universe has a cause or, as we should say nowadays, is 
‘subject to evolution'. 

Averroes, like all medieval thinkers, pictured the universe as 
finite in space. For a formal denial of that doctrine we have to 
look forward to Nicholas of Cusa (p. 17 1) ^nd Giordano Bruno 
(p. 185). 

With the thirteenth century there sets in a very definite de- 
terioration in the quality of Arabic science. The future lay with 
the Latin West on which Arabic thought was now setting its 

Perhaps the most significant of all Moslem influences on the 
West has been the philosophy transmitted through Averroes and 
chiefly by Jewish agents. By his doctrine of the eternity of the 
world, his denial of Creation in time, and his conception of the 
unity of the soul or intellect, Averroes split Western thought 
from top to bottom. Orthodox Catholic philosophy of the Middle 
Ages may be regarded as an organized attempt to refute his views. 
The fact that this seemed necessary tells of the gravity of the 
opposition. His influence may be traced in many medieval heresies, 
in the works of Nicholas of Cusa (p. 171), and of several Renaissance 
thinkers, in the standpoint of Copernicus (p. 179), in the thought 
of Giordano Bruno (p. 185), and beyond. It may seem strange 
that a professedly faithful exponent of Aristotle should have 
initiated that movement which led to the final overthrow oi 
Aristotelian cosmology in the Insurgent Century (Ch. VII). It 


The Middle Ages: Theology y Queen oj the Sciences 

must be remembered, however, that Averroes, like the other 
Arabic philosophers, saw Aristotle through Neoplatonic spectacles^ 
though he was himself unconscious of the fact. The Neoplatonic 
tinge became, moreover, intensified in the Latin versions and 
commentaries on his works. 

3. Oriental Penetration of Occident (1000-1300). 

The eleventh century and those that follow brought the West 
into relation with the wisdom of the East. In these centuries the 
relation of East and West with which we are nowadays familiar 
is reversed. 

In our time most Oriental peoples value Western civilization 
and accord it the sincerest form of flattery. The Oriental recog- 
nizes that with the Occident are science and learning, power 
and organization, and business enterprise. But the admitted 
superiority of the West does not extend to the sphere of religion. 
The Oriental who nowadays gladly accepts the Occidental as his 
judge, his physician, or his teacher, repudiates, and perhaps 
despises, his religion and his philosophy. 

In the Europe of the eleventh and twelfth centuries it was far 
other. The Westerner knew full well that Islam held the learning 
and science of antiquity. Moslem proficiency in arms and ad- 
ministration had been sufficiently proved — the Occidental belief 
in them is enshrined in our Semitic words ' arsenal ' and * admiral 
'tariff, 'douane', and * average'. There was a longing, too, for 
the intellectual treasures of the East, but the same fear and re- 
pugnance to its religion that the East now feels for West. And 
the Western experienced obstacles in obtaining the desired 
Oriental learning analogous to those now encountered by the 
Eastern in the Occident. 

We may consider Arabic influence on Western Europe in two 
stages, an earlier indirect stage, ‘the Age of Rumours', and a later 
direct stage, ‘The Age of Translations'. 

(i) The Age of Arabian Rumours (looo-iioo). 

The first definitely Oriental influence that we can discern as 
affecting ideas about nature is of the character of infiltration 
rather than direct translation. Thus gerbert, who died in 1003 


The Failure of Knowledge 

as Pope Sylvester II had studied in north-east Spain, beyond the 
Moslem zone. He described an abacus (p. 112) that was almost 
certainly of Arabic origin though he used for it counters bearing 
numerals similar to those of Boethius (p. 129). He also instigated 
a translation from Arabic of a work on the astrolabe. He was 
clearly in touch with some sort of Arabic learning. 

Similarly with Herman the cripple (1013-54) who spent his 
life at the Benedictine Abbey of Reichenau in Switzerland. He 
wrote certain mathematical and astrological works which were 
extensively used in the following century. Herman was unable 
to read Arabic, and could not travel by reason of his infirmity. 
Yet his writings display much Oriental influence, which must 
have been conveyed to him by wandering scholars. Similar evi- 
dence of Arabic infiltration is exhibited in lapidaries and herbals 
of the eleventh and twelfth centuries. 

By the mid-eleventh century, Arabic learning was thus- begin- 
ning to trickle through to the West. It was derived ultimately, 
as we have seen, from Greek sources (p. 130). There was, how- 
ever, just one channel by which the original Greek wisdom might 
still reach Europe, though in a much debased form. Communica- 
tion between the West and the Byzantine East was very restricted 
in the Dark Age, but a Greek tradition still lingered in south Italy 
and Sicily. These remained for centuries under the nominal 
suzerainty of Byzantium, and the dialects of the ‘ many-tongfied 
isle* still bear traces of the Greek spoken there, as in Calabria and 
Apulia, until late medieval times. But Saracens had begun their 
conquest of Sicily in the eighth century, and did not loosen their 
hold until the Norman attack of the eleventh. The Semitic 
language of the Saracens left the same impress on the island as did 
their art and architecture. Thus between the tenth and thirteenth 
centuries the 'Sicilies* were a source of both Greek and Arabic 

One seat of learning in the southern Italian area felt especially 
the influence of both Greek and Arabic culture. Salerno, on the 
Gulf of Naples, had been a medical centre as far back as the ninth 
century. There was a Greek-speaking element in the town and 
some traces of ancient Greek medicine lingered there as in other 
parts of south Italy after the downfall of the Western Empire. 


The Middle Ages: Theology^ Queen oj the Sciences 

There were, moreover, a number of Jews in the town and many of 
these had affiliations with the Orient. Such learning as was found 
at Salerno was galvanized into life by Saracenic energy. From 
about 1050 onwards medical works were produced at Salerno. It 
is easy to understand why some of them contain Semitic words, 
and why others present unexpected and strangely altered Greek 

A very important carrying agent of the Arabic learning was 
CONSTANTINE THE AFRICAN (1017-87), a native of Carthage. He 
reached Salerno about 1070 and some years later acted as secretary 
to the Norman conqueror of that city. Later he retired to a 
monastery and spent the rest of his life turning current Arabic 
medical and scientific works into Latin. 

Constantine’s sources are mainly Jewish writers of North 
African origin and Arabic language, among them Isaac Judaeus 
(p. 134). In his desire for self-exaltation Constantine often con- 
ceals the names of the authors from whom he borrows, or he gives 
them inaccurately. His knowledge of both the languages which 
he was treating was far from thorough. Yet his versions were very 
influential, and remained current in the West long after they had 
been replaced by the better workmanship of students of the type 
of Gerard of Cremona (p. 148). With Constantine is linked 
ALPHANUS, Archbishop of Salerno (d. 1085), who was himself the 
first medical translator direct from the Greek, and who turned 
a Neoplatonic physiological work of the fourth century into Latin. 

(ii) The Mechanism of Translation. 

The earliest Oriental influences that reached the West had thus 
been brought by foreign agents or carriers, but the desire for 
knowledge could not be satisfied thus. The movement that was 
to give rise to the universities was shaping itself during the twelfth 
century. Tl;ie Western student was beginning to become more 
curious and more desirous of going to the well-springs of Eastern 

Language was his main difficulty. The idiom of Arabic was 
utterly diflerent from the speech of the peoples of Europe. More- 
over, its grammar had not been reduced to rule in any Latin work, 
nor could teachers be easily procured. The only way to learn the 


The Failure of Knowledge 

language was to go to an Arabic-speaking country. This was a 
dangerous and difficult adventure, involving hardship, secrecy, 
and perhaps abjuration of faith. Moreover, a knowledge adequate 
for rendering scientific treatises into Latin meant a stay of years, 
since some understanding of the subject-matter as well as the 
technical vocabulary was needed. There is good evidence that 
such knowledge was very rarely attained by western Christians, 
and probably never until the later twelfth, century. 

At the period during which Western science began to draw from 
Moslem sources there were only two areas of contact of the rival 
civilizations: Spain and 'the Sicilies*. The conditions in the two 
were somewhat similar. In the tenth century the Iberian penin- 
sula was Moslem save for Leon, Navarre, and Aragon, small 
kingdoms of the French march. In that northern area the grip of 
Islam had soonest relaxed, and this territory remained religiously 
and linguistically a part of the Latin West. The Moslem south 
was ruled from Cordova, which became a very Islamic stronghold. 
At the more northern Toledo the townsfolk while speaking an 
Arabic patois, were chiefly Christian, though with a large Jewish 
element. In 1085, Alphonso VI of Leon, aided by the Cid, con- 
quered the town. A lalrge Arabic-speaking population remained. 
It was at Toledo that most of the work of transmission took place 
(Figs. 51 and 52). 

The question is often asked why in the Middle Ages, the pre- 
vailing tendency was to translate works from the Arabic rather 
than from the Greek, and why this tendency affected even works 
originally written in Greek. The reasons may be set forth 

(a) Between 1000 and 1300 Moslem learning was better organ- 
ized, more original, more vital in every way than Byzantine 

(b) Byzantine Greek is far distant from the classical tongue. 
The language of Aristotle was incomprehensible to the 
monastic guardians of his manuscripts. On the other hand, 
classical Arabic was intelligible to every well-educated man 
— Moslem or other — ^who spoke and wrote Arabic. 

(c) The whole trend of Byzantine learning was to theology and 
away from philosophy and science. 


The Middle Ages: Theology, Queen oj the Sciences 

{d) The channels of trade with the West were rather with Islam 
than with the Byzantine Empire. 

{e) In the Middle Ages languages were learned by speaking and 
not from grammars. Spoken Arabic was more accessible 
than spoken Greek. 

(/) Latin Christendom made little progress in occupying Byzan- 
tine territory. On the other hand, from 1085, when Toledo 
fell, Islam was in retreat in the West. It was thus easier 
to find a skilled Arabic than a skilled Greek teacher. 

(g) Jewish help could be obtained for Arabic, but seldom for 

The process of translation from Arabic, especially in Spain, was 
frequently carried on by the intervention of Jewish students. 
Many of the translated works were themselves by Jews. The 
tenth, eleventh, and twelfth centuries, a time of low degradation 
of the Latin intellect, was the best period of Jewish learning in 
Spain. Arabic was the natural linguistic medium of these learned 

L 145 


The Failure oj Knowledge 

Jews, among whom were Solomon ibn Gabirol (1021-58 ?) of Sara- 
gossa, who was disguised in scholastic writings as avicebron, and 
Moses ben Maimon (1135-1204) of Cordova, more familiarly known 
as MAiMONiDES (p. 139). The writings of these two authors 
together with the Jewish version of averroes were the most 
philosophically influential of those rendered into Latin from Arabic 

during the Middle Ages. Their works helped to mould Western 

Despite the activity of the translators, medieval Latin was not 
yet equipped with an adequate supply of technical terms. The 
meanings of some of these in the Arabic were imperfectly knowh 
to the translators themselves. Such words were therefore often 
simply carried over, transliterated from their Arabic or Hebrew 

The Middle Ages: Theology^ Queen of the Sciences 

form. The early versions are full of Semitic expressions. Thus of 
chemical substances we have realgar (red sulphide of arsenic), 
iutia (zinc oxide), alkali, antimony, zircon, and of chemical 
apparatus alembic for the upper, and aludel for the lower part of 
a distillation vessel. A new chemical substance unknown to the 
Greeks which appears for the first time in the works of Geber is 
sal-ammoniac. The ammoniacon of the Greeks was rock-salt, and 
it seems that the transference of the old names to a new salt was 
effected by the Syrians. Of pharmaceutical terms, we have a 
number of Persian terms that have passed through Arabic, such 
as zedoary, alcohol, sherbet, camphor, lemon, and syrup, while 
more purely Arabic are alizarin, borax, elixir, natron, talc, and 
tartar. In astronomy there are numerous Arabic star names as 
Aldebaran, Altair, Betelgei^se, Rigel, Vega, some astronomical 
terms as nadir, zenith, azimuth, azure, a few instrumental designa- 
tions as alidade and theodolite, and at least one word which has 
passed into common language, almanac. To these may be added 
the mathematical terms zero, cipher, sine, root, algebra (p. 135), 
algorism (see below). Music was also deeply affected, as witness 
lute, guitar, shawm, rebeck. There was a complete Arabic-Latin 
anatomical vocabulary of which almost the sole remains is nucha, 
though the titles of the cephalic, basilic, and saphenous veins have 
passed through Arabic. The modem botanical vocabulary pro- 
vides us with many plant-names of Arabic origin such as artichoke, 
coffee, lilac, musk, ribes and sumach or names that have passed 
through Arabic as jasmine, mezereon, saffron, sesame, and 

(iii) The Translators. 

Among the pioneer Western translators from Arabic to Latin 
was ADELARD OF BATH (c. logo-c. 1150), who joumeyed both to 
Spain and the Sicilies. His services to mathematics were very 
distinguished. He began early with a treatise on the abacus. 
Then he turned to Arabic mathematics and translated into Latin 
the Arithmetic of Al-Kwarizmi involving the use of the ‘Arabic', 
i.e. Indian, numerals (p. 135), which he thus introduced to the 
West. Al-Kwarizmi has, through him, left his name in algorism, the 
old word for arithmetic. Moreover, Adelard also rendered Euclid 


The Failure oj Knowledge 

from the Arabic and so made the Alexandrian mathematician 
known for the first time to the Latins. He wrote a popular 
dialogue, Natural Questions, which is a sort of compendium of 
Arabic science. 

A generation later than Adelard was Robert of Chester {c. 
iiio-c. ii6o), who lived long in northern Spain (1141-7). He was 
the first to translate the Koran (1143). Among his scientific 
renderings was the first alchemical text to appear in Latin 
(1144). His translation of the Algebra of Al-Kwarizmi (p. 135) in- 
troduced the subject to the Latins (1145). Later he returned to 
England and settled in London (1147). There he produced astro- 
nomical tables for the longitude of London (1149-50) based on 
Albategnius (p. 135) and for the latitude of London based on Al- 
Kwarizmi and Adelard. 

Contemporary with Robert and perhaps stimulated by him, 
were certain native translators who worked at Toledo. One of 
these was domenigo gonzalez (fi. 1140), a Christian who ren- 
dered into Latin from Arabic the Physics and other works of 
Aristotle. Another, John of Seville (fi. 1139-55), a converted 
Jew, was very active and translated among many other works 
a pseudo-Aristotelian treatise which greatly influenced Roger 
Bacon, * as well as astronomical and astrological works of Al- 
battani, Alfarabi, Alfargani, Al-Kwarizmi, Alkindi, and Messahala. 

The greatest and most typical of all the translators from the 
Arabic was gerard of cremona (1114-87), who spent many years 
at Toledo and obtained a thorough knowledge of Arabic from 
a native Christian teacher. He is credited with having translated 
into Latin no less than ninety-two complete Arabic works. Many 
of them are of very great length, among them the Almagest of 
Ptolemy (p. 84) on which Georg Purbach (p. 171) began his work 
in the fifteenth century, and the enormous Canon of Avicenna 
(p. 134), perhaps the most widely read medical treatise ever 
penned. Latin editions of Avicenna continued to be issued right 
down to the middle of the seventeenth century. The Canon is still 
in current use in the East. 

Among the other achievements of Gerard are translations frbm 
the Arabic of Archimedes On the Quadrature of the Circle (p. 67), 
of an optical work of Apollonius (p. 69) , of many of the works of 

The Middle Ages: Theology^ Queen oj the Sciences 

Aristotle both spurious and genuine, of Euclid’s Elements, of many 
medical works of Galen, Hippocrates, Isaac Judaeus (p. 134), 
Rhazes (p. 133), and Albucasis (p. 138), of alchemical works of 
Geber (p. 132), of mathematical and astronomical works by 
Alkindi (p. 136), Alfargani (p. 135), Alhazen (p. 136), Alfarabi 
(p. 137), Messahala (p. 135), and others. He also translated 
certain important Neoplatonic works. 

The Sicilian group was less active. Among its products was the 
Optics of Ptolemy (p. 83), translated about 1160 by the Sicilian 
admiral eugenius of Palermo. He rendered it from the Arabic, 
though he had an effective knowledge of Greek. The great astro- 
nomical and mathematical system of Ptolemy known to the 
Middle Ages as the Almagest (p. 84) was also first translated into 
Latin from the Greek in Sicily in 1163, some twelve years before 
it was rendered from the Arabic by Gerard at Toledo (p. 148). 
This version from the Greek gained no currency and only that from 
the Arabic was available until the fifteenth century. 

The last important medieval translator from the Arabic was 
of Sicilian origin. He was the Jew moses farachi (d. 1285), a 
student at Salerno, and his works were among the latest of 
influence that issued from that ancient seat of learning. His great 
achievement was the translation for his master Charles of Anjou 
(1220-85), King of the Sicilies, of the enormous Liher continens of 
Rhazes (p. 133), a standard medical work of the Middle Ages. 

Special consideration among the translators may be given to 
MICHAEL THE SCOT (c. 1175-C. 1235) because we have more 
picturesque details of him than of the others. He had a career 
similar to Adelard. He visited Toledo and afterwards northern 
Italy, staying at Padua, Bologna (1220), and Rome (1224-7). He 
ended his days in the south in the service of the ‘Stupor Mundi’, 
Frederick II. He rendered into Latin from Arabic the astronomy 
of Alpetragius (p. 138), a number of Averroan commentaries, and 
the biological works of Aristotle. His pseudo-Aristotelian com- 
pendium, the Secrets ef Nature, from a number of Greek, Arabic, 
and Hebrew sources, contains a section on generation that is still 
reprinted in the European vernaculars. Michael also produced a 
great treatise on astrology. 

Michael’s activity was significant for several reasons. His version 


The Failure of Knowledge 

of Alpetragius contained the first attack on traditional astronomy. 
His translations of Averroes were among the first works of 
that heresiarch available to the Latins. His version of Aristotelian 
biology gave Aristotle’s own scientific observations for the first 
time to the West. His work on astrology was the first major 
treatise on the subject available in Latin. Michael certainly had 
Jewish and Moslem help and was long associated with the arch- 
enemy of the papacy, Frederick 11. Thus it is no great wonder 
that in the popular imagination his name became associated with 
sorcery and black magic. This was the fate of other translators 
from the Arabic. The vulgar attitude towards such men is faith- 
fully reflected in Sir Walter Scott’s Lay of the Last Minstrel where 
a monk tells us that 

Paynim countries I have trod. 

And fought beneath the Cross of God. 

In those far climes it was my lot 
To meet the wondrous Michael Scott ; 

A wizard of such dreaded fame, 

That when, in Salamanca’s cave. 

Him listed his magic wand to wave, 

The bells would ring in Notre Dame I 
Some of his skill he taught to me ; 

And, warrior, I could say to thee. 

The words that cleft Eildon hills in three. 

And bridled the Tweed with a curb of stone: 

But to speak them were a deadly sin. 

And for having but thought them my heart within, 

A treble penance must be done. 

When Michael lay on his dying, bed, 

His conscience was awakened ; 

He bethought him of his sinful deed. 

And he gave me a sign to come with speed. 

I was in Spain when the morning rose. 

But I stood by his bed ere evening close. 

4. Scholasticism and Science (1200-1400). ^ 

The view of the material universe conveyed by Arabic science 
to Latin Christendom was new in tone and presentation rather 
than in kind. The thought of the Latins in their Dark Age on 


The Middle Ages: Theology^ Queen oj the Sciences 

material things was Neoplatonic, with the Timaeits as text-book 
and the theory of macrocosm and microcosm as key. With the 
advent of Arabic thought the outlines of this vision were sharp- 
ened, and details were elaborated from the Arabian commentators 
on the Aristotelian corpus. 

Thus Aristotle^s views or supposed views as to the structure of 
the universe formed the framework on which the whole of medi- 
eval science, from the thirteenth century onward, came to be built. 
Aristotle conceived the stars as beings whose nature and substance 
were purer and nobler than that of aught in the spheres below. 
This was a point of departure frpm which the influence of the 
heavenly bodies over human destinies might be developed. 
Changes undergone by bodies on the earth — all the phenomena of 
our life — ^were held to be paralleled and controlled by movements 
in the heavens above. 

The theory carried the matter farther. Taking its clue from the 
Aristotelian conception of the 'perfection' of the circle among 
geometrical figures (p. 46), it distinguished the perfect, regular, 
circular motion of the fixed stars from the imperfect, irregular, 
linear motion of the planets.. The fixed stars, moving regularly in 
a circle, controlled the ordered course of nature, the events that 
proceeded in recurring, manifest, and unalterable rounds, such as 
winter and summer, night and day, growth and dec^y. The 
planets, on the other hand, erratic or at least errant in their move- 
ments, governed the more variable and less easily ascertainable 
events in the world around and within us, the happenings that 
make life the uncertain, hopeful, dangerous, happy thing it is. 
It was to the ascertainment of the factors governing this kaleido- 
scope of life that astrology set itself. 

Thus the general outline was fixed, death in the end was sure, 
and, to the believing Christian, life after it. But there was a 
zone between the sure and the unsure that might be predicted 
and perhaps avoided, or, if not avoided, its worst consequences 
abated. It was to this process of insurance that the astrologer set 
himself, and his task remained the same throughout the Middle 
Ages. In this hope, savoir afin de prevoir, the medieval astrologer 
was at one with the modem man of science. The matter is sum- 
marized by Chaucer (1340-1400) : 


The Failure of Knowledge 

Para venture in thilke large book, 

Which that men clepe the heven, y- written was 
With sterres, whan that he his birthe took, 

That he for love sholde han his deeth, alias ! 

For in the sterres, clerer than is glas. 

Is written, God wot, whoso coude it rede. 

The deeth of every man, withouten drede. 

. . . But mennes wittes ben so dulle 
That no wight kan wel rede it atte fulle. 

{Jf}xe Man of Lawes Tale, 11 . 190-6 and 202-3.) 

With the advent of the Arabian learning, astrology had become, 
in fact, the central intellectual interest. It retained this position 
until the triumph of the experimental method in the seventeenth 

Especial attention had always been paid to the zodiacal signs 
(p. 1 1 8) and to the planets. Each zodiacal sign was held to govern 
some region of the body, and each planet to influence a special 
organ. The supposed relations of zodiacal signs, planets, and 
bodily parts and organs, in relation to the advent of disease and 
calamity, had been set forth in many texts of late antiquity. This 
belief, conveyed to the Dark Age, but much corrupted and 
attenuated during its course, was reinforced and developed in the 
West by translations from the Arabic during the scholastic period 
which followed. 

Doctrine of this type, once received into Europe, was stamped 
with the special form of Western thought. Now, it was character- 
istic of the scholastic thinker that, like the early Greek philosopher 
and unlike his predecessor of the Dark Age, he sought always a 
complete scheme of things. He was not content to separate, as we 
do, one department of knowledge or one class of phenomena, and 
consider it in and by itself. Still less would he have held it a virtue 
to become a 'specialist', to limit his outlook to one department with 
the object of increasing the sum of knowledge in it, and in it alone. 
His universe, it must be remembered, so far as it was material, 
was limited. Its frontier was the sphere of the fixed stars. Of the 
structure and nature of all within this sphere he had been pro- 
vided with a definite scheme. The task of medieval science was to 


The Middle Ages: Theology^ Queen oj the Sciences 

elaborate that scheme in connexion with the moral world. This 
was first especially undertaken by mystical writers working under 
the stimulus of the new Arabian influence. Such authors as HUGH 
OF ST. VICTOR (1095-1141), who drew on the earlier and more 
vague Arabian rumours, Bernard Sylvester (c. 1150) of Chartres, 
who relied on Herman the Cripple (1013-54, p. 142), and ST. hil- 
DEGARD (1099-1180) of Bingen, who was influenced by Bernard 
Sylvester and by other Arabicized writings, all produced most 
elaborate mystical schemes based on the doctrine of the macro- 
cosm and microcosm. These schemes took into account the form 
of the world and of man as derived from Arabian sources, and read 
into each relationship a spiritual meaning. 

For such an attitude of mind there could be no ultimate dis- 
tinction between physical events, moral truths, and spiritual 
experiences. In their fusion of the internal and the external 
universe, these mystics have much in common with the mystics 
of all ages. The culmination of the process is reached with Dante 

There were other typical currents of medieval thought that 
were susceptible of more systematic development. It was the 
age of the foundation of universities and of religious orders. 
Among these new orders were two that specially influenced the 
universities, the Dominicans or Black Friars founded at Toulouse 
in 1215 by the austere and orthodox Dominic (1170-1221), and the 
Franciscans or Grey Friars founded in 1209 by the gentle and 
loving Francis of Assisi. The name of Dominic is associated with 
the terrible extermination of the Albigenses, and the Dominicans, 
whose title was paraphrased as Domini canes, ‘hounds of the 
Lord', set themselves to the strengthening of the doctrine of 
the Church and to the extirpation of error. The activity of the 
Inquisition was one of the less edifying interests of the ‘hounds' 
of whom Torquemada was a specially unamiable representative. 
The work of the Franciscans led up more clearly to the scientific 
revival. During the thirteenth century these two orders provided 
most of the great university teachers, who occupied themselves 
in marshalling the new knowledge and making it more accessible. 
Alexander of Hales (d. 1245), Robert Grosseteste (d. 1253), and 


The Failure of Knowledge 

Roger Bacon (d. 1270) were Franciscans, Albertus Magnus 
(1206-80) and St. Thomas Aquinas (1227-74) were Dominicans. 

A foreipost influence in the revival was the recovery of the 
writings of Aristotle. It was the interpretation of these works by 
a few great thinkers that gave to Scholasticism its essential 
character. The first scholastic to be acquainted with the whole 
works of Aristotle was Alexander of hales, albert was the first 
who reduced the whole philosophy of Aristotle to systematic order 
with constant reference to the Arabian commentators, while 
ST. THOMAS AQUINAS remodelled the Aristotelian philosophy in 
accordance with the requirements of ecclesiastical doctrine. As 
time went on, the works of Aristotle, at first represented in 
translation from Arabic, became partially accessible in renderings 
direct from the Greek. A very important translator from the 
Greek was the Dominican william of moerbeke (d. 1286), who 
was in close contact with St. Thomas. 

It is remarkable that the process of codifying the new know- 
ledge derived from the Arabic, involving as it did a rapid develop- 
ment in the whole mental life, did not early give rise to a more 
passionate and more conscious faith in the reality and value of 
progress in knowledge. The test of such faith, so far as nature is 
concerned, must be the direct appeal to nature. Yet there is very 
little evidence of direct observation of nature in the great physical 
encyclopaedias of the thirteenth century, such as those of the 
Dominican Vincent of beauvais (1190-1264), or of the Fran- 
ciscan Bartholomew the Englishman (c. 1260). The explanation 
is that the medieval mind was obsessed with the idea of the world as 
mortal, destructible, finite, and therefore completely knowable in 
both space and in time and as being, at once, both fully knowable 
and not worth knowing. Hear St. Augustine : 

'Men seek out the hidden powers of nature, which to know 
profits not and wherein men desire nothing but knowledge. With 
the same perverted aim they seek after magic arts. ... As for me, 
I care not to know the courses of the stars, while all sacrilegious 
mysteries I hate ' (Confessions, x. 35) . ‘ Even if the causes the 
movements of bodies were known to us, none would be important 
except such as influence our health. But since, being ignorant of 
these, we seek physicians, is it not clear that we should rest con- 


The Middle Ages: Theology, Queen of the Sciences 

tent to be ignorant of the mysteries of the heavens and the earth * 

(De fide, i6). 

Thus medicine is the one science that St. Augustine would 
allow. Is it wonder that medicine had deteriorated into mere 
traditional drug lists until the Arabian revival? In the Latin 
West during the Middle Ages the motive for detailed research, 
in our modern sense of the word, was absent. 

One great Islamic philosopher there was, Averroes (p. 139), 
who took another view of the universe, denying it to be finite, 
at least in time. His works were available in Latin, but the great 
ecclesiastics set their faces against him, though he was widely and 
illicitly read. His theories were adopted mainly by Jews and by 
Latins with heretical leanings. 

5. Main Personalities of Scholastic Science {Thirteenth century). 

The medieval world thus knew nothing of that infinite sea of 
experience on which the man of science nowadays launches his 
bark in adventurous exploration. Medieval science tended to the 
encyclopaedic form. The task of the writer of the encyclopaedia 
was to set forth such a survey of the universe as would be in 
accord with spiritual truth rather than to reveal new truths or 
new relations. The framework on which this scheme was built 
was Aristotle, largely as conveyed by commentaries upon 
his works. Yet it affords a reflection on the incompleteness of all 
philosophical systems that the great teacher and systematist, 
ALBERTUS MAGNUS (1206-80), who perhaps more than any other 
man was responsible for the scholastic world-system, was. among 
the very few medieval writers who were real observers of nature. 
It is, after all, in the very essence of the human animal to love the 
world around it and to watch its creatures. ‘Throw out nature 
with a pitchfork and back she comes again.' Albertus, scholastic 
of the scholastics, drowned in erudition and the most learned man 
of his time, has left us evidence in his great works on natural 
history that the scientific spirit was beginning to awake. As an 
independent observer he is not altogether contemptible, and this 
element in him marks the new dawn which we trace more clearly 
in his successors. 

Contemporary with' the Dominicans, Albert (1206-80) and St. 


The Failure of Knowledge 

Thomas Aquinas (1227-74), were several Franciscan writers who 
form the earliest group with whom the advancement of knowledge 
was a permanent interest. These men were the first consciously 
forward-looking thinkers since antiquity. The most arresting of 
them was Robert Grosseteste (c. 1175-1253), Bishop of Lincoln. 
Grosseteste determined the main direction of physical interests 
during the thirteenth century. He knew something of the action 
of mirrors and of the nature of lenses. It would appear that he 
had actually experimented with lenses, and many of the optical 
ideas of Roger Bacon were taken from his master. The main 
Arabian source of Grosseteste was a Latin translation of the 
mathematical work of Alhazen (p. 136). The great Bishop of 
Lincoln was an enthusiastic advocate of the study of Greek and 
Hebrew and an important forerunner of the Revival of Learning. 

An important writer was the Pole witelo (fl. 1270), an acute 
mathematical investigator and writer who worked in northern 
Italy and wrote a commentary on Alhazen. The Franciscan Roger 
Bacon was largely dependent on Witelo for his optical views. 
Another optical writer dependent on Alhazen was the English 
Franciscan john of peckham (c. 1220-92) , who became Archbishop 
of Canterbury. His works exhibit some mathematical skill, and 
one of them continued to be printed in the seventeenth century 
after the appearance of the writings of Kepler and Galileo! 

The greatest figure in medieval scientific thought is unquestion- 
ably ROGER BACON (1214-94). He was a Franciscan who taught at 
Paris and Oxford. He was essentially an encyclopaedist who 
realized better than most the urgent need for the enlargement of 
the basis of knowledge, especially in connexion with accurate 
knowledge of language and the collection and collation of scientific 
data. In setting forth these needs he made an appeal, verbose, 
diffuse, yet definite, for the encouragement of the experimental 
spirit. He was not himself an experimenter or mathematician, but 
he clearly saw that without experimentation and without mathe- 
matics, natural philosophy is but verbiage. 

Perhaps Bacon's greatest claim on our attention is tliat he 
recognized the usefulness of natural knowledge, foreseeing man's 
control of nature set forth more clearly, three and a half centu- 
ries later, by his great namesake Francis (p. 226). Vaguely, too, 


The Middle Ages: Theology^ Queen oj the Sciences 

he foresaw a number of important modern scientific ventures, 
flying, the use of explosives, circumnavigation of the globe, 
mechanical propulsion, &c. A single anticipation of this kind 
would hardly deserve mention, but the convergence of so many 

Figs. 53 and 54. Roger Bacon’s diagrams of the paths of rays through 
a spherical glass and through a plano-convex lens. 

in one head is impressive. Specially noteworthy — not so much 
for their originality as for their clarity — are Bacon's excursions 
into optics. He understood the nature of refraction and grasped 
its implications for curved surfaces. He thus attained to an 
approximately accurate view of the path of the rays in a burning- 
glass and he had more than an inkling of the mode of action of 
convex lenses. He seems to have been the first to suggest the 
use of lenses for spectacles and, perhaps, from hinting at the 
combination of lenses can be regarded as the progenitor of 
optical apparatus. 


The Failure of Knowledge 

Despite all this Bacon must not be considered as a man bom out 
of his time. On the contrary, he was in many ways very typical of 
the scholastic movement and an important link in the chain of 
scholastic scientific development. In especial, so far from seeing 
any opposition between science and religion, he regarded the 
advancement of science as important for the support of religion. 
That he was frequently in trouble with his superiors there can be 
no doubt, but to suggest that these differences were caused by his 
scientific views is not only to go beyond the facts but beyond all 

Diuing the century after Bacon, though his other works were still 
at times studied in the schools, it happened that for a variety of 
reasons mathematics and philosophy, in which he was chiefly 
interested, fell into abeyance. In this interval the chief advances 
were made by medical men of whom the last half of the thirteenth 
and the first half of the fourteenth century exhibit an especially 
brilliant group. Bologna and Montpellier were the centres at which 
this progress was made. 

Bologna had possessed a medical school since the twelfth 
century, and had inherited the learning of Salerno. At Bologna 
surgery may be said to have been bom again with roger of 
SALERNO (c. 1220) and his successor and faithful follower roland 
OF PARMA (c. 1250), who link the new ' Arabic ' medical movement 
with the old that had survived in southern Italy (p. 142). At 
Bologna, above all, the later thirteenth century saw established 
a regular tradition of anatomization. This was expounded by 
MONDINO DA Luzzi (1276-1328), whose work, despite its practical 
character, was based on translations from the Arabic text of 
Avicenna. The Anatomy of Mondino became the general text-book 
of the subject in the later Middle Ages. By the fourteenth century 
the practice of dissection of the human body had become well 
recognized in several universities. 

At the end of the thirteenth century the ancient foundation of 
the medical school of Montpellier was coming to the fore. The 
Catalan arnald of villanova (c. 1240-1311), one of the most 
remarkable personalities of medieval medicine, taught there. 


The Middle Ages: Theology, Queen oj the Sciences 

Amald was not only the earliest modern exponent of the Hippo- 
cratic method of observing and carefully recording actual cases 
of disease, but he also deeply influenced alchemy. That study was 
effectively of Arabian origin so far as the Western world is con- 
cerned (p. 132). It begins in 1144 with the translation into Latin 
by Robert of Chester (p. 148) of an important alchemical work by 
MORiENUS ROMANUS, a Contemporary Arabic Christian of Jeru- 
salem who derived it from an earlier Arabic source. Alchemy 
had taken its rise with a real effort to understand the properties 
of metals, prompted by the hope of transmuting the baser into the 
more precious (p. 132). Like other medieval studies, it became 
linked with astrology. Thus the 'seven metals' were each con- 
trolled or influenced by one of the 'seven planets' much in the 
same way as were the organs of the human body (p. 152). 

Of such ideas, Amald was a prolific exponent. He had direct 
access to both Arabic and Hebrew and had personal relations with 
both Moslems and Jews. A student at Naples and Salerno, a 
traveller in Italy, Sicily, France, and Spain, he served as medical 
adviser to the Papal Curia both at Rome and Avignon, and was 
employed as ambassador on more than one special mission. 
Amald influenced politics no less than learning and ended his 
adventurous life at sea. 

Astronomy — ^which cannot at this stage be distinguished from 
astrology — ^was certainly the main scientific interest of the 
scholastic age. The practical results of scholastic astronomical 
activity are, however, pitifully meagre. Western knowledge of 
astronomy was largely based on the activity of King alfonso the 
WISE (1223--84) of Castile. He collected at Toledo a considerable 
body of scholars, mostly Jews, who calculated a set of astro- 
nomical tables (1252). These Alfonsine tables spread rapidly 
through Europe. They contain few new ideas, but several 
numerical data, notably the length of the year, were calculated 
with very remarkable accuracy. Alfonso is also responsible for 
a vast encyclopaedia of astronomical knowledge compiled by a 
similar group from Arabic sources. 

The standard astronomical text-book of the scholastic period was 
by the Yorkshireman john holywood (Sacrobosco, died 1250) 
who was long a teacher at Paris. The work was universally 


The Failure oj Knowledge 

popular, exists in numerous manuscripts, and was translated into 
most European vernaculars. It contains, however, no new or 
original element and is put together from translations of the 
works of Albattani and Alfargani. Holy wood wrote also a book 
on arithmetic, or rather 'algorism' (p. 147). It was extremely 
popular and did more to introduce the Arabic notation than any 
other. Both the astronomy and arithmetic were very frequently 

Apart from the Alfonsine tables the best astronomical work of 
the period is that of the French Jew levi ben gerson (1288- 
1344) . His great astronomical treatise is essentially an attempt to 
demonstrate the falseness of the prevalent homocentric theory 
(p. 152). It is, in a sense, a return to Hipparchus (p. 76) and a pre- 
decessor of Copernicus (p. 179). It was written in Hebrew, but 
part of it, under the title The Instrument that reveals Secrets ^ was 
translated into Latin in 1342 by order of Pope Clement VI. The 
instrument is 'Jacob's staff'. This well-known surveying imple- 
ment was invented by Levi's countryman and co-religionist Jacob 
BEN MAKIR (died 1308). 

After medicine, alchemy, and astronomy, the practical sciences 
in which the West exhibited activity in the Middle Ages were 
botany and optics. Botany was always studied in connexion with 
medicine. No advance was made in the use of drugs save what 
was borrowed from the Arabs. There is, however, some indication 
of a revived interest in nature in the graphic representation of 
plants. Numerous optical texts exhibit a certain advance in ideas. 
Nevertheless, neither any of the Latin texts nor even all of them 
together are equal in value to the great work of Alhazen (p. 136) 
that itself became available in Latin about the middle of the 
thirteenth century. 

In pure mathematics the original achievement of the scholastic 
age was small. There was, however, a borrowed element that was 
to prove of high significance. At the end of the twelfth century 
a merchant Leonardo of pisa (c. 1170-c. 1245) travelled for 
commercial purposes in the East and especially in Barbarj^ There 
he learnt of that use of Indian numerals in which the value of 
a digit depends on its place in a series. It is the ordinary method 
of numeration that we now employ. In 1202 Leonardo produced 

The Middle Ages: Theology, Queen of the Sciences 

his famous of the Abacus, in which he advocates this system 
with great skill. It is the first book by a Latin Christian that em- 
ployed this system and is the essential source of our modern system, 
which, however, was extremely slow of general adoption. Other 
works of Leonardo were much more original, but being before their 
time had less influence. He was undoubtedly a mathematician of 
extraordinary ability, but his positive contributions are as nothing 
compared to his importance as the carrier of the new method. A 
much more popular work than Leonardo's that employs the 
'Arabic' numerals was the Algorismus of John Holywood (died 
1250). It appeared about 1240, was very frequently printed in 
the fifteenth and sixteenth centuries, and was still being reprinted 
in the seventeenth century. 

It is one of the puzzles of history that the great improvement 
represented by the 'Arabic' as against the Latin system of 
numerical • notation took three centuries to gain general accep- 
tance. The scholastic age was over before the modem system 
came into general use. 

Many attempts have been made to rehabilitate the intellectual 
achievement of the Middle Ages. So far as science is concerned 
they have been unsuccessful. There is no reason to reverse the 
decision that in this domain the period is one of intellectual 





The Rise of Humanism {1250-1600). The Attempted 
Return to Antiquity 

I. Humanism. 

The advent of Catholic philosophy is one of the most impressive 
events in the whole history of thought. This great effort to 
rationalize Christianity is closely linked with the recovery of the 
Aristotelian texts. 

Until the thirteenth century the only works of Aristotle avail- 
able were those on logic. These had been turned into Latin from 
Greek by Boethius in later antiquity (p. 127). Early in the thir- 
teenth century versions from the Arabic associated with the 
commentaries of the Moslem philosopher Averroes (p. 139) began 
to circulate. The centre of the intellectual world at that period 
was the University of Paris. There the reading of these Av^rroan 
interpretations of Aristotle met with ecclesiastical opposition. 
This was, however, lifted by the middle of the thirteenth century, 
perhaps because versions less coloured by the Averroan outlook 
had become available. The architect of Catholic philosophy, the 
Dominican St. Thomas Aquinas (p. 154), was able to work largely 
on versions of Aristotle prepared directly from the Greek by 
William of Moerbeke (p. 154) and others. These medieval Greek 
versions remained in use until the end of the fifteenth century. 

This summary of the knowledge of Aristotle in the thirteenth 
century requires some explanation. Before the days of printing 
a work seldom replaced completely another that was actually in 
circulation. Manuscripts were too expensive to jettison. Libraries 
were small, scholars conservative and uncritical, catalogues in- 
adequate. The better or newer versions did not commonly drive 
out the worse or older. The two generally continued in use, some at 
one centre, some at another, and often both at the same seat of 
learning. \ 

So far as science is concerned the versions of Aristotle, and the 
Aristotelian commentaries and interpretations in most common 
use, long continued to be those from the Arabic and not those from 


Rise of Humanism. Attempted Return to Antiquity 

the Greek. The hold of the Arabic-Latin versions began to be 
somewhat shaken by two important events ; [d) the rise of human- 
ism and {b) the advent of printing. But though these versions of 
Arabic origin had now competitors they were by no means dis- 
credited. Indeed * Arabist* versions retained their supremacy 
through the fifteenth and sixteenth centuries. Even in the seven- 
teenth century they were still in use in universities where the old 
Aristotelian philosophy flourished. The true and ultimate Arabist 
defeat was not the work of the Greek scholars who ranged them- 
selves under the banner of 'Humanism*. It was rather the men 
of science, adherents of the new ' Experimental Way*, who swept 
away the whole medieval philosophic approach — whether based 
on Greek or Arabic or Aristotle or Averroes. Their triumph was 
not fully apparent till the eighteenth century. There are back- 
ward centres where it is not complete even now. 

In the nineteenth century scholarship itself was transformed 
by the experimental method. Adepts in that method came at last 
to study modem critical versions of the Aristotelian corpus. Then, 
and in the fullness of days, the scientific powers of the great 
teacher came to be properly appreciated. The beauty and sym- 
metry of his mind appeared as never before and are not likely again 
to escape the historian of science. 

We turn now to consider the small beginnings of a true apprecia- 
tion of ancient science. The process is wrapped up with the advent 
of the versions of scientific works prepared from the Greek. One 
of the first to appreciate these was the heretical peter of abano 
(1250-1318). He had a knowledge of Greek, acquired at Constan- 
tinople, and he translated works from that language. He professed 
medicine at Paris and later at Padua in the generation after that 
in which the newly won Aristotelian works on physics had entered 
the curriculum. He earned a reputation as a magician, and only 
his natural death saved him from an unnatural one at the hands 
of the Inquisition. 

The best-known work of Peter, the Conciliator, expresses his 
mediation between the new Greek and the old Arabist school. It 
shows traces, too, of wider contacts, for from it we learn that he 
had met the great traveller Marco Polo (c. 1254-1324). He was 
much less conservative than most medieval writers on scientific 


The Revival oj Learning 

themes. Among Peter's views most worth record may be men- 
tioned his statements that the air has weight, that the brain is the 
source of the nerves, and the heart the source of the blood-vessels 
— novel ideas in his time. He made a remarkably accurate measure 
of the length of the year as 365 days, 6 hours, 4 minutes. 

With the fourteenth century appeared a great movement the hand 
of which is still heavy on our own day. The ancient classics began 
to be recovered and Greek began to be studied. Historians have 
perhaps linked the ' humanistic ' movement too intimately with a 
knowledge of the Greek language. Instances of familiarity with 
that language in the West can be adduced far back into the Dark 
Age (e.g. John Scot Erigena, c. 850), while many of the greatest 
of the humanists, including petrarch himself (1304--74), were 
without any facility in Greek. It is worth noting, too, as linking 
humanism with the Middle Ages, that Petrarch's epistolary style 
was still moulded on St. Augustine rather than on Cicero. 

The backward-looking habit, strong in man from his nature and 
strengthened by Christian teaching, was yet further enforced by 
the humanists. From Petrarch onward the humanist was brooding 
on the past that had been Greece and Rome. Seeking to penetrate 
the dark shadows of what was now recognized as a ‘Middle Age', 
the humanist tried hard to discern the antiquity that was beyond. 
And as he strained his eyes another vision, a reflection perhaps of 
himself, came sometimes to him. In the cloud-land of the past he 
caught or thought he caught a glimpse of what was to come — nay 
of what was in the act of becoming. And then again the vision 
would be clouded over by that terrible erudition, which, in the 
absence of general ideas, has been and is one of the enemies of 

Even in the thirteenth century Roger Bacon and a few isolated 
souls had had this double vision, but for a whole school to possess 
it was something new. In his Book of Memorable Things Petrarch 
says outright, ‘Here stand I as though on a frontier between two 
peoples, looking both to the past and to the future.' While studying 
the classics some of these men were also forging new intellectual 
weapons by developing those national vernaculars that have made 
possible modem literature,modem philosophy, andmodem science. 
It is no mere coincidence that Boccaccio (1313-75), friend and 

Rise oj Humanism. Attempted Return to Antiquity 

contemporary of Petrarch, should have been at once the first 
modern literary man to study Greek and the first great master of 
Italian prose. 

Italy was the birthplace and nursery of humanism. We would 
emphasize that save for reference to the one supreme poet in their 
own tongue, dante (1265-1321), the backward gaze of the Italian 
humanist is always fixed on the more distant classical past, not on 
the nearer period that came to be regarded as an abyss across 
which he sought to reach back to the thought of antiquity. To 
him the abyss seemed real enough and dark enough. It stood for 
the period during which the sweet Greek literature had been for- 
gotten. Even in this new age it could be understood by few except 
in Latin dress, and the work of translation and interpretation 
remained a specialist’s occupation. To the end of the fifteenth 
century an effective knowledge of Greek continued to be rare even 
among the learned. Some of the most important philosophical 
teachers even of the sixteenth century were still quite without it. 

The great influence of the masterpieces of Greece, therefore, 
was then as now something indirect, often conveyed through 
translators and special interpreters ; something esoteric, the full 
intricacy of which was shared only by a few adepts ; a subtle thing 
that influenced men’s way of thinking rather than the actual 
content of their thought. The mere capacity for translation from 
the Greek goes back very far. It was not simply the discovery of 
the actual Greek language which brought about the revival of 
letters. How, then, can we account for the change of heart that 
came over the world when humanism was bom? Or is that 
change of heart but an illusion, a difference of degree rather than 
of kind, in a world where ever3d:hing is in a state of becoming ? 

Some answer to this absorbing question we may glean by com- 
paring the earlier Greek works which came to the West with those 
of later advent. The general character of the earlier translations 
was determined by the outlook of a world becoming ever more 
deeply Arabicized. Islam, the inheritor of antiquity, entered 
into the enjoyment of its legacy with great spirit, but with a 
taste already fixed. The ancient literary and artistic works were 
debarred to the Moslem scholar. Homer and Hesiod, Sophocles 
and Euripides, Greek Art and Greek Architecture, were chapters 


The Revival of Learning 

as closed and forbidden to Islam as to early Christian Europe. 
It was the philosophical, the scientific, the mathematical, the 
medical works that made an appeal. The bulk and number of 
these gave sufficient material for thought and gave an iUusory 
impression of completeness with which Islam long rested content. 

It was these very works, to which the world of Islam clung, that 
were the first to be rendered into Latin from the Arabic. The 
Latin taste being thus determined, the mere knowledge of Greek 
wrought little change. It was works similar to those already 
rendered accessible from the Arabic that were the first to be turned 
into Latin direct from the Greek, for, in fact, Byzailtine literary 
taste was not very different from Arabic taste. The texts were 
merely improved by direct access to the tongue in which they had 
been written, but they were still the same philosophical, medical, 
mathematical texts. 

Such material — and it is bulky and intricate enough— repre- 
sents the Western access to Greek wisdom before the fourteenth 
century. It does not lack quantity — it lacks life. They err who 
think the discovery of the humanists was the Greek language — 
here the humanists were but followers where others had been 
pioneers. It is something much deeper and more fundamental 
which they have handed on, something the nature of which they 
hardly knew and the meaning of which they missed — and perhaps 
still miss. 

,The humanists discovered the literary works of antiquity. 
In them they became absorbed to the exclusion of all else. Their 
eagerness passed into a literary vogue, and cast the blight of a 
purely literary education on the modem world. The barren 
striving after form as distinct from substance, the miserable 
imitativeness that is an insult to. its model, these features, ex- 
hibited typically in the literature of the late Empire, were repeated 
by the humanists as they have been often repeated in modem 
times. They still remain the curse of our educational system. The 
importance of the humanist is not that he gave u^ the knowledge 
of a language, nor that he gave us an insight into the life of anti- 
quity. What the humanist really gave was a something which, 
added to the heritage already there, made possible a completer 
reconstruction of the Greek spirit. That reconstruction, indeed, 


Rise oj Humanism. Attempted Return to Antiquity 

he was himself never able to make. It was the succeeding genera- 
tions that made it for themselves. With that reconstruction 
Greece lived again, the modem world was ushered in, and modem 
science, art, literature, and philosophy were bom. It is an 
illuminating reflection, not without bearing on our present state, 
that both the medieval heritage of Greek science and the Eenais- 
sance heritage of Greek literature proved barren by themselves. 
It was not until the one fertilized the other that there was 
vital growth. 

Modern thought, modern science, modem art, modern letters 
are offspring of that union. Let us put from our minds the time- 
worn fallacy that they are the virgin births of one of these 
elements alone. Men accomplished alike in the arts and in the 
sciences, Leonardo (p. 172), Vesalius (p. 177), Galileo (p. 195), 
are more truly the heirs of Plato and Aristotle than are the men 
who spent their lives in editing the works of these giants of old. 
It is literature, art, and science, not classical scholarship, that 
has inherited the legacy of ancient wisdom. 

2. Recovery of the Ancient Scientific Classics. 

An event of primary importance for the history of science as 
for that of all branches of culture was the introduction of the art of 
printing into Europe about the middle of the fifteenth century. 
There are certain aspects of early printing in connexion with 
science to which attention must be directed. 

{a) We now use the printed page to express our views on current 
matters. In science we mark a discovery by its first publication, 
while both publishers and readers demand of a new book that 
it should contain at least something new. But in the early days 
of printing the press was not thus employed. The Bible and 
other sacred writings were the first to be printed. Then followed 
the works of medieval authors of theological authority. Next 
medieval treatises on law and especially ecclesiastical law, occu- 
pied the press, and were followed by medieval medical texts. 
The writings of classical antiquity came later. Only a very small 
proportion of early printed books are by contemporary writers. 
Almost all are either medieval or ancient texts or compilations 


The Revival of Learning 

therefrom. The custom of using the printed page to record one’s 
own views or experiences crept but slowly into practice. 

{h) In the process of recovery of the classical originals the atten- 
tion of scholars was first directed to works of literary merit. 
Scientific treatises appealed to a much smaller audience and, 
moreover, few scholars were adequately equipped to deal with 
them. Thus the revival of classical science came later than the 
revival of other sections of classical literature. 

(c) There has arisen a curious misconception of the importance 
of the classical literature in the fifteenth and sixteenth centuries. 
The great influence of the Revival of Learning on the subsequent 
history of thought and of education has distorted our view of 
fifteenth-century cultural interests. Even in the great days of 
humanism, in the later fifteenth century, Greek was a very rare 
accomphshment. Those who had any facility in it were extremely 
few, even among the best-educated class. Right through the six- 
teenth century and even into the seventeenth century, the over- 
whelming mass of published philosophical and scientific literature 
was still of the medieval type. 

{d) The publication of Greek scientific writings had little 
influence unless or until such works began to appear in Latin or 
vernacular translations. The humanists seldom had adequate 
scientific equipment and the men of science seldom had ade- 
quate linguistic equipment. 

Bearing these matters in mind, it is interesting to follow the 
chronological course of the appearance in print of the classical 
scientific works of antiquity. For the progress of’ science at the 
time it was the printing of these works rather than the discovery 
of their manuscript texts that was of chief significance. 

The' earliest scientific classics to be printed were naturally those 
of the Latins. The first was the Natural History of Pliny, which 
appeared at Venice as early as 1469. But Pliny, it must be remem- 
bered, was in no sense * recovered*. On the contrary h^ had never 
ceased to be read throughout the Middle Ages (p. mS) . The work was 
in fact so familiar that the Venetian printer id not think it worth 
while to attach the name of an editor to his work. Throughout 
the sixteenth century Pliny was as popular as diuing the Middle 
Ages and was very frequently reprinted. In 1601 his Natural 

Rise of Humanism. Attempted Return to Antiquity 

History was translated by Philemon Holland into English and 
was the second work of ancient science to appear in that language, 
the first being Eudid (1570, p. 170). 

Following on Pliny were editions of Varro (p. 97, Rome, 1471), 
of a collection of agricultural writers (Venice, 1472), and of the 
poem of Manilius (Nuremberg, 1472). These were all of practical 
application. Manilius is interesting as the earliest classical 
scientific treatise to appear outside Italy. It was printed at the 
private press of Regiomontanus (p. 171). The interest in it is 
explained by its astrological content, for astrology had become 
part of the University curriculum. Lucretius followed in 1473 
(Brescia). But Lucretius, as we have seen (p. 95), is not properly 
speaking a scientific writer. Celsus (p. 107), again of immediate 
practical value, followed some years later (Florence, 1478). The 
medical work of Celsus was thus the first technical scientific 
classical work to appear. It had been unknown in the Middle Ages 
and was a real discovery. It began at once to influence the practice 
of medicine. The architectural writers, Vitruvius, Frontinus, and 
Vegetius (Rome, 1486-7) — again practical works — complete the 
short list of early printed ancient Latin science. 

The Greek writings that deal with the true abstract sciences 
are both more numerous and have a more complex history. We 
may first note how backward was the treatment of the Aristote- 
lian scientific corpus. For the most part the Renaissance reader 
was content with the medieval Latin versions mainly from Arabic 
(p. 162). The first ‘modem’ translation and the first important 
scientific book to be printed was the Latin version by Theodore 
Gaza (1400-78) of the three great Aristotelian biological treat- 
ises (Venice, 1476). 

Actual Greek type was hardly used before 1476, and it was near 
the end of the fifteenth century before the scholar-printer Aldo 
Manuzio (1449-1515) produced an adequate edition of the Greek 
text of Aristotle and Theophrastus (Venice, 1495-98) . He added to 
his services by issuing the Greek text of Dioscorides (p. 89, 1499), 
of Pollux, a classical scholar who determined Renaissance anato- 
mical nomenclature (1502), and of Strabo (p. 100, 1516). Aldo's 
successors in the ‘Aldine’ firm were responsible for the first Greek 
editions of Galen (1525) and Hippocrates (1526). 


The Revival of Learning 

Very influential for the whole course of Renaissance science 
were the editions of Euclid. He first appeared in Latin dress at 
Venice in 1482. Editions continued to flow from the press through- 
out the sixteenth century. The first edition in Greek appeared at 
Basel in 1533 and the first in English in London in 1570. 

A work that had a large share in fixing the geographical ideas 
of the Renaissance was the Geographia of Ptolemy, which first 
appeared in Latin at Vicenza in 1475 and in Greek at Basel in 1533. 
The maps illustrating early editions of Ptolemy are most interest- 
ing (p. 88). Even more influential was the Almagest y which was 
first printed in Latin at Basel in 1538 and very frequently at later 
dates. The works of Ptolemy in Renaissance versions are common 
in comparison to those of early Greek mathematicians and astro- 
nomers. Thus a collection of Archimedes was not made until 1544 
(Basel) and was not reprinted till the seventeenth century. 

The most frequently printed of the ancient scientific works at 
this time were undoubtedly the medical. Hippocrates, Dioscorides, 
Galen, and others appeared in scores of editions in Greek, Latin, 
and the vernacular throughout the sixteenth century. They were 
very generally studied, and in conjunction with the Arabic medical 
writers Rhazes, Mesue, Avicenna, and Albucasis they came to 
provide the basis of the actual medical practice of the age. 

3, Scientific Atmosphere of the Early Renaissance, 

The humanists as a class exhibited little sympathy with the 
scientific outlook. Their interests were literary; their peculiar 
aversion was the Arabist tendency of the age that they were 
leaving behind. Arabism expressed itself rather in comment than 
in development of ancient scientific and philosophical themes. 
In the movement typified by Roger Bacon in the thirteenth 
century a new element had entered (p. 156). That movement had 
fallen into the background after Roger's death. It had not entirely 
died, but it had remained as the seldom expressed faith of a small 
band of philosophically minded recluses. At^last faith in the 
appeal to nature found more open expression. With the fifteenth 
century, discontent with the entire medieval scientific scheme 
becomes more generally obvious. The idea that it may be possible 
to adjust theory by experiment again comes to the fore. 


Rise of Humanism. Attempted Return to Antiquity 

The earliest open suggestion is made by a man of lofty philoso- 
phic genius and penetrating scholarship, the Rhinelander nicolas 
OF cusA (1401-64), who became a cardinal and made a fruitless 
attempt to reform the calendar. Nicolas was groping towards 
a philosophical basis for the experimental method. He records a 
careful experiment on a growing plant — afterwards pirated by 
the seventeenth-century writer van Helmont (see p. 231) — proving 
that it absorbs something of weight from the air. This is the first 
biological experiment of modem times, and incidentally the first 
experimental proof that air has weight. Nicolas wrote a book on 
the employment of the balance in physical experimentation. In 
more than one of his works he showed that he knew how to apply 
the experimental method in detail, and he suggests in outline many 
investigations which were not taken in hand until the time of 
Galileo, 150 years later. His theoretical views led him to a belief 
that the Earth is moving and the universe infinite, though he 
attained to no formal astronomic theory. He certainly influenced 
Bruno (p. 185) and gave philosophical assent to the proposition 
that the universe is boundless in both space and time. 

The tradition of the combination of scholarship and observation 
that Nicolas had practised was carried on by several astronomers 
in the second hah of the fifteenth century. For much of this 
we are indebted to the far-sightedness of another cardinal who, 
though bom long before Nicolas, died long after. This was 
JOHANNES BESSARiON (1389-1472), a Greek by birth, who w^.s 
equally anxious to aid the progress of astronomical knowledge and 
to diffuse Greek literature in the West. Bessarion’s friendship, 
extended to two German students in Italy, Purbach and Regiomon- 
tanus, made possible their work which formed the foundation of 
that of Copernicus. 

GEORG PURBACH (1423-61) foUowed with great avidity the 
study of Ptolemy's Almagest (p. 148). He died prematurely and 
had only translations from the Arabic on which to base his work. 
He improved on his original, however, by calculating a table for 
every ten minutes, using sines instead of chords. 

Johannes Muller (1436-76) of Konigsberg (=‘ king's mountain '), 
usually known from his birthplace in Bavaria as Regiomontanus, 
lived hardly longer than Purbach. He had, however, the .good 


The Revival oj Learning 

fortune to have Greek originals on which to work. He completed 
his predecessor’s digest of Ptolemy. He also produced the first 
systematic treatise on trigonometry* and a table of sines for every 
minute and of tangents for every degree. His astronomical tables 
were used by Columbus. Regiomontanus died at Rome, whither 
he had been summoned by the Pope to aid in the long-contemp- 
lated reform of the Calendar. This, in the event, was deferred for 
more than a century. The important works of Regiomontanus 
were only published after his death. 

The Renaissance of Letters was contemporary with the Renais- 
sance of Art, which had its reaction upon scientific thought. 
The great painters had begun to study nature more closely. 
Antonio Pollaiuolo (1428-98) and Andrea del Verrocchio (1435- 
99), among others, made careful investigations of surface ana- 
tomy, while the exquisite figures of plants in the pictures of Sandro 
Botticelli (1444-15 10) mark him out as a very accurate observer. 
There was, hoWever, one artist of the time who takes a quite 
peculiar place among students of nature. Leonardo da vinci 
(1452-15 19) stands for many as the turning-point of the Renais- 
sance into modem times. The ingenuity of his ideas, the mar- 
vellous rapidity of his insight, the sureness of his intuitions, the 
exactness of his observations, the extreme versatility of his 
extraordinary genius, made earlier students place him in an 
isolated and almost superhuman position. His very limitations 
increase the apparent gulf which separates him from other men, 
and hamper us in our comprehension of him. To understand his 
scientific work and its fate we must recognize his defects. 

Leonardo's great limitations were literary and linguistic. He 
hardly acquired even an elementary knowledge of Latin, and he 
exhibited no power of literary expression. The vernacular that 
he employs is that of a Florentine shopkeeper of the lower class. 
He created no great phrase or saying. His sentences are often 
ungrammatical and frequently unfinished. a literary sense 
he was incoherent. The very rush of his ideas obstructed the 
channels for their expression. He might have said, with Petrarch, 

* It was not printed till 1533, that is 57 years after its author’s 


Rise oj Humanism. Attempted Return to Antiquity 

E Tamor di saper che m’ha si acceso 
Che Topera h retardata dal desio. 

My love of knowledge so inflamed me 

That my work was retarded by my very desire. 

Among the great artists he was notorious for the smallness of 
his output and for the extreme slowness with which he worked. 
Did his art consume the major part of his energy and his thoughts ? 
His private papers contain evidence not only of a unique scientific 
insight but of an industry which is almost incredible. He covers 
the whole field of science from mathematics to physiology, and 
there is nothing that he touches which he does not illuminate. 
Thus he presents us with a model of a flying machine and sugges- 
tions for a helicopter and a parachute and, interested in the 
problem of flight, he analyses the nature of the flight of birds in 
a way that has only been surpassed during the last few years. 
He designed a parabolic compass on a principle adopted only late 
in the seventeenth century. He hints at a heliocentric view of 
the world. He has drawings of quick-firing and breech-loading 
guns. He makes many ingenious suggestions for engineering 
apparatus. He has mastered the theoretical principles of per- 
spective. He sets forth some of the homologies of the vertebrate 
skeleton. He has passages which suggest the laws of motion. 
His anatomical and embryological studies were not passed in 
certain respects for hundreds of years. 

Marvellous as were the attainments and achievement of 
Leonardo, he does not occupy a completely isolated position. 
Others of his age rival him both in versatility and penetration. 
Thus his German contemporary albrecht durer of Nuremberg 
(1471-1528), apart from his achievement as an artist, studied the 
details of human anatomy, made a profound and painstaking 
investigation of the proportions of the human body at different 
ages and in the two sexes, was an exceedingly close observer of 
the habits and growth of animals and plants, conducted experi- 
ments in optics, perspective, and the properties of sound, had 
a remarkable command of the mathematics of his day, and, in his 
great drawing, Melancholia^ set forth in allegorical form the changes 
in thought and attitude with which the age was instinct. Diirer 


The Revival of Learning 

worked long in Italy. He is a German, but all that he does and 
says is touched by the spirit of the Italian renaissance. 

Diirer’s work was done under strong Italian influence. This is 
less true of the Swiss writer Aureolus Philippus Theophrastus 
Bombastus von Hohenheim, more compendiously known as 
PARACELSUS (1493-1541). He was a person of violent, boastful, 
and repellent temper, whose iconoclasm, garrulous and often 
incoherent though it was, probably did something to deter men 
from the worship of the old idols. His symbolic act of burning 
the works both of the Greek Galen and of the Arab Avicenna, as 
an introduction to his lecture course at Basel, was meant to 
typify the position of the independent investigator. A writer of 
excessive obscurity, an obscurity of language and of form as well 
as of thought, very few claim the privilege of penetrating to his 
full meaning. It is unfortunate that these few have developed a 
vagueness of expression and an obscurity of style that rival those 
of their original. There is, however, a general agreement among 
the saner Paracelsists that their hero did in a vague sense fore- 
shadow the *New Instauration \ His aim was to see the world 
in the ' light of nature \ That light of his is dimmed for us because 
of his extreme gullibility in some matters, his violence and self- 
contradiction in others, and his involved and mystical present- 
ment in all. 'Nature* included for him the influence of the stars 
upon the lives of men and many other relationships then generally 
credited and now universally discredited. He believed still in 
a relation of microcosm and macrocosm — as in a residual sense 
we all do — but his free modification of that theory may have 
helped to pave the way for its rejection in the generation which 

It is not easy to ascribe any positive scientific contribution to 
Paracelsus. He did, however, give currency to one important 
modification of Aristotelian doctrine whereby alchemy was de- 
flected into a direction which led to chemistry. He held that, apart 
from the 'four elements* of Greek philosophyv there were certain 
proximate principles that gave matter its distinguishing charac- 
teristics. The principles were three in number. Unfortunately the 
names that he selected for these, 'mercury*, 'sulphur*, and 'salt*, 
were already in use for definite substances. Thus confusion was 


Rise of Humanism. Attempted Return to Antiquity 

worse confounded. By mercury he means the nature, principles, or 
characteristics which are common to the metals ; by sulphur he 
means the power of combustibility and the essence of change- 
ability and chemical impurity ; and by salt the principle of fixity 
and of resistance to fire. This was an advance in the sense that 
these principles relate to experience and do not demand that nature 
must of necessity be simple and accord to some rigid scheme. 

A much more coherent author than Paracelsus was the German 
mining engineer georg agricola (1490-1555) *the father of 
mineralogy In his work Concerning Metals (‘De re metallica') of 
1546 he summarizes from experience the metallurgical knowledge 
of his day. In an admirable series of illustrations and descriptions 
he sets out for us the whole technology of mining. It is difficult to 
say how much of the book is original, but there are a number of 
devices and of processes that are mentioned by him for the first 
time. In other works he laid the foundations of physical geo- 
graphy and also devoted considerable attention to fossils, which 
he regarded as remains of extinct organisms. 

The period of activity of Paracelsus represents the beginnings of 
the modern study of mathematics. The best exponent of the 
subject was the unprincipled genius jerome cardan (1501-76), 
whose name is still remembered in ' Cardan's rule ' for the solution 
of cubic equations and the Xardan shaft' of the motor-car. 
Cardan's rule was, in fact, shamelessly pirated from another who 
had imparted it to him \mder a pledge of secrecy. Nevertheless, 
the appearance of Cardan's work on algebra (1545) undoubtedly 
marks for mathematics the end of the Middle Ages and the 
openings of a new era. 

4. Revival of Direct Study of Nature, 

The sixteenth century brought with it a combination of circum- 
stances particularly favourable to certain types of observational 
activity. The printed page had grown familiar. Books were be- 
coming commoner and were now the recognized means for the 
conveyance of new knowledge. The many new and strange forms 
that explorers were bringing back to Europe were drawing atten- 
tion to the beauty and variety of living things. The medicine of 
the age laid special emphasis on vegetable drugs, so that physicians 


The Revival of Learning 

were accustomed to distinguish a large variety of native and 
foreign plants. The artists adso had paid much attention to plants, 
and several had devoted themselves to the study of their habits 
and habitats. Lastly, the arts of the woodcut and the copper 
engraving had been perfected, and there was a number of crafts- 
men capable of producing admirable illustrations of living things 
and especially of plants. Thus books began to appear in which 
plants were portrayed with lively skill. No better botanical 
figures have ever been produced than some issued from the 
presses of the sixteenth centiuy. 

The special development of plant portraiture began in Germany, 
the home of printing, where that art had reached a very high 
standard, otto brunfels of Mainz (1489-1534) was the first to 
produce a work on plants, the figures of which rely wholly on 
observation (Strasbourg, 1530). The drawings are firm, sure, 
faithful. It is very interesting to compare them with those of 
a good modem text-book. The text, however, is befogged by an 
error from which botanists took long to free themselves. Bmnfels 
identifies his plants — gathered in the Rhineland— with those of 
Dioscorides, who worked in eastern Mediterranean lands. The 
equation was impossible and confusion results. 

A younger German botanist was Jerome bock of Heiderbach 
(1498-1554), who escaped some of the errors of Brunfels. Bock's 
careful descriptions of plants and of their mode of occurrence (Stras- 
bourg, 1539) are the first of the kind since Greek times. Only by 
collating a large number of such descriptions did botanists outgrow 
the habit of comparing all their plants with those of the ancients. 

The most remarkable of the early German botanists was 
LEONA^ID FUCHS (1501-66). His botanical work (Basel, 1542), 
intended as a guide to the collector of medical plants, is a land- 
mark in the history of natural knowledge. Fuchs had a good 
acquaintance with the Greek and Latin classics, and was, withal, 
an excellent observer, so that his identifications are supported by 
adequate knowledge. His woodcuts are o^extraordinary beauty 
and truth. They established a tradition of plant illustration 
traceable to the present day. Fuchs enjoys a verdant immortality 
in the beautiful group of American plants, the * Fuchsias'. 

Fuchs arranged his plants alphabetically. He gives us nothing 

Rise oj Humanism. Attempted Return to Antiquity 

of classification, hardly anything that can be called plant geo- 
graphy, little concerning the essential nature of plants or of their 
relation to other living things. His book is, in fact, a 'herbal* pure 
and simple. Yet by its close observation of details and by their 
accurate record on the printed page, it may claim a place among 
the pioneer works of modem science. Fuchs includes in his work 
an admirable glossary of botanical terms. 

Modem plant study thus became effective with this happy 
combination of humanistic learning. Renaissance art, and the 
perfected craft of printing. The same is no less true of the study 
of the animal body. The real father of modem anatomy was the 
Fleming, andreas vesalius (1514-64;, whose work brings out 
this combination admirably. 

Even as a boy Vesalius was always observing Nature and dis- 
secting the bodies of animals. He studied first at Louvain in his 
native Belgium and afterwards at Paris. Both universities were 
extremely conservative. Anatomical instruction was still medieval 
and pinned to the texts of Galen. Vesalius was highly successful 
as student and teacher there, and he became very learned in 
Galen. Foiftunately for himself and for the world he quarrelled 
with his superiors and decided to seek his fortune elsewhere. He 
determined on Italy, was appointed professor at Padua (1537), and 
immediately introduced sweeping reforms. 

In the old days of Mondino (p. 158) the professor had dissected 
on his own account. The successors of Mondino abandoned this 
difficult and tiring process. They were content to read their 
lectures from the text of Galen, while a demonstrator (Latin 
demonstro, 'I point out*) indicated the parts to the students. 
Hence our modem academic titles Reader or Lecturer (}ego, 'I 
read *) and Demonstrator, The basic reform of Vesalius was to do 
away with demonstrators and other intermediaries between him- 
self and the object — 'to put his own hand to the business*, as he 
called it. His drive was irresistible. In five years he had com- 
pleted and printed the masterpiece on which his fame is based, and 
he was still only twenty-eight. He did no further important work. 
Vesalius*s On the Fabric of the Human Body (Basel, 1543) is both 
the first great modem work of science and a foundation-stone of 
modem biology. 




The Revival of Learning 

The book opens with a description of the bones and joints, the 
general classification of which is from Galen. The first bone con- 
sidered is the skull. It is astonishing to find here an examination 
in the modem manner of the different shapes of human skulls. 
Anthropologists to-day attach great importance to these. Skulls 
are systematically measured and individuals and races classed as 
broad-headed, long-headed, round-headed. This is exactly what 
Vesalius does. He follows this matter up by comparing the skull 
of man with that of certain animals, notably the dog. 

Of all the subjects of which Vesalius treats, he is most successful 
with the muscles. In certain respects his representations of these 
are actually superior to most modem anatomical figures. Vesalius, 
with an artistes eye, has succeeded in representing the muscles 
with their normal degree of contraction.^ In other words, he has 
represented living anatomy. This is a more difficult task, and one 
involving more real knowledge, than any presentation of the 
details of dead stmctures. For this reason naturalists still return 
to these figures of Vesalius and have something to learn from them, 
although they were prepared 400 years ago. 

The account by Vesalius of the stmcture of the heart has a 
special interest. The workings of the heart and blood system had 
always been a puzzle. The current solution was that of Galen, 
which depends on the supposed existence of pores in the septum 
between the ventricles (p. 91). Vesalius generally follows the 
physiological view of Galen. When, however, he comes to the 
septum between the ventricles he is mystified. He teUs us that 

'The septum is formed from the very densest substance of the 
heart. It abounds on both sides with pits. Of these none, so far as 
the senses can perceive, penetrate from the right to the left ventricle. 
We wonder at the art of the Creator which causes blood to pass 
from right to left ventricle through invisible pores.* 

Thus he was not satisfied with Galen's view. Twelve years later 
he brought out a second edition of his great book. He has again 
examined the pits on the septum. This timrf he says : 

' Although sometimes these pits are conspicuous, yet none, so far 

I In fact most of the drawings are not by Vesalius himself, but there can 
be no doubt that he supervised them in every detail and determined the 


Rise oj Humanism. Attempted Return to Antiquity 

as the senses can perceive, passes from right to left ventricle . . . 
not long ago I would not have dared to turn aside even a hair's 
breadth from Galen. But the septum of the heart is as thick, dense, 
and compact as the rest of the heart. I do not see, therefore, how 
even the smallest particle can be transferred from the right to the 
left ventricle through the septum.' 

This attitude to Galen makes it evident that we are on the eve 
of a scientific revolution. Men are no longer satisfied with the 
traditions of the ancients. In this Vesalius was not alone. He was 
but the first of a whole line of Paduan anatomists that leads on 
continuously to the great biological awakening of the seventeenth 

5. Astronomical Observation and Hypothesis in the Sixteenth 

The astronomy of the earlier sixteenth century exhibits certain 
activities that mark it off with some definiteness from that of the 
Middle Ages. The work of Regiomontanus (p. 171) was widely 
known and was in large part responsible for this. 

Leonardo da Vinci (p. 172) about 1510 explained correctly the 
dim illumination of the surface of the Moon, when the bright part 
is but a narrow crescent — * the new Moon in the arms of the old * — 
as due to earthshine. It is light reflected from the Earth. His 
younger contemporary Jerome fracastor of Verona (1483- 
1543), an able writer on the revived atomism of Lucretius and 
founder of the modem view of infection, made contributions both 
to astronomical theory and practice. He observed that the tails 
of comets are always turned from the Sun. This fact throws ligjit 
on the nature of these bodies. The French physician jean fernel 
(1497-1558) made a calculation of the size of the Earth (1528) 
accurate within i per cent. The fame of all these writers has, 
however, been wholly overshadowed by that of Copernicus (i 473 “* 


The Pole, nicolas copernicus (1473-1543)1 despite the vast 
change that was introduced in his name into men's ideas, was him- 
self more in the line of such comparatively conservative scholars 
as Regiomontanus than the more revolutionary Leonardo, Fra- 
castor, or Femel. He was a student rather than an observer, and 


The Revival of Learning 

he continued to attend university courses until over thirty years 
of age. He studied at several Italian universities, giving attention 
to classics, mathematics, astronomy, medicine, law, and theology. 
It was in Italy that he first discussed the Pythagorean theory with 
which his name has become associated. Copernicus had skill in 
painting which suggests that he had that type of visualizing 
imagination frequently associated with scientific power. He was 
not at all active as a practical astronomer. He had, it is true, taken 
a few observations of eclipses and oppositions of planets, but for 
the most part his results were obtained in the study. 

Copernicus tehs us that he was induced to seek a new theory of 
the heavenly bodies by finding that mathematicians differed 
among themselves on this subject. He had considered the various 
motions of the heavenly bodies according to the old system, and 
concluded that some essential factor had been missed. He found 
his hint in the traditions that had survived of the thought of 
Philolaus the Pythagorean (p. 21) and of Aristarchus (p. 59). 

'Occasioned by this’, he says, ‘I decided to try whether, on the 
assumption of some motion of the Earth, better explanations of the 
revolutions of the heavenly spheres might not be found. Thus 
assuming the motions which I attribute to the Earth ... I have 
found that when the motions of the other planets are referred to the 
circulation of the Earth and are computed for the revolution of each 
star, not only do the phenomena necessarily follow therefrom, but 
also that the order and magnitude of the stars and of all their 
orbits and the heaven itself are so connected that in no part can 
anything be transposed without confusion to the rest and to the 
whole universe.' (Copernicus, Introduction to De Revolutionihus). 

The new or rather renovated scheme of Copernicus retained 
much of the ancient theory. It still assumed that the universe is 
spherical and finite, terminating in the sphere of the fixed stars. 
It stiU assumed that the movements of the celestial bodies are 
always circular and always with uniform volocities. It still in- 
voked epicycles. It still demanded the excentnc (p. 77). In fact 
Milton’s description of the Ptol^aic world fits not ill with the 
attempt to ‘save the phenomena’ by means of a system of circles 
and spheres that was made by Copernicus. In Farwike Lost the 
Archangel Raphael tells that 


Rise oj Humanism. Attempted Return to Antiquity 


Is as the Book of God before thee set 
Wherein to read his wondrous works, and learn 
His seasons, hours, or days, or months, or years. 

This to attain, whether Heaven move or Earth 
Imports not. . . . 

and then goes on to the * conjectures' of those who would 

model Heaven 

And calculate the stars : how they will wield 
The mighty frame ; how build, unbuild, contrive 
To save appearances ; how gird the sphere 
With Centric and Eccentric scribbled o’er, 

Cycle and Epicycle, Orb in Orb. 

(Paradise Lost, viii. 70-84.) 

The simplicity of the Copemican system — ^which has been inferred 
rather from his famous diagram (Fig. 55) than from his book 
itself — is really more apparent than real. Thus while he reduced 


The Revival of Learning 

the number of circles demanded to explain celestial movements, 
he still invoked no less than thirty-four. 

The immediate influence of the teaching of Copernicus on con- 
temporary thought was, in fact, much less than might be supposed. 
Notices of it, for a generation or more, are surprisingly few and not 
always unfriendly. Religion was the main interest of the day. 
Religion is, by its nature, extremely conservative, and any scien- 
tific advance of the first magnitude usually disturbs its professors. 
Nevertheless Christian doctrine, guided by St. Thomas Aquinas, 
had adapted itself to the Aristotelian system (pp. 150-1). During 
the Middle Ages the doctrine of a spherical Earth had normally 
been taught in the schools. A spherical Earth is neither more in 
accord nor less in accord with the Biblical account than is a 
world system of which the Sun rather than the Earth is the centre. 
Christian doctrine accommodated itself to the one ; it might have 
accommodated itself to the other. There were, however, certain 
extraneous circumstances that intervened in determining the 
reception of the Copernican system. 

One group of these had relation with current religious teaching 
which was greatly disturbed by Giordano Bruno (p. 185). 

A second group had to do rather with the contemporary view of 
the nature of the physical universe. It was an age that believed in 
astrology, and astrology had become part of the university curri- 
culum (p. 169). 

Now astrology was based on the doctrine that the outer spheres 
of the universe influenced the inner sphere (Figs. 20, 40) . This con- 
ception coloured all departments of thought and imbedded itself 
so deeply in speech that many expressions stiU current are based 
on it. ' The scheme was conceived under an evil star', ‘ His fortune 
is in the ascendant ' The seventh heaven of delight ', ' He has gone 
to a higher sphere', 'The British sphere of influence', Xanst thou 
bind the sweet influences of the Pleiades' [Job xxxviii. 31), ‘He 
has the influenza' are such cases. All the coijceptions on which 
these phrases were originally based — and they covered a large part 
3f life — ^were disturbed by the Copernican view. Remove the Earth 
from her central position among the spheres and the whole astro- 
logical system becomes unworkable. It is too much to expect such 
disturbance to be accepted calmly. 


Rise oj Humanism. Attempted Return to Antiquity 

The Dane tycho brake (1346-1601) was born three years after 
the death of Copernicus. Unlike Copernicus he was, before every- 
thing, a patient and accurate observer. He was provided by his 
sovereign with a magnificent observatory which was the scene, 
during twenty-one years, of Tycho's labours in the systematic 
collection of astronomical observations for the correction of cosmic 

theories. The records of Brahe were much the most extensive and 
accurate that had been made up to their time. Brahe's actual 
scientific achievements and contributions may be summarized: 

[a) He set forth a planetary system with the Earth central to 
the orbits of Moon and Sun and central also to the fixed stars. The 
Sun revolves round the Earth in twenty-four hours carrying all 
the planets with it. Of the planets. Mercury and Venus have orbits 
smaller than that of the Sun while the other three have orbits that 
encircle the Earth (Fig. 56). Mathematically this system works 
out as identical with that of Copernicus (1588). 

[h) Examining a comet he was able to determine its parallax and 


The Revival of Learning 

thus proved that it was farther off than the Moon. It was thus 
outside the sphere of the 'elementary* world (see Fig. 20). This 
was equivalent to introducing the principle of change into the 
changeless spheres and therefore contrary to Aristotelian prin- 
ciples (1577). 

(c) He suggested that the movement of a comet might be 'not 
exactly circular but somewhat oblong *. This is the first suggestion 
that a celestial body might move in a path other than circular 
( 1577 )- 

[d) He described very accurately perturbations in the Moon*s 
motion (1599) • These had to await explanation by subsequent 
generations and new astronomical systems. 

{e) His numerous observations on the planets enabled Kepler 
to reveal the true nature of their orbits. 

Tycho*s attempt to represent the structure of the Universe as 
according to the ideal form of the circle was the last great effort 
of the Pythagorean spirit save for that of his pupil Kepler. The 
insurgent century sought for direct evidence as to the nature of 
the world. The new science concerned itself neither with ideal 
forms nor with the theory of knowledge nor with the nature of 
reality nor with the principles of investigation, but with the 
evidences of the senses. 


Downfall of Aristotle. New Attempts at Synthesis 
I. Doctrine of the Infinite Universe. 

Copernicus worked in Poland, the eastern march of European 
civilization. It was at the western limit of Europe, in England, 
where the spirit of the great intellectual revival had not yet ob- 
tained full hold, that his message was first translated into philo- 
sophic form. 

In 1583 there came to London giordano bruno (1547-1600), 
a native of Nola near Naples and a renegade monk. He was in his 
thirty-seventh year and had already sojourned as a teacher at the 
Universities of Lyons, Toulouse, Montpellier, and Paris. At each 
of these centres of learning his restless and turbulent spirit had 
combined with an aloofness from the affairs of men to make him 
unwelcome. Throughout his life he showed a lofty indifference 
to the dictates of common sense that cannot fail to command 
our respect — at a distance. He was accustomed to make a pre- 
carious livelihood by lecturing on a barren logical system which 
he had partly invented. It was intimately linked with an absurd 
principle of mnemonics which he had partly borrowed. So way- 
ward a genius was predestined to tragedy. 

It was during his visit to England that Bruno at length de- 
veloped philosophical coherence. Even then his period of illumina- 
tion lasted but a few months. In 1584 he published in London, 
though with the false impress of Venice, three tiny Italian works. 
The Ash-W ednesday Supper {Cena de le Ceneri), On Cause, 
Principle, and Unity, and On the Infinite Universe and its Worlds. 
These booklets contain weUnigh the whole of his effective philo- 
sophy, which was based in essence on Nicolas of Cusa (p. 171) and 
in form on Copernicus. Essential parts of the thought of Bruno 
are the doctrines that not only does the Earth move round the Sun 
but that the Sun itself moves, that there is no such thing as a point 
absolutely at rest, that the stars are at vast but various distances 
from the solar system and are themselves centres of comparable 
systems, that the universe, being itself infinite, can provide no 


The Insurgent Century 

criterion of fixity, and that our planetary system is in no sense the 
centre of the universe. 

*The Nolan maintains*, he says, *that the world is infinite. 
Therefore there is no body that can be said to be in the centre of 
the world or at the frontier thereof or between two of its frontiers. 
Bodies can only be said to have certain relations to other bodies or 
to frontiers that are chosen arbitrarily. Thus the motions of natural 
bodies are far from being simple circles with a single centre.* (Cena 
de le Ceneri,) 

‘ All these innumerable worlds which we see in the universe are 
not contained therein as in a vessel but rather are comprehended or 
conserved by the efficient cause which moves them. Moreover, as 
the common soul is within the whole to which it gives being and at 
the same time is individual and yet is in all and every part, so the 
essence of the Universe is one in the infinite and in whatsoever thing 
you take as a member thereof. . . .* {On the Infinite Universe.) 

In such a universe where may Paradise and Purgatory be 
placed ? And is not the ' common soul *, which uniformly permeates 
it, a memory of Neoplatonism which in turn took the idea from 
Stoicism (pp. 123-4)? Bruno's vision of an 'infinite Universe', 
endless both in time and space, whose soul abides uniformly in 
every part, differs utterly from the ' created Universe ' of medieval 
Christian philosophy, the Creator of which must, of His nature, 
be separate from that which He has created. The universe of 
medieval Christian philosophy was necessarily centred in Man, 
for into Man alone, among created mundane things, the Divine 
Spirit had entered. Small wonder that the Church was disturbed 
by Bruno's thought. His revolution was incomparably greater 
than any dreamed of by that academic and conservative mathe- 
matician, Copernicus. 

The issues involved were not at first generally recognized. 
Some who were profoundly stirred by the pagan character of 
Bruno's thought fixed on the irrelevant detail of the Earth mov- 
ing round the Sun as contrary to scriptur?: This idea Bruno had 
certainly taken from Copernicus whose work was not, as yet, pro- 
hibited. But Bruno's vision had far deeper implications than a 
mathematical readjustment of the current world scheme. A finite 
universe, spherical or not, with or without the Earth as its centre, 


Downjall oj Aristotle. New Attempts at Synthesis 

can be conceived as 'created*; an infinite universe cannot be so 
contemplated. Creation is fundamental to Christianity — at least to 
the Christianity of that age — and it need not surprise us that the 
Christianity of that age struck at Bruno. In 1600 he was burned 
at the stake, having passed seven years in the prisons of the 
Inquisition. His philosophical writings were suppressed, but their 
seed had been sown. 

Bruno perished miserably without the hope or thought that he 
had a disciple. And yet his view was soon to displace that of 
medieval Christianity. Before he had been dead for thirty years, 
the world was, for the man of science, no longer a diagrammatic 
scheme which required investigation only as regards its details. 
It had become a world without bounds and therefore of infinite 
possibilities. And yet it was a world whose parts were uniformly 
related by mathematical rules, the physical bases of which were in 
process of discovery. 

It was of course true then, as it is of course true now, that the 
view of universal law did not and does not occupy the whole mind of 
all men of science. Most men of science reserved, and still reserve, 
some department of experience in which they forbid full play to 
their vision of universal law. But when and where they give rein to 
that mood, then and there it is bound to displace the mood of 
faith, nor can the medieval compromise (p. 154) stand against 
it. Thus the three little tracts of Bruno printed in London in 1584 
mark the real change from medieval to modem thought and 
especially to modern scientific thought. The change was long in 
coming, longer for some topics than for others, longer in some 
minds than in others. But the coming of that change was inevit- 
able once these three tracts had got abroad. Every attempt was 
made to suppress them, but they had done their work. Bruno was 
right when he said at his trial ‘Perchance you who condemn are 
in greater fear than I who am condemned*. 

In summary we may express Bruno *s thought thus: 

(а) There are other worlds than ours. The Universe is made up of 
many worlds comparable to that in which we live. Our world is 
not the centre of the Universe. 

(б) The Universe is infinite in space and time. This implies that 
conceptions of fixity of points in space or time or of movement 


The Insurgent Century 

in either space or time must be relative to other points arbitrarily 
regarded as fixed. 

(c) The Universe is permeated throughout by a common soul. This 
carries the implication of a uniformity in all the workings of the 
parts of the universe and is easily adapted to the conception of 
uniform natural laws. 

It is important to remember that Bruno's views were not 
based on experiment or observation. His contribution was a 
philosophy, not a scientific method or system, and was, in fact, 
a development of the thought of Nicolas of Cusa (p. 171). The 
doctrine of relativity in space, in motion, in thought, promulgated 
by the calm spirit of Nicolas became in the passionate Bruno an 
ardent and soul-absorbing faith. 

It is not easy to trace in detail the progress of the dissemination 
of the ideas of Bruno. His life was obscure, the propagation of this 
thought fiurtive, his influence secret, indirect, unacknowledged. 
Yet his ideas crop up where they might not be expected. We will 
consider one such case. 

In 1600 there appeared in London a Latin work On the Magnet 
and on Magnetic Bodies and concerning that great magnet, the Earth, 
a New Physiology, by william gilbert (1546-1603), personal 
physician to Queen Elizabeth, a man in authority, respectable 
and respected. His book is the first major original contribution to 
science that was published in England. It earned the admiration 
of Francis Bacon and of Galileo. Gilbert's work has medieval 
elements, still unpurged, but its main section sets forth his inves- 
tigations of the properties of the magnet in thoroughly modem 
form. This section is entirely experimental in outlook, and opens 
the new era of physical research. It records numerous experiments 
and is illustrated by clear diagrams. The properties of the lode- 
stone and of the magnet, the direction that the compass assiunes 
in relation to the poles of the earth, its variation, its inclination 
and its declination are systematically treated- 

The last section of the book is devoted to an exposition of the 
system of the imiverse. The universe of Gilbert is that of Bruno, 
whose name, however, he does not mention. Gilbert must have 
met Bruno at Elizabeth's court, probably in the company 
of Sir Philip Sidney (1554-86). It is to be remembered that 

Downjall oj Aristotle. New Attempts at Synthesis 
this book of Gilbert was published in the year that Bruno was 
bmned tod that Bruno 's views and mode of expression were well- 
nigh as inacceptable in Protestant England as in Catholic Italy. 
The work On the Magnet was the only publication issued by 
Gilbert. Long after his death, however, another work by him On 
our Sublunary World, a New Philosophy, was seen through the 
press by a surviving brother (1651). It expounds in detail, quoting 
Bruno, the idea that the ‘fixed stars’ are at differing distances 
from our planetary system and that these stars are the centres of 
other planetary systems. 

The seventeenth century opened lurid with the fires that 
formed Giordano’s shroud. That hideous event was the herald 
of a period that has no rival for the number and importance of 
its sckntific discoveries. A glance at the mass of fundamental 
scientific work of the seventeenth century shows the major depart- 
ments of science becoming clearly differentiated. The acceptance 
of observation and experiment, as the only methods of eliciting 
the laws of nature, reaches an ever-widening circle. The very 
first scientific generation of the century saw the development of a 
mathematical technique that became the instrument of the new 

2. Mathematics becomes the Instrument of Physical Investigation. 

The improvement in the means of mathematical expression was 
a main condition for the development of exact conceptions of a 
new cosmology and physics. These were an intellectual necessity 
to replace the tottering Aristotelian scheme that Bruno had 
attacked. The insurgent century found a qualitative world based 
on abstract values. ,It bequeathed a quantitative world based on 
concrete impressions. The senses came to reign on that Olympus, 
where Platonic Ideas had once held divine court. Mathematics 
was the mercurial messenger of the new gods. 

A beginning had been made in the later sixteenth centuiy. 
Thus the French lawyer fran^ois viktE (1540-1603) was among 
the first to employ letters to represent numbers. He applied 
algebra to geometry in such a way as to lay a foundation for 
^alytical trigonometty (1591). At about the same time was 
introduced the decimal scheme for representing fractions (1586) 


The Insurgent Century 

by the Fleming simon stevin (1548-1620). This ingenious man 
preceded Galileo in experimenting on the relative rate of fall of 
bodies of different weight {1586). His name is also associated 
with the method of resolution of forces, with the distinction of 
stable and unstable equilibrium, with the law of equilibrium on 
inclined planes (Fig. 57), and with the 'hydrostatic paradox', that 
is that downward pressure of a hquid on the base of its containing 
vessel is independent of its shape and size and depends only on 

Fig. ^7. Stevin* s proof of conditions of equilibrium on inclined planes. 
Around the vertical angle of an upright triangle, of which the opposite side 
is horizontal, hang a ring-chain. It will be in equilibrium, for if not it would 
be in perpetual motion. Remove the suspended loop. Equilibrium remains. 
Therefore weights on planes inclined to each other are in equilibrium if 
they are proportional (as are those of the pieces of chain) to the lengths of 
the planes as cut by the horizontal. 

the depth of the contained vessel and area of the base. Stevin 
was able also to calculate the pressure on any given portion of 
the side of the containing vessel. He laid the essential founda- 
tions for the whole science of hydrostatics (1586). 

By the use of an improved form of Stevin's decimal notation 
calculation was much facilitated. Contemporary astronomical 
activity, however, still carried with it an endless task of computa- 
tion. No technical advance was more needed than some further 
alleviation of this deadening burden. Thus the invention of 
logarithms by Napier was greeted with enthusiasm. 

JOHN NAPIER (1550-1617), Laird of Merchiston in Scotland, 
began his investigations (1573) with an attempt to systematize 


Downfall of Aristotle. New Attempts at Synthesis 

algebraic knowledge. In his earliest work he says that in consider- 
ing imaginary roots he discovered a general rule for roots of all 
degrees. He conceived the principles of logarithms in 1594. The 
next twenty years were spent in developing thQ theory and 
computing the 'canon' or table of logarithms itself. While thus 
engaged he invented the modem notation of fractions. His 
Description of the Marvellous Canon of Logarithms appeared in 
Latin at Edinburgh in 1614. An extension of Napier's long effort 
to do away with the tediousness of calculation was his Rabdologia 
(1617). It contains the description of 'Napier’s bones’, devices 

(a) Cb) Cc) 

Fig. 58. The Circle as special case of the Ellipse. Keeping the major 
axis AA' of constant length, construct a series of ellipses with the two 
foci SS' successively closer, until they coincide. The process is also indicated 
in Fig. 26. 

designed to simplify multiplication and division. These were in 
use for about a century and long attracted even more attention 
than his logarithms. 

An advance, significant for the whole subsequent astronomical 
development, was made by Kepler (p. 200) in a commentary 
(1604) on the work of the thirteenth-century mathematician 
Witelo (p. 156). Kepler regarded conic sections as forming five 
species passing from the (i) line-pair, through (2) hyperbola, 
(3) parabola, and (4) ellipse, to (5) circle. In order to indicate the 
nature of this process Kepler designated as foci the fundamental 
points connected with these curves. The foci of the circle coalesce 
at the centre. Ellipse and hyperbola have two foci equidistant 
from the centre. The parabola has two foci, one within it and 
the other at an infinite distance on the axis, within or without 
the curve (Figs. 58, 26, 17). 

Even more fxmdamental for future mathematical development 
were the ideas introduced by Descartes (p. 221). His analytic^ 
method appeared in his Geometry (1637). Its essential novelty is 


The Insurgent Century 

the introduction of the conception of motion into the geometric 
field. There is a well-known story that, lying late abed, as was his 
wont, and observing a fly hovering in the comer of his room, it 
occurred to him that its position in space could be defined at any 
moment by its distance from the three planes formed by the 
adjacent walls and ceiling. If two instead of three dimensions be 
considered, a point in a plane can be defined by its relation to 
two instead of to three 'Cartesian co-ordinates* as they have come 
to be called after him. 

Thus Descartes saw a curve as described by a moving point, 
the point being the intersection of two moving lines which are 
always parallel to two fixed lines at right angles to one another. 
As the moving point describes its curve, its distances from the 
two fixed axes will vary in a manner characteristic of that particu- 
lar curve. An equation between these distances can be formed 
which would express some property of the curve. The conception 
has had innumerable developments and has been adopted in every 
department of science. Its most familiar development is the 
‘graph*. Important parts of our mathematical notation are due 
to Descartes. 

There is a basic conception in the mathematical attitude of 
Descartes that is far more significant than any technical addition 
that he made. His analytical procedure displayed the fimda- 
mental correspondences of number and form. Pythagoras and 
Plato perceived this correspondence. The Alexandrians tended to 
study the two in isolation. The separate development of algebra 
by the Hindus and of geometry by the Arabs, and the general 
trend of western mathematical studies in the Middle Ages and the 
fifteenth and sixteenth centuries concealed a most essential truth. 
Descartes, despite professed indifference to historical considera- 
tions, called men back to the old paths of Pythagoras and Plato 
on this most fundamental issue. It is probable that the application 
of algebraic methods to the geometric fieldjs the greatest single 
step ever made in the progress of the exact sciences. Descartes 
himself insists on the unity of the study of mathematics. 

* All sciences which have for their end investigations concerning 
order and measure are related to mathematics, it being of small 
import whether this measure be sought in numbers, forms, stars, 


Downfall of Aristotle. New Attempts at Synthesis 

sounds, or any other object; there ought therefore to be a general 
science, namely mathematics, which should explain all that can be 
known about order and measure, considered independently of any 
application to a particular subject. ... A proof that it far surpasses 
in utility and importance the sciences which depend on it, is that 
it embraces at once all the objects to which these are devoted and 
a great many besides.’ {Rules for Direction of the Mind, 1628.) 

The expression of this Platonic view makes it evident that the 
reaction against the long reign of Aristotle has begun. (For 
Aristotle's own criticism on the point see p. 34-5.) 

About the beginning of the seventeenth century were made the 
first decided advances since antiquity in synthetic geometry. In 
this department the leading name is that of Descartes' fellow 
countryman blaise pascal (1623-62). He also added much to 
mathematical theory especially in connexion with probability. 
Pascal invented one of the first arithmetical machines. 

A versatile mathematician of the age was the learned Oxford 
Professor john wallis (1616-1703). His first great mathematical 
work, Arithmetica infinitorum (1655), contains the germ of the 
differential calculus. Newton read it early and derived his bi- 
nomial theorem from it. Wallis wrote the first mathematical 
work devoted to tides, in which he introduces the assumption 
'that, for purposes of calculation, earth and moon can be treated 
as a single body concentrated at their centre of gravity.' His 
Algebra (1657) contains the idea of the interpretation of imaginary 
quantities in geometry which was fundamental for the develop- 
ment of analytic methods. Wallis introduced the symbol 00 for 

A younger man of mathematical genius was the polymath 
CHRISTIAN HUYGENS (1629-95). His mathematical skill early drew 
the attention of Descartes, who predicted his future eminence. 
Before he was twenty he did good work on the quadrature of the 
circle and conic sections (1651-4). He diffused his mathematical 
abilities in many departments, optics, astronomy, mechanics, 
theory of light, and elsewhere, and thus missed reaping some of 
the fame that his abilities justified. 

Mathematical activity early influenced optics, a favourite 
subject for discussion by mathematicians even during the Middle 




The Insurgent Century 

Ages (p. i6o). The leading problem was the nature of the laws of 
refraction. Ptolemy (p. 83), Alhazen (p. 136), Witelo (p. 156), and 
their medieval followers were aware that light rays are bent or 
'refracted' when passing from a rarer to a denser medium. In a 
commentary on Witelo, Kepler (p. 200) gives his measurements 
of the incident and the refracted rays in special cases, but failed 
to reach a general law (1604) . This was successfully elicited (1621) 

medium, are bent toward the vertical to a definite amount. If AA' and BB' 

be two such rays ^ at whatever angle they strike the surface. 

A a B u 

This ratio differs for different media and the less it is the higher is the 
* refractive power ' of the medium. 

by the Hollander willibrord shell (1591--1626). Descartes 
placed the results in a more acceptable form and published them 
without acknowledging their source (1637).^ 

The nature of the advance can be illustrated by a simple dia- 
gram. Rays of light AA' and BB' pass at different angles from air 
into water (Fig. 59). In all such cases they are bent toward the 

vertical and bent in such a 


degree that the ratio -r — is the same 
A a 


Downjall oj Aristotle. New Attempts at Synthesis 

as the ratio . This ratio for water is 3 : 4, which is said to be 

the refractive index of water. Each substance has its own charac- 
teristic refractive index. Different kinds of glass were, for instance, 
soon found to have different refractive indices. 

The laws of refraction of light have been a most important 
factor in the construction of optical instruments. In that art the 
effective beginning was made by Galileo (1609). The optics of 
his compoimd systems of lenses were investigated by Kepler 
(p. 200), who first expressed in intelligible mathematical form the 
action of telescope and microscope (1611). Kepler's work led to 
further advance by Descartes (1637) who also produced a geo- 
metrical theory of the rainbow based on the law of refraction. 
The study of refraction occupied Huygens. His knowledge of the 
subject enabled him to improve lenses and to produce telescopes 
with much clearer definition than heretofore (1655). 

If the development of optics was determined by mathematical 
advance the same is no less true of mechanics. In the latter case, 
however, the whole body of new teaching was in effect the work of 
one man, Galileo, to whom we now turn. 

3. Physico-Mathematical Synthesis, 

GALILEO GALILEI (1564-1642) lived a long life of unparalleled 
intellectual activity. Many of the products of his genius were of 
immediate practical application, many more involved profound 
modification of the current scientific opinions, yet others struck 
at the very basis of the general beliefs of the day. 

The early training of Galileo had been along strictly scholastic 
and Aristotelian lines. In 1585 he began a systematic experi- 
mental investigation of the mechanical doctrines of Aristotle. By 
1590 he had developed a number of objections to Aristotelian 
physical teaching. Notably he had accumulated his records of 
experiments on falling bodies. These were announced from his 
professorial chair and illustrated in 1591 from the leaning tower 
of Pisa. By that most famous of experiments he unmasked an 
Aristotelian error. Weights of i lb. and of 100 lb., dropped from 
the top of the tower, reached the earth together. How then was it 


The Insurgent Century 

possible to maintain with Aristotle that the rate of fall was a 
function of the weight of the falling object?^ 

For the rest of his life Galileo was constantly occupied with 
physical investigations. Of these the most famous resulted in his 
great astronomical discoveries (pp. 206-12). It is not, however, in 
his discoveries, numerous, fundamental, superb though they were, 
that we sense the full significance of Galileo in the history of 
thought. It is rather in his initiation of a new attitude toward 
the objective universe and in his construction of an enduring 
mathematico-physical scheme that would fit that attitude. More 
than to any other man, we owe to him the conception of our 
world in terms of interplay of calculable forces and measurable 
bodies. And moreover, to him more than to any other man we 
owe the experimental employment of tliat conception. 

‘Dynamics*, says Lagrange (p. 266), ‘is a science due entirely to 
the moderns. Galileo laid its foundations. Before him philosophers 
considered the forces which act on bodies in a state of equilibrium 
only. Although they attributed in a vague way the acceleration of 
falling bodies and the curvilinear movement of projectiles to the 
constant action of gravity, nobody had yet succeeded in determin- 
ing the laws of these phenomena. Galileo made the first important 
steps, and thereby opened a way, new and immense, to the advance- 
ment of mechanics as a science.' {Micanique analytique, 1788.) 

He set forth his views in his great Discourses concerning two new 
Sciences (1638). The work at one step advanced the subject from 
the medieval to the modem stage. The two new sciences deal 
respectively with (a) ‘ Coherence and resistance to fracture ' and 
(6) 'Uniform, accelerated, and violent or projectile motions'. 

The first part of the work is mainly concerned with the resis- 
tance of solids to fracture, and the cause of their coherence. The 
value of this section lies in the incidental experiments and observa- 
tions on motion through resisting media. The current belief that 
machines built on exactly similar designs, but on different scales, 
are of strength in proportion to their linear dimensions is discussed. 

* The story of the weights dropped from the top of the leaning tower 
of Pisa is here told in its traditional form for which there is no satisfactory 
evidence. There is, however, adequate evidence that by the year 1590 he 
had attained to the attitude set out in the traditional account. 


Downjall oj Aristotle. New Attempts at Synthesis 

It is shown that the larger machine will equal the smaller in all 
respects, save that it will be less strong and less resistant to 
violent actions. The machines discussed include animal bodies 
(p. 214). 

After explaining the strength of ropes of fibrous materials, 
Galileo turns to the cause of coherence of the parts of such thing s 
as stones and metals, which do not show a fibrous structure. 
What prevents a glass or metal rod, suspended from one end, 
from being broken by a pull at the other? The explanation 
suggested depends upon nature’s so-called 'abhorrence of the 
vacuum’ supposedly produced by the sudden separation of two 
fiat surfaces. This idea is extended, and a cause of coherence is 
found by considering every body as composed of very minute 
particles, between any two of which is exerted a similar resistance 
to separation. 

This line of reasoning leads to a very important experiment for 
measuring what is called the force of a vacuum. It occasions the 
remark that a pump will not work when the water had sunk 35 
feet below the valve. This is sometimes told as if Galileo had said, 
jokingly, that native’s horror of a vacupm does not extend beyond 
35 feet, but it is plain that the remark was made seriously. He 
held the conception of suction then current, for he compares the 
column of water to a rod of metal suspended from its upper end, 
which may be lengthened till it breaks with its own weight. It is 
strange that he failed to see how simply this phenomenon could 
be explained by the weight of the atmosphere, with which he was 
well acquainted. A fuller explanation had to await Torricelli 
(p. 232). 

Aristotle’s ideas on motion and especially that bodies fall with 
velocities proportional to their weights and inversely proportional 
to the densities of the media through which they fall, are examined. 
The end result is to substitute for Aristotle’s assumption that law 
of the motion of falling bodies which is the foundation of modem 

The discussion of the strength of beams opens with a considera- 
tion of the resistance of solid bodies to fracture. This is very great 
in the case of a direct pull, but is less for a bending force. Thus, a 
rod of iron will bear a longitudinal pull of, say, 1,000 lb., while 


^he Insurgent Century 

50 lb. will break it if it be fastened by one end horizontally into a 

Galileo assumed, as the basis of his inquiry, that the forces of 
cohesion with which a beam resists a cross fracture in any section 
may all be considered as acting at the centre of gravity of the 
section, and that it breaks away at the lowest point. An elegant 
result deduced from this theory is that the form of a beam, to be 
equally strong in every part, should be that of a parabolic prism, 
the vertex of the parabola being the farthest removed from the 
point of support. As an approximation to this curve he recom- 
mends tracing the line in which a heavy flexible string hangs when 
supported from two nails. 

The curvature of a beam under any system of strains is a 
subject into which, before the days of Newton, it was not possible 
to inquire, and even in the simpler problem considered by Galileo 
he makes assumptions which require justification. His theory of 
beams is erroneous in so far as it takes no account of the equili- 
brium which must exist between the forces of tension and those of 
compression over any cross-section. 

The theorems and formulae deduced geometrically from the 
phenomena of imiform and accelerated motion lead to a more 
detailed statement of the principle of inertia. The definition of 
uniformly accelerated motion is given as that of a body which so 
moves that in equal intervals of time it receives equal increments 
of velocity. 

There follows an application of the results. He examines the 
times of descent down inclined planes, assuming the velocity to 
be the same for the same height whatever the inclination. This he 
verified by careful experiments, although he was unable at the 
time to prove it mathematically.^ 

The next section plunges at once into the consideration of the 
properties of a body whose motion is coijapounded of two other 
motions, one uniform, and the other naturdly accelerated. Such 
is the motion of a projectile. The law of the independence of the 

* Viviani relates that, soon after he joined Galileo in 1639, he drew his 
master's attention to this. The same night, as Galileo lay sleepless in bed, 
he discovered the mathematical demonstration. It was introduced into the 
subsequent editions of the Discourses. 


Downfall of Aristotle. New Attempts at Synthesis 

horizontal and the vertical motions is here laid down. A body 
projected horizontally would — but for its weight and external 
impediments — continue to move in a straight line. Again, the 
effects of gravity acting by itself on the projected body would be 
entirely downwards. But gravity acting on the projected body 
can neither increase nor diminish the rate at which it travels 
horizontally. Therefore, whatever the path or the direction of 
motion at any moment, the distance 
travelled horizontally is a measure of 
the time that has elapsed since motion 
began. He proves that the path des- 
cribed has the geometrical properties of 
a parabola (Fig. 6o). 

Galileo drew up a table giving the 
position and dimensions of the parabola 
described with any given direction of 
projection. He showed that the range 
on a horizontal plane is greatest when 
the angle of elevation is 45°. He was 
essentially applying the principles of 
the Differential or Fluxional Calculus. 

Had pure mathematics attracted him 
as .strongly as its applications, he 
would have founded the Fluxional 
Calculus, which is the glory of Newton and of Leibnitz. 

No sooner was the manuscript of these dialogues out of his 
hands in 1636 than Galileo began to occupy himself with new pro- 
jects which he left unfinished at death. In them he approaches the 
laws of interdependence of force and motion which appear at the 
beginning of Newton’s Prindpia (1687). But Galileo not only 
prepared the way for Newton : he supplied him with much of his 
materials. Thus, Newton’s first law — that a body will continue in a 
state of rest, or of uniform motion in a straight line, until compelled 
to change its state by some force impressed upon it — is a generaliza- 
tion of Galileo’s theory of uniform motion. Since all the motions 
that we see taking place on the surface of the earth soon come to 
an end, we are led to suppose that continuous movements, such, 
for instance, as those of the celestial bodies, can only be maintained 


Fig. 60. AB, BC,CD... 
represent equal forward 
displacements in equal 
increments of time of an 
horizontally ejected pro- 
jectile. The distances of 
fall BF, CG, DH . . . in- 
crease as the ' square of 
the time. The actual path 
AFGH is a parabola. 

The Insurgent Century 

by a perpetual consumption and a perpetual application of force, 
and hence it had been inferred that rest is the natural condition 
of things. We make, then, a great advance when we comprehend 
that a body is equally indifferent to motion or to rest, and that it 
perseveres equally in either state until disturbing forces are 

Newton’s second law — that every change of motion is propor- 
tional to the force that makes the change, and in the direction of that 
straight line in which the disturbing force is impressed — is involved in 
Galileo’s theory of projectiles. Before his time it was a commonly 
received axiom that a body could not be affected by more than 
one force at a time. 

But now the establishment of this principle of the composition 
of forces supplied a conclusive answer to the most formidable of 
the arguments against the rotation of the earth. It is employed 
by Galileo in his Dialogue of the Two Systems of the World (1632, 
p. 211). The distinction between mass and weight was, however, 
not valued, and, consequently, Galileo failed to grasp the fact 
that acceleration might be made a means of measuring the mag- 
nitude of the force producing the motion, that is to say of the 
mass of the earth. 

Of the third of Newton’s laws of motion — that action and 
reaction are always equal and opposite — we find traces in many of 
Galileo’s researches, as in his theory of the inclined plane, and 
in his definition of momentum. It is adumbrated in a little work 
on mechanics written by him in youth but published after his 
death. It is developed in his latest ideas on percussion. 

4. The Re-Formation of the Heavens, 

The first to apply mathematics as an empirical instrument in 
seeking the laws of celestial motion was the German Johannes 
KEPLER (1571-1630). He had strong mystical leanings, and a large 
proportion of his writings seem now unreadable foolishness, but 
there is a residuum of his works that is of the very highest 
scientific importance. His idea of the universe was, from the first, 
essentially Platonic and Pythagorean. He was convinced that the 
arrangement of the world and of its parts must correspond with 
some abstract conception of the beautiful and the harmonious 


Downfall of Aristotle. New Attempts at Synthesis 

and, further, must be expressible in numerical and geometric form. 
It was this belief that sustained him in his vast and almost in- 
credible labours. He spent years of his life chained to the mere 
drudgery of computation without assistance and without any of 
the devices, such as logarithms or reckoning machines, that now 
lighten the computer’s task. Nothing but a burning yet steady 
faith could make such drudgery endurable. 

We gain an insight into the transition state between the old and 
the new in which Kepler worked when we recall that his professed 
occupation was largely astrological calculation. Nor was he cyni- 
cally sceptical as to the claims of astrology, but sought in the events 
of his own life a verification of the theory of the influence of the 
heavenly bodies. 

Kepler adopted the Copemican view from an early date. He 
turned his mind to the question of the number, size, and relation 
of the orbits of the planets. He was ever seeking a law binding 
together the members of the solar system. After trying various 
simple numerical relations, after attempting to fill the gaps by 
hypothetical planets and after discarding various other sugges- 
tions, he lit, at last, on a device which satisfied him (1596). There 
are only five possible regular solid figures (i.e. figures with equal 
sides and equal angles) — 'Platonic bodies’ as they were called 
(p. 22) — and there are only five intervals between the six planets 
that he recognized. As far as the calculations of Kepler extended 
at that time, the five regular solids could be fitted between the 
spheres of the planets so that each polyhedron was inscribed in the 
same sphere about which the next outer one was circumscribed 
(Fig. 61). Thus 

Sphere of Saturn 

Sphere of Jupiter 
Sphere of Mars 
Sphere of Earth 
Sphere of Venus 
Sphere of Mercury 


The Insurgent Century 

For the first time a unitary system had been actually introduced 
in explanation of the structure of the universe. We may well smile 

Fig. 6i. From Kepler’s Mysterium Cosmographicum (Tubingen 1596)* 
illustrating supposed relationships between the five Platonic bodies (p. 22) 
and the number and distances of the planets. The concentric figures are 
inscribed within each other thus : 

Outermost Sphere bearing sign of Saturn. 


Sphere bearing sign of Jupiter. 

4-sided regular pyramid. 

Sphere bearing sign of Mars. 

12-sided regular body. 

Sphere bearing sign of Earth. 

20-sided regular body. 

Sphere of Venus (hardly traceable).. 

8-sided regular body. 

Sphere of Mercury. 

Innermost Central body of the Sun. 

at this instance of human presumption. Kepler soon found that he 
had wrongly estimated the distance of the planets from their 

* The reproduction is from the second edition of 1621 because the block 
recut for it gives a little clearer result than that of the first edition. 


Downjall oj Aristotle. New Attempts at Synthesis 

centre! The basis of this unitary system was a miscalculation I 
It endured but a day. But to Kepler, who, like the medieval 
thinkers, held that the universe was designed on a moral plan, 
these new mathematical relationships — :f alse as we know they are — 
came as a confirmation of what he conceived to be the divine 
purpose. The regular solids, he observed, were of two classes: 
primary (cube, tetrahedron, dodecahedron) and secondary (ico- 
sahedron, and octahedron), differing in various ways. What 
more fitting than that the earth, the residence of man ' created in 
God’s image’, be placed between the two kinds of solids? The 
scheme was confirmatory of many of the main tenets of his 
Pythagorean faith! 

That Kepler sought so persistently for a simple mathematical 
scheme of the material world, and that, having found one, he 
regarded it as fitting his scheme of the moral world, suggests 
certain reflections on the workings of the mind itself. Whatever 
reality may be, we seem to be so made that we aspire towards an 
interpretation of the universe that shall hold together in a complete 
and reasonable scheme. The fact that we thus aspire does not in 
the least prove that such a scheme corresponds to reality. Never- 
theless, all great religions attempt to provide such an interpreta- 
tion. All become skilfully 'rationalized’. 

It is because science disturbs part of this already carefully 
rationalized field that rehgion resents its intrusion. The mind 
recoils from a dualistic universe, and rationalized religion usually 
seeks to minimize even such remnants of dualism as the con- 
ception of a spirit of evil. It is easy for us now to regard the 
opponents of Galileo and Kepler as purblind fools. Base motives 
certainly prompted some of the opposition; but in essence the 
opposition expresses the reluctance of the human mind to adopt 
any teaching which disturbs its unitary conceptions. A reasoned 
view of the universe, physical and moral, had grown up during 
the Middle Ages. It would have been indeed a marvel if this had 
been relinquished without an embittered struggle, for faith is not 
necessarily accompanied by either wisdom or learning, or foresight. 

Despite the failure of his first attempt, Kepler still pursued his 
life aim, the foundation of an astronomy in which demonstrable 


The Insurgent Century 

mathematical principles should replace arbitrary hypotheses. He 
examined the relation of the distances of the planets to their 
time of revolution round the central sun. It was clear that the 
time of revolution was not proportional to the distance. For that 
the outer planets were too slow. But why ? There is, he suggested, 
'one moving intelligence in the sun that forces all round, but most 
the nearest — languishing and weakening in the more distant by 
attenuation of its virtue by remoteness'. How different from the 
phraseology of modem astronomy which dates from Newton! 
In such phrases as ' moving intelligence *, ' languishing of its virtue 
etc., Kepler was employing the Aristotelian phraseology that had 
arisen during the Middle Ages. The conception was familiar to the 
medieval philosophers, Christian, Moslem, and Jewish. Aquinas 
(p. 182), Averroes (p. 140), and Maimonides (p. 146) all had a 
clear conception of intelligence moving the planets. They had 
derived this conception ultimately from Greek thinkers, and they 
had adapted it each to his own theology. The conception was 
quite familiar to all in the sixteenth and seventeenth centuries. 

As the sixteenth century turned into the seventeenth, Kepler 
received a great incentive to work by joining Tycho Brahe (p. 183) 
as assistant. On the death of Tycho in 1601 Kepler became his 
literary legatee. The next nine years saw him largely occupied 
with the papers of Tycho and with work on optics, in the course 
of which he developed an approximation to the law of the re- 
fraction of light. In 1609 he issued his greatest work the New 
Astronomy with Commentaries on the Motions of Mars, It is full of 
important suggestions, notably that the earth attracts a stone just 
as the stone seeks the earth, and that two bodies near each other 
will always attract each other if adequately beyond influence of 
any third body. It also develops a theory of the tides in relation to 
attraction by the moon. But above and beyond all, the work sets 
forth the cardinal principles of modem astronomy, the so-called 
first two planetary laws of Kepler by which 

(а) Planets move round the sun not in circles, but in ellipses, 
the sun being one of the foci. 

(б) A planet moves not imiformly but in such a way that a line 
drawn from it to the sun sweeps out equal areas of the ellipse in 
equal times (Fig. 62). 


Downfall of Aristotle. New Attempts at Synthesis 

It was another nine years before Kepler enunciated in the 
Epitome Astronomiae (i6i8) his third law to the effect that 
(c) The squares of the period of revolution round the sun are 
proportional to the cubes of their distance. 

For one who accepted these principles of Kepler the Aristote- 
lian cosmolpgy lay derelict. Its foundations were undermined and 




Fig. 62. Planets sweep out equal areas in equal times. PPi, P2P3, P4P6 
are distances along its orbit around the Sun S traversed by a planet in equal 
times. Areas SPPi, SPgPa and SP4P5 are equal. 

their place taken by an intelligible mathematical relationship. 
The scholastic Aristotelianism was to become as much an embar- 
rassment to official religion as the narratives of miracle became 
at a later date. It was, however, as hard for one section of the 
Church to rid itself of its scholastic heritage as it was for another 
at a later date to disembarrass itself of the dead-weight of miracle. 

Certain further reflections on Kepler's work rise to the mind. 
It is a fundamental error to separate science from learning or, 
perhaps, it would be best to say from tradition. By the Greeks 
the study of conic sections had been prosecuted as an intellectual 
exercise. These figures, hyperbola, parabola, ellipse, existed, so 
far as they knew, in the mind and in the mind alone. They 
corresponded to nothing in the natural world. And then, after 
two thousand years, Kepler shows that these ancient concepts 
correspond to something that is also revealed by the use of the 
sense. Is not the mind then somehow attuned to nature ? It has 


The Insurgent Century 

been well said by a great historian of science that ‘if the Greeks 
had not cultivated conic sections, Kepler could not have super- 
seded Ptolemy ; if the Greeks had cultivated Dynamics, Kepler 
might have anticipated Newton' (Whewell). 

Dynamics as we have seen, was in fact a creation of Kepler’s 
contemporary, Galileo. In character and temper Kepler and 
Galileo form an extraordinary contrast. The German Protestant, 
mystic and dreamer rather than observer and experimenter, 
produced voluminous, numerous, and wholly unreadable volumes. 
He stands over against Galileo, the Italian Catholic, clear and 
cold of intellect, unrivalled in experimental skill, witty and happily 
endowed with artistic and literary prowess, who wrote never a 
work and hardly a line that was not significant. In sheer genius, 
however, the two men were not rivals but peers and comrades. 
On them, in equal measure, rest the foundations of the conception 
of a mathematical universe. 

Galileo’s astronomical activity began in 1604. In that year, 
in the constellation Serpentarius, there appeared a new luminous 
body. He demonstrated that it was without parallax, that is to 
say there was no difference in its apparent position in the heavens, 
from whatever point it was viewed. Now parallax decreases with 
distance. In Galileo’s time the planets were known to have paral- 
lax, but the parallax of the fixed stars was so small, by reason of 
their vast distance, that it was unmeasurable by the instruments 
of the day. This new body was thus in the remote region of the 
fixed stars. Now that outer zone had been regarded by Aristotle 
and his followers as absolutely changeless (p. 47). New stars 
when previously noticed had been considered to belong to the 
lower and less perfect regions nearer to earth. To the same lower 
region were assigned such temporary and rapidly changing bodies 
as meteors and comets. Galileo had thus attacked the incorrupt- 
ible and unchangeable heavens and hac^ delivered a blow to the 
Aristotelian scheme, wellnigh as serious as the experiment on 
the tower at Pisa (p, 195). 

In 1609 Galileo made accessible two instruments that had the 
profoundest influence on the subsequent development of science, 
the telescope and microscope. His earliest discoveries with the 


Downfall of Aristotle. New Attempts at Synthesis 

telescope were issued in a little pamphlet of 24 leaves, his Messen- 
ger of the Heavens ('Sidereus nuntius’) in 1610. There are no 24 
leaves in all scientific literature that contain more important 

The first half of that famous booklet is occupied by observations 
on the moon. The surface of the moon, far from being smooth and 
polished, as it appeared to the naked eye, was now seen to be 

Fig. 63. The Moon as seen by Galileo in 1609. 

rough, with high mountains and deep depressions. The latter 
Galileo interpreted as rivers, lakes, and seas. From the appearance 
of illuminated mountain tops he could estimate the height of some 

of them. He found them to rise four or five miles above the general 
level (Fig. 63). 

Galileo s lunar observations have an interesting relationship 
with English literature. In 1638 he was old and blind and nomin- 
ally a prisoner of the Inquisition at Fiesole. He was visited there 
by Milton. The incident has inspired several artists and writers. 
In 1658, nine years after Galileo^s death, Milton began his Para- 
dise Lost, completing it in 1666. Its cosmology is deliberately 
Ptolemaic, not Copemican (p. 180). Nevertheless, Paradise Lost 
does recall the poet's induction into the new astronomy twenty- 
seven years previously. It describes Satan's shield of which the 

broad circumference 

Hung on his shouldere like the moon, whose orb 


The Insurgent Century 

Through optic glass the Tuscan artist views 
At evening, from the top of Fesole, 

Or in Valdarno, to descry new lands, 

Rivers, or mountains, in her spotty globe. 

{Paradise Lost, i. 286-91.) 

The Messenger of the Heavens discusses the revelation by the 
telescope of an immense number of hitherto unobserved fixed 
stars. These were seen to be at least ten times as numerous as 
those that had been catalogued. The more conspicuous star 
clusters were found to contain many stars too faint for recognition 
by the naked eye. Parts of the Milky Way and some of the nebu- 
lous patches in Orion, the Pleiades and elsewhere were resolved 
into groups of stars of various magnitudes. 

The remainder of the little book is devoted to an account of the 
satellites of Jupiter which Galileo discovered on one of the first 
occasions when he used his telescope. The existence of these 
bodies was of peculiar interest at the time, since the planet was 
seen to be itself a sort of little model of the solar system, with 
minor bodies centering round a great central body. The contem- 
porary discussion as to the 'plurality of worlds' (pp. 186-7) was 
given a new turn by this discovery of a world modelled on the 
Copemican solar system. 

There were other observations made by Galileo about this time 
that were later the subject of much discussion. Important were 
the observations on the inner planets and notably on Venus. It 
had been a real objection to the Copemican hypothesis that if the 
planets resemble the Earth in revolving roimd a central sun, they 
might be expected to be luminous only when exposed to the Sun's 
ra]fs. In other words, they should exhibit phases like the Moon. 
Such phases were now actually observed in Venus by Galileo. 

In the same year the outermost of the known planets, Saturn, 
was investigated. Peculiar appearances in him were noted, though 
their interpretation as rings was the wirk of Christian Huygens 
(1629-95) at a later date (p. 195). 

Soon after this Galileo first observed dark spots on the surface of 
the Sun. These he saw narrowed continuously as they approached 
the edges of the Sun's disk. He rightly regarded the process as 
foreshortening and as indicating that they were on the surface of 


Downjall of Aristotle. New Attempts at Synthesis 

the Sun's orb which was itself rotating. The date and circum- 
stances of the announcement (1612) were unfortunate, since they 
involved him in a controversy with a powerful Jesuit rival who 
not only claimed priority of observation, but also put another 
interpretation on the spots. 

The controversy spread far beyond its original focus. An aspect 
of the dispute was the question of the habitability of the Moon, 
the planets, and even of the stars, for these, too, some thought to 
be worlds. His critics believed this a natural corollary of Galileo's 
development of the ' Copemican ' view which he had now openly 
espoused. The conception of the 'plurality of worlds' gave rise 
to a very considerable literature. The doctrine, it was believed, 
was contrary to Aristotelian and Christian teaching. It had been 
enunciated by the heretical Bruno (p. 185). 

Thus became united against Galileo a variety of interests. The 
band of academic Aristotelians had long been fuming against him. 
Jesuits who were actively engaged in teaching, as well as many 
political churchmen, now joined them. Pious folk were outraged 
by the conception of the plurality of worlds. To them were further 
united many of that intellectually timid class that forms the mass 
of every population in every age and is by no means rare in uni- 
versity circles. Deeper though less expressed was the great philo- 
sophic fear of the infinite universe that Bruno had suggested. The 
matter came before the Inquisition early in 1616. Galileo was 
admonished ' to abandon these opinions and to abstain altogether 
from teaching or defending or even discussing them'. A few days 
later a decree was issued ordering the work of Copernicus to be 
'suspended till corrected'. 

In 1624 Galileo published II Saggiatore (‘The Assayer’), a work 
which contains a conception of great import for the subsequent 
development of science. This conception, moreover, was destined 
to colour deeply much of the philosophical thought of later ages. 
He here distinguishes sharply between those qualities of an 
object that are susceptible of exact numerical estimation and those 
which cannot be treated in this way. 

* No sooner ', says Galileo, * do I form a conception of a material or 
corporeal substance, than I feel the need of conceiving that it has 
boundaries and shape,; that relative to others jit is great or small ; 

3012 P 209 

The Insurgent Century 

that it is in this place or that; that it is moving or still; that it 
touches or does not touch another body ; that it is unique, rare, or 
common; nor can I, by any effort of imagination, disjoin it from 
these (primary) qualities. On the other hand, I find no need to 
apprehend it as accompanied by such conditions as whiteness or 
redness, bitterness or sweetness, sonorousness or silence, well- 
smelling or ill-smelling. If the senses had not informed us of these 
(secondary) qualities, language and imagination alone could never 
have ariived at them. Wherefore I hold that tastes, colours, 
smells, and the like exist only in the being which feels, which being 
removed, these (secondary) qualities themselves do vanish. Having 
special names for them we would persuade ourselves that these 
(secondary qualities) have a real and veritable existence. But I 
hold that there exists nothing in external bodies for exciting (the 
secondary qualities) tastes, smells, and sounds, but (the primary 
qualities) size, shape, quantity, and motion. If, therefore, the 
organs of sense, ears, tongues, and noses were removed, I believe 
that (the primary qualities) shape, quantity, and motion would 
remain, but there would be no *more of (the secondary qualities) 
smells, tastes, and sounds. Thus, apart from the (percipient) living 
creatures, I take these (secondary qualities) to be mere words.' 

This distinction between primary qualities and secondary 
qualities, as they came afterwards to be called, has been made 
by men of science ever since. Galileo was the prime mover in 
that development which is summed up in the phrase Science is 

As to whether men of science have been right or wrong in their 
view that primary qualities have a reality lacking in secondary 
qualities, we need not for the moment consider. It is evident that 
ordinary experience is almost entirely made up of secondary 
qualities. The fact that men of science have dwelt chiefly on 
something else, something which ordinary men do not ordinarily 
consider, has separated them from their fellows. Since Galileo, 
men of science have formed a sort of priesthood which has been, 
not infrequently, opposed to another priesthood. Nor has the 
distinction which Galileo made remained with the working men 
of science. Through Thomas Hobbes (1588-1679) and John Locke 
(1632-1704) in England, and through Marin Mersenne (1588-1648) 
and Rene Descartes (1596-1650) in France, it has passed into 
general philosophy. 


Downfall of Aristotle. New Attempts at Synthesis 

By 1630, after many years’ work, Galileo had at last completed 
his epoch-making Dialogue on the Two Chief Systems of the World, 
that is the Ptolemaic and the Copemican. Quite apart from the 
discussion of the relative position of Earth and Sun in the uni- 
verse, the Dialogue is the consummation of the labours of Galileo 
in that it seeks to present the doctrine of uniformity in the 
working of the material universe. 

The point of view expressed by the doctrine of uniformity, the 
view that corresponding causes are everywhere producing corre- 
sponding effects, is so familiar to us nowadays as to be a part of 
our manner of thinking. We are brought up to it from our earliest 
years. The only occasions on which it is ever questioned by 
educated men of our own time are {a) in the discussion of the 
nature or reality of miracles, and (&) in the discussion of the 
relation of mind and matter. But in the seventeenth century it 
was not so. The Aristotelian conception of the universe still ruled 
supreme. According to that view the events in the high supra- 
lunary spheres — ' celestial physics ’ as we may call them — were of 
a very different order to our earthly happenings — ‘terrestrial 
physics’. A large part of medieval philosophy may indeed be 
regarded as a debate, prolonged through hundreds of years, of the 
relation of celestial to terrestrial physics. That there was a differ- 
ence between the two had hardly yet been questioned, save by 
Bruno (p. 185). Even Galileo was in no strong position to discuss 
celestial physics. It is of interest, however, that he throws out 
a definite suggestion that it can be discussed on the terrestrial 
basis, thus foreshadowing the doctrine of universal gravitation. 

* Since, as by a unanimous conspiracy of all the parts of Earth for 
the formation of its whole, those parts do congregate with equal 
inclination and, ever striving, as it were, at union, adapt themselves 
to the form of a sphere, so may we not also believe that Moon, Sun, 
and the other members of the solar system [corpi mondani) are 
likewise of spherical form by a concordant instinct and natural 
concourse of all their parts ? And if any of their parts were violently 
separated from the whole, might we not reasonably suppose that 
they would revert spontaneously by natural instinct ? May we not 
therefore conclude that as regards their proper motion, all members 
of the Solar System [corpi mondani) are alike ? ' 

Permission to print this dialogue Was obtained from the eccle- 


The Insurgent Century 

siastical authorities on the express condition that the subject was 
to be treated theoretically as a convenient hypothesis and not as 
representing the facts. It was issued in 1632. 

The debate in this work is carried on by three persons, an open 
advocate of the Copernican doctrine, an obtuse and obstinate 
follower of Aristotle and Ptolemy, and an impartial participator 
open to conviction. The conditions of publication are only 
superficially complied with, and the tone leaves no doubt as to 
Galileo's real opinions. The work is full of prophecies of the 
development of cosmic theory. 

The Aristotelian in the dialogue is represented as hopelessly 
stupid, and the Copernican has the best of the dispute. In fact, 
however, the Copernican passes far beyond Copernicus, notably 
in his total rejection of the idea of the stars as fixed in a crystal 
sphere. The stars, as in the works of Bruno, are held to be at 
inconceivable but differing distances from our Earth, and the 
absence of visible stellar parallax is considered as due to the vast- 
ness of this interval.^ 

The Dialogue brought matters to a head. Oddly enough, it was 
not the sweeping generalizations on which Galileo's opponents 
seized — maybe they did not realize their full significance. It was 
rather certain details opposed to the current view that were 
specially suspected. In August 1632 the sale of the book was pro- 
hibited and its contents submitted for examination to a special 
commission. They reported against Galileo. The end is well 

5. Implications of the Galilean Revolution. 

Galileo, more than any other man, had introduced the change in 
our manner of thinking that broke with ancient and led on to 
modern science. Contributions had also been made by Copernicus, 
by Vesalius, by Bruno, by Tycho, and by Kepler and others. 
TTie share of Galileo is, however, so bverwhelming that it is not 
unfair to call it the 'Galilean Revolution'. The change was more 
than an addition to knowledge. It was more even than an altera- 
tion in the conception of the structure of the universe. It was 

I The measurement of the paraUax of a fixed star was not made until 
1838, when it was achieved by Bessel (p. 269). 


Downfall of Aristotle. New Attempts at Synthesis 
rather a change in mood as to the kind of knowledge that was to 
be sought. It partook of the nature of a philosophical crisis. Its 
implications are so fundamental for science that we must attempt 
to review them. This we can most conveniently do under various 
headings which, it must be recognized, are incommensurable. 
They are not divisions of the subject, but themes which suggest 
themselves in connexion with Galileo's life work. 

(a) The Mechanical World. 

(b) Extension of the Senses. 

(c) The Universe as Mathematical and Boundless. 

(d) Religion and Science. 

{a) The Mechanical World. The science of elementary mechanics 
exists to-day in substantially the state in which Galileo left it. Its 
formulation was his real life task. Among his earliest observations 
were those on the pendulum — made when he was eighteen years 
of age. In explaining its movements, in the draft of a work on 
mechanics prepared a few years after these observations, he 
invoked the action of gravity. Nevertheless Galileo conceived no 
exact idea of the action of gravity-^of which the pendulum is 
a special case — until many years later. His conclusions on that 
topic are embodied in his Discourses concerning two new sciences 
(1638) published when he was seventy-four years old. The wide 
separation in time of these two events illustrates how wholly 
different is the order and manner of presentation of the thought 
of a scientific investigator from the order and manner in which he 
reaches his conclusions. 

In this, his final work, the results of his investigation extending 
over more than half a century are placed in logical or rational 
order. Thus their historic sequence is concealed. The process of 
setting forth a scientific discovery involves of necessity the cover- 
ing up of the true historic sequence. This is one of the reasons that 
make the history of science difficult to master. 

Of all Galileo's contributions to mechanical conceptions perhaps 
the most fundamental was that the continuous application of 
a force produces either an increment or decrement of velocity at 
every moment. The conception of acceleration as a constantly 
changing velocity accompanying the application of force was in 
contradiction to the Aristotelian principle that terrestrial bodies 


The Insurgent Century 

tend of their own nature to come to rest at a level which is natural 
for them. Acceleration, as we understand it, was one of Galileo's 
fundamental contributions. It involves the conception of the 
indefinite splitting up of time and thus of the application to time 
of the doctrine of limits as Archimedes had applied it to space. 
Through his mathematical teaching concerning moving bodies 
Galileo leads on to Newton. 

Again, the philosophers of the Middle Ages and the mathe- 
maticians of the sixteenth century had found great difficulty in 
conceiving a body as the subject of several simultaneous move- 
ments. For them the t3^e of 'perfect' motion was to be seen in 
the supposedly circular path of the heavenly bodies. Galileo by 
introducing the idea of acceleration, and especially of acceleration 
as natural to falling bodies, made familiar the idea of compoimded 
motion. By his analysis of the path of projectiles (p. 199) he intro- 
duced that view into curvilinear as well as rectilinear motion. 
Thus he paved the way for Newton's synthesis of terrestrial and 
celestial mechanics, 

Moreover Galileo's developments of the science of mechanics 
were applicable to all visible and tangible objects. His con- 
ception of a mechanical universe swiftly reacted even on the 
biological sciences. In the rebound of sentiment against Aristotle, 
biologists sought to explain the animal body as a machine. The 
first important biological works of the seventeenth century — ^for 
example those of Sanctorius (p. 236), of Harvey (p. 237), of 
Descartes (p. 191) — all sought thus to explain the body. Though 
Galileo in general eschewed the investigation of living things, in 
this matter he was himself a pioneer. He pointed out that a 
machine to be most efficient must be of a particular size. If one 
dimension is increased it is not enough to increase the others in 
proportion. The machine must be designed anew. 

Arising out of this principle he^shows it to be impossible for 
a swiftly moving land animal to increase its size, retaining its 
proportion of parts, and at the same time to maintain its agility. 
Increase in size increases weight as the cube of the length, but 
areas of cross-section of bones or muscles only as the square of the 
length. Thus if an animal's dimensions are doubled, its ability to 
overcome forces is quadrupled, but the forces to be overcome are 


Downfall of Aristotle. New Attempts at Synthesis 
increased eight times. But Galileo also saw that if an animal be 
immersed in water, then the weight is counterpoised to the extent 
of an equivalent volume of water. Under such circumstances 
the character of the physical barrier to increase in size is altered. 

The importance of this principle has only been appreciated in 
modem times. Thus each species has, of its physiological nature, 
a limit of growth, which is enormously higher for certain water 
animals, as whales among vertebrates and cephalopods among 
invertebrates, than for any land animals. The change in the pro- 
portions of the parts during growth had, in fact, already been 
made a subject of special study by the artist Albrecht Dlirer a 
century earlier. But Diirer had not subjected the basic principle 
to mathematical analysis as did Galileo (p. 173) 

In sum Galileo produced a conception of a world in which 
search might reasonably be made for mechanical principles alike 
in the movements of the heavens and the changes on the earth, 
in the circulation of a planet's satellites as in the structure of a 
minute insect. It is an increasingly mechanic world with which 
men of science have henceforth to deal. Astrology had laid sacri- 
legious hands on the heavens. The new determinism was to be 
a much more intimate thjng which concerned the stars no less 
than men and men no more than mice. This was evident enough 
to the lofty genius of Spinoza, but these complications of the 
mechanical conception of the world were almost wholly missed 
by Galileo’s leading opponents. They saw in him, as they had 
seen in the astrologers, merely another disturber of traditional 
religion. Had the real nature of the Galilean revolution been 
realized, it would have fared even worse than it did with its 
author and his followers. 

We may here say a word concerning Galileo’s opponents. They 
have been the objects of contumely because of his base and cruel 
treatment by the Inquisition and by those in high authority in the 
Church. We need not stop to defend these inane pomposities, nor 
need we pause to denounce the dishonesty and foolishness of 
other of his opponents. But not all those who were opposed to 
Galileo were fools or rogues. A great body of not unreasonable 
opinion hesitated to accept his physical philosophy. It is right to 
remember that a'complete system of philosophy, weaving into one 


The Insurgent Century 

vast scheme the moral and physical, the terrestrial and celestial 
worlds, had been built up during the Middle Ages. This satisfied 
the need of the day. The fact that Galileo had made a breach in 
that scheme was no clear reason to abandon the whole. Would the 
fact that recognized scientific laws were shown to be inapplicable 
to some particular group of phenomena be a reason nowadays for 
abandoning the scientific method of exploring nature ? Remember 
that Galileo had to offer his audience no complete system even of 
physical philosophy — that was reserved for successors of Newton. 
Even if the contemporary critic were a specialist in physics — and 
such were few in those days — a reasonable attitude would surely 
have been one of friendly and non-committal suspension of judge- 
ment not so much as to Galileo's findings, but as to their implica- 

It is true that the older astronomical position had been shaken 
also by Kepler’s demonstration that the movements of the 
planets are more easily understood if we suppose them to follow 
elliptical and not circular courses. But Galilean physics and Kep- 
lerian astronomy had not been linked together. That again was 
reserved for Newton’s generation. Moreover many of the exem- 
plars of Aristotle’s science were taken from the world of life. 
Aristotle’s biological system was still the best, and it was the 
Aristotelian physical system that Galileo was attacking. Further, 
as things then stood, abandonment of the Aristotelian scheme of 
the universe meant abandonment of much religious teaching. 
We are entitled to expect that judges should be both just and 
merciful. The judges of Galileo were perhaps neither. But the 
facts of human nature offer no warrant for the hope that all 
teachers will have the insight and understanding of a great 
master’s immediate following. Suspension of judgement as to the 
validity of Galileo’s arguments was thus a necessary consequence 
of the imperfect nature of man. To note this is not to justify 
either the ignorance, the duplicity^ or the cruelty of some of his 

Apart from professional theologians on the one hand and 
Spinozists on the other, most reasonable men in the seventeenth 
century were, in fact, content with a compromise. *The heavens 
are the heavens of the Lord ; But the earth hath he given to the 


Downjall of Aristotle. New Attempts at Synthesis 

children of Men. * This was the atmosphere in which arose and 
flourished the great scientific movement of the age. 

(6) Extension of the Senses. Galileo is best remembered for his 
wonderful astronomical observations. But at the back of these 
observations lay his invention of the telescope and his successive 
improvements in the construction of that instrument. And at the 
back of that lies yet another movement, the introduction of the 
skilled mechanic into the service of science. In this movement, 
too, Galileo may be said to be an important figure. 

Apart from the striking changes, artistic, literary, intellectual, 
during the fifteenth and sixteenth centuries, there were other 
changes, less dramatic but affecting even more closely and deeply 
the lives of men. One of these was the refinement of craftsmanship 
incident on the greater accessibility of good steel for tools. The 
houses, the furniture, the apparatus of life of, say, the year 1600 
represent great technical advances on the year 1450. A well- 
known exhibition of that improvement was in the building of sea- 
going ships which had made transoceanic exploration possible. 
One reason for the forwardness of Germany and of Germans in the 
art of printing was the excellence and reliability of German crafts- 
men. Regiomontanus (p. 171) left Hungary for Niimberg (1470) 
because he could there obtain good workers for his astronomical 
instruments. But until the seventeenth century highly skilled 
craftsmen were seldom invoked by the man of science. No 
small part of Galileo’s success as an experimenter was due to 
his constant employment of specially trained mechanics. He thus 
laid the foundation of the profession of scientific instrument 
maker. The existence of that cleiss became a main condition of the 
advancement of science in the centuries which followed. Com- 
pound optical apparatus had been constructed by others before 
Galileo. The results obtained were negative till the great dis- 
coverer perfected the method of manufacture. 

With such instruments in his hand Galileo was in a position to 
observe with an accuracy and a detail that had previously been 
quite unknown. He is the effective inventor of the telescope and 
the father of modem observational astronomy. There is, how- 
ever, another aspect of his optical discoveries that is less often 
recalled. He is the inventor also of the compound microscope, and, 


The Insurgent Century 

indeed, revelations of that instrument are mentioned in one of the 
earliest independent accounts of his work. The minute world 
revealed by this instrument was almost as wonderful as the new 
discoveries in the starry sphere. The heavens had always been 
recognized as vast almost beyond the power of thought. But the 
incomparable complexity of life and of matter close at hand was a 
wholly new conception. That beings, minute beyond the powers 
of our vision, could have structures as complete and complex as 
ourselves was a truly startling thought. If there was world beyond 
world in the heavens there was world beyond world within us. 

It is interesting to see how these matters looked in the eyes of 
the first generation of professed microscopists. In England the 
pioneer of such studies was henry power (1623-68), disciple of 
Sir Thomas Browne, who writes in his Experimental Philosophy 

‘Dioptrical Glasses are bat a Modern Invention neither do 
Records furnish us with anything that does antedate our late dis- 
coveries of the Telescope and Microscope. The want of which 
incomparable Artifice made the Ancients not onely erre in their 
fond Coelestial Hypothesis and Crystalline wheelwork of the 
Heavens but also in their nearer observations of the smallest sort 
of Creatures which have been perfunctorily described as the dis- 
regarded pieces and huslement of the Creation. ... In these pretty 
Engines are lodged all the perfections of the largest animals: . . . 
and that which augments the miracle, all these in so narrow a room 
neither interfere nor impede one another in their operations. 
Ruder heads stand amazed at prodigious and Colossean pieces of 
Nature, but in these narrow Engines there is more curious Mathe- 

In the time of Galileo atomic views were coming again to the 
fore. There was as yet no experimental evidence for the existence 
and nature of atoms. It remained a philosophical doctrine. But 
it seemed to fit the revelations of the microscope. Were these tiny 
beings atoms ? Were atoms alive These questions gave rise to a 
considerable literature which, since it led nowhere, has been almost 
forgotten. Yet it fitted and stimulated current philosophical views, 
and the curiosity which it aroused had a very definite influence 
in directing the biological observation of the generations which 


Downfall oj Aristotle. New Attempts at Synthesis 

(c) The Universe as Mathematical and Boundless, With the ad- 
vent of the Galilean physics and the Keplerian astronomy, it began 
at least to appear possible that all parts of the universe were 
mechanically interrelated. The astrological teaching of antiquity 
and of the Middle Ages had treated the inner spheres of the world 
scheme as dependent on the outer spheres. In this sense the 
extreme expression of astrological doctrine was determinist. But 
now Galileo, following Bruno and Gilbert, thought of the world 
as boundless. In such a universe no part could be said to be inner, 
none outer, none centre, none circumference. In such a universe 
the mechanics of one part are presumably the mechanics of 
another, though proof of this had to await Newton. Of such 
a boundless universe no beginning in time can be intelligibly 

The implications of this view represent a series of enormous 
changes some of which we have already discussed. Especially it 
affected the conception of the task of the man of science. 

The physical world, in the thought of Galileo, was a separate and 
mathematical conception, a piece of machinery, the action of any 
part of which was calculable. It was thus quite separate from the 
moral world with which it had been united in the medieval 
scheme. The knowledge of the world as a whole — philosophy — 
was thus divided into two categories, natural philosophy and 
moral philosophy, a distinction which is still recalled in the naming 
of the departments of the imiversity where Newton taught. In 
the main we may say that the division has held from Galileo’s day 
to our own. 

A further implication in the conception of a boundless physical 
universe and the separation of natural from moral philosophy is 
the movement known in modem times as 'scientific specialization.’ 
Science, natural philosophy, proceeds on the information given by 
the senses. The line of its attack is thus limited and we cannot 
hope that anything but limited objectives can be reached. Science 
does not seek to solve universal problems. On the other hand 
it does seek to solve its limited problems with a known degree 
of accuracy and a known margin of error. The desire for exact 
expression and for the translation of observation into terms of 
measurement has penetrated every department of science from the 


The Insurgent Century 

time of Galileo onwards. Even the biological sciences have been 
affected. The physico-mathematical form in which the biological 
works of Sanctorius (1600) , Harvey (1628) , and Descartes (1637) 
cast may be contrasted with the beautiful but not mathematically 
controlled works of the 'German fathers of botany' (1530-42, 
pp. 176-7) or of Vesalius (1543, p. 177). Since the work of Galileo 
there has always been a group of biologists that has sought to 
represent biology as a department of physics. 

[d) Religion and Science. Medieval philosophy had presented a 
view of the world as a whole. Looking back on it, from our modern 
point of view, we can see two breaches of continuity. One between 
the celestial and the terrestrial, the other between the living and the 
not living. These two gaps were, however, well concealed from all 
but the most acute, until displayed in the seventeenth century by 
the work of such men as Galileo and Harvey. But thought could 
not rest content with the multiple system thus revealed. There is 
an insatiable demand for explanation of the world on a unitary 
basis. Law must reign, and if not divine law then physical 
law. This call for an explanation of all things in terms simpler 
than themselves was first met in modem times by the philosophy 
of Descartes (p. 221). 

The conception of a mechanical and mathematical universe 
affected other philosophers whose world schemes have endured 
better than that of Descartes. The model suggested by the new 
science of mechanics involves the belief that any event in one part 
of the world must, of necessity, have its consequences in another 
part. Each event gives rise to its own chain, circle, sphere of 
events. Events are never without consequences which go on like 
waves caused by the dropping of a pebble in water producing ever 
widening if less apparent circles which are reflected and reflected 
again from the margins of the pool. This view of the world was 
essential to the thought of Spinoz^ (1632-77). In such a view we 
can think of the dissipation of neither matter nor energy. The 
belief in the conservation of both was implicit in all of Galileo's 
work though not expressed tmtil he had been dead for two 
hundred years. 

The whole question leads on to the philosophical problem of 
'causality' where we cannot follow it. But science, true to its 


Downjall of Aristotle. New Attempts at Synthesis 

principle of limited attacks and limited objectives, has its own 
working rules of causality. It follows Galileo in agreeing to 
discuss only certain particular types of sequence and treating 
them as related, the relation being regarded as cause and effect. 
Thus the physicist will deal only with physical, the chemist 
only with chemical sequences, the biologist only with biological 
sequences. In the course of this process new relationships may 
be discerned or become more apparent, as for instance in the 
physical state of the heavenly bodies or of the relative constitution 
of parents and offspring. Thus will arise new sciences — astro- 
physics and genetics — ^which will limit their scope to the relations 
in their particular fields. All departments will agree, however, 
that only those sequences shall be considered that can be measured 
or at least estimated. From Galileo's day onward we see science 
as measurement. 

But since science must limit its objectives, the world based on 
science, as Galileo the artist weU knew, is not a complete world. 
The appearance of our world depends on how we look at our world 
— that is, on our 'mood'. We may be jn a scientific, an artistic, 
an emotional, a social mood. The resultant of all the ways that we 
have of looking at our world — the resultant of our moods — is, in 
effect, our religion. Galileo founded a new conception of the world 
— he almost founded a mood in which to regard it. In doing so he 
certainly affected the religion of all men who are able to accept or 
partake of his mood. But to say that that mood was all of Galileo, 
to say that the universe as he looked at it was wholly mathematical 
and physical, is not only going beyond his teaching but also going 
beyond all that we can learn of the nature of the man. Reasons 
are doubtless at hand for the rejection of any established religious 
formula, but it would be perverting the historical record to ascribe 
the desire to do so to Galileo or to men of science in general and 
as a whole. 

6. Prophets of Science, 

DESCARTES (1596-1650), the 'first modern philosopher' and the 
most dominant thinker of the seventeenth century, made striking 
contributions both to scientific theory and practice. 

{a) He set forth views as to how science should be prosecuted. 


The Insurgent Century 

(b) He was the first in modem times to propound a unitary 
theory of the universe that became widely current. 

(c) He made important contributions to mathematical, physical, 
and physiological science. 

These three activities of Descartes are not as essentially con- 
nected as he would have wished. In 1633 he was about to pub- 
lish his cosmic view in a work which he termed The World, when 
he heard of the condemnation of Galileo. He promptly withdrew 
the book. In the event his first publication was the Discourse on 
Method (1637). 

(a) Descartes on Scientific Method, 

From an early date Descartes felt great dissatisfaction with the 
results of the usual studies of his time. It seemed to him that there 
was no clear distinction between facts, theories, and tradition. 
Want of clarity was abhorrent to hipi. He attempted to divest 
himself of every preconceived notion and then to build up his 
knowledge. With this end in view he tells us in his Discourse that 
he made certain resolutions: 

(i) ' Never to accept anything for true which he did not clearly 
know to be such, avoiding precipitancy and prejudice, and compris- 
ing nothing more in his judgment than was absolutely clear and 
distinct in his mind.* 

(ii) * To divide each of the difficulties under examination into as 
many parts as possible.* 

(iii) * To proceed in his thoughts always from the simplest and 
easiest to the more complex, assigning in thought a certain order 
eyen to those objects which in their own nature do not stand in a 
relation of antecedence and sequence — ^i.e. to seek relation every- 

(iv) * To make enumerations so complete and reviews so general 
that he might be assured that nothing was omitted.* 

He believed that such truth as is ascertainable is so only by 
the application of these princiffles. These, he thought, are the 
true principles of science, and only by their application can science 
advance. They apply, he held, as much in the sphere of religion 
as in mathematical or physical matters. In essence, therefore, 
revealed religion in the ordinary sense is superfluous. For him the 
fundamental test of a truth is the clearness with which we appre- 
hend it. I think, therefore I am, is the most clearly apprehended 


Dowrifa/l of Aristotle. New Attempts at Synthesis 

of all truths, and, therefore, personality cannot be an illusion. 
Similarly, to him, the conception of the soul as separate from the 
body was clear and even obvious; therefore, he maintained, it 
must be true. Moreover, he considered that the mind could not 
create something greater than itself. Therefore, the conception 
of infinite perfection transcending humanity must have been put 
into our minds by infinite perfection itself ; that is, by God. 

It is noteworthy that in reaching his scientific results he did 
not employ the method that he advocates. It is doubtful if any 
one actively and successfully prosecuting scientific discovery has 
ever or could ever proceed on the lines that he lays down. It may, 
indeed, be doubted whether scientific discovery ever follows any 
prearranged system. The spirit bloweth where it listeth and 
discovery is a thing of the spirit. There is no one method of 
discovery but as many methods as there are discoverers. There is 
no human faculty or power that has not at times been pressed into 
the service of scientific discovery. There is a method of scientific 
demonstration, but that is a very different thing from a method of 
discovery. The setting forth of the one must almost necessarily 
conceal the nature of the other. We, therefore, consider Descartes 
separately as a scientific discoverer and as a prophet and critic 
of science. 

Of the achievement of Galileo, Descartefe formed no high esti- 
mate. Galileo was eliciting mechanical laws. Descartes belittled 
this effort since it included no analysis of the basic conceptions 
with which Galileo was dealing, force, motion, matter, space, time, 
number, extension, and the like. The obvious retort is that had 
Galileo done these things, philosophy might have been richer, but 
science would certainly have been poorer in being deprived of 
the most successful experimenter and the most acute exponent 
of natural law that had yet arisen. 

(&) Descartes* Cosmology, 

We may now turn to the conception of the material universe as 
formed by Descartes. Here, too, we may honour him as a pioneer, 
while we regret that he is less critical of himself than of others. 
The form of the world, according to him, is inevitable, in the sense 
that, had God created more worlds, 'provided only that He 


The Insurgent Century 

had established certain laws of nature and had lent them His 
concurrence to act as is their wont, the physical features of 
these worlds would inevitably form as they have done on ours.’ 
Descartes accepts the probability of creation of matter as a 
momentary act, but holds that this act of creation was the same 
as that by which creation is now sustained. 

Descartes regards the universe as infinite and devoid of any 
empty space. The primary quality of matter is extension, but 
there are also the secondary and derived qualities of divisibility 
and mobility, which are created by God. We may connect the 
assertion of Descartes that divisibility and mobility are derived 
qualities with the formulation of the law that matter, in so far as 
it is unaffected by extraneous forces, remains in motion or at rest. 

He regarded matter as uniform — i.e. made of the same basic 
stuff — though divided and figured in endless variety. Matter is 
closely packed, without any vacuum. Therefore, the movement 
of any part of matter produces the movement of all matter. It 
thus follows that throughout the universe there are circular vor- 
tices of material particles that vary in size and in velocity. If one 
considers any limited part of the universe, the particles in it, as 
they whirl around their vortices, get their comers rubbed off. 
These being rubbed finer and finer become a minutely divided dust 
which tends to centripetal action. This fine dust is ‘first matter' 
and forms the sun and the stars. Ultimately these spherical 
globules acquire a contrary or centrifugal action. They then form 
‘second matter’, which constitutes the atmosphere enveloping 
first matter. The centrifugal tendency of the second matter pro- 
duces rays of light which come in waves from the sun or the stars 
to our eyes. In the process of vortex formation particles are liable 
to get detained on their way to the centre. These settle round the 
edge of the sun or star, like froth or foam. This ‘third matter’ 
can be recognized as the sun-spots (p. 208) and certain other 
celestial phenomena. Major vortices are responsible for planetary 
movements, minor vortices for terrestrial phenomena. The action 
of gravity is identified with centripetal action of a vortex. 

The theory of vortices failed to explain a multitude of known 
phenomena, including Kepler’s laws of planetary motion (p. 204) . 
It became, however, very fashionable. It was elaborated and a 


Downjall of Aristotle. New Attempts at Synthesis 
whole system of physics and cosmology erected on it. It survived 
in France until near the middle of the eighteenth century though 
it had less influence in other countries. From the first it was 
subject to destructive criticism, and it was made untenable by the 
work of Newton. 

{c) Descartes on the Nature of Man. 

For the completeness of his system it was necessary for Des- 
cartes to include the phenomena presented by living things. Here, 
too, his work was of a pioneer character though he invented a 
number of structures and functions that had no existence outside 
his mind. The analogies that he draws, however, are sometimes 
both striking and valuable. 

‘I remained satisfied that God first formed the body of man 
wholly like to ours, as well in outward shape as in inward conforma- 
tion, and of the same matter ; that at first He placed in it no rational 
soul, nor any other principle, beyond kindling in the heart a flame- 
less fire similar, as I think, to the heat generated in damp hay, or 
to that which causes fermentation in must.' 

Descartes is here trying to co-ordinate combustion, metabolism, 
respiration, and fermentation. 

'For, when I examined the kind of functions which might, as 
consequences of this supposition, exist in this body, I found pre- 
cisely all those which may exist in us independently of all power of 
thinking, and consequently without being in any measure owing to 
the soul ; in other words, to that part of us which is distinct from 
the body, and from that of which it has been said above that the 
nature distinctly consists in thinking — functions in which the 
animals void of reason may be said wholly to resemble us; but 
among which I could not discover any of those that, as dependent 
on thought alone, belong to us as man, while, on the other hand, I 
did afterwards discover these as soon as I supposed God to have 
created a rational soul, and to have annexed it to this body.' 

He thus considered that man once existed without a rational 
soul and that animals are stiU automata. He knew, for instance, 
William Harvey's account of the circulation of the blood, and he 
based upon it a most elaborate and carefully worked-out theory of 
the action of the animal body. Man, however, at least in his present 
state, Descartes considered to differ from animals, in the possession 

The Insurgent Century 

of a soul. This he believed to be especially associated with a 
particular part of the body, the pineal gland, a structure within 
the brain which, in his erroneous opinion, was not found in animals. 
In the piheal gland two clear and distinct ideas produce an absolute 
mystery. It is there that the mystery of creation is concentrated. 

The Cartesian philosophy was the first complete and coherent 
system of modem- times. It rapidly found adherents, spread in 
every country, and was popular for several generations. In Des- 
cartes’ native land it won its way even among churchmen. 
Gradually, however, the numerous physical errors which it in- 
volved were exposed. Towards the end of the century the theory 
of vortices became quite untenable. It was then shown to be incon- 
sistent with astronomical observation, and to harmonize neither 
with the cosmical system of Newton nor with the revived atomic 
theory. As an explanation of cosmic phenomena it could no longer 
be held. Important scientific works that professed to be based on 
the Cartesian system appeared, however, as late as the middle of 
the eighteenth century. 

Further, the advance of physiological knowledge exposed basic 
eiAorc of Descartes in the interpretation of the workings of the 
animal body. Descartes, however, had laid the foundations of 
modem philosophy, and from his time on there has been a con- 
tinuous chain of thinkers who have claimed to interpret the world 
by the unaided powers of their own minds. 

{d) Francis Bacon as Prophet of Science, 

Less adapted than Descartes by his powers, his temper, and his 
outlook, to make a great philosophical synthesis was Francis 
BACON Lord Verulam (1561--1626). The Englishman was, more- 
over, less efficient in the actual handling of scientific material and 
incomparably below Descartes in scientific achievement. Despite 
the fact that Bacon was the>)lder of the two, his influence made 
itself felt -somewhat later than that of Descartes. Bacon’s scientific 
ineffectiveness prevented his works and their author from gain- 
ing an entry into circles occupied in the actual advancement of 
science. * He writes philosophy (i.e. science) ', said William Harvey, 
like a Lord Chancellor/ While no one ever worked on the scien- 
tific principles laid down by Descartes, we must, nevertheless, 

Downjall of Aristotle. New Attempts at Synthesis 

remember that there were three Descartes, the cosmic philosopher, 
the prophet and critic of science, and the investigator. There was. 
however, only one Bacon, the author of the Projiciencie and 
Advancement of Learning (1605) and the Instauratio niagna or 
Novum Organum (1620). 

Let us consider Bacon's attitude towards the investigation of 
Nature as set forth in these works. What was this new scientific 
process which he practised worse than he preached ? Bacon was 
for conducting his investigations by collecting all the facts. This 
done, he thought, the facts might be passed through a sort of 
automatic logical mill. The results would then emerge. But this 
method cannot be applied in practice, since facts, phenomena, are 
infinite in number. Therefore, we must somehow choose from 
among them, though Bacon thought otherwise. How then shall 
we choose our facts? Experience shows that they only choose 
profitably who have a knowledge of how their predecessors have 
succeeded or failed in their choosing. In other words, the process 
of choosing facts is an act of judgement on the part of the learned 
chooser, the man of science. So it is also with the process of choos- 
ing words on the part of the word-chooser whom we call a poet* 
The choice of the man of science, as of the poet, is controlled by 
knowledge of his art — of 'his subject' as we are wont to call it at 
the universities or in the laboratories. The man of science, like 
the poet, exercises his judgement to select those things which bear 
a certain relation to each other. And yet no skill in reasoning, 
however deft, no knowledge of the nature of scientific method, 
however profound, no acquaintance with his science, however 
complete, will make a scientific discoverer. Nor, for that matter, 
will any learning in the lore of metre or in the nature and history 
of poetry make a poet. Men of science, like poets, can be shaped, 
but they cannot be made. They must be born with that incom- 
municable power of judgement. 

The scientific man in the prosecution of his art of discovery has 
to practise three distinguishable mental processes. These may be 
distinguished as firstly, the choosing of his facts ; secondly, the 
formation of an hypothesis that links them together; and thirdly, 
the testing of the truth or falsehood of the hypothesis. When this 
hypothesis answers numerous and repeated tests, he has made 


The Insurgent Century 

what is usually called a 'scientific discovery*. It is doubtless true 
that the three processes of choosing facts, drawing a hypothesis or 
conclusion, and testing the conclusion, are often confused in his 
own thinking by the man of science. Often, too, his demonstra- 
tion of his discovery, that is the testing of his hypothesis, helps 
him, more or less unconsciously, to new acts of judgement, these 
to a new selection of facts, and so on in endless complexity. But 
essentially the three processes are distinct, and one might be largely 
developed while the others were in a state of relative arrest. 

In this matter scientific articles, and especially scientific 
text-books, habitually give a false impression. These scientific 
works are composed to demonstrate the truth of certain views. 
In doing so they must needs obscure the process by which the 
investigator reached those views. That process consists, in effect, 
of a series of improvised judgements or 'working hypotheses*, 
interspersed with imperfect and merely provisional demonstra- 
tions. Many hypotheses and many demonstrations have had to 
be discarded when submitted to a further process of testing. Thus 
a scientific article or book, which tells nothing of these side issues, 
blind alleys, and false starts, tends, in some sort, to conceal the 
tracks of the investigator. For this reason, among others, science 
can never be learned from books, but only by contact with 

The distinction between the process of discovery and the 
demonstration of discovery was constantly missed during the 
Middle Ages. On this point, in which our thought is separated 
from that of the men of those times. Bacon remained in darkness. 
He succeeded, indeed, in emphasizing the importance of the 
operation of collection of facts. He failed to perceive how deeply 
the act of judgement must be involved in the effective collection 
of facts. 

As an insurance against bias in the collection and error in the 
consideration of facts, Bacon warned men against his four famous 
Idols, four false notions, or erroneous ways of looking at Nature. 
There were the Idols of the Tribe, fallacies inherent in humankind in 
general, and notably man*s proneness to suppose in nature greater 
order than is actually there. There were the Idols of the Cave, 
errors inherent in our individual constitution, our private and 


Downjall oj Aristotle. New Attempts at Synthesis 

particular prejudices, as we may term them. There were the Idols 
of the Market-place, errors arising from received systems of 
thought. There were the Idols of the Theatre, errors arising from 
the influence of mere words over our minds {Novum Organum, 

But did not Bacon hithself fail to discern a fifth set of idols ? 
These we may term the Idols of the Academy. Their worship in- 
volves the fallacy of supposing that a blind though learned rule 
can take the place of judgement. It was this that prevented 
Bacon from entering into the promised land, of which but a Pisgah 
view was granted him. 

Yet despite Bacon^s failure in the practical application of his 
method, the world owes to him some conceptions of high impor- 
tance for the development of science. 

{a) He set forth the widening intellectual breach which separated 
his day from the Middle Ages. He perceived the vices of the 
scholastic method. In the clarity and vigour with which he de- 
nounced these vices, he stands above those of his contemporaries 
who were striving toward a new form of intellectual activity. 

{h) He perceived, better than any of his day, the extreme 
difficulty of ascertaining the facts of nature. He forecast the 
critical discussion that characterizes modern science. He missed, 
however, the important point that the delicate process of obser- 
vation is so closely interlocked with discussion that both must 
almost necessarily be performed by the same worker. 

(c) English writers of the later seventeenth century concur in 
ascribing to the impetus of Bacon's writings the foundation of the 
Royal Society. Thomas Sprat (1635-1713), Bishop of Rochester, 
the first historian of the Society, assures us of this (1677), do 
Oldenburg and Wilkins, its first secretaries. The opinion is fully 
confirmed by Robert Boyle (1627-91), the most effective of its 
founders, and by John Locke (1632-1704), the greatest of English 

{d) It is, perhaps, in the department of psychological speculation 
that the influence of Bacon has been most direct. The basic 
principle of the philosophy of John Locke is that all our ideas are 
ultimately the product of sensation {Essay concerning Human 
Understanding, 1690). This conception is implicit in Bacon's great 


The Insurgent Century 

work, his Novum Organum (1620). Through the 'practicaT 
tendency of his philosophy and especially through Locke, Bacon 
was the father of certain characteristically English schools of 
thought in psychology and ethics. These have affected deeply the 
subsequent course' of scientific development. 

Whatever his scientific failures, we may thus accord to Bacon 
his own claim that 'he rang the bell which called the wits to- 

7. Character and Conduct of Matter, 

Our word matter is derived from the Latin materia, which in its 
turn is connected with mater, 'mother'. Originally materia was 
a general term for the stuff of which things are composed and 
especially things employed in buildings. So in the medieval 
nomenclature and in that of the alchemists materia prima was the 
stuff of which all things were built, the 'primal matter' that lay 
at the back of all four elements. Both alchemists and the medieval 
philosophers were prepared to believe that matter of one type, by 
a mere rearrangement of its four elements, could be transformed 
into matter of another type. Nor were they convinced that, in 
some circumstances, matter might not appear ' out of the air ' or out 
of nothing. They did not in general regard air as possessing weight, 
and some of them would have claimed that it had 'negative 
weight' since like fire it tended to rise. Nevertheless, it is not 
exactly true to say that the medieval writers had no idea at all 
of wh^t we call the 'conservation of matter' Had that been so 
no trade that used Weights would have been possible. Had there 
been no constancy in weight such stories as that of Hiero's crown 
(p. 64) would have been meaningless. We would rather say that 
in the Middle Ages the idea of conservation of matter was 
indefinite, inexact, unexpressed, and implicit, whereas now it has 
become definite, exact, forlhulated, and explicit. Three centuries 
of application of experimental methods has made this difference. 

There was one particular aspect of matter that had special 
bearings on the early development of modem ideas on the subject. 
The question as to the nature of the air that we breathe and 
whether or not it has weight had been debated since antiquity. 
One of the most popular of the pagan systems of physical philosophy 

Downfall of Aristotle. New Attempts at Synthesis 

— to which Galen adhered — ^held that the ' pneuma * of the world soul 
is inhaled during the act of breathing, which on that account is 
necessary for life. On the cessation of breathing the individual soul 
joined again the world soul (p. 91). Such a view was contrary 
to the medieval Christian attitude. Medieval Christian thought 
generally ignored the objective existence of air as either a material 
or spiritual entity. Nevertheless, Peter of Abano (p. 163) in the 
fourteenth century on theoretical grounds, and Cardinal Nicholas 
of Cusa (p. 171) in the fifteenth century on experimental grounds, 
had held that something material was in fact drawn from the air. 
The problem was given a new aspect by van Helmont. 

The Belgian, jan baptist van helmont (1577-1644), was a 
pious mystic who devoted his life to the investigation of chemical 
processes basing himself largely on the views of Paracelsus 
(p. 174). He published little. Soon after he died his son, who 
occupied himself with similar pursuits* collected his father's 
writings and issued them as The Fount of Medicine [Ortus medicinae 
1648). These writings are in extremely obscure language. More- 
over, the alchemical school, to which van Helmont belonged, was 
justly despised by the clear thinkers, such as Galileo and Descartes, 
who were attacking Aristotelianism and contributing to the up- 
building of the new physical philosophy. Thus van Helmont 
exerted little influence on scientific writings until his works were 
translated and interpreted in the 'sixties of the seventeenth 

Van Helmont concluded from a repetition of the experiments of 
Nicolas of Cusa (p. 171) that plants draw their whole substance 
from water. (He did not, of course, know the part played by 
the atmosphere, especially by carbon dioxide, in the growth of 
plants.) Further, he showed that vapours, though similar in 
appearance, may be very different in character and conduct. 
In other words, there are many kinds of * gas ' The idea is so 
familiar to us that it is hard to realize it as an innovation. Yet 
the very w6rd gas was invented by van Helmont. Etymologically 
it is chaos phonetically transmuted in his native Flemish speech. 

Galileo also was well aware that the atmosphere has weight. 
Nevertheless, he failed to invoke it to explain the failure of a 
suction pump to lift water higher than 35 feet. The explanation was 


The Insurgent Century 

adduced by Galileo’s pupil and secretary, Evangelista Torri- 
celli (1608-47). He reasoned that as mercury is about 14 times 

as heavy as water the atmosphere should support ^ — i.e. about 

2 \ feet of mercury. He selected a glass tube of J-inch calibre and 
4 feet long and closed at one end. This he filled with mercury, 
applied his finger to the open end and in- 
verted it in a basin of mercury. The mercury 
sank at once to 2\ feet above the basin, 
leavingi^feet apparently empty (1643). This 
was the Torricellian vacuum as it came to 
be called. 

Torricelli had in fact constructed a baro- 
meter (Greek 'weight measurer’). He ob- 
served that at times his barometer stood 
higher than at other times. He inferred that 
when the barometer stood high the air was 
heavier, when low, lighter. Descartes pre- 
dicted that at greater altitudes the mercury 
column would stand lower since there was 
less atmosphere to support it. Experiments 
suggested by Pascal confirmed this. The 
matter was further investigated by Huygens, 
Halley, Leibniz, and others. The barometer 
has since been greatly improved, but in 
essence it is still that suggested by Torri- 

The thermometer has had a somewhat 
different history. An air thermometer was 
invented by Galileo. It consisted of a glass 
bulb containing air connected to a glass tube dipping into a liquid 
(Fig. 64). It was very seneitive to temperature changes, but was 
very inexact as it was also subject to barometric changes. About 
1612 Gahleo invented the modem type of sealed tube with glass 
bulb filled with liquid. Technical difficulties in construction, 
however, prevented a delicate and accurate instmment from being 
made until the eighteenth century. 

Very great advances in our knowledge of physical and chemical 

Fig. 64. Galileo’s 

Downjall oj Aristotle. New Attempts at Synthesis 

states are due to the air-pump. This instrument was invented in 
1656 by OTTO VON GUERICKE (1602-86), burgomaster of Magde- 
burg in Prussia. With it he gave a direct and convincing demon- 
stration that air has weight. Guericke is remembered by the 
‘Magdeburg hemispheres’ which, though easily separable under 
normal conditions, could not be separated by two teams of sixteen 
horses each when he had drawn out the air with his air-pump. 
Guericke also invented the first electrical machine. It consisted 
of a globe of sulphur which was made to rotate. Pressure of the 
hands upon the rotating globe charged it electrically. He also 
showed that bodies charged with the same kind of electricity 
repel each other. 

The air-pump of Guericke was considerably improved (1658-9) 
by ROBERT HOOKE (1635— 1703) Working at Oxford for his employer 
ROBERT BOYLE (1627-91). Hooke was one of the most skilf ul and 
ingenious of physical experimenters, Boyle one of the ablest and 
most suggestive of scientific investigators. A large part of the 
foundations of the modem sciences of chemistry and physics in 
their various departments was laid down by these two men. 

By means of the air-pump Boyle and Hooke examined the 
elasticity, compressibility, and weight of the air (1660). The 
necessity of air for respiration and combustion was later demon- 
strated by means of the same instrument (1662). Finally, Boyle 
showed that a part only of the air was used in the process of 
respiration or combustion. The matter was well expressed by 
Hooke in his great work Micrographia (1665) • 

‘ The dissolution of sulphureous bodies is made by a substance 
inherent and mixt with the Air, that is like, if not the very same, 
with that which is fixt in Salt -peter. . . . That shining body which 
we call flame is nothing else but a mixture of Air and volatile 
parts of combustible sulphureous bodies which are acting upon 
each other whilst they ascend. 

This substance ‘inherent and mixed with the air’ is oxygen, of 
which Hooke and Boyle may be regarded as the discoverers. 

Boyle’s name is familiarly recalled in ‘Boyle’s law’ which states 
that the volume of a gas varies inversely as the pressure upon it, 
provided temperature be constant. Boyle took a U-shaped tube 
with a shorter closed and a longer open limb. By pouring mercury 


The Insurgent Century 

into it he cut off air in the short limb and, by shaking, the mercury 
was brought to the same level in both limbs. The air in the short 
limb was now under atmospheric pressure. Adding mercury to 
the long limb he could increase the pressure continuously, thereby 
reducing the bulk of contained iair. Thus when the barometric 
pressure stood at 30 inches, by adding mercury in the long limb till 
it stood 30 inches above the level in the short limb, the pressure on 
the iihprisoned air was doubled. The bulk of that air was then 
found to be reduced to one half. Under three times the atmo- 
spheric pressure it was reduced to a third and so on. Moreover, 
he could reverse the process. 

Boyle’s more purely chemical investigations and speculations 
were of high importance. His most famous work, the Sceptical 
Chymist (1661), opens the modem period of chemistry, and marks 
the end of the doctrine of the four elements of the Aristotelians. 

*To prevent mistakes,* he says, *I must advertize to you, that I 
now mean by Elements . . . certain Primitive and simple . . . 
bodies ; which not being made of any other bodies, or of one another, 
are the Ingredients of which all those call'd perfectly mixt Bodies 
are immediately compounded and into which they are ultimately 

This, in effect, is the modem definition of an element. There can 
be little doubt that he derived his view of chemical elements in 
part from the modest German teacher, joachim jung (1587-1657) 
of Hamburg. Jung had enunciated similar views as early as 1634 
and published them in 1642. Boyle had received a draft of Jung’s 
physical philosophy in a letter received by him in 1654. 

Among other important contributions of Boyle must be included 
the suggestion of chemical ‘indicators’ for testing the acidity or 
alkalinity of liquids, and his isolation of elemental phosphoms. 
He was extremely active in the scientific life of the later seven- 
teenth century. .Almost every aspect of contemporary science is 
discussed in the course of his numerous and diffuse works. 

There is one doctrine popularized by Boyle to which we must 
pay especial attention. In his Origin of Forms and Qualities (1666) 
he defeitely ‘espoused the atomical philosophy, corrected and 
purged from the wild fancies and extravagancies of the first 


Downjall of Aristotle. New Attempts at Synthesis 

inventors of it'. He assumes the existence of a universal matter, 
common to all bodies, extended, divisible, impenetrable. This 
matter consists of innumerable particles, each solid, impercep- 
tible and of its own determinate shape. ‘ These particles are the 
true prima naturalia/ There are also multitudes of corpuscles 
built up from several such particles and substantially indivisible 
or at least very rarely split up into their prima naturalia. Such 
secondary 'clusters' have each their own particular shape. 

' Clusters ' and ' prima naturalia ' may adhere to form characteristic 
and similar groups which are not without analogy to molecules 
and atoms in the modem acceptance of these terms. Neverthe- 
less, the analogy of Boyle's atomism to either modem or ancient 
atomism is far from close. 

Boyle had certainly derived his atomic views from the French 
philosopher, pierre gassendi (1592-1655), 'the reviver of Epicur- 
eanism '. Gassendi adapted that system of thought to the exigencies 
of the philosophy of his time. Boyle's nomenclature is taken direct 
from Gassendi who devoted at least twenty years to his great work 
on atomic philosophy (1649). 

Some form of corpuscular philosophy was widely accepted by 
Boyle's contemporaries, especially in England, where it was 
espoused by the philosopher, john locke (1632-1704) . The corpus- 
cular philosophy, however, though much discussed, was not de- 
veloped on the experimental side for more than a century. 
Chemical observations were collected in pienty and science 
became overwhelmed by a vast number of disconnected chemical 
facts and records, inadequately linked by generalizations. 

An idea of the estimate which seventeenth-century thought 
placed upon a corpuscular (or atomic) hypothesis can be 
gathered from John Locke's Essay concerning Human Under- 
standing (1690). Whenever he deals with the ultimate physical 
cause of secondary qualities and of powers of material substances, 
it is to 'the corpuscularian hypothesis' that he appeals. 'These 
insensible corpuscles', 'the active parts of matter and the great 
instruments of nature', are for him the source of all secondary 
qualities. He maintains that if the figure, size, texture, and 
motion of the minute constituent parts of any two bodies could 
be known, then the mutual operations of bodies could be foretold. 


The Insurgent Century 

Thus 'the dissolving of silver in aqua-fortis and gold in aqua- 
regia and not vice versa, would then, perhaps, be no more difficult 
to know than it is to a smith to imderstand why the turning of one 
key will open a lock and not the turning of another'; 

8. Mechanization of Physiology, 

(a) First Application of Physics to Physiology, 

Biological science, it is often said, always lags behind physical 
science and is always in a more elementary stage. The statement 
is hardly borne out by history. It depends for any truth that it 
may possess upon a particular conception of the nature of science. 
In antiquity, in the hands of Aristotle, biological science was far 
ahead of physical. Again the earliest modem scientific work of 
a monographic character, the great book of Vesalius (p. 177) , is 
exclusively biological. The treatise of Copernicus, published in the 
same year, is medieval by comparison, and contains very few 
original observations (p. 179). To justify the doctrine of the re- 
lative backwardness of biological science it is necessary to postu- 
late that the aim of biology is to represent biological phenomena 
in physical terms. Thus expressed the statement becomes a self- 
evident proposition for, if the postidate be granted, biology can 
never advance beyond its physical data. A large school of bio- 
logical thinkers does not accept this postulate. Nevertheless, it is 
true that the most significant biological advances of the insurgent 
century were, in fact, attempts to express biological findings in 
physical terms. 

The first to apply the new physical philosophy to biological 
matters was santorio santorio (1561-1636), a professor of 
medicine at Padua, in his little tract De medicina statica (1614). 
Inspired by the methods of Galileo who had been his colleague at 
Padua, he sought to compare the weight of the human body at 
different times and in different circumstances. He found that the 
body loses weight by mere exposure, a process which he assigned 
to 'insensible perspiration'. His experiments laid the foundation 
of the modem study of 'metabolism'. Santorio also adapted 
Galileo's thermometer to clinical purposes. It marks the medieval 
character of much of the thought of the day that his account 


Downjall of Aristotle. New Attempts at Synthesis 
of this (1626) is concealed in a commentary on a work of Avicenna 
(P* 134)- 

The Englishman, william harvey (1578-1657), is also to 
be regarded as a disciple of Galileo though he himself was, perhaps, 
little aware of it. Harvey studied at Padua (1598-1601) while 
Galileo was active there. By 1615 he had attained to a conception 
of the circulation of the blood. He published his demonstration 
in 1628. The story of that discovery is very accessible. We 
would emphasize that the essential part of its demonstration is 
the result not of mere observation but of the application of 
Galileo’s principle of measurement. Having shown that the blood 
can only leave the ventricle of the heart in one direction, he turns 
to measure the capacity of the heart. He finds it to be two ounces. 
The heart beats 72 times a minute so that in the hour it throws into 
the system 2 x 72 x 60 ounces = 8,640 ounces = 540 pounds, that 
is to say about three times the body weight ! Where can all this 
blood come from ? Where can it all go to ? The answer to that is 
that the blood is a stage army which goes off only to come on 
again. It is the same blood that is always returning (Fig. 65). 

The knowledge that the blood circulates has formed the founda- 
tion on which has since been built a mass^of physical interpretation 
of the activities of living things. This aggregate forms the science 
of physiology. The blood is a carrier, ever going its rounds over 
the same route to return whence it came. What does it carry ? 
And why? How and where does it take up its loads? How, 
where, and why does it part with them ? The answering of these 
questions has formed the main task of physiology since Harvey’s 
time. As each generation has obtained a more complete and a 
more rational answer for one organ or another, so it has been 
possible to form a clearer picture of some part of the animal body 
as a working mechanical model. 

Yet despite the triumphs of physical methods in physiology, we 
cannot suppose, with Descartes, that the clearest image— which 
is certainly at first sight the most satisfying— is of necessity also 
the truest, for the animal body can be shown on various grounds 
to be no mechanical model. A machine is made up of the sum of 
its parts. An animal body, as Aristotle perceived, is no more 
the sum of its parts than is a work of art. The Aristotelian 


The Insurgent Century 

world-system was falling. The Aristotelian biology held and 
still holds. 

(6) Physiological System of Descartes, 

Nevertheless, the physical discoveries of Galileo and the de- 
monstrations of Santorio (p. 236) and of Harvey (p. 237) gave a 

great impetus to the attempt to 
explain vital workings on mecha- 
nical grounds. A number of 
seventeeiith-century investiga- 
tors devoted themselves to this 
task . The most impressive expon- 
ent of physiological theory along 
these lines was Descarteshimself. 
His account of the subject ap- 
peared posthumously (1662 and 
1664). It is important as the 
first modem book devoted to 
the subject of physiology. 

Descartes had not himself any 
extensive practical knowledge 
of physiology. On theoretical 
grounds he set forth a very com- 
plicated apparatus which he be- 
lieved to be a model of animal 
stmcture. Subsequent investi- 
gation failed to confirm many of 
his findings. For a time, how- 
ever, his ingenious scheme at- 
tracted many. A strong point in his physiological teaching was 
the stress laid on the nervous system, and on its power of co- 
ordinating the different bodily activities. Thus expressed, his 
view may sound modem, but i^is, in fact, grotesquely wrong in 

An important part of Descartes' theory is the position accorded 
to man. He regarded man as unique in his possession of a soul. 
Now in the view of Descartes the special prerogative of the 
soul is to originate action. Animals, he thought, are machines, 


Fig. 65. Diagram to illustrate 
Harvey’s Theory of the Circulation 
of the Blood. 

Downfall of Aristotle. New Attempts at Synthesis 

automata. Therefore, given that we know enough of the works of 
the machine, we can tell how it will act under any given circum- 
stances. But the human soul he regarded as obeying no such 
laws, nor any laws but its own. Its nature he believed to be a 
complete mystery for ever sealed to us. Descartes conceived that 
the soul governs the body through the action of the nervous 
system, though how it does so he again leaves as a mystery. The 
two insoluble mysteries come, he believed, into relationship to 
each other in a structure or organ in the brain, known to modem 
physiology as the * pineal body'. This organ he wrongly believed 
absent in animals other than man. All their actions and move- 
ments, even those which seem to express pain or fear, are purely 
automatic. It is the modem 'behaviourism' with man expressly 

The word 'mystery' is not popular among modem men of 
science. It is, therefore, right to point out that the processes by 
which a sensory impression passes into sensation, by which sensa- 
tion educes thought, and by which thoughts are followed by acts, 
have been in no way elucidated by physiological science. In these 
matters we are in no better case than Descartes. If we have 
abandoned his terminology we are no nearer a solution of his 
leading problems. The basic defects of Descartes system were 
errors in matters of fact. It was on account of these that he 
ceased to have a physiological following with the first generation 
after the publication of his essay on man. 

(c) I atrophy sicists. 

One of the ablest critics of the physiological system of Descartes 
was the Dane, niels steno (1648-86), whose scientific work was 
done mostly in Italy and France. Steno, like Descartes, was a 
mechanist, but unlike Descartes applied himself to the explora- 
tion of bodily structure. He found a pineal gland like that of man 
in other animals, and he could not persuade himself that it had the 
connexions, material or spiritual, described by Descartes. His 
criticism of Descartes in detail was very damaging (p. 278). 

More constmctive was the achievement of giovanni alfonso 
BORELL i (1608-79), an eminent Italian mathematician, astrono- 
mer, and pol5unath, a- friend of Galileo and Malpighi. Borelli's 


The Insurgent Century 

work On motion of animals (1680) is the classic of what is variously 
called the ' iatrophysical ' or ' iatromathematical ' school. It stands 
as the greatest early triumph in the application of the science of 
mechanics to the working of the living organism. Stirred by 
the success of Galileo in giving a mathematical expression to 
mechanical events, Borelli attempted to do the like with the 

Fig. 66. Modified from Borelli to illustrate bodily action as mechanism. 

animal body. In this undertaking he was, in fact, very successful. 
That department of physiology which treats of muscular move- 
ment on mechanical principles was effectively founded and largely 
developed by him. Here his mathematical and physical training 
was specially useful. He endeavoured, with some success, to 
extend mechanical principles to such activities as the flight of 
birds and the swimming of fish. His mechanical analyses of the 
movements of the heart, or of the intestines, were less successful, 
and he naturally failed altogether in his attempt to introduce 
mechanical ideas in explanation of what we now know to be 
chemical processes, such as digestion. 

{d) latrochemists. 

Just as Descartes and Borelli sought to explain all animal 
activity on a mechanical basis, so others resorted to chemical 
interpretation. Forerunners of this point of view were Paracelsus 
(p. 174) and van Helmont (p. 231). A more coherent attempt was 
made by franciscus sylvius (1614-72), professor of medicine at 

Downfall oj Aristotle. New Attempts at Synthesis 

Leyden. That university had become in the second half of the 
seventeenth century the most progressive scientific centre north 
of the Alps. It was the seat of the first university laboratory, 
which was built at his instance. 

Sylvius devoted much attention to the study of salts, which he 
recognized as the result of the union of acids and bases. Thus he 
attained to the idea of chemical affinity— an important advance. 
With a good knowledge of anatomy and accepting the main 
mechanistic advances, such as the doctrine of the circulation of 
the blood and the mechanics of muscular motion. Sylvius sought 
to give a chemical interpretation to other vital activities, express- 
ing them in terms of 'acid and alkali' and of 'fermentation'. In 
this attempt he made no clear distinction between changes induced 
by 'unorganized' ferments, as gastric juice or rennet, and changes 
induced by micro-organisms, as alcoholic fermentation or leavening 
by yeast. Nevertheless, he and his school added considerably to 
our knowledge of physiological processes, notably by their 
examination of the body fluids, especially the digestive fluids 
such as the saliva and the secretions of the stomach and of the 

The views of yet another group of biological theorists were 
best expressed by another expert chemist, georg ernst stahl 
(1660-1734). He is remembered in connexion with phlogiston 
(p. 288) and also stands as protagonist of his age of that view of 
the nature of the organism which goes under the term vitalism 
(p. 42). Though expressed in obscure and mystical language, 
Stahl's vitalism is in effect a return to the Aristotelian position 
and a denial of the views of Descartes, Borelli, and Sylvius. To 
Descartes the animal body was a machine, to Sylvius a laboratory. 
But for Stahl the phenomena characteristic of the living body are 
governed neither by physical nor chemical laws, but by laws of a 
wholly different kind. These are the laws of the sensitive soul. 
This sensitive soul in its ultimate analysis is not dissimilar from the 
psyche of Aristotle (p. 41). Stahl held that the immediate instru- 
ments, the natural slaves of this sensitive soul, were chemical 
processes, and his physiology thus develops along lines of which 
Aristotle could know nothing. This does not, however, alter the 
fact of his hypothesis being essentially of Aristotelian origin (p. 347) . 




The Insurgent Century 

(e) Plant Physiology, 

Most of the physiological discussion of the seventeenth century 
turned on the vital process of animals and especially those of 
man. The plant physiology of the age was of a more elementary 

Van Helmont had shown that plants draw something of nutri- 
tive value from water (p. 231). This was contrary to the Aristote- 
lian teaching that plants draw their food, ready elaborated, from 
the earth. The generation following van Helmont sought to 
erect a positive scheme ol plant physiology without, however, very 
much success, marcello malpighi (1628-94), the great Bolo- 
gnese microscopist (p. 243), held wrongly that the sap is brought 
to the leaves by the fibrous parts of the wood. The leaves, he 
thought, form from the sap the material required for growth. 
This, he knew, is distributed from the leaves to the various parts 
of the plant. He conceived a wholly imaginary ' circulation of sap ' 
comparable to the circulation of the blood in animals. The 
respiration of plants, he falsely believed, is carried on through the 
' spiral vessels ' which bear a superficial resemblance to the breath- 
ing tubes or tracheae of insects with which he was very familiar. 

The earliest experimental work on the physiology of plants was 
that of the French ecclesiastic, EDMt mariotte (died 1684). This 
able physicist observed the high pressure with which sap rises. 
This he compared to blood pressure. To explain the existence of 
sap pressure he inferred that there must be something in plants 
which permits the entrance but prevents the exit of liquids. He 
held that it is sap pressure which expands the organs of plants 
and so contributes to their growth (1676). 

Mariotte was definitely opposed to the Aristotelian conception 
of a vegetative soul (p. 41). He considered that this conception 
fails to explain the fact that every species of plant, and even the 
parts of a plant, exactly reproduce their own properties in their off- 
spring, as with 'cuttings'. He wSs, so far as plants are concerned, 
a complete 'mechanist', and, therefore, anti- Aristotelian. All the 
'vital' processes of plants were for him the result of the interplay 
of physical forces. He beUeved, as a corollary to this view, that 
organisms can be spontaneously generated (p. 245). 


Downfall of Aristotle. New Attempts at Synthesis 

(/) The Classical Microscopists. 

The interpretation of vital activity in chemical and physical 
terms has had a continuous history to our own time. It is far 
other with the very striking microscopical researches with which 
the second half of the seventeenth century is crowded. Five 
investigators of the front rank, marcello malpighi (1628-94) at 
Bologna, Robert hooke (1635-1703) and nehemiah grew (1641- 
1712) in London, jan Swammerdam (1637-80) at Amsterdam, 
and ANTONY VAN LEEUWENHOEK (1632-1723) at Delft, all busied 
themselves with microscopic investigations of the structure and 
behaviour of living things. Their results impressed their con- 
temporaries as deeply as they have modem historians. Neverthe- 
less, their labours gave rise at the time to surprisingly few 
general ideas. Moreover, none of these microscopists inspired a 
school. Thus the following century hardly extended their observa- 
tions, and we have to turn to the nineteenth century for their true 
continuators. On this account the ‘classical microscopists’ must 
be accorded a less prominent place in a general history of science 
than the great interest of their biological observations might 
suggest. We may briefly consider the general ideas that they 

(i) The infinite complexity of living things in the microscopic 
world was nearly as philosophically disturbing as the unexpected 
complexity and ordered majesty of the astronomical world which 
Galileo and Kepler had unveiled to the astonished gaze of a 
previous generation. Notably the vast variety of minute life 
gave at once new point and added new difficulty to the conception 
of ‘Creation’. 

(ii) In a few notable respects the microscopic analysis of the 
tissues of animals aided the conception of the living body as a 
TnArhatiism- Thus Harvey had shown that the blood in its circula- 
tion passed from arteries to veins. The chaimels of passage were 
unknown to him. They were revealed as ‘capillary vessels’ by 
Malpigbi and Leeuwenhoek. These observers also discovered the 
corpuscles of the blood, the secretory functions of ‘glands’, and 
the fibrillary character of muscles, thus helping to complete details 
of the ‘ animal machiiie ’. 


The Insurgent Century 

(iii) The nature of sexual generation had been a subject of secular 
dispute. The discovery (1679) in the male element of 'animalcules’ 
— 'spermatozoa’, as we now call them — aroused new speculations. 
The sperm then was organized. How was it organized ? The eye 
of faith, lit within by its own light, locking through an imperfect 
microscope, lit without by a flickering candle, saw many a 
' homunculus ’ in many a spermatozoon and even the piercing eye 
of a Malpighi or a Leeuwenhoek saw that which was not (Fig. 67). 

Fig. 67. Spermatozoa as seen in the seventeenth century : a, h, c, by 
Leeuwenhoek (1679), d, by Hartsoeker (1694), man, e, f, g, by 
Plantades (1699), in man. 

The faith of others demanded that the homunculus should be carried 
by the female element, by the germ rather than by the sperm. 
That, too, was seen by the eye of faith. The more sober and con- 
servative Harvey insisted that the production of the complex 
embryo in the simple substance of the egg was a 'new appearance’, 
a recurring miracle, induced or excited by that magic imponderable, 
the 'generative force’. 

(jy) Microscopic analysis revealed some similarity between the 
structures of plants and animals. False analogies were drawn and 
carried at times to fantastic lengths. For some such fantasies, 
justification at least appeared. The 'loves of the plants’, on which 
poets had dwelt, were not wholly fables. It began to be realized 
that flowers contained the sexual elements, and a real parallel was 
perceived between their reproductive processes and those of 

(v) Lastly, there is an, aspect of minute life that came to the fore 

Downjall of Aristotle. New Attempts at Synthesis 
in the later seventeenth century that requires some special dis- 
cussion. It is the theme of spontaneous generation of living things, 
that is, the generation of living things from non-living matter. 

(g) Spontaneous Generation, 

Neither ancient nor medieval nor renaissance scientific writers 
doubted that spontaneous generation took place on occasion. The 
subject has a considerable literature. In familiar language corpses 
were said to 'breed* worms, dirt to 'breed* vermin, sour wine to 
'breed* vinegar eels, and so forth. The doctrine of spontaneous 
generation is often fathered on Aristotle and is certainly encount- 
ered in his writings, but in truth it was not so much a doctrine as 
a universal assumption. It so fell out that when the reality of 
spontaneous generation was first questioned, the authority of 
Aristotle — or rather the contemporary misunderstanding of him — 
was a very real obstacle to scientific advance. It is also true that 
Aristotle gave spontaneous generation a place in his biological 
scheme. But his error was shared by every naturalist until the 
seventeenth century, and indeed it is hard to see how these men, 
with the knowledge at their disposal, could take any other view. 

With the advent of effective microscopes in the second half of 
the seventeenth century, new tendencies set in. On the one hand, 
exploration of minute life showed many cases of alleged spontaneous 
generation to have been falsely interpreted. Thus plant galls had 
been regarded as spontaneously generated, but Malpighi showed 
that these curious growths are related to the action of insect larvae. 
On the other hand, the microscope revealed minute organisms 
which seemed to appear out of nothing. Thus Leeuwenhoek saw 
excessively smaU creatures in infusions of hay and other substance. 
Such infusions, perfectly clear when first prepared, become in a 
few days or even hours cloudy with actively moving microscopic 
forms. These seemed to be spontaneously generated. 

The first scientific treatment of the question was made by 
FRANCESCO REDi (1621-97), a physician of Florence. He tells us 
(1668) that he 

'began to believe that all worms found in meat were derived from 
flies, and not from putrefaction. I was confirmed by observing 


The Insurgent Century 

that, before the meat became wormy, there hovered over it flies 
of that very kind that later bred in it. Belief unconfirmed by 
experiment is vain. Therefore, I put a (dead) snake, some fish, 
and a slice of veal in four large, wide-mouthed flasks. These 
I closed and sealed. Then I filled the same number of flasks in 
the same way leaving them open. Flies were seen constantly 
entering and leaving the open flasks. The meat and the fish in 
them became wormy. In the closed flasks were no worms, 
though the contents were now putrid and stinking. Outside, on 
the cover of the closed flasks, a few maggots eagerly sought 
some crevice of entry. 

'Thus the flesh of dead animals cannot engender worms unless 
the eggs of the living be deposited therein. 

‘Since air had been excluded from the closed flasks I made a 
new experiment to exclude all doubt. I put meat and fish in a 
vase covered with gauze. For further protection against flies, I 
placed it in a gauze-covered frame. I never saw any worms in 
the meat, though there were many on the frame, and flies, ever 
and anon, lit on the outer gauze and deposited their worms there.' 

It is odd that, despite these admirable experiments, Redi con- 
tinued to believe that gall insects were spontaneously generated. 
This subject was taken up by another eminent Italian physician, 
ANTONIO VALLiSNiERi (1661-1730), who again demonstrated that 
the larvae in galls originate in eggs deposited in the plants (1700). 
VaUisnieri compared the process of gall formation, as well as 
infection of plants by aphides, to the transmission of disease. 
Other investigators showed that fleas and lice — to this day popu- 
larly thought to be ‘bred by dirt' — are, in fact, bred only by 
parents like themselves. 

Thus the matter closed in the seventeenth century with the 
general balance of opinion against spontaneous generation. The 
possibility had been disproved — ^so far as a universal negative 
can be disproved — for visible organisms. The question was still 
open for the minute organisms encountered in infusions, the 
miscellaneous biological group classed in the language of the day 
as Infusoria, 

In summary we may say that for Biology the Insurgent Century 
closed with a strong mechanistic bias. The microscopic world, 

Downjall oj Aristotle. New Attempts at Synthesis 

however, remained an enigma, a land of wonders where all laws 
seemed at times to be broken. De minimis non curat lex ('The law 
does not concern itself with the most minute things*) was not 
infrequently quoted, but the lex of the lawyer was a very different 
thing from the lex naturae. 


Enthronement of Determinism 
I. The Newtonian Key to the Mathematics of the Heavens. 

ST. AUGUSTINE, about A.D. 427. 

‘ This glorious doctor, as he went by the sea-side studying on the 
Trinity, found a little child which had made a little pit in the sand, 
and in his hand a spoon. And with the spoon he took water and 
poured it into the pit. And St. Augustine demanded what he did. 
And he answered: “I will lade out all the sea into this pit." 
"What ? " said St. Augustine, "How may it be done, sith the sea 
is so great, and thy pit and spoon so little?" "Yea", said he, 
"I shall lightlier draw all the water of the sea and bring it into 
this pit than thou shalt bring the mystery of the Trinity into thy 
understanding, for it is greater to the comparison of thy wit than 
is' this great sea unto this little pit." And therewith the child 
vanished.' — Abbreviated from ‘The Golden Legend', as englished 
by William Caxton in 1483. 

ISAAC NEWTON, A.D. 1727, shortly before his death. 

‘ I do not know what I may appear to the world, but to myself 
I seem to have been only like a boy playing on the sea shore, and 
diverting myself in now and then finding a smoother pebble or a 
prettier shell than ordinary, while the great ocean of truth lay all 
undiscovered before me.' — From the Anecdotes of Joseph Spence 

Nothing emerges more clearly from a survey of the history of 
science lhan the lasting and essential sameness of the human spirit. 
The same aspiration for a coherent and comprehensive plan of his 
imiverse has characterized the mind of man from his very dawn and 
has survived a thousand defeats. It is therefore by no means strange 
that two men widely separated in time, genius, mood should take 
refuge in the same image to express their thought of infinity. 

St. Augustine (354-430 ; p. 124) marks the effective beginning 
of a great epoch — a space of thirteen centuries — of which the 
effective end is marked by the arrival of Isaac newton (1642- 
1727). In his Confessions Augustirfe says that the sole funda- 
mental truth lacking to the ‘ Platonists ' — by which he means his 
Neoplatonic teachers (p. 124) — ^wasthe doctrine of the Incarnation. 
It was Augustine who determined that Christian thought should 


Newtonian Key to the Mathematics oj the Heavens 
be cast in a Neoplatonic mould, the impress of which it has borne 
to our own day. It was his specifically Christian contribution to 
award to man a unique dignity that was denied by certain pagan 
philosophers. The Augustinian Neoplatonist is still working in 
John Dryden (1631-1700). He is still straining his ears to hear 
the 'music of the spheres' in the very year in which Newton’s 
greatest work appeared : 

From harmony, from heavenly harmony, 

This universal frame began. 

From harmony to harmony 

Through all the compass of the notes it ran, 

The diapason closing full in Man. 

(A Song for St. Cecilia's Day, 1687.) 

In the Neoplatonic Christian world there was a hierarchy of 
existences from purely spiritual to purely physical, the whole 
linked together in God's heavenly harmony. The centuries rolled 
on, and still that music of the spheres lulled man's mind to sleep 
while his spirit waked. At last ‘Aristotle' — a strangely changed 
Aristotle — was recovered by the Latins from his Arabian custo- 
dians (p. 162), and Scholasticism was born. Thus the ancient 
cosmic scheme was enlarged by a Neoplatonic Aristotelianism 
and the ‘Dark Ages' of Faith gave place to the ‘Middle Ages’ of 
Reason. Yet the spell of Plato and of his mouthpiece Augustine 
stiU remained unbroken. The spiritual realm of the medieval 
Christian stretched to the infinite, aspiring to the timeless God. 
But the Christian's material world, the world of Augustine, of the 
Neoplatonists, of the Stoics, and of Aristotle remained limited by 
those flaming ramparts beyond which even thought could hardly 

The change came with the sixteenth century. Copernicus put 
Earth from her ancient seat (p. 179) in a new form of an old con- 
vention. But it was Bruno who proclaimed a universe of world 
beyond world, without centre or circumference, in which all place 
and all motion were relative. For him the stars were no longer 
fixed and the frontiers of the universe were an idle dream. Next 
Kepler reduced the movements of the heavenly bodies to intel- 
ligible mathematical rules. Galileo developed the system of 
earthly mechanics with which, he hinted, the heavenly bodies 


The Mechanical World 

must somehow show accord. The conduct of matter was explored 
by Boyle and the new experimental school in a new and exact 
spirit, without the older presuppositions. While Harvey, Des- 
cartes, Borelli, expounded the living body as a mechanical system, 
Malpighi, Hooke, Grew, Leeuwenhoek, Swammerdam revealed, 
with their microscopes, vast and unsuspected regions and forms 
of life and the endlessly complex structure of even the minutest 
living things whose very existence had not been conceived. 

In the third quarter of the seventeenth century learned societies 
in France, England, and Italy became centres for the exchange of 
scientific ideas. Perhaps the greatest achievement of these socie- 
ties was the development and perfection of the manner of present- 
ing inquiries. Thus the form of scientific communications became 
standardized and the demand for rigorous demonstration insis- 
tent. To quote authority was useless. Nullius in verba (‘On the 
word of no man *) stands on the crest of the Royal Society, whose 
publications began in 1664. The demand for evidence, for tangible 
data, for experience that can be repeated at will, had created 
science as we know it. 

A fruitful source of misunderstanding of the aims and methods 
of the new science has been the unfortunate necessity that its 
technique of presentation must conceal the investigator himself. 
With the advent of the ‘scientific joumar it becomes increasingly 
difficult to reach behind the text to the mind of the author. The 
new method of scientific publication does not allow us to see 
the trial attempts and tentative views of the men who wrote these 
books and papers. The point comes out admirably in the career 
of New;ton himself. 

The demonstrations of Galileo and Kepler, while they banished 
the earth-centred universe, did not at once destroy the conception 
of a sun-centred universe. No one had proved that the fixed stars 
were at various distances from our planetary system, and that 
view was not generally expressed. Nevertheless, such an opinion 
was certainly widely held in scientific circles. The varying size 
of the stars, the occasional appearance of new stars and many 
other phenomena, suggested that the stars were of the same order 
as our sun, or earth, and the planets of our system. The leaven 
of Bruno had worked. In 1686, the year before the publication of 


Newtonian Key to the Mathematics oj the Heavens 

Newton's Principia, appeared the very famous work On the 
Plurality of Worlds by the French writer Le Bovier de Fontenelle 
(1657-1757). There were many who were thinking the same 
thought. * I am of like opinion with all the great philosophers of 
our age', wrote Huygens, ‘that the sun is of the same nature as 
the fixed stars. And may not every one of the stars or suns have 
as great a retinue of planets with moons to wait upon them as 
has our own sun?* (1698). The earth, then, being but a moving 
particle in space, space itself must be infinite, as Bruno had 
claimed. The Cosmos, not' Man, must be the prime reality. In 
that new-found Cosmos the philosophers vied with one another in 
tracing laws, and the music of the spheres grew more distant and, 
at times, even discordant. 

The change was at first one of degree rather than of kind. Law 
had been traced in the heavens from of old. The rules of planetary 
and stellar motion had been gradually developed from the astro- 
nomical theories of antiquity. Even in the Middle Ages a few new 
mathematical relationships of the heavenly bodies had been dis- 
cerned. In the sixteenth century astronomy under Tycho (p.183) 
put her house in order for the Great Instauration (p. 227) of the 
coming age. And then Galileo startled the world with his proof 
of change in the uttermost heavens (p. 206) in the very region held 
by the Aristotelian and Platonic schemes to be utterly changeless. 

By 1618 Kepler had enunciated his ‘three laws of planetary 
motion', bringing these movements into an intelligible relation 
with each other (pp. 204-5). Then Galileo determined the rule of 
action of gravitation and came near to the ‘ three laws of motion' 
which we call Newton's (pp. 199-200). Others, Hooke and Wallis 
among them, were feeling their way in the same direction. But 
it was Newton who first affirmed these laws and succeeded in link- 
ing them with Kepler's laws of planetary movement. Before 
Newton, no man had shown, or clearly and demonstrably per- 
ceived, how the complex movements of the heavenly bodies were 
in relation to the natural succession of earthly phenomena. Reason 
no less than Faith would have been against such a view. Newton's 
unique achievement was to prove that this relationship amounted 
to identity. It was Newton who moved men's minds to see that 
the force that causes a stone to fall is that which keeps the planets 


The Mechanical World 

in their path. It was Newton who first enunciated a law the writ 
of which ran no less in the heavens than on the earth. With New- 
ton the Universe acquired an independent rationality quite un- 
related to the spiritual order or to anything outside itself. The 
Cosmology of Plato, of Aristotle, of Augustine, of the theologians 
was doomed. 

Newton knew that if a stone be let drop, its weight — ^which is 
another name for Earth's attraction — ^will cause it to fall a certain 
measurable distance in the first second of its fall. He came early 
to suspect that the force which kept the moon in her orbit was 
none other than this terrestrial attraction. The period of the 
moon's revolution round the earth, and the dimensions of her 
orbit, were alike susceptible of estimation, so that her velocity 
could be calculated. Now the moon, like any body pursuing a 
curved course, is moving at any particular moment in a direction 
tangential to her orbit. But the moon, as we know, does not con- 
tinue to move along the tangent, but is constrained to follow her 
elliptic path round the earth. At the end of the second, she, like the 
stone, has ' fallen ' a certain distance toward the earth (Fig. 68) . The 
earth has drawn her to herself. Now, from Kepler's laws, Newton 
had reason to suspect that the attractive power of the earth on 
any body decreases as the square of the distance from the centre 
of the earth. If the conjecture were correct, he had the equation : 

Distance fallen by Moon _ (Distance of stone from Earth's centre)^ 
Distance fallen by stone (Distance of moon from Earth's centre) ^ 

When Newton first approached this problem (1666) he found 
that the moon's ‘ fall' was but seven-eighths of what he expected. 
But he had seized on the conception of universal gravitation, that 
is, that every particle of matter attracts every other, and he 
suspected that the attraction varied directly as the product of 
the attracting masses, and inversely as the square of the distance 
between them. It was still years before he was armed with the 
knowledge and means to show that the ‘ fall of the Moon * had the 
value required by his theory. By that time (1671) he had developed 
the wonderful mathematical method of dealing with curves which 
has since, with another nomenclature, become familiar under the 
name of ‘Calculus'. 


Newtonian Key to the Mathematics oj the Heavens 

The action of gravity on the earth and in the heavens was now 
seen to be the same, at least for a particular case. Newton^s grand 
hypothesis was launched, though not yet worked out in detail. 
We owe it to the astronomer edmond halley (1656-1742) — whose 
name is recalled periodically by his comet (p. 260)— that Newton 
undertook to attack the whole problem of gravitation. He had 
years of labour before he could show that the attraction of a 
spherical body on an external point was as if the spherical body 

Fig. 68. Illustrating the orbit of the moon as compounded of 
tangential and centripetal movements. 

were concentrated at its centre (1685). He had no expectation of 
so beautiful a result till it emerged from his mathematical in- 
vestigations. With this theorem in his hands, all the mechanism 
of the universe lay spread before him. The vision was set forth 
in the Philosophiae Naturalis Principia Mathematica of 1687. 
Halley bore all the stress, set aside his own researches, sacrificed 
himself to forward what is regarded as the greatest of all scientific 
works. The Principia — as the work is usually called — established 
a view of the structure and workings of the universe which sur- 
vived to our own generation. 

The full extent and revolutionary character of the change that 
Newton was working in men's minds was not at first recognized 


The Mechanical World 

even by himself, but it became apparent in the course of the 
eighteenth century. The essential revolutionary element was that 
Newton had conceived a working universe wholly independent of 
the spiritual order. This was the profoundest break that had yet 
been made with all for which the Middle Ages stood. With Newton 
there set in an age of scientific determinism. 

But if the nature of the Newtonian revolution was not at first 
apparent, the scientific importance of the Principia, as of New- 
ton's other contributions, was recognized immediately on publica- 
tion. Newton wrote for mathematicians, and his full significance 
was beyond the comprehension of any others. He needed inter- 
preters. Of these the ablest and most effective was voltaire 
(1694-1778), who spent the years 1726-9 in England. To him 
we owe the well-known story of Newton and the falling apple. 
Voltaire was aided in the. preparation of his version of the New- 
tonian philosophy by his mistress, £milie de Breteuil, Marquise 
du Chastelet (1706-49), who was a competent mathematician and 
herself translated the Principia into French (published post- 
humously 1759). Voltaire's delightful and lucid exposition (1737) 
marks the real victory of the Newtonian philosophy and the final 
submergence of Aristotelianism. 

The changes in method and outlook introduced by Newton were 
so great that their general conformity as members of an historical 
series is sometimes lost to view. The issue is further obscured by 
the use or misuse of certain well-worn phrases. Newton's phrase 
‘ I invent no hypotheses ' is often quoted. The prestige of his name 
led to the assertion that ‘whereas his predecessors described the 
motions of the heavenly bodies, Newton was the first to explain 
them'. Scrutiny of these statements throws light on the nature 
of scientific process. 

Newton's famous phrase Hypotheses non Jingo occurs at the end 
of the Principia, ' I have not yet been able to deduce from the 
phenomena the reason of these properties of gravitation and / 
invent no hypotheses. For whatever cannot be deduced from the 
phenomena should be called an Jiypothesis,* 

Now Newton is here giving to the word hypothesis its exact 
original meaning. In the works of Plato^ as well as in yet earlier 

e.g. Phaedo, 101 d, e. 


Newtonian Key to the Mathematics oj the Heavens 

works bearing the name of Hippocrates (p. 30) the word ‘ hypo- 
thesis ' is used for a postulated scheme or plan which must be 
accepted if discussion is to take place. It is literally a ' founda- 
tion' (Greek hypo thesis, *a thing placed under'). We have such 
hypotheses constantly before us in law. Some are mere legal 
fictions, as that ' the King can do no wrong ' ; others are convenient 
presentations of a remote possibility, as ‘ the lease that runs for 
999 years' ; others refer to procedure, as' that 'a man is innocent 
(i.e. treated as innocent) until proved guilty'. All these are hypo- 
theses in the Platonic, Hippocratic, and Newtonian sense. None 
are deduced from the phenomena. None are verifiable. All are 
parts of a working scheme into which certain phenomena can be 
conveniently and tidily fitted. In this use of the word Newton 
was certainly right when he said ' I invent no hypotheses'. 

But if hypothesis be taken to mean what we usually understand 
by a scientific hypothesis, that is a generalization drawn from a 
series of observations which, it may reasonably be hoped, will be 
confirmed by yet further observations, then we must say that 
Newton was constantly both inventing and employing hypotheses. 
His application to the movements of the moon of the doctrine of 
gravity as he knew it on earth (p. 252] was an obvious example. 
Once he had such an 'hypothesis' that would fit the moon, he 
could and did apply it to other members of the planetary system. 
Its verification from the planets strengthened his conviction of the 
value of his first inference. The whole of his scientific activity was 
remarkable for invention of hypotheses. The successful invention 
of hypotheses is indeed the mark of his scientific eminence. 

As regards the distinction between description and explanation, 
the position is somewhat the same. Newton knew that a property 
which we ceJl gravity is associated with all matter of which we have 
direct experience. Having reached an exact conception of this 
property, he proceeds to examine the motions of the planetary 
bodies and finds that they may be re-expressed in terms of 
gravity. To do this is to give a description, not an explanation. 
It may reasonably be claimed that ' description is the true aim of 
science '. Let us apply the claim to some of Newton's predecessors. 

Ptolemy represented the apparent movements of the heavenly 
bodies in terms of epicycles. This was his method of description. 


The Mechanical World 

If he were asked ‘Why were the epicycles thus disposed?* he 
could have given no answer. He described ; he did not explain. 

Copernicus displaced the geocentric scheme. He expounded 
the appearances more simply and fully by ascribing them to the 
motion of the earth round a sun that was at rest. If asked ‘ Why 
does the earth move so ? * he could have given no answer. He 
described ; he did not explain. 

Kepler represented the appearances more simply and fully by a 
system of ellipses. If asked ‘Why should this form have been 
chosen ? * he could have given no answer. He described ; he did 
not explain. 

Newton*s completer scheme was based on the mutual attrac- 
tion of bodies. If asked ‘Why do they mutually attract each 
other ? * he could have given no answer. * If^ therefore, his account 
of the planetary system may be called an explanation, then such 
an explanation is indistinguishable from a description. The distinc- 
tion between description and explanation cannot be ultimately 
maintained. It is the function of science to describe in terms that 
are as simple as possible. Ultimately the description must be in 
terms that defy further analysis, if such terms there be. 

There is a significant change in nomenclature that expresses 
epigrammatically the change that came into men's minds with the 
acceptance of a mechanical world. For fourteen centuries, between 
St. Augustine and Newton, the Christian philosophic synthesis 
had reigned supreme ; undisputedly at first, a little uneasily at last. 
But during the succeeding two centuries the results of the investi- 
gation of Nature appeared to fit less and less neatly with the 
accepted philosophic scheme. Changes in ^he meanings of words are 
sometimes straws that tell how the winds of thought are blowing. 
It is no accident that, precisely during these two centuries, certain 
kinds of ‘ philosophical enquiries ' — as Newton and his contempor- 
aries always described their labours — came gradually to be known 
as ‘scientific researches*. Science, the knowledge of nature, was 
separated from philosophy, the search for the key to the universe. 
The change represents a fragmentation of interests that has lasted 

* Newton did attempt to give an answer. He sought to * explain’ gravi- 
tation in terms of ether. Even had his attempt been successful, which it 
was not, it would have been of the nature of a re-description. 


Newtonian Key to the Mathematics of the Heavens 

beyond the period that we are considering. For this reason, 
among others, it is peculiarly difficult to present the history of 
modern science as a coherent whole. From now on, our narrative, 
to become intelligible, needs a minuter subdivision. Science does 
not describe the world as a whole, but only a little bit of it at a 
time, each science choosing its own bit. This departmentalism 
now becomes self-conscious. 

2. Morphology of the Universe, 

Investigations on the general structure of the cosmos associated 
with Newton’s conceptions fall naturally under three heads: 

(i) Observational astronomy, that is, the direct investigation of 
the heavenly bodies by means of the telescope. 

(ii) Dynamical ■ astronomy, that is, the reduction to mathe- 
matical form of the movements of the heavenly bodies and 
the prediction, on a gravitational basis, of the movements 
of those bodies based on the mathematical expressions thus 

(iii) Astrophysics, that is, the investigation of the physical and 
chemical constitution and state of the heavenly bodies. 

(i) Observational Astronomy, 

At the command of Louis XIV, the great scientific architect 
CLAUDE PERRAULT (1613-88) built an observatory at Paris. This 
was the first State observatory of modern times. It was expressly 
intended to provide there facilities for men of science, whatever 
their country of origin. Soon after its completion the Frenchman 
Jean Picard, the Hollander Christian Huygens, the Dane Olaus 
Roemer, and the Italian G. D. Cassini were all at work there. 

JEAN PICARD (1620-82) was an exact and careful observer, 
remembered for his measurements of the dimensions of the 
earth (1671, p. 271). These formed the basis of Newton’s calcula- 
tions. He recognized the astronomical value of the pendulum 
clock invented by Huygens, and he was the first to introduce the 
systematic use of telescopic ‘sights'. 

CHRISTIAN HUYGENS (1629-95, pp. 193-4), before coming to the 
new observatory, had already completed much important scientific 
work. Thus, he had improved the telescope, and had proved that 




The Mechanical World 

the changes in the appearance of Saturn — its * horns* as Galileo 
called them — ^were due to a ring inclined at 28 degrees to the 
ecliptic (1653-6). The micrometer, a telescopic device for measur- 
ing small angular distances, was effectively introduced by him 
(1658).^ His astronomical experiences raised in him a desire for 
an exact mode of measuring time. With this in view he attached 
a pendulum to a clock driven by weights, so that the clock kept 
the pendulum going but the pendulum regulated the rate of move- 
ment of the clock. The device was made public in his Horologium 
(1658), a work universally regarded as the foundation of the 
modem clock-maker*s art. 

Huygens began work at the royal observatory at Paris in 1671, 
and in 1673 published his famous Horologium oscillatorium,^ a 
work of the highest genius which has influenced every science 
through its mastery of the principles of dynamics. It is second in 
scientific importance perhaps only to the Principia, which is in 
some respects based on it. It is primarily a mathematical analysis 
of the principles of the pendulum clock. It devotes attention to 
the composition of forces in circular motion. A memorable sen- 
tence in the work is the formulation of what has since become 
known as Newton’s 'first law of motion’ (p. 199) Huygens 
writes: 'If gravity did not exist nor the atmosphere obstmct the 
motions of bodies, a body would maintain forever, with equable 
velocity in a straight line, the motion once impressed upon it.’ 
The work presents the modem view of the nature of inertia 
with great clearness.-^ 

Huygens measured the acceleration due to gravity by experi- 
ments with a seconds pendulum, that is to say, a pendulum the 
oscillations of which occupy exactly one second. It is possible to 
calculate this acceleration at any spot of the earth’s surface from 
the accurate measurement at that spot of the distance between 

* The micrometer had been invented about 1640 by the Englishman 
William Gascoigne (1612-44). Huygens’s device was improved about 1666 
by the Frenchman Adrien Auzout (d. 1691). 

^ Not to be confused with the HoThlogium of 1658. 

3 The ideas of mass and of inertia were implied by Huygens in his 
statement of the laws governing the collision of elastic bodies as presented 
to the Royal Society in 1669. In this matter he had been preceded to 
some extent (1668) by Wallis (p. 193) and Christopher Wren (1632-1723). 


Morphology oj the Universe 

the point of suspension and the centre of gravity of a seconds 
pendulum. Huygens's own result was 32-16 feet per second. 

In 1681 Huygens returned to Holland and devoted himself once 
more to optical investigations and devices. He introduced a prin- 
ciple of optical construction which obviated much of the difficulty 
of chromatic aberration by employing lenses of enormous focal 
distance for his very long 'aerial telescopes'. The 'Huygenian 
eyepiece ' invented by him is still in use. 

OLAus ROEMER (1644-1701) was the first to show that light has 
a definite velocity (1675). His conclusion was based on his 
observation that the intervals between the eclipses of Jupiter's 
moons were less when Jupiter and Earth were approaching each 
other than when they were receding. His discovery was of 
the highest importance, but it was rejected by the conservative 
Cassini, the astronomical dictator of the age. 

G. D. CASSINI (1625-1712) began life as an engineer in the papal 
service. He established an astronomical reputation by his writing 
on comets (1652) and by his observations of the rotation periods 
of Jupiter, Mars, and Venus (1665-7). He was called to Paris by 
Louis XIV in 1669 and became the most influential figure in the 
observatory. Under his auspices it was shown that the earth was 
flattened towards the poles, a discovery that had important 
astronomical implications (p. 272). Under him, too, the parallax 
of Mars was measured. This led to an estimate of the distance 
of Mars from the sun (1673). His estimate of the distance of the 
sun from the earth, though by far the best up to its date, was 
some 7 per cent, in error. 

Cassini was a man of conventional piety and — remarkable at 
that date — ^was an anti-Copernican. He was succeeded at the 
Paris observatory by three generations of descendants. The Cas- 
sini regime at the observatory lasted for a century and a quarter 
(1671-1794) and their lives extended over more than two cen- 
turies (1625-1845). Their conservative bias gradually weakened 
as the dynasty came to an end, but it was very injurious to French 

In England, interests were increasingly maritime, and a scheme 
for finding longitude at sea was propounded in 1675. John 
FLAMSTEED (1646-1719), already recognized as a promising 


The Mechanical World 

astronomer, showed this to be impracticable without a more accu- 
rate knowledge of the positions of the fixed stars than was then 
available. Charles II, hearing of this, declared that ‘ he must have 
them anew observed, examined and corrected for his seamen An 
observatory was erected for Flamsteed at Greenwich. His in- 
dustry there was enormous, and between 1676 and 1689 he deter- 
mined the positions of some twenty thousand fixed stars. His best 
observations were made with a mural arc, which he erected in 
1689. This marked a great instrumental advance, and made pos- 
sible far more accurate determinations than had before been at- 
tempted. His star catalogue forms the basis of modern astronomy. 

Flamsteed was succeeded at Greenwich (1720) by edmond 
HALLEY (1656-1742). This remarkable man had detected dis- 
crepancies between the observed and the theoretical paths of 
Jupiter and Saturn before he was twenty. Perceiving that 
observations in the southern hemisphere were needed for the 
adjustment of these differences, he embarked for St. Helena 
(1676), where he observed for eighteen months. During this 
period he improved the seconds pendulum (p. 258) and determined 
the position of 341 stars of which no accurate record then existed. 
At the same time he made many other contributions to science 
and, notably, made a series of meteorological observations. These 
led to his publication of the first map of the winds of the globe 
(1686) and an attempt at their explanation (p. 275). He also made 
the first complete observation of a transit of Mercury. 

In 1680 Halley began the study of the orbits of comets. In 1682 
a comet appeared, the course of which was watched by several 
observers. Newton had suggested that comets might move in 
very elongated ellipses, indistinguishable from parabolas — as 
such ellipses must be — ^when near the sun (Fig. 69). Halley calcu- 
lated the form, position, and measurements of the path of the 
comet of 1682, and noted their likeness to those of similar comets 
of 1531 and 1607. He inferred that his comet was a return of 
these. Other returns were traced. In 1705 he expressed the view 
that his comet returns every s^enty-five and a half years, follow- 
ing an immensely long elliptical orbit extending far beyond the 
orbits of the planets (Fig. 70). Halley's comet is now known to 
have reappeared at about that interval from \2 b.c. to a.d. 1910 — 


Morphology oj the Universe 
twenty-six appearances in all. A famous appearance of this comet 
was that of 1066, which undermined Harold’s morale, being inter- 
preted as indicating his defeat by William the Conqueror. It is 
represented in the Bayeux tapestry. 

Halley was succeeded at Greenwich by James Bradley (1693- 
1762), who contributed to observational astronomy two important 
conceptions, aberration of light (1729) and nutation of the earth's 
axis (1748). 

Fig. 69. Parabola and elongated ellipse, showing how they become 
indistinguishable from each other as they approach their common focus. 

The aberration of light is most simply explained by the very 
illustration which suggested the idea to Bradley himself. Imagine 
travelling in a boat in a wind and with a flag at the mast-head. If 
the course be changed, the flag alters its apparent direction. Re- 
place, in imagination, the wind by light coming from a star, and 
the boat by the earth moving round the sun and ever changing 
its direction. The result must be a cyclic change in the apparent 
position of a star. This Bradley was the first to observe and to 

The nutation (Latin * nodding’) of the earth’s axis is an undula- 
tory movement grafted on to that simple movement of the axis 
which corresponds to the precession of the equinoxes (p. 77). 
Thus the movement of the axis is not in a circle, as it would be 
if the precessional movement were uncomplicated, but in a figure 
of crenated outline (Fig. 71). Since Bradley’s time many astro- 
nomers have studied the conduct of the earth’s axis. It has trans- 
pired that nutation is only one of a whole series of complications 
of its motion. 


The Mechanical World 

The most impressive figure among eighteenth-century observa- 
tional astronomers was Frederick william herschel (1738- 
1822). Bom in Hanover — ^then a possession of the British Crown 
—he came to England (1757), turned early to astronomy, and 
acquired great technical skill in constmcting instruments. He 
conducted four complete reviews of the heavens, with telescopes of 
increasingly greater power. The second review revealed Uranus 
(1781), the first new planet to be discovered in historic time. 

Fig. 70. Path of Halley’s Comet. The position at various dates, with 
reference to the Perihelion, P, and Aphelion, A, is indicated. 

Further improvements in his instruments led to his discovery of 
the satellites of Uranus (1787) and of Saturn (1789). 

Herschel’s industry and accuracy as an observer were un- 
rivalled and his skill as an instrument maker was of the highest 
order. His most striking investigations were directed to the 
distribution of the stars. He concluded that the entire sidereal 
system is of lens shape, the edge being formed by the Milky Way.^ 
The diameter of the lens is about five times the thickness. Our 
sun is not far from the centre of this lens (Fig. 72). 

Closely linked with HerscheFs conception of the form of the 
Universe was his immense series of observations on nebulae, of 
which he discovered many hundreds. He found, as had Galileo 

* A similar conclusion had been reached in 1750 by Thomas Wright 
(1711-86) and in 1755 by the philosopher Immanuel Kant (1724-1804). 


Morphology of the Universe 

before him, that some of the nebulous appearances could be re- 
solved into star clusters by instruments of sufficiently high power. 
At first he considered that all nebulae were of this nature and that 
they represented ‘island universes* outside our own. Later, how- 
ever, he concluded that some nebulae, at least, were composed of 
‘a shining fluid, of a nature totally unknown to us* (1791). He 
finally came to the conclusion that such shining fluid might gradu- 
ally condense, the points of condensation forming stars and the 

Fig. 71. Precession and Nutation. The axis of the earth moves, in the 
course of centuries, in such a way that a point on it, the North Pole for 
instance, describes a circle (dotted line). This produces the phenomenon 
known as ‘ precession of the equinoxes Added to this motion, as Bradley 
showed, was another, that of 'nutation', producing waves in the circle, in 
fact a ‘gently undulating ring'. In the figure the undulations are enor- 
mously exaggerated. 

whole forming a star cluster which might pass into a single star 
or star group (1814). 

Linked also with his conception of the general form of the 
sidereal system was his view as to the movement within it of the 
solar system. It had been known since the time of Halley that 
certain stars move relatively to each other. Basing his opinion 
on the nature of their apparent movement, Herschel concluded 
that the entire solar system is itself progressing towards a point 
in the constellation Hercules (1805). 


The Mechanical World 

Herschel always emphasized the fact that stars are not merely 
scattered at random. In considering their distribution he noted 
that many were in closely contiguous pairs, ‘ double stars On an 
average the less bright would be the more distant. Owing to the 
orbital displacement of the earth, such pairs can be viewed, at 
intervals of six months, from two points i8o million miles apart. 
The perspective relations thus involved make it theoretically pos- 

Fig. 72. Section of the Universe according to Herschel’s Lens-theory. 

sible to estimate the relative distances of the two members of a 
pair. Herschel pursued this idea with extraordinary tenacity over 
a period of many years, mapping out the places and aspects of 
numerous double stars. At last (1802) he was able to show that 
some of these stars circulate round each other. In their manner 
of doing this they follow the mathematical formulae of the laws 
of gravitation. Those laws, enunciated by Galileo for bodies on 
our earth and shown by Newton to rule the solar system, were 
now to be demonstrated among the distant stars. 

(ii) Dynamical Astronomy, 

In the eighteenth century, in the absence of any knowledge of 
the exact distances and movements of the stars, mathematical 
analysis could be applied only to the solar system. The distances 
from each other of the members of this system as well as their 
proportional sizes became fairly known. The demonstration of 
Newton for certain of them-^ad left a presumption that all 
attracted each other according to the law of gravitation. The 
problem was to fit the exact consequence of that law to the move- 
ments which were revealed by progressively more exact observation . 


Morphology of the Universe 

This was the main task of the mathematicians of the age. 
Among them a foremost place must be accorded to the German 
philosopher and statesman g. w. leibniz (1646-1716), a man of 
very varied talents. His mathematical and scientific activity began 
after a visit to Huygens in Paris (1672) and to Boyle and others in 
London (1673). During three years* subsequent residence in Paris 
he devoted himself to mathematical study under Huygens. From 

Fig. 73. Illustrating the path of a point moving in a varying ellipse. 

this there resulted the conception of the ‘differential calculus* 
on which the work of subsequent mathematicians was based. 

The first formal publication of the method (1684) was preceded 
and followed by many years of controversy in the learned world 
on the question as to whether the priority rested with Newton 
(p. 252) or Leibniz. In fact, however, the nomenclature adopted by 
subsequent investigators was that of Leibniz. 

LEONHARD EULER of Basel (1707-83), who early became blind, 
showed that certain irregularities in the earth*s movement between 
the time of Ptolemy (p. 83) and his own were best explained by 
supposing that our planet is moving in a path which is a ‘ varying 
ellipse* and not a fixed one (1756, Fig. 73). This variation had 
pursued such a course that the axis of the earth's orbit had 
altered about five degrees since the time of Ptolemy. 


The Mechanical World 

j. L. LAGRANGE (1736-1813), of Turin and Paris, one of the 
greatest mathematicians of all time, made an important contribu- 
tion concerning certain irregularities in the moon's motion. It 
had been known since Galileo that while the moon always turns 
the same face to us, yet there are parts near her edge that are 
alternately visible and invisible to us. Lagrange showed that this 
was best explained on the assumption that neither earth nor moon 
is truly spherical. Neither could therefore be treated as though 
the force of gravity acted at its centre (1764), as Newton originally 
thought (p. 253). 

Lagrange distinguished two types of disturbance of members 
of the solar system : {a) periodic, which complete a cycle of changes 
in a single revolution or a few revolutions of the disturbing body, 
and (^)) secular, in which a continuous disturbance acts always in 
the same direction and presents no evidence of a cyclic factor. 
The disturbance of one member of the solar system by another 
depends both on the relative position of the two bodies and also 
on their orbital sizes, shapes, planes of movements, &c., the quanti- 
ties that are known mathematically as the elements of the orbit. 
The relative position of the planets is constantly changing. Thus 
they produce changing disturbances one upon the other, the 
effects going through periodic cycles. But apart from these, there 
are disturbing forces based on the orbital elements themselves 
which give rise to changes in the orbital elements of other bodies. 
These secular changes in the orbital elements are in general very 
small, but they accumulate continually. 

In the discussion of the periodic and secular movements of the 
members of the solar system there was a constant interdigitation 
of the work of Lagrahge and that of p. s. laplace (1749-1827). 
That remarkable man spent his life at Paris pouring out a stream 
of books on astronomical and mathematical subjects. He did not 
permit his activities to be greatly interrupted either by the 
Revolution or by later successive governmental changes. His first 
major contribution was to show that an observed, very slow in- 
crease in the moon's rate of motion round the earth is explicable 
as due to a corresponding slow decrease of the eccentricity of the 
earth's orbit. This change in its turn is being produced by the 
gravitational action of the planets (1787). The order of change is 


Morphology oj the Universe 

such that the length of the month decreases by about ^ second 
per century. 

As long ago as 1650 irregularities in the motion of Jupiter and 
Saturn had been suspected. Halley had noted them (1676). They 
were thought to be of a secular nature. Laplace, working on 
suggestions of Lagrange, showed that the inequalities corresponded 
to a period of about 900 years. This was the starting-point of a 
series of most remarkable investigations by Lagrange and Laplace 
on secular inequalities (i773-*84). The final result was the follow- 
ing general law : 

Take for each planet the product 

mass X Ij (axis of orbit) X (eccentricity) 

Add together these products for all the planets. 

The resulting sum is then invariable, except for periodic in- 

This law establishes the existence of a constant stock or fund 
of eccentricity for the solar system. The total of this fund cannot 
be altered. If the eccentricity of one planet be increased, that of 
another must be diminished. (In fact nearly the whole fund is 
absorbed by Jupiter and Saturn.) The law forms a sort of guaran- 
tee of the stability of the solar system. 

The work of the eighteenth-century astronomers was summed 
up by Laplace in his great Celestial Mechanics (1799-1825). Its 
object he declares to be *to solve the great mechanical problems 
of the solar system and to bring theory to coincide so closely with 
observation that empirical equations should no longer be needed'. 
It is the most comprehensive attempt of its kind ever made. With 
its completion the Newtonian problem seemed solved. The move- 
ments of the known members of the solar system were deducible 
from the law of gravitation. The discrepancies were so small, 
compared to those which had already been removed, that the 
impression was created that they too would be removed by more 
careful observation or by some correction of calculation. 

Laplace's name is indissociably linked with his ‘nebular 

* * Eccentricity ’ is the technical term for the ratio, in an ellipse, of the 
distance between the foci to the whole length of the major axis. For 
ellipses approaching a circle it is very small and it approximates to unity 
as the ellipse lengthens (see Fig. 26). 


The Mechanical World 

hypothesis ' which appeared in his popular but nevertheless scientifi- 
cally valuable Essay on the System of the World (1796) . He pointed 
out that the motions of all the members of the solar system — some 
thirty to forty motions — were in the same direction.* All the 
motions were in planes but slightly inclined to each other, and 
the orbits of none were very far from circular. Attention was 
at the time being drawn to the nebulae by Herschel (p, 262). 
Laplace suggested that the whole solar system had condensed out 
of a vast rotating atmospheric mass, a huge gaseous nebula, that 
filled the bounds of the present solar system. The conception 
struck the imagination of the age and has remained an integral 
part of general thought concerning the cosmos. 

The death of Laplace took place just a century after that of 
Newton. The two events provide convenient landmarks in the 
history of science. 

Two most remarkable observations, the direct result of theo- 
retical considerations, were made in the first half of the nineteenth 

The first of these was made on the basis of the numerical 
sequence known as 'Bode's law' (j. E. bode, 1747-1826) which 
had been set forth as early as 1772. If to each member of the 
simple sequence 0, 3, 6, 12, 24, 48, 96. (each figure being double 
the previous) the number 4 be added, producing 4, 7, 10, 16, 28, 
52, 100, we obtain approximately the proportionate distances from 
the sun of Mercury, Venus, Earth, Mars, Jupiter, Saturn with blank 
for the number 28. Unsuccessful search was long made for this 
missing planet. In 1801 giuseppe piazze (1746-1826) of Palermo 
found a very small planet, which he named Ceres, about a quarter 
the size of the moon, at the required distance. This directed the 
general attention of astronomers to the possibility of finding more 
such small bodies. Since that time over a thousand of these 
‘minor planets' or asteroids have been found, most of them in 
very similar orbits to that of Ceres and nearly all circling between 
the orbits of Mars and Jupiter. It is suggested that they represent 
an exploded larger planet of which meteors may also have been 

* The motion of the satellites of Uranus is, in fact, in the opposite direc- 
tion, but this had not emerged very clearly at the time Laplace was writing. 


Morphology of the Universe 

The second and more famous of these discoveries anticipated 
on theoretical grounds was that of a major planet. The existence 
of this body was betrayed by irregularities in the movement of 
the planet Uranus. In 1846 John couch adams (1819-92) of 
Cambridge and u. j. j. le verrier (1811-77) of Paris, working 
quite independently, indicated the part of the heavens where the 
perturbing body was to be found. Telescopic search revealed it 
as foretold and it was given the name Neptune. 

A constant desideratum of astronomy has been a determination 
of the distance of stars. This can be done by measuring the angle 
that the earth’s orbit subtends to a star. The angle is so exces- 
sively small that its observation presents great experimental diffi- 
culties. These were first overcome in 1832 by thomas Henderson 
(1798-1844). His result was not published till 1893, while that of 
F. w. BESSEL (1784-1846) appeared in 1838. 

(iii) Astrophysics, 

By the first quarter of the nineteenth century there had 
developed clear ideas of the general structure of the universe and 
mathematical conceptions of the forms, dimensions, and relations 
of its constituent members. There was, however, little positive 
knowledge of their physical and none of their chemical constitution. 

The possibilities of a science of astrophysics may be said to have 
opened with the nineteenth century, w. h. wollaston (1766- 
1828), examining the solar spectrum in 1802, observed dark 
streaks crossing the coloured band, which he took to be boundaries 
of the natural colours. Some twelve years later a self-educated 
Bavarian instrument-maker, Joseph fraunhofer (1787-1826) 
attached a telescope to the prism and examined the spectrum 
much more closely. He found that the resulting spectrum ex- 
hibited numerous black transverse lines of constant position 
(1814). Similar lines were visible in all forms of sunlight, whether 
direct, as from the sun itself, or reflected as from the clouds, 
moon, or planets. In the spectra from the stars, on the other hand, 
the distribution of lines was different. 

In 1859 the two Heidelberg professors, gustav Robert kirch- 
HOFF (1824-87) and R. w. bunsen (1811-99), succeeded in showing 
that there was an invariable connexion between certain rays of 


The Mechanical World 

the spectrum and certain kinds of matter. The assurance of their 
conclusion was certified by their discovery, through the spectra 
alone, of two new elements [Caesium and Rubidium), Kirchhoff 
went on to demonstrate certain essential characteristics of spectra 
and so was able to determine the existence in the sun of a large 
number of elements. 

With the advent of the spectroscope and its application to the 
heavens, all departments of astronomy became intimately linked. 
It must suffice to attempt a mere enumeration of, some of the 
results of this modern phase which opened with William Herschel. 

The subject of double stars, to which Herschel drew attention, 
was particularly developed by f. g. w. strove (1793-1864) and 
his successors at St. Petersburg, working at first with telescopes 
constructed by Fraunhofer. A great many multiple stars have 
been made known. Their numbers render it certain that the forces 
that have given rise to our universe have a special tendency to 
the production of these multiple bodies. 

No general picture of the universe can be formed unless the 
laws of the motions of the stars are known. The proper motions 
of a few stars were known to Herschel. In 1837 w. a. argelander 
(1799-1875) knew about 400. The number now known is many 
thousands. In recent years great stress has been laid on the preva- 
lence among brighter stars of opposite stream-flows towards two 
regions in the Milky Way. This is presumably due to the motion 
of the solar system as a whole, which can thus be estimated. 

Spectroscopic research from Kirchhoff's time has been persis- 
tently directed towards the sun. The majority of elements have 
been identified in the sun. During an eclipse of 1869 the solar 
spectrum was found to include a gas to which the name ' helium' 
was given. Twenty-seven years later the gas was obtained on our 

The conception of the physical conditions of the sun has under- 
gone a very great change in the century since Herschel. Much 
attention has been paid to the sun-spots which were shown, as 
early as 1843, to have a definite period, a definite distribution and 
order of appearance, and a rate of rotation which is different in 
different solar latitudes. The relation of sun-spots to terrestrial 
magnetic storms is remarkably constant. 


Morphology oj the Universe 

The solar prominences observable by the eye only during eclipses 
can be examined by means of the spectroscope during full day- 
light (1868). Investigations have shown that the prominences 
increase and decrease in harmony with the sun-spots. The pro- 
minences originate in a shallow gaseous layer, the chromosphere, 
which is distinguished from the brilliantly incandescent inner 
layer the photosphere. Between the two is a narrow ‘reversing 
layer* detectable only during eclipses and exhibiting special 
spectroscopic properties. 

A very important principle associated with the name of Chris- 
tian DOPPLER (1803-53) was introduced in 1842. According to 
‘Doppler’s principle’ the movement of a spectrum-yielding body 
or part of a body can be measured by the shifting of lines in its 
spectrum. This has rendered possible the estimation of the sun’s 
rotation rate and also of the rate of approach and recession 
towards or away from us of various stars. 

3. The Terrestrial Globe, 

(i) Measurement of the Earth, 

The size of the earth was the subject bf discussion from an early 
date. That it was an exact sphere was assumed at least from 
Aristotelian times (p. 47). An exacter mode of measuring angular 
elevation became possible with the invention of the telescope. 
With its aid an estimation of the length of a degree was under- 
taken (1669-71) for the Academie des Sciences by jean Picard 
(1620-82, p. 257). The figure reached was 69*1 miles, which was a 
large variant from that of 60 miles which had been the estimate 
generally accepted. The method adopted by Picard was in prin- 
ciple that of Eratosthenes (p. 70), a star being used instead of 
the sun. Picard’s result was issued in a somewhat inaccessible 
form (1671). Thus it was at first missed by Newton, who, in 
ignorance of it, abandoned for some years his calculations, based 
on earlier measurements, seeking to identify gravity as the force 
that kept the moon and planets in their orbits (p. 252). 

Soon after Picard’s determination the Academie organized an 
astronomical expedition (1671-4) to Cayenne in French Guiana, 
then occupied by a Fre'nch commercial company. Cayenne is in 


The Mechanical W arid 

latitude 5®. It was found that, to keep time there, the pendula 
of the clocks set for Paris in latitude 49® had to be shortened. 
The explanation of this, as we now know, is the bulging of the 
earth in the region of the equator. Gravitation decreases as 
we pass southward, since we are also getting farther from the 
earth*s centre, and the pendulum therefore swings slower and has 
to be shortened if it is to keep time. 

The results of the Cayenne expedition were published in 1684. 
In 1673 Huygens in his Horologium oscillatorium (p. 258) had set 
forth the relation between the length of a pendulum and time of 
oscillation. This principle, together with the measurement of 
Picard, was utilized by Newton for the investigation of the figure 
of the earth in the Principia (1687). 

Between 1684 and 1714 long series of pendulum measurements 
were undertaken in France by G. D. Cassini (p. 259) and his son 
Jacques (1677-1756). The results of these suggested that the 
form of the earth is that produced by the rotation of an ellipse 
round its major axis (a prolate spheroid). 

This conclusion was in discord with that of Huygens and New- 
ton. Thus the form of the earth became a main subject of scientific 
discussion, and several expeditions went forth to make measure- 
ments and to take pendulum observations. Of these, the most 
important left Paris in 1735 for South America under c. m. de 
LA CONDAMINE (1701-74) to determine the length of a degree of 
longitude in the neighbourhood of the equator. The expedition 
laid down a famous and well-measured base, still spoken of as the 
‘Peru line'. In 1738 it was proved by p. L. m. de maupertuis 
(1698-1759), who had been a member of a similar expedition to 
northern Sweden, that the form of the earth was that derived from 
the rotation of an ellipse round its minor axis (an ohlate spheroid). 
These results came to be finally accepted about the middle of the 
century, when the era of exact geodetic survey begins. 

If the French excelled during this period in the exactness of 
their observations, the English made such observations possible 
by the skiU and ingenuity of their instrument-makers. Thus 
GEORGE GRAHAM (1673-1751) invented the so-called 'dead beat 
escapement' of clocks and also the mercurial pendulum which 
remains always of the same effective length, since any expansion 


The Terrestrial Globe 

by heat of the rod is compensated by expansion of mercury in a 
suspended jar. He constructed astronomical instruments for 
Halley and Bradley and geodetic instruments for Maupertuis. 
JOHN HARRISON (1692-1776) — ‘Longitude Harrison’ — devised the 
self-compensating gridiron pendulum (1726) and also amaintaining 
mechanism by which a clock continues to go during the process of 
winding. He is especially remembered for his chronometer which 
made possible, for the first time, the exact determination of longi- 
tude at sea. The instruments of jesse ramsden (1732-1800) were 
no less renowned. Best known of them was his instrument known 
as an ‘Equatorial' (1774), which can be adjusted so as to cause a 
telescope to follow by clockwork the apparent motion of any point 
in the heavens to which it was directed. Modifications of it are in 
use in every modern observatory. Of comparable value was his 
engine for dividing mathematical instruments. He also completely 
transformed the surveying instrument for measuring angles, 
known from Elizabethan days as the ‘ theodolite'. 

(ii) Cartography. 

It was a period of great exploratory activity. Exacter deter- 
minations of the position of geographical points were constantly 
being recorded, and a more scientific cartography came into being. 
The numerous longitudes observed by Picard and his associates 
were utilized in 1679 ^ France drawn up for the 

Academic by G. D. Cassini (p. 259), who also issued a good map of 
the world in 1694. The interest thus aroused produced a number 
of firms of map-makers, and several States appointed carto- 
graphers. At Venice was founded the earliest geographical society, 
the Accademia Cosmographica dei Argonauti. The French excelled 
in cartography for most of the eighteenth century. Especially 
prominent was j. b. bojrguignon d'anville (1697-1783), many 
of whose admirable maps were in current use until a century ago. 
He was merciless to legend, preferring to leave the interior of 
Africa blank to filling it fancifully, and rejecting the conception 
of an Antarctic continent covering half the southern hemisphere. 
He portrayed China (1718) according to surveys conducted by 
Jesuit missionaries under the Emperor Kanghi (reigned 1661- 
1721). D'Anville devoted much attention to the history of his 




The Mechanical World 

science. For long the best topographical work was the Carte 
g/om/trique de la France, based on surveys carried out (1744-83) 
by c. F. CASSINI (1714-84) and his son Jacques dominique (1748- 
1845), and issued in 1793. 

In the second half of the eighteenth century a number of factors 
contributed to the furtherance of maritime exploration. The 
accurate determination of longitude at sea was made possible by 
the chronometers of * Longitude Harrison*. The conditions of 
seamen were ameliorated by the use, on the recommendation of 
the British naval surgeon james lind (1736-1812), of orange and 
lemon juice as a preventive of scurvy, then the main obstacle 
to long sea voyages. The three voyages of Captain james cook 
(1728-79) which occupied the last twelve years of his life will 
always be memorable. It has been said that Cook*s monument is 
the map of the Pacific. In cartographical achievement he is, how- 
ever, rivalled by the two French officers j. F. de galaup, comte de 
LA perouse (1741-89), and j. a. bruni d’entrecasteaux (1739- 
93), who began the exact record of geographical points in Chinese 
and Japanese waters and in the Easterh Archipelago. 

The labours of explorers of this type mark the opening of the 
exact scientific stage of topographic development. In 1787, work- 
ing with a theodolite provided by Jesse Ramsden (p. 273), General 
WILLIAM ROY (1726-90) measured a base line for the triangula- 
tion of the British Isles that was to lead up to the Ordnance 
Survey. The primary triangulation was not completed till 1858, 
but the detailed survey was begun in 1791, the first inch-to-the- 
mile sheet was issued in 1801, and the first six-inch-to-the-mile 
sheet (that is i in 10,560) in 1846. 

Other countries have followed along somewhat similar lines but 
at later dates. Proposals in France to replace the Cassini map 
were held up by war, and no steps were taken till 1817, The map 
was brought to final completion only in 1880. Among continental 
surveys, of special interest as presenting peculiar difficulties is the 
beautiful map of Switzerland published in 1842-65 and based 
on a triangulation completed in 1833. The scale, however, as 
with all continental maps, is less than that of the Ordnance 


The Terrestrial Globe 

(iii) Wind and Water. 

Along with the exploration of the globe there developed a desire 
to reach some generalized conception of its phenomena, its 
magnetism, the watery atmospheric envelope, the tides, the cur- 
rents, the winds, and the climates. 'Geophysics', the body of 
knowledge thus collected, is a quite modern term (1888), but the 
kind of inquiry that it represents came into prominence in the 
eighteenth century. 

The knowledge of the prevalent winds was brought into rela- 
tion with the study of the earth as a whole by Halley (p. 260), 
who published in 1686 his account of the trade winds and mon- 
soons. The map which accompanies it shows a clear line of 
demarcation between the variable winds of the temperate zones 
on the one hand and the more reliable tropic winds on the other, 
along a line which runs at about 30 degrees both north and south 
of the equator. Halley was the first to connect the general circula- 
tion of the atmosphere with the distribution of the sun's heat over 
the earth's surface. In a later version of this map (1700) he added 
observations of the deviations of the magnetic compass, indicating 
the lines of equal variation (see p. 277). 

GEORGE HADLEY (1685-1768) enunciated in 1735 the still cur- 
rent theory of trade winds as the resultant of the rotation of the 
earth and the displacement of air by tropical heat. Later the 
same view was taken by Dalton (1793). The first general work on 
winds was produced in 1742 by the French mathematician jean 
LE ROND D'ALEMBERT (1717-83). Of the meteorological advances 
during the century, following the appearance of this work, the 
most significant were perhaps the investigations on the watery 
content of the atmosphere (1783) by H. B. de saussure (1740-99) 
of Geneva, the balloon ascents to ascertain the properties of air 
at high altitudes, notably by Gay-Lussac (1804), the introduction 
of the 'wind scale' (1805) by Admiral Beaufort (1774-1857), and 
the theory of dew set out (1814) by the American Charles wells 

A new outlook on geophysics was introduced by the American 
naval officer Matthew fontaine maury (1806-73). From 1839 
onward he occupied himself in extracting from logbooks great 


The Mechanical World 

numbers of observations of winds, currents, temperature, and so 
forth. By collating these he was able to draw up marine charts 
which led to such shortening of passages that an international 
conference was called in 1853 consider further organization of 
such observations. Maury's Physical Geography of the Sea (1855) 
is the foundation work of modem knowledge on the subject. 
Largely as the result of his work, meteorological offices were 
established by several governments, and the international meteoro- 
logical services initiated. In England the first director of the 
Meteorological Office, Admiral Robert fitzroy (1805-65), was 
appointed in 1855. Darwin had sailed with him twenty years 
previously in the Beagle, and he is still remembered by the ‘ Fitz- 
roy barometer'. 

Of all aspects of geophysics, the theme of the tides has perhaps 
attracted the greatest amount of scientific ability. Kepler and 
Galileo devoted attention to the subject. Newton, in the Principia 
(1687), placed the theory of the tides on a gravitational basis. 

An adequate exposition of the tides is a very difficult task, nor 
is the tidal theory of Newton applicable to the prediction of the 
times or the height of tide at any required place. Newton, however, 
did give a satisfactory explanation of many of the characteristics 
of tides. The Newtonian view was expounded by Halley for the 
benefit of King James II, and this exposition has since become 
traditional in text-books. It is illustrated by a diagram to be 
found on the first plate of nearly every school atlas. The diagram 
is misleading since the problem is represented as one of statics 
when it is, in fact, one of dynamics. An easy presentation of the 
problem of tides is one of the desiderata of the art of scientific 

(iv) Terrestrial Magnetism. 

The subject of terrestrial magnetism has been especially studied 
because of its importance to navigation. An immense mass of 
data was collected, though there were few general ideas to connect 
them until long after our period. That the magnetic compass does 
not normally point to the true north is said to have been discovered 
by Columbus during his first voyage to America in 1492. The 
degree by which it departs from this line is known as the declina- 

The Terrestrial Globe 

Hon or variation. That the compass suspended about a horizontal 
needle in the magnetic meridian will also dip was discovered at 
the end of the sixteenth century. The degree of dip is known as 
the inclination, Gilbert (1600, p. 188) knew that both declina- 
tion and inclination were different in different places. In the early 
years of the seventeenth century it was found that the declination 
varied in the course of years in the same place. George Graham 
(p. 272) showed in 1724 that there was also a diurnal change in 
the declination. Much work was done by Halley on the difference 
in the degree of declination in different parts of the world. In 
1700 he drew up an interesting chart in which the distribution of 
equal degrees of declination in the earth's surface is represented 
by lines, isogonic lines as we now call them. The method, here used 
for the first time, has since been adopted for innumerable other 
terrestrial variations such as isoclinals (lines of equal magnetic 
dip), isomagnetics (lines of equal magnetic force), isobars (lines 
of equal barometric pressure), isotherms (lines of equal tempera- 
ture), and the like. 

Between 1756 and 1759 ^ number of observations by John Can- 
ton showed that on certain days the movements of the compass 
were conspicuously irregular and that the Aurora borealis was then 
often visible. These phenomena, it was soon realized, were related 
to the occurrence of sun-spots. 

Another landmark in the history of terrestrial magnetism was 
the discovery, towards the end of the eighteenth century, that the 
intensity of the magnetic force varies at different parts of the 
earth. The first published observations on this subject were those 
made in equatorial America (1798-1803) by Humboldt. In 1827 
Arago showed that this intensity also exhibits diurnal variation. 
In 1834 the mathematician k. f. gauss (1777-1855) instituted at 
Gottingen the first special observatory for terrestrial magnetism. 
He greatly improved the type of instrument for magnetic observa- 
tions. In 1840 a number of magnetic laboratories were estab- 
lished in various parts of the British Empire under the general 
superintendence of edward sabine (1788-1883), who had long 
been occupied on the subject. His numerous publications on 
terrestrial magnetism issued between 1823 ^ind 1871 are still 
currently referred to. 


The Mechanical World 

(v) Early Views of Earth History, 

That something of the history of the earth might be learned 
by a study of its crust was believed from of old. Much positive 
mineralogical knowledge accumulated from the mining industry. 
Among the most puzzling phenomena presented by the crust of 
the earth was that of fossils. The Dane niels steno (1648-86), 
who spent some years in Italy, discussed the formation, displace- 
ment, and destruction of the stratified rocks in Tuscany (1669) 
and recognized the orgahic origin of fossils. A number of Italian, 
English, and French writers concurred with Steno, and during 
the first three-quarters of the eighteenth century there was an 
extensive accumulation of geological data and many theories 
were proposed to explain them (p. 239). 

The first comprehensive general account of the history of the 
earth, which included a consideration of the nature of fossils* 
was put forward by georges louis leclerc, comte de buffon 
(1707-88) in his tipoques de la Nature (1778). Buffon in forming 
his theory laid special stress upon certain data not all of which can 
now be interpreted as he would have had them. He held in mind 
primarily [a) the oblate spheroid form of the earth ; (6) the con- 
trast between the small amount of heat received from the sun 
and the large supply possessed by the earth ; (c) the effect of the 
earth's internal heat in altering the rocks ; and (d) the presence of 
fossils in all sorts of situations, even mountain tops. In associa- 
tion with the last he noted that limestone in north Europe, Asia 
and America often consists largely of the remains of marine 
organisms; and that the remains of large terrestrial animals, 
more or less similar to living forms, often occur near the surface, 
showing that they were recently living, whereas the deeper-lying 
remains of marine creatures in the same region belong to extinct 
forms or to forms related only to the inhg.bitants of far distant 
seasw He conceived that the earth (and other planets) arose from 
the collision of a comet with the sun. Thus arose a molten spheroid, 
the history of which can be divided into seven epochs, thus: 

ist epoch. Incandescent to molten. 3,000 years. 

2nd epoch. Gradual consolidation. Rents in crust allow influx of 
molten metallic ores. 35,000 years. 


The Terrestrial Globe 

3rd epoch. Atmospheric vapours precipitated as the primitive 
universal ocean. Continents appear. Life begins in 
waters and marine sediment accumulates. 15-20,000 

4th epoch. Access of internal heat. Period of violent volcanic 
activity. 5,000 years. 

5th epoch. Calm restored. Equatorial regions still too hot for 
habitation. Life over polar areas where dwell huge 
terrestrial animals, elephants, mastodons,, rhino- 
ceroses, &c., which now came into existence. Fauna 
and flora gradually migrate southward. 

6th epoch. Land mass broken up. Man appears. 

7th epoch. Man asserts his supremacy. This epoch will continue 
till the earth cools and life becomes extinct. 

The scheme is historically important both as the first effective 
attempt to explain observed and collected facts bearing on the 
history of the earth, and also as an estimate of many geological 
formations as of very slow growth and of great antiquity. It pro- 
vided a basis for inquiry. In common with most early schemes it 
laid great stress on volcanic activity, earthquakes, explosions, 
and other dramatic events. 

Despite the remarkable insight of the accomplished Buffon, 
and the attractiveness and popularity of his literary style, the 
geological dictator of the age was abraham gottlob werner 
(1750-1817), a teacher at the school of mines at Freiburg, who wrote 
hardly anything at all, did not travel, and whose teaching was 
vitiated by his belief that the sequence of rock masses which he 
recognized in his native Saxony was of universal application. 

Werner was an unusually successful teacher, and through his 
pupils the physical features of rocks all over the world became 
more widely known. His main doctrine was that of the aqueous 
origin of rocks, and his followers, known as Wemerians or 
* Neptunists were opposed by those who stressed the influence of 
subterranean heat, the * Vulcanists'. The influence of Werner 
continued long after his death and reached the youthful Charles 

Very important in the history of geology is the influence of the 
French naturalist Cuvier (p. 329). He realized that the evidence 
of the rocks reveals a succession of animal populations. He 


The Mechanical World 

perceived that vast numbers of species, many no longer existing, 
appeared upon the earth at different periods. Following Lin- 
naeus, he was a firm believer in the fixity and unalterability of 
species, though his contemporary Lamarck (p. 379) was engaged 
in putting forward the opposite view. Cuvier had, however, to 
account for the extinction of some forms of life, and for what 
seemed the creation, or at least the appearance, of new forms. His 
explanation of these remarkable facts was that the earth has 
been the scene of a series of great catastrophes. He believed that 
of the last of these catastrophes we have an historic record. It 
is the flood recorded in the Book of Genesis. He expressly 
denied the existence of fossil man of great antiquity. 

(vi) Stratigraphy, 

The work of james hutton (1726-97) initiates a more modern 
attitude. He travelled widely in order to study rocks, and satisfied 
himself that it is mostly in stratifications that fossils occur. He 
saw clearly that the imposition of successive horizontal layers is 
inexplicable as a result of a single great flood but suggests 
rather a quiet orderly deposit over a long period. In his Theory 
of the Earth (1795) he interpreted the strata as having once been 
the beds of seas, lakes, marshes, &c. 

It was soon recognized that rocks often contain fragments 
from lower layers, nor could the fact be missed that stratified 
series are often tilted, bent, or broken. Many, encouraged by 
Cuvier's doctrine of 'catastrophes', ascribed these irregularities to 
violent upheavals. In this connexion it is interesting to observe 
that the Essai sur la geographie mineralogique des environs de 
Paris (1811) of Alexandre brongniart (1770-1847), though 
written in collaboration with Cuvier, inclines more to the views 
of Hutton. 

WILLIAM SMITH (1769-1839), a civil engineer, obtained an in- 
sight into the nature of strata while cutting canals. He published 
the first coloured geological map (1815). His Stratigraphical 
System of Organised Fossils (1817) showed that certain layers have 
each their characteristic series of fossils. Some members of a 
series are wont to occur also in the layer below, others in the 
layer above, others in all three. Therefore changes in the flora 

The Terrestrial Globe 

and fauna which these fossils represent could not have been sud- 
den. He saw, too, that the farther back we go, the less like are the 
fossils to forms still living. 

A third British geologist, Charles lyell (1797-1875), finally 
exorcized the catastrophic demon. He took to the study of geology 
while at Oxford, travelled considerably, and was influenced both 
by William Smith and by Lamarck. He saw that the relative ages 
of the later deposits could be determined by the proportion they 
yielded of living and of extinct molluscan shells. In his great 
Principles of Geology (1830-3) he showed that rocks are now being 
laid down by seas and rivers and are still being broken up by 
glaciers, rain, sandstorms, and the like: that, in fact, geologically 
ancient conditions were in essence similar to those of our time. 
Few books have exercised more influence on the course of bio- 
logical thought. Darwin’s early observations were made in the 
light of Lyell’s great work. 

We are struck by the overwhelming share of British investi- 
gators in the early development of geology as a science. The very 
names of the formations suffice to establish the British share in 
the development of the science. Lyell is responsible for Plio- 
cene (Greek, ‘more recent’), Miocene (‘less recent’), and Eocene 
(‘ dawn of recent ’) ; Sedgwick, the Cambridge geologist with whom 
Darwin went on geological excursions, invented Devonian 
(from its predominance in Devonshire), Cambrian (Cambria = 
W ales) , Palaeozoic (Greek, ' ancient life ’) , and C ainozoic (‘ new life ’) . 
Between the last two formations John Phillips of Oxford (1800-74) 
interpolated Mesozoic (‘ intermediate life ’) . Other British contem- 
poraries are responsible for Carboniferous (or ‘ coed-bearing ’) , Ordo- 
vician and Silurian (the Ordovices and Silures are British tribes 
mentioned by Caesar), Permian (from the province of Perm in 
east Russia), and Cretaceous (Latin ' chalky’). On the other hand, 
Triassic (Latin Trias, the number ‘three’) and Jurassic (ivom the 
Jura mountains) were titles given by German geologists at the 
beginning of the nineteenth century. The term Tertiary is older 
and was used by eighteenth-century Italian writers. The tertiary 
formations were held to be the third of a series of which the 
Secondary correspond roughly to the Mesozoic and Palaeozoic, 
and the Primary to the non-fossil-bearing rocks. The word 


The Mechanical World 

Geology itself was effectively introduced (1779) by H. B. de Saus- 
sure (1740-99) of Geneva, founder of modern mountaineering. 

Of all writers on geophysics none has treated the subject so com- 
prehensively and philosophically as Alexander von humboldt 
(1769-1859). His life was largely spent in travel and exploration 
of the most varied kind, and his occupation as diplomatic agent 
in Paris brought him contact with nearly all the leading 
scientific men of his day. Among his positive additions to 
science is the introduction of isothermal lines (1817), and he was 
the first to make a general study of temperature and pressure over 
the globe which has been essential to the modern science of 
meteorology. He was the first to investigate the rate of decrease 
of mean temperature with increased altitude. He made many 
studies of volcanoes and showed that they occur in linear groups, 
presumably corresponding to subterranean fissures. He showed 
that many rocks thought to be of aqueous were really of igneous 
origin. He discovered that the magnetic force of the earth de- 
creases from the poles to the equator (1804). He made the pre- 
liminary steps to a .real geography of plants, studying them in 
relation to the physical conditions in which they grow. None of 
his services, however, is greater than the magnificent production 
in which he summarizes the work of his life, his Kosmos, of which 
the publication was begun in 1845 and completed posthumously 
in 1862. This book has been said to combine the large and vague 
ideas, typical of eighteenth-century thought, with the exact and 
positive science of the nineteenth. It is a truly transitional work, 
but still forms an excellent introduction to the study of geophysics. 

During the first half of the nineteenth century, as geology grew 
into an independent science, the structure of the earth was studied 
from the point of view of the distribution and arrangement of 
its rocks (stratigraphy), from the point of view of the structure 
and composition of its rocks (petrography), and from the point of 
view of the nature and affinities of its fossils (palaeontology). Per- 
haps no country in the world presents so much geological variety 
within so small an area as does England. It is thus not inexpli- 
cable that geology became an especially English science. 'The 
Geological Survey of England and Wales' was begun by Sir 
.THOMAS DE LA BECHE (1796-1855) in 1832. It was far earlier 

The Terrestrial Globe 

in inception and execution than any comparable work produced 
in any other country. 

A series of other English investigators gave to geology its 
rational framework for the detailed research of the next century. 
Thirty years of work by G. poulett scrope (1787-1876), begin- 
ning with his Considerations on Volcanos (1825), marked the end 
of the Wernerian view. He laid the foundations of the current 
theory of volcanic origin and drew attention to their very peculiar 
distribution. Roderick murchison (1792-1871) in his great 
Silurian System (1839) expounded the chronological correspon- 
dence of rocks, introduced much of the nomenclature now in use, 
and explained the nature and incidence of many scenic details. 
His views were shown to be applicable over a wide area by his 
geological exploration of Russia (1841-5). Behind the band of 
British geologists stood adam sedgwick (1785-1873), who 
worked with them all and among them with his pupil Charles 
Darwin (pp. 379 ff.). 

4. Transformations of Matter, 

(i) Rise of Quantitative Method. 

A belief in the indestructibility and uncreatability of matter is, 
in some degree, implicit in many operations outside the scientific 
sphere (p. 230). In the seventeenth century the belief sometimes 
became explicit. Thus Francis Bacon wrote: ‘It is sufficiently 
clear that all things are changed, and nothing really perishes, and 
that the sum of matter remains absolutely the same* {Cogitationes 
de natura rerum, published posthumously, 1653), and there are 
comparable passages in the writings of Boyle (p. 233). The doc- 
trine was given express form by Newton. 

The law on which gravity acts, that of inverse squares, implies 
that the weight of a body is not constant, but varies according to 
its relation with other bodies. But Newton*s second law of motion, 
that ‘ change of momentum^ is proportional to the impressed force * , 
implies that quantities of matter, that is to say masses, are equal 
if they suffer equal changes of motion under the action of equal 
forces, and that, conversely, forces are equal if they produce the 

^ Newton's word is motion, not momentum, but he means what we mean 
by the latter word. 


The Mechanical World 

same changes of motion in the same body. Thus Newton distin- 
guished clearly between mass and weight. The mass of a body is 
proportional to the force that produces a given acceleration in 
the body. This force, in the case of a freely falling body, is the 
weight. Since all bodies fall at the same place with the same 
acceleration, their masses are proportional to their weights at the 
same place. 

This exact and express doctrine of the constancy of weight at the 
same place (provided that other attracting bodies are unmoved) 
was a condition for the development of conceptions concerning 
the nature of physical changes. Without that doctrine the belief 
in any sudden inexplicable or magical appearance is possible. 
With it all changes in the state of matter can, in theory, be ex- 
pressed in terms of number, wdght, and measure. The changes 
that are specially investigated on the basis of weight are those 
known as ‘chemicar. Thus the Newtonian conception gave a 
special impetus to the rationalization of chemistry and provided, 
in effect, the doctrine of the indestructibility and uncreatability 
of matter. 

The investigation of chemical processes in the seventeenth cen- 
tury had yielded, by the dawn of the eighteenth, a vast accumula- 
tion of data for which no satisfactory system of classification had 
been suggested. Antitheses, as acid and alkali, were emphasized 
and tests for them were devised. Categories were invented and 
defined, such as salts (that is soluble, sapid, and crystalline sub- 
stances), earths (that is friable, fire-resisting, and tasteless sub- 
stances), and calces (that is powdery products of heated minerals). 
JAN BAPTIST VAN HELMONT (1577-1644) had indicated the exis- 
tence of various aeriform substances, for which he devised the 
name gas (1644),* which could be condensed, as he supposed, into 
solid bodies and released therefrom by chemical change. He had, 
however, no method of collecting gas. Chemical theory, though it 
had emerged from the alchemical stage, was a confused mass of 
doctrine and tradition. 

The Rev. Stephen hales (1677-1761) devised an apparatus 
for collecting gases by leading them, from the retorts in which 

* Helmont introduced the word *gas' as a representative of the Greek 
word chaos, 


Transformations of Matter 

they were produced by heating, through a pipe to a vessel filled 
with and inverted over water, in the so-called ‘ pneumatic trough 
He was able to measure the volumes of gases produced from 
weighed amounts of solids. He made, howeVer, no further 
chemical examination of these gases because he supposed the 
product to be, in all cases, 'air' which had functioned as a kind 
of cement binding together the particles of the solids that he had 

Chemical technique was, in other respects, advanced and re- 
fined. This process was aided, from about 1670 onwards, by 
apparatus made from the newly introduced transparent flint glass 
in place of the older opaque vessels. The knowledge of the age 
was admirably summarized by the distinguished Dutch physician 
HERMANN BOERHAAVE (1668-1738). His Elements of Chemistry 
(1732) is among the very few great works written expressly as a 
students' text-book. Though exhibiting few new departures, it 
is firmly based on personal experience and is exceptionally lucid. 
Boerhaave held that all chemical events are ultimately reducible to 
relatively few and simple categories, and he believed vital processes 
to be expressible in chemical terms. Boerhaave's attitude gave to 
experimental chemistry a hopeful outlook which supported it for 
more than a generation, despite the paucity of important general 

The most notable chemical development of the earlier eighteenth 
century was the idea of 'affinity'. In 1718 the French physician 
^:tienne FRAN901S GEOFFROY (1672-1731), influenced by Boer- 
haave, drew up tables in which acids were arranged in the order 
of their affinity for certain bases, and metals were arranged in the 
order of their affinity for sulphur. The relative degrees of affinity 
were estimated by ascertaining whether one base turned out 
another base or one metal another metal from a given compound. 
This idea of Geoffroy was further pursued by Black and others 
and notably by Bergman and Berthollet (p. 291). 

(ii) Intensive Study of Chemical Reaction, 

The Scottish investigator Joseph black (1728-99) published 
in 1756 his Experiments upon Magnesia alba, Quicklime, and some 
other Alcaline Substances, Perhaps no brief chemical essay has 


The Mechanical World 

ever been so weighted with significant novelty. Black was a 
cautious investigator and his success was due to the accuracy of 
his measurements. He knew that chalk, by being heated and thus 
turned into quicklime (equation i), ceases to effervesce with acids 
but gains the power of absorbing water (equation 2). As we would 
now formulate it : 

(1) CaCOg = Ca0+C02 (Chalk into quicklime. Gas evolved). 

(2) CaO+HgO = Ca (OHjg (Slaking of quicklime. Water 

Moreover, Black showed that, in the prpcess of heating, the chalk 
loses weight, a loss which, by applying the methods of Hales 
(p. 284), he attributed to the removal of air in the process. And 
it had long been known that if the slaked lime be treated with a 
mild alkali, e.g. carbonate of soda, it is changed back into the state 
in which it was before heating, in fact, into chalk, while the mild 
alkali is converted into a caustic alkadi. The process would now 
be represented thus : 

(3) Ca(0H)2+Na2C03 = CaC03+2Na0H. 

Moreover, he showed that a definite amount of chalk, whether 
heated into quicklime or not, neutralizes an equal weight of acid, 
the only difference being that the neutralization takes place with 
effervescence and loss of weight if the chalk is unheated, and with- 
out effervescence or loss of weight if the chalk is first heated into 
quicklime. Thus: 

(4) Unheated CaCOa (chalk) +2HCI = CaClg+HgO+COg. 

(5) Heated CaO (quicklime) +2HCI = CaClg+HaO. 

The gas given off by chalk in (i)* transferred from one alkali 
to the other in (3) and given off in the effervescence produced by 
the reaction (4), he named * fixed air', thus differentiating it from 
the ordinary air of the atmosphere more clearly than van Hel- 
mont (p. 284) had been able to do in his tentative and chemically 
incomplete work. We now call it ‘carbon dioxide'. The conver- 
sion of quicklime into ordinary chalk by exposure to air: 

(6) CaO+COa = CaCOa, 

proved that carbon dioxide is a normal constituent of the air. 

Black's work is of very great importance as the first intensive 
and detailed study of a chemical reaction. His especial triumph 
consisted in showing that the chemical changes occurring in this 


Transformations of Matter 

series of reactions could, without isolating the 'fixed air’, be 
detected by subjecting them at every stage to the arbitrament 
of the balance. Black had thus discovered a gas different from 
air, which could exist in either the free or combined state, 
could be transferred from combination with one substance to 
another, and had many properties peculiar to itself. It had not 
hitherto been generally and clearly realized that there were any 
kinds of gases distinct from air. Attention was now drawn to this 
fact. The development of a technique for the isolation and study 
of gases and the discovery of the characters and laws of combina- 
tion of gases was the main task of chemical endeavour of the later 
eighteenth and early nineteenth centuries. 

(iii) Gases. 

In 1766 the eccentric philosopher henry cavendish (1731-- 
1810), as exact an experimenter as Black, sent his first paper to 
the Royal Society. It bore the title On Factitious Airs, by which 
he meant gases produced artificially in the laboratory as distinct 
from 'natural’ air. He discovered that a definite, peculiar, and 
highly inflammable gas, which he called 'inflammable air’ — 
'hydrogen’, as we now call it — is produced by the action of acids 
on certain metals. Continuing his investigations on an exact 
quantitative basis he published his Experiments on Air (1784). 
These demonstrated that the only product of the combustion of 
'inflammable air’ (hydrogen) and ' dephlogisticated air' — that is 
oxygen — is water. His figures give an approximately correct 
estimate of the proportions of the two in water. 

Cavendish ascertained the amount of hydrogen evolved by 
action of acids on different metals. Adjusting his figures according 
to modern findings, we may say that he found that one part by 
weight of hydrogen was displaced by twenty-four parts of iron, 
twenty-eight of zinc, or fifty of tin. These numbers correspond 
to the 'equivalents’ of these elements, and were used by him in 
1766 to describe the different weights of different bases that 
neutralized a fixed amount of a given acid. He was the first to 
determine the weights of equal volumes of gases, a very fruitful 
line of research. 

The chemical activities of the Unitarian divine, Joseph priest- 


The Mechanical World 

LEY (1733-1804), were contemporary with those of Cavendish. 
He greatly developed and improved the technique of the prepara- 
tion, manipulation, and study of gases. A series of important 
observations was made by him in the seventies and eighties. He 
showed that green plants would make respired air again respir- 
able, and that they gave off a respirable gas. He prepared and 
studied a number of gases (ammonia, hydrogen chloride, sulphur 
dioxide, nitric and nitrous oxides, nitrogen peroxide), he investi- 
gated nitrogen and silicon tetrafluoride, and he isolated oxygen 
(1774-5) by heating certain oxides. He was hampered by his 
obstinate adherence to the old phlogiston theory. Phlogiston was 
a hypothetical substance supposed to exist in all combustible 
bodies and to be disengaged during combustion. It was ‘the 
matter of fire’ The word phlogiston had been introduced by 
Stahl in 1702 (p. 241). 

Contemporary also with Cavendish and Priestley was carl 
WILHELM SCHEELE (1742-86), a Swedish apothecary and one of 
the greatest of chemical experimenters and discoverers. His 
Treatise on Air and Fire (1777) proved that air consisted of two 
different gases now known as oxygen and nitrogen. Most of this 
research had been carried out before 1773. Thus Scheele’s recog- 
nition and isolation of oxygen really preceded Priestley’s. 
Scheele’s numerous chemical discoveries include, not only oxygen, 
but also chlorine, manganese, baryta, silicon tetrafluoride, hydro- 
fluoric acid, various inorganic acids, and the first extensive range 
of organic acids, glycerol, arseniuretted hydrogen, copper arsenite 
(still known as ‘Scheele’s green’), and many other substances. 
His Treatise and his many memoirs mark him as a rigorous 
experimenter and a concise writer. 

(iv) The Elements. 

The work of Black, Cavendish, Priestley, and Scheele assumed 
that matter was completely ‘conserved’, that is to say, neither 
came into being nor passed out of being in the course of their 
experiments. Further, they assumed weight to be the measure of 
the amount of matter. 

In their day the old view of the four elements, earth, water, 
air. and fire, had not quite gone out of currency. It was, in fact, 


Transformations of Matter 

widely mooted that prolonged boiling converted water into earth. 
This question was tstken up and finally resolved by the great 
French chemist antoine laurent lavoisier (1743-94). He 
began the investigation with a simple but extremely carefully 
conducted series of experiments. By exact weighing he showed 
(1770) that if ordinary water be boiled in a suitably designed vessel 
in such a way that the steam produced is condensed and it and the 
residue weighed, then the weight of the solid particles that remain 
behind corresponds to the weight lost by the water. Thus nothing 
is lost and nothing gained. 

Lavoisier next, investigated the phenomena of calcination of 
metals. This process, it had long been known, results in the 
increase in weight of the calcined metal, an increase which 
Lavoisier was able to show as due to something taken from the 
air (1774-8). This was a serious blow to the phlogiston theory 
(p. 297) . He proceeded to an extensive and quantitative investiga- 
tion of the changes occurring during breathing, burning, and other 
forms of combustion (1772-83). Ip the course of these he dis- 
covered the true nature of respired air, and showed how both 
carbon dioxide and water are products of the normal act of 

If clear grasp of its implication be accepted as the test of a dis- 
covery, Lavoisier was the discoverer of oxygen. We owe the word 
oxygen to him. He proved that in all cases of combustion there 
is a combination of oxygen with the substance burned. He 
repeated the experiments of Cavendish on exploding ‘inflam- 
mable air' (hydrogen) and ‘ dephlogisticated air' (oxygen), and 
thence concluded that water was a compound of these two gases 
(1784). These experiments mark the end of the phlogiston theory. 
Men of science had now in their hands a technique by which the 
laws of chemical combination could be investigated. 

Among Lavoisier's major contributions to science was his 
establishment, once and for all, of the conception of chemical 
‘elements' in the modem sense — ‘simple radicles' was the title 
attached to them by one of his French contemporaries. These 
‘simple radicles', foUowing Boyle, he defines as substances which 
cannot be further decomposed. He divides them into four 
groups: [a) The gases oxygen, nitrogen, and hydrogen, and the 




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‘imponderables 'light and caloric; (6) Elements such as sulphur, 
phosphorus, andcarbon which, on oxidation, yieldacids ; (c) Metals, 
of which he distinguished seventeen ; {d) The ‘ earths ’, lime, mag- 
nesia, baryta, alumina, and silica. These last had not yet been 
decomposed. The same might be said of the ‘alkalis', potash and 
soda, but Lavoisier was so certain that the alkalis were compound 
substances, produced by the union of oxygen with other ‘simple 
radicles', as yet undiscovered, that he refused to include them 
among the ‘simple radicles'. 

Lavoisier was able to recognize correctly twenty- three elements 
in the modem sense, though his actual list was considerably longer. 
Together with de Morveau and Berthollet, in their joint work, A 
New Chemical Nomenclature (1787), he introduced a new system 
of naming substances according to their chemical composition, 
a reform that contributed greatly to the progress of chemistry 
by its rejection of the fanciful and often ridiculous alchemical 
names and the substitution of many now in use. 

Lavoisier is generally regarded as the founder of the modern 
phase of chemistry, which he set forth in his classic Elementary 
Treatise on Chemistry (1789). His writings were widely studied. 
His experiments were models of painstaking ingenuity. Perhaps 
his numerous and varied achievements may be summed up in the 
statement that he gave coherence and clarity to the conception of 
the conservation of matter. All his work was based on the explicit 
assertion of the principle that, within experimental limits, the 
same weight of simple bodies can be drawn from compound bodies 
as had been put into them, no more and no less, and that compound 
bodies represent the combined weight of the simple bodies of 
which they are composed. This view became, with Lavoisier, 
explicit and axiomatic. 

(v) Atomism, 

As the eighteenth century turned into the nineteenth, the ques- 
tion of the innate constitution of matter was again raised. In the 
seventeenth century ‘Epicureanism' based on atomic views had 
become a philosophic vogue. It was opposed to the current 
Cartesianism which it survived. Among early exponents of the 
atomic view were Gassendi (p. 235), whose main work appeared 


Transjormatiom oj Matter 

in 1649, Boyle (p. 233), who treated the subject at intervals 
between 1661 and his death in 1691. Huygens also supported the 
atomic view. Newton, in his calculations of the motions of the 
planets, found it necessary to assume interstellar space to be a 
vacuum. He extended this conception to terrestrial matter and 
thus the conception of atoms naturally arose {Principia, 1687). 
It is, however, difficult to find any definite formulation regarding 
the exact nature of his * corpuscles* or 'particles* in his works. 
But from his time onward, despite the opposition of Leibniz 
(p. 265), the constitution of matter was generally donsidered as 
atomic by physical investigators. The view was popularized and 
widely disseminated by Voltaire (p. 254). 

The older investigators had great difficulty in obtaining their 
substances in a pure state. Indeed, chemical purity is an idea of 
very gradual growth, and is perhaps hardly consistent with the 
older doctrine of the four elements. The work of Black, Cavendish, 
and Lavoisier, however, drew general attention to the high degree 
of exactness possible in chemical operations. This conception was 
pressed by Lavoisier’s fellow countryman Joseph louis proust 
(1755-1826), who was the first to emphasize the constant com- 
position of chemical compounds. With the improved methods 
available for the preparation of pure substances he was able to 
show that a definite compound, however formed, whether in 
Nature or by the hand of man in the laboratory, always contains 
the same 'simple bodies* (i.e. elements) combined in the same 
proportions by weight. This fact is expressed as the so-called 
' Law of Definite Proportions *. Working on this law were several 
chemists. Notable among them was e. g. fischer {1754-1831), 
who prepared a table of equivalents (1802) from the figures of 
j. B. RICHTER (1762-1807) to Correspond to the law of equivalent 

Proust’s conclusions were disputed by claude louis berthol- 
LET (1748-1822), who in his Essay on Chemical Statics (1803) had 
set forth his views on chemical affinity and had criticized the 
development of Geoffrey’s affinity table (p. 285) by tobern olaf 
BERGMAN (1735-84). Bergman, recognizing (1773) that affinity 
tables should be double, one table showing the affinities for 
reactions in solution {the 'wet way*) and the other showing the 

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affinities when the substances were heated together (the *dry 
way*), had drawn up large duplicate tables in his Elective 
Attractions (i775>-83). 

Bergman, moreover, recognized that in some reactions the 
chemical change could be carried to completion only if the amount 
of the reacting substance added exceeded that demanded by the 
amount of the substance acted upon. In more familiar phraseo- 
logy he showed that it was necessary to add more than the 
amount * chemically equivalent *. Berthollet clearly demonstrated 
that the relative amounts of the substances concerned in a 
chemical reaction, together with such factors as insolubility and 
volatility, affected the completeness of the reaction ; that increas- 
ing proportions of one reactant caused the reaction to proceed 
still farther in one direction; and that chemical reactions in 
general were incomplete, the substance upon which two other 
substances acted with opposing forces being divided between 
them in proportion both to their affinities for that substance and 
to the quantities of those substances present. 

From these theoretically sound principles, unfortunately 
neglected for many years, but later to become the basis of modem 
chemical dynamics, Berthollet erroneously concluded against 
Proust that chemical compounds were produced in analogous 
ways, and that their constituents were therefore combined, not in 
fixed and constant proportions, but in proportions that varied 
with the conditions under which the compounds were formed. 
Proust's conclusions were, however, accepted by chemists, and 
his law presently received a new and wider interpretation as a 
result of the atomic speculations of Dalton. 

JOHN DALTON (1766-1844), a Quaker teacher of Manchester, 
had greater philosophic insight than Proust. Dalton’s first im- 
portant contribution to science was his rule that all gases expand 
equally with equal increments of temperature (i8oi). This law 
was about that time more explicitly formulated by the French 
chemist Joseph louis gay-lussac (1778-1850), and his name is 
not unjustly associated with it.' His own ’ law of partial pressure ’ 
(1801) Palton decided might be explained on the atomic basis, ‘ a 
conclusion’, he assures us, ’which seems universally adopted’. 

* Gay-Lussac himself indicated that J, A. C. Charles {1746-1823) had 
preceded him in this discovery but had published no results. 


Transjormations oj Matter 

Dalton's line of thought on the constitution of matter had 
come to him first through his interest in meteorology. His analyses 
of air showed that it was always composed of the same proportion 
of oxygen and nitrogen, with small quantities of water vapour 
and carbon dioxide. He knew that these gases are not in combina- 
tion and have different densities. Why then does the heaviest not 
sink to the bottom and the lightest rise to the top ? These facts 
might be explained if they were all composed of minute particles 
of different sizes in the manner suggested by philosophers of anti- 
quity such as Lucretius (p. 95). Adding to the ancient atomic 
conception the new view that matter was composed of a large 
number of elementary, homogeneous, and distinct substances, 
themselves composed of indivisible, indestructible, uncreatable 
atoms, it must also be assumed that all the atoms of any parti- 
cular element are like each other but different from the atoms of 
other elements. 

This view fitted well to Proust's recently formulated 'Law of 
Definite Proportions' (p. 291). In applying his theory to the facts 
of chemistry, Dalton started with the assumption that chemical 
combination takes place in the simplest possible way, one atom 
of one element combining with one a'tom of another, water being 
composed of H and 0 in a i : i ratio, and ammonia of N and H 
also in a I : i ratio. He assumed also that when two elements 
form more than one compound, higher ratios are possible, as for 
instance with the oxides of carbon (CO and COg). 

Dalton had been working on his theory since the beginning of 
the century and gave it formal enunciation in 1808. The first 
number of his New System of Chemical Philosophy (1808-27) which 
appeared in that year has gained general acceptance as a classic. 
In it he pointed out that, though atoms must be far too small to 
measure or weigh directly, yet nevertheless it should be possible 
to determine the relative weights of atoms of different elements. 
For this we need only know the relative number of atoms combin- 
ing to form a compound, and the relative weights in which* the 
constituent elements combined to form that compound. 

Dalton had very little real experimental guidance as to the 
number of atoms that form compounds. Thus he wrongly assumed 
that, in water, hydrogen and oxygen are combined in the ratio of 


The Mechanical World 

I atom to I atom, instead of in the ratio 2 to i. He then introduced 
experimental error in estimating the relative weight of the hydro- 
gen and oxygen in water as i to 7 (instead of i to 8). Thus he 
ascribed to oxygen the relative atomic weight of 7 instead of 16. 

(vi) Molecular Theory, 

The publication of the atomic theory attracted much attention 
in France, gay-lussac (p. 292) was already working on similar 
lines. He was interested in the combination of gases and showed 
that, when gases combine, their relative volumes bear a very 
simple numerical relation to each other and to the volume of their 
product, if gaseous (1808). Thus one volume of oxygen combines 
with two volumes of hydrogen to form two volumes of water 
vapour ; one volume of nitrogen combines with three volumes of 
hydrogen to form two volumes of ammonia gas, and so on. 

The atomic theory and the findings of Gay-Lussac were clearly 
linked together in the exposition of the Italian amedeo avogadro 
(1776-1856). Avogadro pointed out (1811) that if there is a simple 
numerical relation between combining volumes of gases and if 
they combine into uniform atomic groups, then there must be 
some simple connexion between the actual numbers of these 
atomic groups in equal volumes of combining gases. The simplest 
relation — and that which has been shown to be the real one — is 
that equal volumes of all gases contain in similar conditions the 
same number of atomic groups. Avogadro assumed that the 
atomic groups, as conceived by Dalton, were not indivisible but 
in the simplest case consisted of two parts, separable during 
chemical reaction. The divisible groups he named molecules 
(Latin = ‘ little masses ') . Avogadro also assumed that these mole- 
cules, and not the individual atoms, were equally distributed 
throughout space in the case of all gases (1811). Both assump- 
tions, he observed, fitted Gay-Lussac's law. 

Avogadro's hypothesis, that 'equal volumes of all gases under 
the same conditions of temperature and pressure contain the 
same number of molecules ', was, to the confusion of their subject, 
imfortunately not received by chemists, owing, firstly, to the small 
number ol cases to which it could then be applied, and, secondly, 
to the fact that several of those cases gave anomalous results not 

Transjormations oj Matter 

understood until much later. It was not until 1858, after 
Avogadro's death, that authoritative attention was called to it 
by another Italian chemist, Stanislao Cannizzaro (1826-1910). 
This long eclipse of an important law rendered the results of 
physical chemistry far less profitable than they might have been 
for nearly half a century. 

During this period there was enunciated a hypothesis that 
has had a somewhat similar history. In an anonymous paper 
published in 1815, the English physician william prout (1785- 
1850) called attention to the closeness with which the atomic 
weights of the elements, expressed in terms of relation to hydro- 
gen, approximated to whole numbers. Hydrogen, therefore, he 
regarded as the universal substance. In more modem times there 
was a general movement towards Front's hypothesis of a materia 
prima, and his conception of atomic weights approximating to 
whole numbers has assumed a new significance. 

Much of the chemical activity of the first half of the nineteenth 
century naturally went to the exact determination of atomic and 
molecular weights. Notably the Swede j5ns jakob berzelius 
(1779-1848) devoted himself to this task from 1811 onwards, as- 
certaining the molecular weights of tBousands of substances. He 
also did important work as the founder of electrochemical theory. 
He developed the conception that a group of atoms or radicle can 
form an unchanging constituent through a series of compounds, 
behaving as though it were an element. He rendered a great 
service in establishing chemical nomenclature and developed the 
convenient mode of formulating elements by the capital initial 
letters of their Latin names, adding numerals to indicate the 
numbers of the various atoms present in a compound. 

Many of the most fruitful lines of Lavoisier's work were con- 
tinued by sir HUMPHRY DAVY (1778-1829). Notably he succeeded 
by means of the electric current (p. 307) in resolving the alkalis, 
potash, and soda, and the alkaline earths, baryta, strontia, lime, 
and magnesia, into their elements. Those elements were oxygen 
on the one hand, and a series of metals which he called potassium, 
sodium, barium, strontium, calcium, and magnesium, deriving 
these names from the old terms for the substances in which the 
respective elements were contained (1807-8). He also showed that 


The Mechanical World 

the gas chlorine, prepared by the Swedish chemist Scheele in 1774 
and thought to contain oxygen, was of elementary character 

Davy was especially fortunate in the practical application of 
much of his work. His ‘safety-lamp* still bears his name, and 
deservedly so, for his detailed and important researches on flame 
and explosions made it practicable, though the principle on which 
it is based was discovered by George Stephenson, the engineer. 
He performed a great service to agriculture by codifying, for the 
first time, the mass of chemical knowledge applicable to it. His 
Elements of Agricultural Chemistry (1813) contains the first use in 
the English language of the word Element defined in the modem 
chemical sense : 

‘All the varieties of material substances may be resolved into 
a comparatively small number of bodies, which, as they are not 
capable of being decomposed, are considered in the present state 
of chemical knowledge as elements.* 

At that date Davy recognized forty-seven of these elements. 

An impressive figure in the scientific world of the thirties and 
forties was Justus von liebig (1803-73), professor of chemistry 
first in Giessen and then in Munich. He applied to organic sub- 
stances the exact methods that had been developed in the previous 
decades. Over his laboratory was inscribed ‘ God has ordained all 
things by measure, number and weight*. His great achievement 
was his application of exact chemical knowledge to the processes 
and products of vital activity. (For Liebig's physiological work 
see p. 352.) 

With the work of lothar meyer (1830-95) and dmitri men- 
DELEEFF (1834-1907) the study of chemistry passed into an entirely 
different phase. Their work demonstrated (1869-70) that there 
is a connexion between the atomic weights of the elements and 
their properties. The periodic table which is known by Men- 
deleeff*s name enabled him and other workers to prophesy the 
existence and properties of elements, then undiscovered, but sub- 
sequently isolated. The table in an elaborated and modified form 
is still the basis of modem systematic chemical exposition. 


Transjormations oj Forces 

5. Transformations of Forces. 

(i) The Imponderables. 

The seventeenth century — the age of Galileo — and the eighteenth 
— the age of Newton — established a view of a universe maintained 
by a balance of forces acting on bodies. There was still much 
vagueness as to the limits of the two. Thus, ‘phlogiston*, which 
was supposed to go forth from a body on combustion, and ‘ether* 
which was at once agent and medium of light, no less than the 
electric and magnetic ‘fluids*, remained ambiguous conceptions 
to the very end of the eighteenth century and even into the nine- 
teenth. This group of imagined entities, phlogiston, ether, the 
electric and magnetic fluids, were regarded as weightless sub- 
stances : ‘imponderables*. The confusion of language created by 
the ‘imponderables* persisted in its crudest form. ‘It is the im- 
ponderables — ^heat, electricity, love — that rule the world*, wrote 
Oliver Wendell Holmes — himself a man of science — as late as 
1858 {The Autocrat of the Breakfast Table). 

Among the imponderables a place of special importance was 
occupied by the supposed substance of heat: ‘caloric*. During 
the earlier eighteenth century two views of the nature of heat 
were current. On the one hand, it was generally conceived as a 
fluid held in greater or less quantity within the pores of all bodies. 
Thus when a metal grows hot on being hammered, the heat be- 
comes more perceptible because the caloric, it was thought, was 
squeezed out by the pressure. The material and fluid nature of 
heat was a generally accepted idea which was not greatly dis- 
turbed by the victorious advance of the Newtonian philosophy. 

On the other hand, there were adherents to the suggestion made 
by Boyle (1664), Hooke (1665), and Huygens (1690) that all basic 
physical phenomena — ^heat, light, chemical action, electricity, 
magnetism — ^were susceptible of mechanical explanation. It was 
believed that all were due to the movements on the part of small 
particles of the affected bodies, varying in form, velocity, order 
of arrangement, attractive power, and the like. 

Certain relations between forces of different kinds were, of 
course, evident to every observer. This was the case, for example, 
with the general interconnexions of light with heat and again 


The Mechanical World 

with electricity, and especially of heat with work. The production 
of fire by friction was a device of the highest antiquity ; frictional 
electricity was well known ; the steam-pump was becoming fami- 
liar; the production of heat, light, and sound in a variety of 
chemical and physical Operations was also naturally very familiar. 
Nevertheless no exact relation between these various phenomena 
was yet recognized. 

(ii) Temperature Measurement, 

Methods of estimating temperature were greatly improved 
even before the elucidation of what may seem now the obvious 
distinction between heat and temperature. An air thermometer 
or rather thermoscope had been invented by Galileo about 1592, 
and an open-ended water thermoscope had been described by Jean 
Rey in 1632. A distinct advance, making the passage from the 
thermoscope to thermometer,, was the sealed alcohol indicator, 
invented about 1641, probably by Ferdinand II, Grand Duke of 
Tuscany. It was used for the experiments of the Italian Acca- 
demia del Cimento during its brief life (1657-67). All these instru- 
ments were provided with arbitrary scales. 

At the very beginning of the eighteenth century (1701) Newton 
suggested an oil thermometer with a rational thermometric scale, 
in which the temperature of freezing water was taken as 0° and 
that of the human body in health as 12*". By assuming that the 
rate of cooling of a hot body is proportional to the ' whole heat * 
[= temperature] of that body, he was able to estimate higher 
temperatures, such as 'red-heat', by observing the times taken 
by hot bodies to cool down to temperatures measurable on his 
thermometer. The proportionality here assumed has since be- 
come known as 'Newton's Law of Cooling'. This, more exactly, 
is that, for small ranges of temperature, the rate of cooling of a 
hot body is proportional to the difference in temperature between 
that body and the medium by which it is surrounded. 

The mercury thermometer was introduced and thermometric 
standards fixed about 1715 by d. g. Fahrenheit (1686-1736) and 
described in a communication to the Royal Society in 1724. A 
maximum and minimum thermometer was constructed in 1757 by 
CHARLES CAVENDISH (1703-83), whose son Henry (p. 287 f.) ex- 


Transjormations of Forces 

plored the thermometric conduct of mercury in 1783. This 
instrument was improved in the later years of the eighteenth cen- 
tury into the form we know. The maximum and minimum ther- 
mometer assumed its modern form in the hands of daniel 
RUTHERFORD (1749-1819) in I794. 

The invention of a satisfactory instrument for the measure- 
ment of temperature, with fixed points giving concordant read- 
ings in all circumstances to investigators in different places, had, 
as its most immediate important result, the foundation of the 
quantitative science of heat by Joseph black (1728-99). About 
1760 Black introduced the method of measuring quantities of 
heat by the number of degrees of temperature imparted to a 
definite quantity of matter, a method destined to have far-reach- 
ing effects. At the same time Black set forth clearly the distinc- 
tion between heat and temperature, or quantity of heat and inten- 
sity of heat. Rejecting the older view that the quantities of heat 
necessary to produce equal increments of temperature in different 
bodies were proportional to the quantities of matter in these 
bodies, he showed that every kind of substance had its own 
characteristic 'capacity for heat', which appeared to bear no 
relation to the quantity of matter in the body investigated. 
Black's term 'capacity for heat' has since been replaced by the 
term specific heat, 

(hi) Heat a Mode of Motion, 

In 1761-4 Black showed that definite quantities of heat dis- 
appear during certain changes of physical states, such as melting 
and evaporation. He also demonstrated that the same quantities 
of heat reappear during the reverse changes, freezing and con- 
densation. Black called this disappearing and reappearing 
factor the 'latent heat'. 

Black's discovery of latent heat was shortly afterwards applied 
by the engineer, james watt (1736-1819), then occupied in im- 
proving the steam-engine (p. 302). Watt found that water, on 
conversion into steam at boiling-point, expanded at atmospheric 
pressure to about 1,800 times its liquid volume. He also 
found that steam at boiling-point, when passed into ice-cold 
water, could raise about six times its weight of that water to 


The Mechanical World 

boiling-point (1764) . This puzzling result Black explained to him in 
accordance with his discoveries of 1761-4 on latent heat; and 
Watt (1765) applied Black’s discovery in his contrivance of the 
separate condenser, the greatest of all his many improvements of 
the steam-engine (Fig. 74). This simple principle is still in use and 
has made possible many subsequent developments. 

The conception of the nature of heat, from being a subject of 

Fig. 74. Diagram of Watt’s model illustrating condensing principle for 
steam-engine, 1765. In older engines the cylinder itself had been cooled 
at each stroke, after entry of steam. Watt attached a condenser and ‘ air- 
pump’ to empty the cylinder, which could then be kept permanently at 
steam heat while the vacuum produced by condensation did its share of 
the work and thus added to the efficiency of the engine. 

Speculation, was now on what seemed an exact basis, susceptible 
of practical application. Heat was held to be an elastic, uncreat- 
hble, indestructible, measurable fluid. To emphasize this new 
outlook, Lavoisier and the French Academicians introduced for it 
the name 'calorique' (1787). 

The theory of caloric was, however, already being undermined 
by the adventurous American, benjamin Thompson, count 
RUMFORD (1753-1814). Employing a balance, sensitive to one part 
in 1,000,000, he showed (1799) that there was no measurable 
alteration of weight in a mass of water on conversion into ice 


Transformations of Forces 

or on the reconversion of the ice into water, despite a heat-change 
of an order that would raise 9J oz. of gold from freezing-point 
to a red heat. Heat, therefore, if a fluid, 'must be something so 
infinitely rare, even in its most condensed state, as to baffle all 
our attempts to discover its gravity*. Therefore to Rumford it 
did not appear likely that heat was a substance distinct from, and 
accumulated in, the heated body. If, however, heat were ‘ nothing 
more than an intestine vibratory motion of the constituent parts 
of heated bodies*, then no change of the weights was to be ex- 
pected on heating, since only the internal motions, not their mass, 
would be affected. 

In 179^ Rumford had published his Inquiry concerning the 
Source of the Heut which is excited- hy Friction, In boring cannon 
he estimated the heat produced by measuring the rise in tempera- 
ture of a mass of water contained in a box suitably arranged 
around the boring-point. The heat generated by the friction of 
the borer and the cannon appeared to be inexhaustible, and he 
reasoned ' that any thing which any insulated body, or system of 
bodies, can continue to furnish without limitation, cannot possibly 
be a material substance*. Heat was therefore, he concluded, ‘a 
kind of motion*. 

Soon after these experiments there appeared the first publica- 
tion (1799) of Humphry Davy (1778-1829, p. 295), describing 
work that he had carried out at the age of nineteen. It contains 
the often misquoted account of an attempt to melt two pieces of 
ice by the heat developed on rubbing them together in a vacuum. 
The arrangement of the experiment was very imperfect and, since 
Davy*s recorded results were thermodynamically impossible, there 
can be little doubt that the proper technique was lacking. Per- 
haps the experiment is even now beyond the powers of any experi- 
menter. The results were assumed, and throughout his brilliant 
career Davy held fast to his youthful and correct conclusion — 
unjustified or at least unconfirmed by his premisses — that heat 
was a vibratory motion of the corpuscles of bodies. It is a remark- 
able case of that feeling or instinct for the correct solution that is 
the special gift of some talented investigators. 

Count Rumford had come very near to a more demonstrable 
treatment of the transformation and conservation of energy, for 


The Mechanical World 

he was not far from revealing the nature of the relation between 
heat and mechanical effort. He observed in his experiments on 
the boring of cannon that two horses, working steadily against 
frictional resistance, produced heat at a steady rate. He even 
compared the heat thus produced with the heat that would result 
from the combustion of the food consumed by the horses. Yet 
since he had no exact and transferable conception of work as a 
measure of mechanical action, he could not develop a com- 
plete doctrine of the transformation of one form of energy into 

The development of the steam-engine by Watt, and its use in 
the pumping of Cornish mines was, about this time, much in 
men's minds. When the firm of Boulton and Watt first began to 
manufacture their engines, the terms of sale devised by Watt 
involved the annual payment by the buyer, over a period of 
years, of one-third of the value of the savings in fuel effected by 
the new engine where it replaced an older type. But since the new 
engines were often for use in new mines, or were to do more work 
than those they replaced, or were required to pump from greater 
depths, a method of comparing engines was needed. Thus the 
determination of the duty of an engine was introduced (1778) as 
a quantitative relation between output of work and consumption 
of fuel. The ‘ duty ’ was the number of pounds of water raised by 
the engine through a vertical height of one foot per bushel of 
coal consumed. From this could be calculated the power of an 
engine, i.e. its rate of doing work. A standard of power was intro- 
duced by Watt in 1782-3 from calculations of the rate of working 
of a mill horse, and the term horse-power was applied to define a 
rate of doing work equivalent to the raising of 33,000 pounds one 
foot per minute. It was not, however, until the middle of the 
nineteenth century that the general convertibility of heat into 
work was finally recognized. 

(iv) Static Electricity. 

In the field of electricity, until the end of the eighteenth cen- 
tury, only the static form was recognized. The process of elec- 
trical conduction was demonstrated in 1731 and it was shown 
that, while some bodies would conduct electricity, others would 


Transformations of Forces 

not. Thus * insulation* became possible. It was shown also that 
all bodies are capable of electrification. 

Early attention was drawn to electrical attraction and repul- 
sion, To explain them a theory of two fluids was introduced (1730) 
by the French experimenter c. f. du fay (1698-1739). These 
fluids were supposed to be separated by friction and to neutralize 
each other when in combination. 

The striking way in which an electric charge may be fixed by 
two conductors separated by a non-conductor, as in the familiar 
‘Leyden jar*, was discovered at that town in 1746 by two Dutch 
experimenters. About this time benjamin franklin (1706-90) 
began to take an interest in electricity and soon observed that 
electric charges could be drawn off with peculiar facility by metal 
points. He supposed that ‘electric fire is a common element* 
existing in all bodies. If a body had more than its normal share 
it was called plus, if less minus (1747). This was the ‘one fluid 
theory* which held the field until the time of Faraday (p. 310). 
Franklin explained lightning as of electrical origin, suggested 
lightning conductors (1749), and put the idea to a practical test 
(1752). Through the survey by Priestley of the general state of 
electrical knowledge in his History and Present State of Electricity 
(1767) such phenomena became generally recognized. A number 
of types of frictional electrical machines were introduced and the 
subject attracted much attention. Electrical investigation had 
hitherto been almost entirely qualitative. In 1767, from the 
observation that there was no charge on the inner surface of a 
hollow electrified metal body, Priestley had suggested that the 
law of electrical attraction was the same as that of gravitational 
attraction, namely, the law of the inverse square of the distance. 
Cavendish gave an experimental proof of this in 1771. Unfor- 
tunately, however, he did not publish his experimental verifica- 
tion, and it remained unknown till 1879. 

The first method of measurement applicable to electricity was 
the action of an electrified object on light suspended bodies such 
as threads, metal foil, or pith-balls. An early attempt at quantita- 
tive expression was made in 1786 with a gold-leaf electroscope by 
measuring the angular divergence of the leaves when charged. 
But the first effective verification of the law of attraction was 


The Mechanical World 

made by the French engineer Charles Augustus coulomb 
(1736-1806), who adapted to electricity Hooke's principle 'ut 
tensio sic vis’. Using hairs and wires he constructed a ‘torsion 
balance' (1785). The principle was to measure the amount of 
torsion required to bring a charged pith-ball within various dis- 
tances of another pith-ball, equally charged with electricity of 
the same sign and therefore repelling it (Fig. 75). This method 

: Mil fed head 

Torsion wire 

S— 5R 

OFixed pith ball 
^Movable pith ball 

Fig. 75. Coulomb's Torsion Balance. Within a closed chamber two 
charged balls are insulated. One is fixed to the framework, the other 
attached to a wire that can be turned by a milled head. The degree of 
torsion needed to bring them together is a measure of the force of their 
mutual repulsion. 

was peculiarly adapted for the investigation of the distribution of 
electricity on surfaces and of the laws of electrical and magnetic 
action. Coulomb was the founder of the mathematical theory of 
these subjects, and by the use of his. 'balance' was able to prove 
that Newton's law of inverse squares (p. 252) holds good for elec- 
tric and magnetic attraction and repulsion. 

In the later eighteenth century there was considerable interest 
in the shock-producing fishes, the skate-hke Torpedo, and the 
electric eel or Gymnotus. Accounts of them were given by John 
Hunter (1773-5), Ingenhousz (1773), and Cavendish (1776), and 
it was realized that their shocks were of an electrical nature. The 


Transformations oj Forces 

attention thus drawn to electricity in the animal body led luigi 
GALVAN i (1737-98) of Bologna to investigate the susceptibility of 
nerves to irritation. He showed that muscular contraction could 
be produced by electrical action and conversely that electric phe- 
nomena could be produced by the muscular contraction. (1791. 
Fig. 76.) 

(v) First Study of Current Electricity, 

Many thought that this ‘animal electricity' was of its own 

Fig. 76. Galvani's experiments on effects of metallic contacts on nerves 
and muscles of frogs’ legs (1791). To left a metal rod establishes electric 
contact between water in two dishes. In one lies the end of the nerves with the 
spinal cord attached, in the other the feet. In the middle there is contact 
by a metal bar between two damp mats, on one of which lies the spinal 
cord and on the other the legs and feet. To the right there is a similar 
preparation with a broken contact which can be completed by bringing the 
rods together. 

peculiar kind and it was dubbed ‘galvanism'. Alessandro 
VOLTA (1745-1827) of Pavia, working on the results of Galvani, 
found that electric discharge through a nerve or sense organ not 
only produced muscular contraction but also sensation. If one 
end of a bent rod with limbs of different metals were held in the 
mouth a sensation of light was immediately produced when the 
other end made contact with the eye. A silver and a gold coin held 
against the tongue gave a saltish taste when the coins were con- 
nected by a wire. The essential thing was the contact of different 
metals. Volta showed that a muscle can be thrown info con- 
tinuous contraction by repeated electrical stimulation, but he 
was also able to demonstrate (1800) that the animal relationship 
of ‘galvanism' is in no way essential, as had previously been 
thought. Volta's device of the ‘voltaic pile', in which the electric 




The Mechanical World 

discharge of coins of the original experiment was replaced by a 
whole series of pairs of coins or disks between cards soaked in brine, 
soon developed into his famous ‘ couronne de tasses ' (1800. Fig. 77) 
and was the foundation of electrochemistry. The invention drew 
immediate and widespread attention. It was the first instrument 
for producing an electric current. 

Fig. 77. Volta’s Pile below and his Crown of Cups above. The pile is a 
series of paired disks of silver and zinc, sandwiched between paper strips 
soaked in salt water. They are supported by glass rods m m. From the 
lowest disk a metal strip goes to vessel h. A current will pass from the top 
disk to the vessel if the two are linked by a conductor. Two piles may be 
linked together by a metal strip, as at 0 c, and the effect doubled. 

The ‘ crown of cups ’ is a series of vessels of salt water or dilute acid in 
which are pairs of plates of different metals, connected by metal strips a a. 
The action is as with the pile. 

In England water was decomposed by current in the very year 
of Volta's publication. It was a generally held view that the 
chemical changes in the pile were the source of the electric current. 
Thus chemical affinity began to be correlated with electricity, 
which Franklin and others after him had come to regard as related 
to *fire' or heat. 

We may note that the ‘crown of cups', each cup containing 
two plates of different metals steeped in salt water or a dilute acid, 
is the direct ancestor of the various forms of electric ‘cell'. 


Transjormatiom of Forces 

The voltaic pile or the crown of cups provided an entirely new 
means for the decomposition of certain substances. In the de- 
composition of water by the current so produced, very great 
interest was aroused by the sight of oxygen and hydrogen bubbling 
off from the separate plates. Humphry Davy was among the 
first to develop this most fruitful mode of analysis, from which 
he had very great hopes, believing that it must * carry with it per- 
fectly new views of corpuscular action'. He himself showed by 
its means that in the decomposition of water the volume of 
hydrogen is double that of oxygen. Before many years electrical 
decomposition in his hands had yielded a whole series of new 
elements, notably sodium and potassium (1807-8). 

The nature of the process of electrical decomposition and the 
cause of migration of its products to the two poles of the electric 
cell gave rise to much speculation. Davy developed or adapted 
a theory that the electric pile breaks the particles near it into two 
factors. Thus in decomposition with a zinc-copper couple the 
copper repels and the zinc attracts the oxygen. Oxygen being 
given off, the hydrogen is thereby set free and attracts oxygen 
from the nearest particle. Thus again hydrogen is released and 
again attracts the nearest oxygen. A chain of decomposition is 
formed resulting in the discharge of hydrogen at the zinc pole and 
oxygen at the copper. 

The process of electrical decomposition was given quantitative 
expression by Faraday (1833, p. 310). Its two primary laws, still 
known by his name, are : 

(a) The mass of the product liberated by electrical decomposi- 
tion is proportional to the quantity of electricity passed. 

{b) When the same current is passed through solutions of dif- 
ferent substances, the masses of the liberated products are 
proportional to the chemical equivalents of those products. 
Thus a definite relation was established between electrical and 
chemical action. 

(vi) Electromagnetism. 

Soon after the completion of Davy’s electro-chemical researches 
a new orientation of electrical science set in. The year 1820 was 
especially eventful. In that year the Dane, mans Christian 


The Mechanical World 

OERSTED (1777-1851), demonstrated exactly the long-suspected 
connexion of electricity with magnetism. He found that if a wire 
carrying an electric current was placed near and parallel to a mag- 
netic needle it deflected it (Fig. 78), but not if the wire carrying the 
current was at right angles to the needle. The direction in which 
the needle turns depends on whether the wire carrying the current 
is above or below the needle, and on the direction of the current. 

The significance of this linking of electricity with magnetism 

Fig. 78. Oersted's experiment on the effect of an electric current 
on a magnetic needle. 

was at once recognized by the French investigator, Francois 
ARAGO (1786-1853) , who showed (1820) that a spiral of copper wire, 
through which a current was passed, attracted previously un- 
magnetized iron filings, which clung to the wire as long as the 
current flowed, but dropped off when the circuit was broken. 
Such a coil, in fact, acts like a magnet. In 1824 he found that 
rotation of a copper disk produced rotation of a magnetic needle 
supported above it (Fig. 79). This phenomenon was rendered 
intelligible by Faraday in 1831 (p. 314). 

ANDRE MARIE AMPERE (1775-1836), very soon after Oersted's 
publication, revealed the laws governing the deflection of the 
magnetic needle by the electric current and the mutual attractions 
and repulsions of electric currents. He showed that two parallel 
wires carrying currents attract each other if the currents flow in 
the same direction, and repel each other if the currents flow in 
opposite directions and he showed, as Arago had already done, 
that a cylindrical coil behaves like a magnet when a current is 
passed through it. He proceeded to a mathematical analysis of 
these phenomena (1822-7) and showed that an electric current 


Transformation of Forces 

is equivalent in its external effects to a magnetic shell. He pro- 
pounded the theory that magnetism is the result of molecular 
electric currents. His memory is perpetuated in the well-known 
'Ampere’s Rule*, formulated by him for determining the deflec- 


Fig. 79. Arago’s experiment of rotating a copper disk below a magnetic 


tion of a magnet by an electric current, and in the umpire, the 
practical unit of electric current, which is named after him. 

The work of these investigators, especially of Ampere, provided 
a means of detecting a current and of measuring it on some arbi- 

Fig, 80. The simplest form of galvanometer or apparatus for measuring 
electric current. It consists of a magnetic needle set in a non-conducting 
rectangular framework around which are wound many turns of wire through 
which passes the current, the effect of which is to be measured. 

trarily chosen scale by means of its magnetic effect. Instruments 
devised for this purpose, galvanometers, appeared in 1821 from the 
hands of several inventors. In their simplest form, they consist 
of a coil of many turns of wire carrying the current and deflecting 
a magnetic needle suspended on a pivot at the centre of the coil 
(Fig. 80). 


The Mechanical World 

(vii) The Dynamo. 

A main achievement of Michael faraday (1791-1867), one of 
the greatest of scientific geniuses, was the demonstration that an 
electric current can be used as a source of power. From the experi- 
ments of Oersted and from his own Faraday realized that a current 
traversing wire creates a magnetic ‘field of force'. Any part of 
this may be presented graphically, in any plane at right angles 

Fig. 81 . Faraday’s apparatus for demonstrating how an electric current can 
be disposed so as to produce a continuous rotational movement. 

to the wire, by a series of circles concentric to the wire (Fig. 84). 
Faraday thought that this force might cause a magnet to move 
round the wire. Moreover he argued that if a magnetic pole can 
be made to rotate round a current it should be possible to cause 
a wire carrying current to rotate round a magnetic pole. 

A circuit, consisting of two vessels of mercury and connecting 
wires, was arranged by Faraday so that in one vessel there was 
a fixed magnet and a wire free to rotate, while in the other the 
wire was fixed and the magnet movable (Fig. 81). Electric cur- 
rent passed from the wire through the mercury in the left-hand 
cup to a copper rod running into the base of the vessel. The 
magnet in this cup was fastened to the copper rod by a thread. 
In the right-hand vessel the fixed magnet was placed in a socket 
in the stem of the vessel, and the wire which dipped into the mer- 


Transformations oj Forces 

cury was able to move freely. As soon as the circuit was com- 
pleted, the magnet in the first vessel and the wire in the second 
commenced to rotate, and continued to do so while the current 
was passing. Faraday had thus transformed electrical current 
into continuous movement (1821). 

Faraday knew of the demonstration by Ampere that a cylin- 

drical coil of wire behaves like a magnet when a current is passed 
through it. The converse that a magnet could produce a current 
was shown by him to be equally true. The experiments that led 
him to this conclusion have become classics. 

Around an iron ring he wound two separate coils of wire. One 
was connected with a voltaic battery, the other with a galvano- 
meter. A key made it possible to break or make circuit. On mak- 
ing or breaking the current in the voltaic circuit, the galvanometer 
showed that a current also flowed for an instant in its circuit, but 
the currents on making and breaking were in the opposite direc- 
tion (1831, Fig. 82). 

But if a circuit can act as a magnet, as Arago had shown, can- 
not a magnet produce this same result with an iron ring ? Is not 
the battery unnecessary ? The testing of this point was a critical 
experiment for the whole future of electrical science. Faraday 
wound a coil of wire round a bar of iron and completed the circuit 
so as to include a galvanometer. He then placed the bar between 
the north pole of one bar magnet and the south pole of another, 
the other ends of the magnets being in contact. Whenever con- 
tact between the magnets was made or broken the galvanometer 
indicated the momentary passage of a current (Fig. 83). 


The Mechanical World 

On this discovery a wit of the time wrote : 

Around the magnet Faraday 

Was sure that Volta’s lightnings play: 

But how to draw them from the wire ? 

He took a lesson from the heart : 

Tis when we meet, ’tis when we part. 

Breaks forth the electric fire. 

Faraday had dispensed with a battery. Could he, by retaining 
the battery, dispense with a magnet, substituting for it a current ? 

Using a wooden bobbin for the iron ring, Faraday wound a coil 
of wire round it, and connected it to a voltaic coil. Round this 
'primary' coil was wound another and much longer coil, the 
'secondary', its ends being joined to a galvanometer. As before, 
both on make and break, momentary currents were indicated by 
the galvanometer. Faraday had revealed the process of 'induc- 
ing' a current, and with the knowledge of induction currents a 
new era in the application of electricity had opened (1831). 

It was now clear that the essential factor in the production of the 
magneto-electric effects was change, movement of the magnet or 
of the coil, or making and breaking of the current or the contact. 
Magneto-electric effects are related somehow to 'fields of force' 
which fade out as we pass farther from the site of the change. 
These fields of force can be arranged or mapped in lines as 
indicated by the behaviour of iron filings placed on cards within 
their area. 

In seeking a general explanation of these phenomena Faraday 

Transjormations oj Forces 

was thinking much about the lines of magnetic force which came 
to play a very important part in electrical sciences. They were 
by no means a new conception. Gilbert (p. i88) had a clear idea 
of them, Descartes had seen in them evidence for his hypothetical 
vortices, and certain eighteenth-century physicists had even 
mapped them, but it was reserved for Faraday to indicate their 

Fig. 84. Lines of force due to current in a straight conductor. 

significance. Throughout the rest of his career he continued to 
speculate and experiment on these lines of force which are now a 
familiar scientific conception. 

The general character of the lines of force due to a current can be 
easily demonstrated either by manipulating a small compass 
needle in the neighbourhood of a current or by running an electric 
wire carrying a current through a card on which iron filings are 
spread. These filings take the position of curves in the neigh- 
bourhood of the wire and the lines of force can similarly be repre- 
sented as concentric circles at right angles to the current (Fig. 84). 

Faraday had already succeeded in making a magnet rotate 
round a wire carrying a current, and a wire carrying a current 
rotate round a magnet. Such movements are related to the 
distribution of the lines of force due to current or magnet setting 
up certain stresses in the medium. This wire or magnet is continu- 
ally urged away from the strong part of the field. Ampere had 
shown that parallel wires carrying current attract one another if 


The Mechanical World 

the currents are in the same direction and repel one another if 
the currents are in opposite directions. This fact Faraday was 
able easily to fit into his conception of lines of force. If currents 

Fig. 86. Field due to currents in the opposite direction. 

run in the same direction in two neighbouring wires, the resultant 
field of lines of force will be such that they will be driven from the 
strong parts of the field to the weaker and so drawn together (Fig. 
85). If the currents run in opposite direction they will again be 
driven to the weaker parts of the field and so driven apart (Fig. 86). 

Arago's demonstration of the effect of a rotating copper disk 
on a magnet suspended over it (p. 308) was now explicable in 
terms of lines of force. As the disk moves, it cuts through the 


Transjormations of Forces 

lines of force of the magnet. Induced currents are therefore set 
up. The movement of the magnet is simply the result of the 
mutual action of. the magnet and of the magnetic fields due to 
the induced current. By visualizing the lines of force as endowed 
with certain physical properties, it is possible to link together 
many otherwise disconnected phenomena. 

Faraday in his very fruitful year 1831 provided also the con- 
verse to Arago's experiment (Fig. 79). He made a copper disk 
rotate between the two poles of a horseshoe magnet. The axis 
and the edges of the disk were connected with a galvanometer* 
As the disk turned, the galvanometer showed that an induced 
current was produced. This was the first magneto-electric machine 
or dynamo. This discovery of electro-magnetic induction was thus 
the starting-point for the utilization of electricity on a large scale, 
and for the application of such power for lighting and traction. 

A dynamo consists essentially of a suitable conductor, built up 
of many coils, which rotates in a magnetic field. The rotating 
conductor cuts through the lines of force of the magnetic field and 
an induced current is thereby set up in the coils of the rotating 
conductor. In each coil the induced current changes its direction 
during each revolution. Such a current is said to alternate. By 
means of a well-known device the alternating current may be made 
direct by reversing the current in each coil of the armature each 
time it passes a pair of conductors. 

With Faraday's ring with two coils of wire (Fig. 82) it is 
possible to obtain a high electromotive force from a current given 
by a very few cells. Many experimenters after him sought to 
construct apparatus which should give a high electromotive force 
by inductive action of one circuit on another. It was h. d. ri'HM- 
KORFF (1803-77), a- Parisian instrument maker, who in 1851 
produced the type of coil still known by his name and so rendered 
practical the development of the electric motor. 

About this time, when Faraday's researches were thus assuming 
practical significance, scientific men began to appreciate the 
exactness and preciseness behind much of his simple language. 
It is astonishing how many general theorems, the methodical de- 
duction of which require the highest mathematical powers, 
Faraday attained by some sort of intuition without the help of 


The Mechanical World 

mathematical formulae. Thus the first important scientific contribu- 
tion of JAMES CLERK-MAXWELL (1831-79) was On Faraday* s Lines 
of Force (1856) . In it he sought ‘ to show how by a strict application 
of the ideas and methods of Faraday, the connexion of the very 
different orders of phenomena which he discovered, may be placed 
before the mathematical mind*. He followed the suggestion of 
William Thomson, later lord kelvin (1824-1907), who had been 
working at the subject since 1849. The analogies that Clerk-Max- 
well worked out were those of heat and of hydrodynamics. These 
gave rise to his conception of electric and magnetic effects as 
due to changes in the ether (1862) and to his great contribution 
On a Dynamical Theory of the Electro-magnetic Field (1864). 
In the latter he showed that electro-magnetic action travels 
through space at a definite rate, in waves, and that these waves 
are, like those of light (pp. 316 ff.), transverse to the direction in 
which the waves are propagated. Since he was able also to prove 
that the velocity of these waves is the same as that of light (1867), 
an electro-magnetic theory of light thereby became possible. 

(viii) Undulatory Theory, 

At the end of the eighteenth century there were in the field 
two rival conceptions of the nature of light, the emission theory 
and the undulatory theory. 

The emission theory is of great antiquity but was given 
modem scientific form by Newton. He treated a luminous body 
as emitting streams of minute corpuscles moving progressively in 
a straight line corresponding to the direction of the ray. Vision 
was supposed to be produced by the impact of these streams 
on the eye. The bending of the ray as it passes from air into a 
denser medium — as, for example, into glass or into water — is ex- 
plained by assuming that as each corpuscle approaches the denser 
surface of the medium at any given angle it begins to be attracted 
towards it. 

The undulatory theory of Christian Huygens, put forward in 
1678 and especially in his famous Treatise on Light (1690), treated 
all space as pervaded by a subtle and elastic medium, the ether, 
through which waves are propagated in all directions from a light- 
source. These undulations spread in a regular spherical form from 


Transjormations oj Forces 

the point of origin, just as waves produced by a stone dropped into 
water spread in circles. 

Huygens applied this theory to explain the phenomena of 
refraction. A source of light may be regarded as emitting a series 
of spherical waves in the ether. Any point A on the surface of 
such a wave (Fig. 87) may in its turn be regarded as a source of 
light. Every other point on the surface of the same wave, as for 
example B, C, or D, emits similarly its own spherical wave. At 
any distance from the 
original source the surface 
of all these waves can be 
regarded as combining to- 
gether to form what is 
called a ‘wave-front’. If 
the source of light be suffi- 
ciently distant the wave- 
front is on so large a sphere 
that a small part of it may 
be treated as flat (or, in 
section, linear), while the 
lines radiating to it from 
the source of light may be 
treated as parallel. 

We have now to con- 
sider, as did Huygens, the application of this wave theory to the 
known facts of refraction and notably to Snell’s law (p. 194). 
Those facts require (as we shall presently see) that the velocity of 
propagation of light should be less in a denser than in a rarer 
medium. The change in the rate of propagation will produce a 
change in the direction of the wave-front. 

In the diagram (Fig. 88) A and C are parallel rays derived from 
a distant source of light with wave-front a plane surface at right 
angles to their line of advance. They strike the surface of a 
denser medium obliquely, A reaching it at A^, along wave-front 
Ai M, before C reaches it at Suppose the velocity in the 
denser to be § of that in the rarer medium. While C advances 
from M to Cj, A will reach a point A 2 which is f as far 
from . 4 i as Af is from^ Cj. For another ray B, that strikes the 


Fig. 87. Huygens’s conception of 

The Mechanical World 

surface at midway between A and C, the wave-front B^N 
may be considered. Now C gets to at the moment when B 
having struck the surface at B^ reaches a point Bg at f the distance 
from B^ that N is from C^, or ^ of | the distance that M is from Cj. 

Fig 88 Refraction in terms of Wave Theory Beads on the lines mark 
equal intervals Velocity of light in denser is represented as twu-thirds of 
that in the rarer medium 

Thus A-^A^is § MC^ and JBj is J MC^. A^ and B^ are located on 
wave-front circles with centres Aj^ and respectively and with 
radii equal respectively to § and ^ of MCj. Thus the wave-front 
when C arrives at will be a straight line A^ B^ C^, which only 
touches but cannot cut either of the two circles. That straight 
line is, in fact, a common tangent to all circles formed on the pro- 
portionate construction here considered. The angular change of 
direction of wave-front from A^M to A^C^ corresponds to the 
necessities of Snell’s law. 

The wave theory of light that prevailed in the nineteenth cen- 
tury was propounded at its dawn by thomas young (1773-1829). 
In two communications (1801), which place him in the forefront of 
scientific investigators, he set out his wave theory and its essential 
principle of interference. 


Transjormations oj Forces 

* Suppose he said, ‘ a number of equal waves of water to move 
upon the surface of a stagnant lake with a certain constant velo- 
city, and to enter a narrow channel leading out of the lake ; sup- 
pose then, another similar cause to have excited another equal 
series of waves, which arrive at the same channel with the same 
velocity and at the same time as the first. One series of waves will 
not destroy the other, but their effects will be combined. If they 
enter the channel in such a manner that the elevations of the one 
series coincide with those of the other, they must together produce a 

cf/vm OF 

Fig. 89. To illustrate the principle of interference. 

series of greater joint elevations ; but if the elevations of one series 
are so situated as to correspond to the depressions of the other, they 
must exactly fill up those depressions, and the surface of the water 
must remain smooth — at least, I can discover no alternative, either 
from theory or experiment. Now, I maintain that similar effects 
take place whenever two portions of light are thus mixed, and this 
I call the general law of the interference of light.* 

This view of interference is perhaps most simply presented if 
we picture waves from one centre of disturbance entering two 
channels of unequal length which subsequently meet. If at the 
meeting-point the waves are in opposite phases they will evi- 
dently neutralize each other (Fig. 89). 

Newton had himself discussed the wave theory, and had dis- 
missed it, saying: 

* If light consisted in motion, it would bend into the shadow, for 
motion cannot be propagated in a fluid in right lines beyond an 
obstacle which stops part of the motion, but will bend and spread 
every way into the quiescent medium beyond the obstacle. ... A 
bell may be heard beyond a hill which intercepts the sounding 
body . . . but light is never known to bend into the shadow.' 


The Mechanical World 

Young proved, however, that light does bend. The bend is 
extremely small, owing to the minuteness and immense speed of 
the waves, but it is greater in some mediums than in others, in 
water for example than in air (Fig. 90). 

Young demonstrated this bending of light-rays by a simple 

experiment. Light reflected from the 
sun was admitted through a pin-hole 
in the side of a dark chamber, making 
a cone of light. In the pathway of this 
cone was interposed a narrow strip of 
card. Faint fringes of colour were seen 
on either side of the shadow thus cast 
on the opposite wall, while in the 
shadow itself was a sequence of faint 
dark and light upright bands, finishing 
off in a faint light band in the middle 
of the shadow. Since light normally 
travels equally in all directions, a part 
of it, passing on each side of the strip 
of card, must spread out behind it. 
But why should the light arrange it- 
self in strips, and not fall equally all 
over the shadow ? When an opaque 
object was placed so as to prevent the 
light from passing one of the edges 
of the card the fringes disappeared. Therefore, so long as the 
light passes in one direction behind the card it spreads itself out 
equally, and only when two sets of rays from the two sides of the 
card meet do ' interference ’ bands appear. This is a close analogy 
to what happens in the case of water-waves. 

Light does not, however, always travel through a transparent 
medium equally in all directions. Thus it had long been known 
that light traversing two crystals of Iceland spar in any but one 
direction gives two streams of (usually) unequal brightness. The 
relative intensity of the two streams was known to depend on the 
relative positions of the crystals. In certain positions one stream 
disappears entirely. The French mathematician Etienne louis 
MALUS (1775-1812) found that he could elicit results comparable 


Fig. 90. Waves diverging 
from centre A, pass through 
aperture BC. They extend 
themselves on each side — that 
is, they ‘ bend into the shade ’ — 
so as to fill the space BCDE 
while affecting the parts out- 
side this area much less or not 
at all. (Young's diagram.) 

Transjormations oj Forces 

to those of Iceland spar by light reflected ftom transparent surfaces. 
Misunderstanding the nature of the process, he called it polariza- 
tion (1805), a misleading title which 
it still bears. Such phenomena as those 
investigated by Malus were inexplic- 
able on the wave theory until it was 
given its modem form by the French 
experimenter auguste j e an fresnel 
(1782-1827), in correspondence with 

In sound-waves, from which Young 
had drawn his picture of light-waves, 
the vibrating particles move in a 
direction parallel to the propagation 
of the wave. This is * longitudinaT 
vibration. In water-waves the water 
particles move up and down at right 
angles to the forward direction of 
the wave. This is ' transverse ' vibra- 
tion. The ether vibrations of a light- 
wave are transverse. They have, 
however, this complication, that the 
plane of vibration is not restricted, 
so that a ray of light may consist of 
waves vibrating in any plane at right 
angles to the direction of the ray. 

Graphically represented (Fig. 91), 
looking ' end-on * at a wave, we can 
visualize a series of short straight lines signifying the extremes 
between which the ‘ether particles’ vibrate. Although vibrating 
in planes at all angles to the line of the advancing light, yet all 
vibrations are at right angles to the direction in which the wave 
advances, that is, for the purposes of our diagram, they vibrate in 
the plane of the paper. The action of Iceland spar upon the light- 
waves impinging on it may be compared to a set of railings with 
vertical chinks. Vibrations parallel to the rails will pass on 
between its chinks, but the remainder wilj be stopped. The light 
that passes on is said to be 'polarized*. 

Light. The observer is sup- 
posed to view a light ray end- 
on as it advances toward 
him. The line of advance is 
along an axis represented by 
the central point. Vibrations 
in the ether take place in all 
planes through which the axis 
passes. These planes, from the 
observer’s point of view, are 
seen as straight lines, of which 
SIX are represented. If the ray 
encounters a medium which 
acts as a grating (such as is re- 
presented by the dotted lines), 
permitting the passage of vi- 
brations in only one plane (i in 
diagram) ,the light is ‘polarized’ . 




The Mechanical World 

Fresnel also used the conception of interference to bring the 
undulatory view of light within mathematical range by making 
possible a quantitative estimate of the length of light-waves 
(1821), Two metal mirrors in almost the same plane (Fig. 92) 
reflect light from a pin-hole in the wall of a dark chamber on to a 
white screen. Looking into the mirrors from the screen the 
observer would see two ' virtual images ' of the Whole, as at A and 
B, and the optical effects are as though the light really proceeds 

from those points. By rotating the mirrors, A and B can be made 
to approach each other until, when the mirrors are in the same 
plane, the points coincide into a single virtual image. A line 
drawn from this, vertical to the screen, meets it at C. Consider any 
point P on the screen in the area that receives light from both 
A and B. PA is longer than PP, but the difference becomes less 
the nearer P is to C. This difference, PA minus PB, can be calcu- 
lated from the known conditions of the experiment. Now P 
sometimes shows a dark, sometimes a light, band. This will be 
according as the difference between PA and PB approximates to 
an odd or even multiple of a half wave-length ; whether, in fact, 
the waves of light as from A and B strike the screen in the same 
or in opposite phases (Fig. 93). 

We have seen (p. 317) that the wave theory requires that the 
velocity of light in rarer media should be greater than in denser, 
the opposite being demanded by the emission- theory. Thus a 
direct proof that light passes more rapidly through air than 
water would be a further confirmation of the wave theory. This 
was achieved by jean leon foucault (1819-68) in a very well- 
known series of experiments begun in Paris in 1850, and described 
in full detail in 1862. He had already done work with his exact 

Transjormations of Forces 

contemporary, hippolytelouis fizeau (1819-96) , on alliedthemes, 
such as chromatic polarization of light and interference of heat- 
rays and of light-rays of greatly differing length of path. He is 
also well remembered for his invention of the gyroscope (1852) 
and for his method of giving the reflectors of optical instruments 
a spheroid or paraboloid form (1857). His name is, moreover, 
attached to several electrical devices. Fizeau had made deter- 
minations of the absolute velocity of light in 1849. These deter- 

Fig. 93. A BCD represents a system of transverse waves propagated 
toward the right. At P it is joined by a second system, of equal amplitude 
and wave-length, but with oscillations half a wave-length later. There 
results a state of oscillatory rest or ‘interference'. Should the wdves of 
the second system have the same wave-length but unequal amplitude, the 
amplitude of the first would be reduced. If the second has a different 
wave-length, a more complex system will arise. 

minations of Foucault and Fizeau — in the neighbourhood of 
300,000 kilometres per second — open the modern classical period of 
optics. Fizeau introduced certain conceptions of the relative motion 
of matter and ether that were later developed by Clerk-Maxwell, 
(ix) Doctrine of Energy, 

The History of Science submits, no more easily than the history 
of other subjects, to arbitrary time divisions. Nevertheless there 
are certain seminal scientific ideas, the appearance of which makes 
it possible for the historian to establish time boundaries sufficient 
for the division of his narrative. Such a one is the doctrine that 
any form of measurable physical activity is convertible into 
any other form, and that the total amount of such activity in the 
world is limited and remains the same. This Doctrine of Energy 
became accepted about the middle of the nineteenth century and 
opened a new era in the history of scientific ideas. 

An important advance in this direction was made by the brilliant 


The Mechanical World 

young Frenchman, sadi carnot (1796-1831), in his only pub- 
lication, Reflexions on the Motive Power of Fire (1824). Carnot 
measured and defined work as 'weight lifted through a certain 
height'. He established quite clearly the principle that heat 
and work are reversible conditions and that the efficiency of a 
reversible engine depends on the temperatures between which it 
works. The work of Carnot attracted little attention during his 
lifetime. The principles involved were grasped some twenty years 
later by the Englishman j. p. joule (1818-89), a pupil of Dalton, 
who developed the subject with great experimental skill. 

Joule's work began to assume significance in 1840, when he was 
emphasizing the idea of the importance of physical units. Those 
which he then adopted involved the conception of the transference 
of chemical into electrical activity in a measurable way. His unit 
of static electricity was the quantity needed to decompose 9 
grammes of water, and his degree of current electricity the same 
amount propagated in an hour. He regarded the consumption 
of the metal in the electric battery as a source of energy analogous 
to that of the coal that drives the steam-engine. 

In considering the electric motor invented by Faraday, Joule 
was able to demonstrate a numerical relation between the chemical 
effect in the battery, the mechanical effect in the motor, and the 
electrical effect in the circuit. Thus, if a given weight of zinc be 
dissolved in acid, a certain measurable amount of heat is given off. 
Make the zinc an element in a battery and a measurably less 
amount of heat is produced in the course of its solution. If the 
current passes through a wire, it heats the wire. This amount of 
heat corresponds, he showed, to the difference between the heat 
produced by the simple solution of zinc in acid and that produced 
when it is dissolved as an element in a battery. Moreover, if the 
current drives a motor yet more heat is missing. The amount miss- 
ing is proportional to the work done by the motor. 

Joule's historic paper of 1843 On the calorific effects of Magneto- 
Electricity and on the mechanical value of Heat brings out very 
clearly the relation between work and heat. It sets forth ' Joule's 
Equivalent', as it is now called, that is, the amount of work which 
must be transformed in order to give one unit of heat. This unit 
of heat was the amount needed to raise one .pound of water one 


Transjormations oj Forces 

degree Fahrenheit. His unit of work was the amount required to 
raise one pound weight a height of one foot. His equivalent, as 
he then determined it, was 838 foot-pounds. 

In the years that followed, Joule pursued his idea with many 
refinements. Thus he measured the work required and the heat 
produced when water is driven through fine tubes, when air is 
•compressed or allowed to expand, when a paddle-wheel is driven 
through water or through more viscous fluids, and so on. But not 
until 1847 did he give the first full and clear exposition of that 
principle now called energy, a term first applied in that capacity 
by William Thomson (Lord Kelvin) in his great paper. Dissipation 
of Mechanical Energy (1852).* Joule's superb exposition of 1847 
had been given in the form of a popular lecture in a church reading 
room! This great scientific pronouncement, after rejection by 
several journals, appeared in a Manchester weekly paper with the 
title : Matter, Living Force and Heat. His living force is, of course, 
what we call * Energy He said : 

'Living force (vis viva) is one of the most important qualities 
with which matter can be endowed, and as such it would be absurd 
to suppose that it can be destroyed. . . . Experiment has shown 
that wherever living force is apparently destroyed, whether by 
percussion, friction, or any similar means, an exact equivalent of 
heat is restored. The converse is also true, namely, that heat cannot 
be lessened or absorbed without the production of living force or 
its equivalent attraction through space. . . . Heat, living force and 
attraction through space (to which I might also add light, were it 
consistent with the scope of the present lecture) are mutually con- 
vertible. In these conversions nothing is ever lost.' 

In the same year appeared the little book of Hermann helm- 
HOLTZ (1821-94), Erhaltung der Kraft ('Conservation of Energy') 
In the same year, too. Joule came in contact with William Thom- 
son, afterwards lord Kelvin (1824-1907), who had long been 
interested in the transformation of heat, Helmholtz, in his famous 
pamphlet, in rejecting the possibility of perpetual motion, sought 
to establish the doctrine that through all transformations of energy 
the sum total of all energies in the universe remains constant. 
Thomson accepted the conclusions of Joule and Helmholtz and 

* Thomas Young had used the word in an analogous sense in 1807. 


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applied himself from 1848 onward to the mathematical implications 
of these doctrines. ‘ The first step toward numerical reckoning of 
the properties of matter', he wrote, 'is the discovery of a continu- 
ously varying action of some kind, and the means of measuring it 
in terms of some arbitrary unit or scale division. But more is 
necessary to complete the science of measurement in my depart- 
ment, and that is the fixing on something absolutely definite, as 
the unit of reckoning.' 

Thomson reached his conception of a fixed point. He was 
familiar with Carnot’s view of a reversible cycle and was one of the 
first to draw attention to it (1848), in illustration of the fact that 
the melting-point of ice is lowered by pressure. He saw clearly 
that the amount of work performed by an engine does not depend 
directly on the thermometer scale value of the temperatures 
between which it is working. Thus, to take a simple example, 
the work done between 100° and 150'' is not the same as the work 
done between 150° and 200^^. Therefore, before it is possible to 
reach a clear conception of the interchange of forces it is necessary 
to find some absolute scale which is not arbitrarily determined by 
the changes of state of a single substance as is that of the ordinary 
thermometer by the freezing-point and boiling-point of water. 
Now for an engine to be theoretically perfect, that is, for all its 
heat to be converted to work, it is necessary that the lower of the 
temperatures between which it works be the minimum possible. 
This minimum point Thomson called ‘ the absolute zero of 

Working between the temperatures 0° and 100° Thomson found 
that for every 373 parts of heat put in at 100° the engine will 
return 273 parts into the receiver, converting 100 parts into 
mechanical work. In other words, if boiling-point under the 
stated conditions be taken as one fixed point and freezing-point 
be taken as another, then — treating the working range between 
these two points as 100 — the lowest conceivable temperature, 
the zero of this absolute scale, would be —273°. This is the zero 
of an ‘absolute thermometric scale’. That scale is concerned 
solely with the work done by the substance employed and has 
nothing to do with its physical properties. 

The recognition of an absolute scale and of its implications with 


Transformations oj Forces 

the doctrines of energy, of the transformation of forces, of the 
ether, and of atoms provides the foundations on which was built 
the impressive structure of classical physics during the second 
half of the nineteenth century. 

6. Multiplicity of Organic Forms. 

(i) Early Classificatory Systems. 

As the exploration of the globe proceeded, the number of kinds 
of living organisms known to science rapidly increased and be- 
came very large. Some system of ccTdification and standardized 
description became an urgent need. Many attempts were made in 
this direction, but the successful and accepted scheme was that 
of the Swede karl linnaeus (1707-78). Its pre-eminent con- 
venience led to its rapid adoption to the exclusion of all other 

Linnaeus took the parts of a plant or animal in regular sequence 
and described them according to a recognized rule. This intro- 
duced what was almost a new international language, very con- 
densed, very clear, and very easily learned. As ‘botanical Latin' 
it has survived and maintained its usefulness. The method was 
a great improvement on the verbose and confused accounts usual 
till that time. It is best expounded in his Philosophia botanica 

(1751)- , .... 

Linnaeus also constructed a system of arrangement m which 
every known species of animal and plant had a position assigned 
to it. This involved grouping the Species into Genera, the Genera 
into Orders, and the Orders into Classes. 

For plants the Classes and Orders were based on the number 
and arrangement of the parts in the flower. Linnaeus had a clear 
though not very accurate or searching conception of the sexual 
character of the floral elements. The number of ‘stamens’ or 
free mal^ parts was his first consideration. Thus Linnaeus grouped 
plants with one stamen in the Class Monandria, plants with two 
in the Class Diandria, plants with three in the Class Triandria, 
and so on. Each Class was then divided into Orders, according 
to the number of ‘ styles or free female parts, in the flower. Thus, 
the Class Monandria was divided into the Orders Monandria 


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Monogynia with one style, Monandria Digynia with two, and 
Monandria Trigynia with three, and so on. 

For animals, Linnaeus distinguished the Classes of Mammals, 
Birds, Reptiles, Fishes, Insects, and Vermes. The first four had 
already been grouped together by Aristotle as * Animals with red 
blood' or, as wenow call them, ‘Vertebrata' or backboned animals. 
The remaining Classes, Insects and Vermes, contain, bundled 
together, all the Orders of animals without vertebrae or back- 
bones. Here Linnaeus was behind Aristotle, who had broken up 
these groups more effectively (p. 41). 

The contribution through which the name of Linnaeus will, 
however, always be remembered and is daily recalled by naturalists 
is his ‘binomial nomenclature', the system of defining every 
known living thing by two Latin names, the first being that of its 
genus and the second that of its species. It will naturally be asked 
what is meant by these words. To this no one can give a clear or 
even an intelligible answer, though there is evidence that an answer 
is slowly emerging from certain current work. Naturalists have 
been occupied for over two centuries with the more exact indi- 
vidual application of these terms without reaching any general 
definition of them. It is unparalleled in scientific history that un- 
defined and undefinable terms should remain indispensable for 
so long and so active a period. 

But although no one can, even now, define species in general 
terms, Linnaeus had certain ideas concerning their nature which are 
of great historical importance. He held that species are constant 
and invariable, a view in which he differed from John Ray. ‘ There 
are just as many species as there were created in the beginning', 
wrote Linnaeus, and again, ‘There is no such thing as a new 
species'. In this matter we have departed completely from his 

The Systema Naturae of Linnaeus is nevertheless a permanent 
contribution. It was first drafted in 1735, and he modified it and 
amplified it in its many editions. Of these, biologists have agreed 
on the tenth, which appeared in 1758, as the permanent basis for 
the scientific names of living things. If a species is given its 
‘Linnaean name' by a modern naturalist, it means that adopted 
in this tenth edition. 


Multiplicity oj Organic Forms 

Linnaeus was an extremely stimulating teacher. He had a 
great number of enthusiastic pupils, many of whom went on 
expeditions to distant lands and discovered and described multi- 
tudes of species. He and his disciples, by concentrating their 
interest on external parts, which are specially valuable for pur- 
poses of classification, withdrew attention from the intimate 
structure and working of the living organism. The search for new 
species thus remained for long the chief aim of most naturalists, 
to the neglect both of anatomical and of physiological studies. 

Much of the immense appeal of Linnaeus to his generation and 
those which followed was due to his appreciation of wild life. 
There have been few greater nature lovers. His tradition can be 
traced especially in Britain. It is commemorated in the ‘Lin- 
nean Society* (established 1790), and its impact happened to 
coincide in time and was ancillary to the literary movement known 
as the * Romantic Revolt*. Natural History in Britain had long 
interested the country gentry and clergy. There came a time when 
these were reinforced by the scientific tastes of the rising and 
wealthy industrial class. Thus the study of Nature became 
' fashionable *. Societies for it were founded in every major centre 
of population in Britain, from Kirkwall in the Orkneys to 
Penzance in Cornwall. Darwin, who approached his great task 
in the dual capacity of systematist and observer of wild life, was 
a typical product of this dual Linnaean tradition. Among its 
gifted literary exponents were the Rev. Gilbert White of Selborne 
(1789) and Charles Waterton of the Wanderings (1823). Other 
eminent and typical figures associated with the movement were 
Banks (p. 340), Lyell (p, 281), Murchison (p. 283), T. A. Knight, 
and the entomologist, the Rev. W. Kirby (i759“i85o). 

Since the time of Linnaeus almost every important biological 
movement has left its mark on the system of classification current 
in its day. The classification of living things adopted by a bio- 
logical writer may often be treated as an epitome of his views on 
many important biological problems, and especially on ' compara- 
tive* studies. This was notably the case with the system of 

The French naturalist georges cuvier (1769-1832) wielded 
great authority and determined the general direction of biological, 


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and especially of zoological, activity in the first half of the nine- 
teenth century. His general approach, unlike that of Linnaeus, 
was analytic. He laid stress on the structure and relations of the 
inner parts rather than on their external characters. 

Cuvier divided the animal kingdom into four great divisions, 
each of which, in his view (1817), is built on its own peculiar and 
definite plan. 

I. Vertebrata, with a backbone. 

II. Mollusca, slugs, oysters, snails, &c. 

III. Articulata, jointed animals, insects, spiders, lobsters, 


IV. Radiata, all remaining animals. 

In drawing up this scheme Cuvier was guided by his analysis 
of two main sets of functions. The heart and circulation provide, 
he considered, a centre for the 'vegetative functions* of growth, 
reproduction. See., to which the breathing apparatus is accessory. 
The . brain and spinal cord he regarded as presiding over the 
‘animal functions* which are associated with active movemeiit 
and are served by the muscular system. We are here reminded 
of the ‘vegetative* and ‘animal soul* of Aristotle. The thought 
of Cuvier is, in fact, infused with that of his great predecessor. 
Though the conception of vegetative and animal functions have, 
since Cuvier*s time, changed beyond recognition, much of our 
modem classificatory system is based on him and through him on 

The Genevan botanist, augustin pyramus de candolle (1778- 
1841), did for plants similar service to that of Cuvier for animals. 
He was a searching and patient investigator. Much of his classi- 
fication of the higher plants (1824) survives in the systems 
developed by modem botanists. 

(ii) Main Subdivisions of Biological Study, 

A feature in the biological outlook of the early nineteenth 
century was the slowness with which microscopical research took 
an important place. The great microscopists of the seventeenth 
century had singularly few successors in the eighteenth. Thus, 
when Humphry Davy needed descriptions of the microscopic 
stmeture of stems and leaves for his Agricultural Chemistry (1813) 


Multiplicity of Organic Forms 

he had to rely on Grew's Anatomy of Plants (1682) of 130 years 
earlier. In the third decade of the nineteenth century certain 
improvements in the microscope began to be available, and awoke 
the interest of biologists. A number of observers were soon devot- 
ing themselves to the intensive study of microscopic organisms, 
and to the microscopic analysis of larger forms. From now on the 
microscope became the essential instrument of the biological 
sciences. Microscopic observations have since provided the build- 
ing material. for a dozen separate departments of biology. 

In the first half of the nineteenth century philosophical natural- 
ists were largely occupied in establishing ‘affinities* between dif- 
ferent types of organisms. These workers may be divided into 
fairly definite groups according to the character of the problems 
that they set themselves to solve. Of these groups five may be 
distinguished as of particular historical importance. 

(a) Those concerned with comparing external characters of 
living forms nearly allied to each other; that is, in the work of 
establishing the nature and limits of species, genera, and families, 
and of their degrees of affinity. These are the systematists or 
‘ taxonomists * (Greek taxis, ‘ arrangement * ; nomia, distribution. 
The word was introduced by de Candolle 1813). A very great 
exponent of this study was Darwin. His concentration on its 
problems led him to his historic consideration of the origin of 
species. An investigator who worked on comparable lines but 
came to different conclusions was Louis Agassiz. Important 
botanical taxonomists were A. P. de Candolle and J. D. Hooker. 

(b) Those occupied in investigating the inner structure of con- 
trasted forms, that is of forms belonging to widely separated groups 
as Orders and Classes. These are the comparative anatomists or 
morphologists, (The term ‘ Comparative Anatomy * was introduced 
in 1672 by Grew. Morphology, Greek morphi, ‘form*, was intro- 
duced by Goethe about 1817.) Typical exponents of this method 
were the versatile Johannes mClIer (1801-58) in Germany, 
RICHARD OWEN (1804-92), opponent of Darwin, and first director 
of the British Museum of Natural History, Robert brown (1773- 
1858), ‘botanicorum facile princeps’, and Etienne geoffroy st. 
HILAIRE (1772-1844), opponent of Cuvier. 

{c) Workers engaged in the comparative anatomy of fossil forms 


The Mechanical World 

are known as palaeontologists. Among the greatest of these were 
RICHARD OWEN (1804-92), and the palaeobotanist w. c. william- 
son (1816-95). The word ‘Palaeontology' was introduced into 
English by Sir Charles Lyell (1838). 

{d) It was early realized that the structure of embryos revealed 
affinities that are less apparent in adults. Moreover, in certain 
respects, the knowledge of the formation of the parts in the 
embryo was found to make the structure of adult forms more 
intelligible. The beginnings of life had always excited wonder and 
curiosity. The investigation of embryos required, however, un- 
usual kinds of skill, and ‘embryologists' were early differentiated. 
(The term emhryologie was admitted into the French language 
by the Academic in 1762. It did not enter English till the nine- 
teenth century.) Important early embryologists were the Ger- 
mans KARL ERNST VON BAER (1792-1876) and ROBERT REMAK 
(1815-65), the Swiss Albrecht kolliker (1817-1905), and the 
Swiss American louis agassiz (1807-73). 

(e) Quite apart from the schools of ‘naturalists' and ‘biolo- 
gists', the first half of the nineteenth century saw a great 
extension of scientific interest in the analytical study of animal 
function by means of physical and chemical experiment. The 
exponents of this science of ‘ physiology ' were mainly preoccupied 
with its medical applications. Such physiologists were not usually 
concerned to compare different forms. Choosing for preference 
those likest to man — the ‘higher' animals — they devoted them- 
selves rather to the examination of the parts and functions in 
their developed state. The results have been portentous in bulk, 
complexity, and interest, and have given rise to a picture of the 
animal machine which has deeply influenced the current concep- 
tion of the nature of Man, and of his place in Nature. Among 
the greatest exponents of this department of science were sir 
CHARLES BELL (1774-1842), JOHANNES MCLLER (180I-58), and 
CLAUDE BERNARD (1813-78). 

(iii) Naturphilosophie. 

The startling revelations of the microscopists and the ‘mechan- 
ist ' physiologists of the seventeenth century induced, especially in 
German thought, an era of speculative activity. The conception 


Multiplicity of Organic Forms 

of the ‘ ladder of Nature ’ assumed a new importance. Aristotle 
had been content with its formal projection (p. 41). During the 
eighteenth century it took the form of a rigid framework into 
which observations were to be fitted. 

Certain microscopic observations had given rise to the false idea 
that the organism is already fully formed in the germinal original, 
that is in the ovum of the female or, alternatively, in the sper- 
matozoon of the male. The Genevan Charles bonnet (1720-93) 
raised this idea of ‘preformation* to the rank of a scientific and 
philosophic doctrine (1762). Both this conception and the processof 
reproduction without fertilization (parthenogenesis, Greek, = virgin 
birth) ,whichhe rediscovered (1745) , he made to serve theological ends. 

In this peculiar intellectual atmosphere Bonnet and his followers 
developed a rigid interpretation of the conception of a ‘ ladder of 
nature*. Passing from the most subtle of the elements, fire, 
through air, water, and the densest, earth, this ‘scala naturae* 
ascended through the finer minerals, such as crystals, to living 
things, proceeding through what were then regarded as the 
lowest of these, namely the moulds, via plants, insects, and worms, 
upward to fish, birds, mammals, and finally to man. The medieval 
and Christian view of ‘ man as the measure of all things ’ was thus 
given a new significance by Bonnet and his school. ‘All beings,* 
he wrote, ‘have been conceived and formed on one single plan, 
of which they are the endlessly graded variants. This prototype 
is man, whose stages of development are so many steps toward 
the highest form of being.* Each being was believed to be 
‘preformed* in the male or female ‘primordium* or germ, the 
spermatozoon or ovum. 

Such views pass insensibly into the attitude, known later as 
N atur philosophies which became especially popular in Germany. 
Some of its developments in that country became fantastic to 
the verge of insanity. Yet there were several effective thinkers for 
whom this attitude became a useftil approach, to natural know- 
ledge. Among these were the two loftiest intellects that Germany 
has produced, Kant and Goethe. 

The thought of the age was given a new direction by the Konigs- 
berg philosopher, immanuel kant (1724-1804) in his famous 
Critique of Pure Reason {1771). He had begun as a man of science, 


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and it was from his treatment of scientific problems that his 
philosophical interest emerged. Beginning with a world of phe- 
nomena, of nature, of experience — the determinate world of the 
man of science — ^he gradually passed into the world of the in- 
telligible, of ends, of the philosopher. 

To most men then, and to most men still, these two worlds 
seem to confront one another. Men of science affirm this when 
they say that 'the study of purpose in Nature is inconsistent with 
the scientific aim, which is the adequate description of pheno- 
mena*. It was Kant*s thought that the two attitudes are neither 
opposite nor irreconcilable. He reduces the problem to the dis- 
cussion of the relation between our perception of things and their 
real nature. Our perceptions, Kant held, come into relation with 
the real nature of things through the character of our processes 
of thought. In other words, our thoughts work along Nature*s 
own lines. Kant pointed out that, if we consider living organisms, 
we perceive that they are composed of parts which are compre- 
hensible only as conditions for the existence of the whole. The 
very existence of the whole implies an end. True, says Kant, 
Nature exhibits to us nothing in the way of purpose. Neverthe- 
less we can only understand an organism if we regard it as though 
produced under the guidance of thought for the end. The naturalist 
tacitly admits this when he considers the different organs or parts 
in relation to their function in the whole living organism. 

The opposition, so familiar to the biologist, between the 
mechanist and the teleological (p. 42) or vitalist view, is, Kant 
held, due to the nature of our knowledge, that is of our experience. 
But our thchights must be distinguished from our experience. In 
thought we pass constantly from the view of the^ar^ as mechanism 
to a view of the whole as purpose, and back again. Nor do we 
separate these two views unless deflected by some specific doc- 
trine that the parts are really separate. There is, Kant believes, 
a hidden basic principle of Nature which unites the mechanical 
and teleological. That principle is none the less real because our 
reason fails to grasp it or our powers to formulate it. So far as 
actual practice and use of language go, such a principle is, in 
fact, accepted by every biologist, the most convinced 'mechanist' 
no less than the most extreme 'teleologist'. 


Multiplicity oj Organic Forms 

Kant's scientific influence is to be traced especially in johann 
WOLFGANG VON GOETHE (1749-1832), whose pre-eminence as a poet 
and writer must not obscure his importance for science. Goethe 
did great service in emphasizing the fact that all organisms accord 
in structure to a certain quite limited number of patterns or plans. 
These represented for him ‘ ideas ' in the mind of God. By search- 
ing for these ideas — ‘plans' or ‘types' as they came later to be 
called— Goethe and his followers did much to stimulate the 
systematic comparison of diverse living things. Not the least of 
their services was that they thus persuaded biologists to abandon 
the point of view, derived from medical applications, that regards 
the structure of man as the type to which that of all other creatures 
must be referred. 

Goethe expounded several doctrines of great importance, some 
of which are still of value. His most valuable scientific concep- 
tions were the following: 

{a) The genera of a larger group (Family, Order, Class, or 
Phylum) present something in the nature of variants on a com- 
mon plan. These are all expressions of the same ‘idea' or ‘type'. 

(b) The various parts of the flower are but modifications of 
leaves. The ‘cotyledons' of germinating seeds (cf. the terms 
‘Monocotyledons' and ‘Dicotyledons') are but the first leaves 
borne by the infant shoot. 

(c) Similarly all the parts of living beings are referable to one 
original model or ‘primordium'. Thus not only is there a pri- 
mordial species of animal and a primordial species of plant, 
corresponding to the animal ‘idea' and the plant ‘idea', but also 
there is a primordial part of each animal and plant. The bones 
of the spine provide a good illustration of this conception. 
These ‘vertebrae', fundamentally of the same origin and struc- 
ture, have different forms, and perform different functions in 
different parts of the backbone. All are variants on the ‘pri- 
mordial' vertebra. Goethe believed that a like story might be 
told of other organs. This position is now indefensible in its 
original form, but it has in it an element of truth which provided 
a basis for much research and a good framework for the classifica- 
tion of observations. 

Bonnet, Kant, Goethe, and their followers, the ‘Nature 


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Philosophers*, were thinkers rather than observers, though their 
observational activities certainly cannot be despised. Some of 
their ideas, strange and strained as they now seem, and repellent 
as they are to many men of science, recur again and again during 
the centuries. 

Whence comes the continued fascination of thoughts so little 
related to the daily task of the scientific observer ? The essence 
of the thought of such men is that the processes of the mind 
reflect the processes of Nature. In this there is surely a truth, 
though it is presumptuous to suppose that we have any deep 
understanding of this parallelism. To say that ' the burnt child 
dreads the fire* is but to give a special instance of the wider 
statement that reason is generalized experience. Our minds, as 
much the product of evolution as our bodies, have in the ages 
developed as mirrors of the world in which we dwell; they are 
attuned to Nature. The mathematical thought of ages on the 
nature of certain curves elaborated a knowledge which Kepler 
and Newton fitted into the phenomena of planetary movements. 
The minds of the pre-Keplerian mathematicians were attuned to 
Nature. They were working on Nature*s lines, though they knew 
it not. To say that we live in a rational world is but to say that 
by reasoning aright we may learn something about that world. 
This is as true for biology as for astronomy, though no such dia- 
grammatic illustration is to hand in the biological realm. Yet by 
those whose minds were specially attuned to biological studies, 
truths have often been discerned which were verified later by 
experience. This in itself is sufficient justification for that specu- 
lative attitude which is more productive during some Scientific 
episodes than during others, but is never without its value. 

(iv) Correlation of Parts, 

GEORGES CUVIER (1769-1832), ‘the dictator of biology*, was 
especially interested in structure rather than function. He was 
essentially a ‘morphologist*. The main conception that guided 
him was that of the ‘correlation of parts*, the nature of which 
must be discussed. 

Organs do not exist or function separately in nature, but only 
as parts of complete living things. In these living things certain 


Multiplicity oj Organic Forms 

relations are observed which are fundamental to their mode of 
life. Thus feathers are always found in birds, and never in other 
creatures. The presence of feathers is related to a certain forma- 
tion of the forelimb, with reference to its action as wing. Feathers 
are never found without wings, and in other winged animals than 
birds the structure of the wing is very different from that of birds, 
and never has feathers. But the wing structure peculiar to the 
bird is in turn related to certain formations of the collar-bone 
and breast-bone, with reference to the function of flight ; these, 
again, to the form and movement of the chest ; these, again, to 
the function of breathing, and so on throughout the entire body 
of the bird. 

This principle of 'correlation' is traceable in the structure and 
working of each and every organ and probably in every part of 
every organ of the bird. Thus, given a feather, it is possible to 
infer that its owner had a particular form of collar-bone, a parti- 
cular kind of skeleton, a particular type of mouth, a particular 
structure of lung, a particular method of breathing, excretion, 
digestion, a particular temperature and heart-beat, even a parti- 
cular kind of mind. Again, given a particular form of collar- 
bone, skeleton, mouth, lung, &c., we can infer a feather. If enough 
be known of the comparative morphology of the bird group, 
it is possible by the use of this principle to make astonishingly 
sweeping and accurate inferences. 

Cuvier was far from being the first to apply his principle. In a 
sense it is obvious. If anyone were to find a severed hand, he 
would know that it had once been attached to the body of a 
human being, and not to that of an animal. He could make a very 
likely guess at sex, occupation, age, state of health, and the social 
position of the owner of the hand. This is nothing but the ' prin- 
ciple of correlation' which is the theme of most detective stories. 
Aristotle had, to some e:ttent, been able to act upon this prin- 
ciple, but Cuvier, out of the great stores of his knowledge of 
organic forms, refined and extended the application of it far 
beyond any of his predecessors. In Cuvier’s hands the principle 
of correlation could often be brought to bear upon the merest 
fragment. From a little bit of leg bone, for example, even the 
'leggy' nature of which no one but a trained naturalist could 




The Mechanical World 

guess, he succeeded in reconstructing an entire giant bird of a 
very aberrant type. His reconstruction was proved to be accurate 
by subsequent discoveries. 

The principle of correlation has been of special value in the 
study of fossils, since these are usually fragmentary. Cuvier was 
therefore in a good position to elucidate the relationship between 
the living and the extinct forms. Thus arose the modern science 
of 'palaeontology* which owes to none so great a debt as to him. 
In his time large numbers of very strange fossil forms were being 

The effect on the mind of Cuvier of these strange discoveries 
may itself seem strange. He realized that the evidence of geology 
showed that there had been a succession of different types of 
animal population, and he recognized that vast numbers of species, 
many no longer existing, had appeared upon the earth at different 
periods. Following Linnaeus, he was a firm believer in the fixity 
and unalterability of species. He had, however, to account for the 
extinction of many forms of life, and the new appearance of many 
other forms. His explanation was that the earth had been the 
scene of a series of great catastrophes, of which the last was the 
Flood recorded in Genesis ! He expressly denied the existence of 
fossil man. 

Cuvier did not commit himself to the doctrine of a special 
creation following each catastrophe. He suggested that on each 
occasion the earth was repeopled from the remnant that survived. 
This did not explain the regular succession of new species in geo- 
logical time. He believed that these came from parts of the world 
still inadequately explored by geologists. His followers carried 
the matter farther, and elevated his teaching into a doctrine of 
successive creations. This came to assume fantastic forms even 
in the hands of serious scientific exponents, one of whom, as late 
as 1849, expounded the science of palaeontology on the basis of 
twenty-seven successive creations. 

Cuvier*s great work Le Rlgne Animal appeared in 1819. With 
various enlargements, modifications, and improvements by his 
pupils it remained standard for many years. To him and through 
his disciples Comparative Anatomy owes so much that the work 
may be said to be still standard. His personality ht up a zeal for 

Multiplicity of Organic Forms 

comparative anatomy and palaeontology which lasted throughout 
the nineteenth century. Of the many inspired by this movement 
a typical representative was Richard owen (1804-92). He 
was also influenced by Naturphilosophie and was an obstinate 
opponent of Darwinian evolution. 

Owen embarked on an immense investigation of the teeth of 
mammals set forth in his Odontography (1840-5). Teeth, being 
the hardest parts of the body, are found fossilized more often than 
any others. Thus his investigations led him into palaeontology, 
of which he became an admitted master. Among his best-known 
works in that department are those on the giant bird, the recent 
but extinct Dinomis of New Zealand (1846), and the much more 
ancient giant walking sloth, the fossil Mylodon of South America 

In 1856 Owen became Director of the Natural History Depart- 
ment of the British Museum, and his activity and. industry rose 
to the occasion. His great Anatomy and Physiology of the Verte- 
brates (1866-8) was based entirely on personal observation, and 
was the most important of its kind since Cuvier. The system of 
classification he adopted has not won favour, but as a record of 
facts the book was of very great value. 

The activity of the comparative anatomists during the nine- 
teenth century was immense. Many new Classes were described 
on the basis of fossil material. The teaching of Darwin, providing 
a framework into which comparative studies could be fitted, gave 
the effective stimulus to such work. The alliance of comparative 
studies with evolutionary doctrine had the effect of focusing atten- 
tion on structure as distinct from function. Comparative physio- 
logy almost ceased to be studied in the later nineteenth century, 
and is only now reviving. Comparative anatomy in its turn be- 
came largely a study of developmental stages, and embryology 
became the comparative study par excellence, 

(v) Biological Exploration. 

In the exploratory voyages of the eighteenth century the prac- 
tice was begun of carrying naturalists with equipment for observ- 
ing and collecting. One of the earliest and most important of the 
expeditions thus provided sailed the Pacific between 1768 and 


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1776 under Captain james cook (1728-79). Joseph banks (1745- 
1820), a young amateur of great wealth and scientific competence, 
accompanied him and provided equipment. The staff included 
several artists, and a pupil of Linnaeus went as botanist. The 
voyage yielded many plants and animals new to science. Cook's 
two other voyages were also very productive. 

^ Among such expeditions a most important place is taken by the 
voyage of the Beagle in 1831-4, which carried as naturalist the 
youthful CHARLES DARWIN (1809-82). His name is so associated 
with the evolutionary idea through which he profoundly influenced 
scientific, philosophical, political, religious, and ethical thought, 
that certain of his other claims are often forgotten. To appreciate 
his distinction, it is necessary to recall that, had he never written 
on evolution, he would still stand in the front rank among 
naturalists, and would have to be included in any history of 
science. Thus, as a single example, even during the voyage in the 
Beagle he reached conclusions that modified and extended the 
fundamental working principles of geology and palaeontology. 

In Darwin’s record of experience in the Beagle in the famous 
Journal of Researches (1839) ^ special interest attaches to his 
observations on the highly peculiar animals and plants connected 
with oceanic islands. The Galapagos and St. Helena are good 
examples. Their extraordinary wealth of peculiar forms and the 
difference of these from those of the nearest neighbouring land — 
either continental or insular — are among the most striking phe- 
nomena in the distribution of living things. They, more perhaps 
than any other, suggested to Darwin his solution of the problem of 
the origin of species. 

Second only in importance to the voyage of the Beagle was that 
of the Erebus and Terror (1839-43) which explored the Antarctic 
under the command of Sir James Ross (1800-62). As naturalist 
there accompanied him Joseph dalton hooker (1817-1911), 
afterwards in charge of the Botanic Gardens at Kew. 

Hooker was an industrious collector and skilled systematist. 
None of his numerous writings is of more weight than those 
(published 1844-60) on the flora encountered in this voyage. They 
include accounts of the plants of the Antarctic area, as well as 
those of Tasmania and New Zealand, and laid the foundation of 


Multiplicity oj Organic Forms 

the systematic study of plant geography. Further Hooker showed 
the vast importance in the economy of Nature of the minute marine 
plants known as 'diatoms'. 

The expedition was also important for its revelation of a very 
varied fauna in a region hitherto unexplored, namely the depths 
of the sea. Four hundred fathoms were sounded by Ross, 
and life was proved to be abundant there. We now know that 
there is life in the open sea at every depth with a great concentra- 
tion near the surface and at the bottom. Until about 1869, how- 
ever, with the laying of the first Atlantic cable, it was not realized 
how vast and varied a fauna and flora there is, and how different 
are the conditions of life at the two levels. The effective knowledge 
of the ocean fauna dates from the work of the Challenger natural- 
ists. They showed that most of the living matter in the world is 
contained in the microscopic plant forms that float at and near 
the surface. 

The greatest of all biological explorations was that under- 
taken by this British Admiralty vessel Challenger in 1872-6. 
She carried full equipment for six naturalists under Charles 
WYVILLE THOMSON (1830-82). She travelled 69,000 nautical 
miles in the course of which every ocean and the least fre- 
quented parts of the world were visited, and hundreds of deep- 
sea soundings were taken. 

The vast collections of the Challenger were investigated by a 
whole army of naturalists under John Murray (1841-1914). The 
results were issued by the British Government in fifty large 
volumes. These provide the best-worked-out account of any bio- 
logical expedition, and form especially the solid bases of a science 
of Oceanography. They made it evident that, for any understand- 
ing of the life of our planet as a whole, an exact knowledge of 
the physical conditions of the sea is essential. Oceanography has 
since developed in a manner which demonstrates the interdepen- 
dence of the biological and the physical sciences. A study which 
involves more than two-thirds of the earth's surface, and impli- 
cates the whole past and future history of the other third, is of 
primary importance to our conception of life as a whole. 

The voyage of the Challenger was succeeded by that of the 
United States Government steamer Tuscarora, whose scientific 


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staff investigated the floor of the Pacific. Other American and 
Norwegian expeditions followed in rapid succession. Alexander 
AGASSIZ (1835-1910) was especially prominent in this work. 
Trained as an engineer, he was able greatly to improve the 
apparatus of oceanic investigation. Among his most remarkable 
results was his demonstration that the deep-water animals of the 
Caribbean Sea are more nearly related to those of the Pacific 
depths than they are to those of the Atlantic. He concluded that 
the Caribbean was once a bay of the Pacific, and that it has been 
cut off from the Pacific by the uprise of the Isthmus of Panama, 

(vi) Distribution of Living Things, 

Many facts significant of the past or present configuration of 
the earth's surface have been revealed by the study of oceano- 
graphy, and it may be said that the subject has greatly modified 
our general conception df the world of life. Nor is this remarkable, 
since the major part of the earth's surface is covered by sea, and 
the general level of depression of the sea is much greater than the 
general level of elevation of the land. 

Oceanic plants dwelling near the surface were studied on the 
Challenger in conjunction with the floating fauna with which they 
dwell. The name plankton (Greek ‘ drifting ') was invented for this 
whole community by victor hensen (1835-1924) of Kiel (1888). 
The study of plankton has become of great importance. Hensen, 
primarily a physiologist, began it while considering the produc- 
tion of nutritive substances under different meteorological condi- 
tions. He thus laid the foundations of the systematic study of 
the economics of the life of the ocean — oceanic bionomics, as we 
may call it. The subject is fundamental for our conception of the 
course of life as a whole upon this planet. 

The circumstances of life on the ocean floor, as revealed by the 
Challenger, and by later expeditions, are entirely different from 
those at the surface. The pressure at 5,000 fathoms is about 5 tons 
to the square inch as against 15 lb. at the surface. No sunlight 
penetrates there ; below 200 fathoms all is dark. The temperature 
in the depths is uniform, and not much above freezing. There are 
no currents, and no seasons. Conditions are substantially uniform 
the world over, on the equator and at the poles. There is no 


Multiplicity of Organic Forms 

vegetable life to build up the bodies of the animals that dwell 
there, and thus the animals prey only on one another, drawing 
their ultimate supplies from the dead matter that rains down from 

The results of the deep-sea dredging have been in certain respects 
disappointing. Specimens of numerous new genera, and species of 
known families have been brought up. Many are interestingly 
specialized, but few are widely different in essential structure from 
more familiar forms. No ' missing links ' have been discovered, no 
new Classes or Orders found. 

The Challenger found, and further exploration has confirmed, 
that the species of plants and animals of the open ocean, whether 
on the surface or at the bottom, are mostly very widespread. An 
exception must be made for the inhabitants of the extremest 
depths. The distribution of oceanic forms is determined by such 
factors as temperature, degrees of saltness, intensity of light, 
pressure, &c. 

The extension of the knowledge of the conditions that prevail 
in the ocean and in its superincumbent atmosphere is leading to a 
new range of scientific ideas. As the laws of oceanic life were seen to 
come into relation with those of physical conditions, a most im- 
pressive physicp-biological parallelism was distinguished which 
may one day provide a real ‘ physiology' of the ocean. The word 
physiologia was, in fact, originally applied to the material working 
of the world as a whole, and not to the individual organism. Thus 
Gilbert ushered in the modem scientific era with his Earth as a 
Magnet, a New Physiology (1600). 

For a philosophical view of our planet as a whole a knowledge 
of the distribution of the life on land as well as in the sea is neces- 
sary. That different countries had different kinds of living forms 
was always obvious. In the eighteenth century Buffon (pp. 
278-9) drew attention to 'natural barriers' delimiting flora and 
fauna. Lyell (1834, p. 287) convinced his readers that the present 
distribution of life is determined by past changes involving the 
major land-masses. The materials obtained by Darwin in the 
Beagle (published 1839-63) brought out striking facts in the geo- 
graphical distribution of animals, both living and extinct. The 
peculiar way in which existing species were placed on the earth's 


The Mechanical World 

surface was, however, a special object of interest to the traveller 
and collector Alfred russel w' allace (1823-1913), known for 
writings on South America and the Eastern Archipelago. 

Wallace produced in 1876 his Geographical Distribution of 
Animals, still the most important work on the subject. He based 
his discussion on mammals, dividing the land-surface of the earth 
into six zoogeographical regions. These he named Palaearctic, 
Nearctic, Ethiopian, Oriental, Australian, and Neotropical, These 
have been retained in great part by more modern workers. The 
most important changes since his time aie [a) the separation 
of Madagascar (Malagasy) from the Ethiopian region; [h) the 
general recognition that the Palaearctic and Nearctic regions are 
more nearly allied to each other than to any other region, and 
their union into a Holarctic region ; and (c) the subdivision of the 
‘Australian’ or Pacific region. 

Wallace, demonstrated many remarkable faunal contrasts. 
None is more striking than that between the islands of Bali and 
Lombok, near Java. These islands are separated by a deep strait 
which at its narrowest is but fifteen miles. Yet, as Wallace re- 
marked, they ‘differ far more in their birds and quadrupeds than 
do England and Japan’. This strait, known as the ‘Wallace Line', 
has been generally regarded as delimiting the Oriental from the 
highly peculiar Australian zoogeographical region. 

The zoogeographical regions into which the earth’s surface can 
be divided must obviously depend upon the particular group of 
animals chosen, since different groups are of different geological 
age and have different modes of dispersal. It happens, however, 
that the division of geographical regions based on mammals 
accords closely with that based on perching birds, and is not 
vastly different from that based on certain invertebrate groups, 
e.g. the spiders, earthworms, &c. Very different from these, on 
the other hand, is the division based on such very ancient groups 
as reptiles or molluscs. 

The general principles that determine plant regions are similar 
to those of animals, but their application is considerably different. 
The subject has been broached mainly in connexion with the 
flowering plants. These are geologically younger than the groups 
on which zoogeographical regions are based. Moreover, tempera- 


Multiplicity oj Organic Forms 

ture and moisture are of overwhelming importance in the life of 
plants. Even between countries in the same regions of plant 
geography which present but slight differences of climate certain 
notable floristic differences may occur. Further, the means of 
dispersal of flowering plants are more effective than those of most 
animal groups. The effects of this are sufficiently evident on 
oceanic islands. 

A pioneer plant geographer was the German philosopher and 
traveller, Alexander von Humboldt (p. 282). Von Humboldt began 

Fig. 94. The main zoogeographical regions. The ‘Australian* region 
includes an immense number of islands, too small to appear on the map. 

his Kosmos (1845-7) when he was seventy-six, and he completed 
it in what he called the ‘improbable years' which followed. This 
great book, now seldom read, did good service in emphasizing 
the relations between the forms and habits of plants and the 
character and soil of their habitat. 

Certain resemblances between the flora of Africa, South America, 
and Australia had impressed Humboldt and other naturalists. 
In 1847 J* Hooker (p. 340) suggested in explanation a land 
connexion between South Americaand Australiaas late as Jurassic 
times. Various names, forms, and areas have been ascribed to this 
now fragmented continent. 

Attempts to delimit definite plant regions have been less suc- 
cessful than those of the zoogeographers. A simple scheme is to 
divide the earth's flora into three primary areas: (a) the North 


The Mechanical World 

Temperate Zone, (&) the Tropical Zone, and (c) the South Tem- 
perate Zone. The northern tropic cuts off {a) from (6) with con- 
siderable accuracy. The southern tropic separates {b) from (c) 
with less precision. 

(а) The North Temperate Zone contains most land. It is con- 
tinuous save for the geologically recent break at the Behring 
Straits. It is characterized (i) by needle-leaved cone-bearing trees ; 
(ii) by catkin-bearing and other trees that lose their leaves in 
winter ; and (hi) by a great number of herbaceous plants that die 
down annually. 

(б) The Tropical Region occupies areas widely separated by 
intervening ocean. It is characterized (i) by giant Monocotyledons, 
notably the palms, by the Banana family, and by the enormous 
grasses known as ' bamboos * ; (ii) by evergreen polypetalous trees, 
and by figs ; (hi) by the rarity of herbaceous plants which, in this 
region, are mostly parasitic on other plants. 

(c) The South Temperate Zone occupies very widely separate 
areas of South Africa, South America, Australia, and New Zea- 
land. It is characterized by a number of peculiar Natural Orders, 
mostly of shrub-like habit. Many are intolerant of moisture. In- 
dividual species are very numerous and often very restricted in 
area of distribution. 

Geographical regions are biologically interesting not so much 
in themselves, but as revealing or summarizing the history of the 
various groups from which they are constructed. Thus the distri- 
bution in space of living forms is ultimately referable to their 
distribution in time. The discussion of the one is of little profit 
without the other. The first systematic efforts to correlate the 
two sets of facts for plants were made by william crawford 
WILLIAMSON (1816-95) of Manchester, who came early under the 
influence of William Smith (p. 280) and began his work on plants 
in 1858. Williamson demonstrated that in coal are to be found 
gigantic woody forms similar to the higher existing flowerless 
plants, such as horse-tails, ferns, and club-mosses. 

Knowledge of the geological succession of plant forms became 
astonishingly detailed, and the floristic landscape at various 
periods and in various parts of the world was confidently restored. 
Moreover, owing to the fact that plant cells have definite and thick 


Multiplicity of Organic Forms 

walls which may be preserved in fossils, it is sometimes possible to 
examine the minute structure of fossil forms. In many cases even 
the reproductive processes are susceptible of close examination. 
Such studies have produced remarkably definite theories of the 
line of descent of plant forms, and of the interrelation between 
the great groups. 

7. Physical Interpretation of the Living Organism, 

(i) Beginnings of Modern Physiology, 

Throughout all history there has been an opposition, alike in 
philosophy and in science, between the interpretation of the nature 
of life in terms of mechanism and that in terms of some other 
entity. In the first quarter of the eighteenth century this conflict 
came into very clear view. 

GEORGE ERNST STAHL (1660-1734), professor at Halle and 
a fashionable physician, was an extremely voluminous writer, 
especially on chemistry. He saddled that science with the unfor- 
tunate theory of ' phlogiston ’ (p. 288) which held its ground until 
Lavoisier. In physiology he set himself especially against the 
mechanism of Descartes. To the French philosopher the animal 
body was a machine. To the German physician the word machine 
expressed exactly what the animal body was not. The phenomena 
characteristic of the living body are, Stahl considered, governed 
not by physical laws but by laws of a wholly different kind. These 
are the laws of the sensitive soul which, in its ultimate analysis, is 
not dissimilar to the psyche of Aristotle. Stahl held that the im- 
mediate instruments, the natural slaves, of this sensitive soul, 
are chemical processes (1708). 

Almost exactly contemporary with Stahl was his rival at Halle 
FRIEDRICH HOFFMANN (1660-1742), who was no less skilled a 
chemist and at least as verbose a writer. In Hoffmann*s view the 
body is like a machine. Nevertheless he separated himself, on the 
one hand from the pure mechanists of the school of Descartes and 
Boerhaave by claiming that bodily movements are the exhibition 
of properties peculiar to organic matter and, on the other, from 
the Stahlian vitalists by denying the need to invoke a sensitive 
soul. 'Life*, he wrote, 'consists in the movements of the blood. 
This circular movement maintains the integrity of that complex 


The Mechanical World 

which makes up the body. The vital spirits which come from the 
blood are prepared in the brain and released therefrom to the 
nerves. Through them come the acts of organic life which can be 
reduced to the mechanical effects of contraction and expansion ' 

An important participator in the controversy was Hermann 
BOERHAAVE (1668--1738), professor of medicine at Leyden, and one 
of the greatest physicians of all time. He, too, was skilled in 
chemistry. His admirable Institidiones medicae (1708) remained 
the standard account of physiology for half a century. In this 
work Boerhaave goes systematically through the functions and 
actions of the body, seeking to ascribe chemical and physical 
laws to each. He does lip-service to the influence of mind on body, 
but in practice is as completely mechanist as Descartes. Thus he 
still believed that something material passes down the nerves to 
cause movement by distending the muscles. He set the tone to 
physiological thought for at least a century. 

Throughout the eighteenth and nineteenth centuries nearly all 
important physiological investigators were medical men. An 
exception was the exemplary parish priest, the Rev. Stephen 
HALES (1677-1761), who made many important advances in both 
animal and vegetable physiology. His work on the functional 
activity of plants was the most important until the nineteenth 
century. His Vegetable Staticks (1727) contains the record of a 
great number of experiments on living plants, devised to inter- 
pret their activity in terms of recognized physical forces. Thus, 
measuring the amounts of water taken in by the roots and that 
given off by the leaves, he estimated what botanists now call 
‘ transpiration He compared this with the amount of moisture 
in the earth, and showed the relationship of the one to the other. 
He calculated the rate at which the water rises in the stems, and 
showed that this has a relation to the rate at which it enters by 
the roots and is transpired through the leaves. He measured the 
force of the upward sap-current in the stems. He sought to show 
that these activitiesof living plants might be explained inmechani- 
cal terms with reference to their structure. 

An interesting contribution by Hales was his demonstration 
that the air supplies something material to the substance of 


Physical Interpretation oj the Living Organism 

plants. This we now know to be carbon dioxide. Following 
upon this he showed with the aid of the air-pump that air 
enters the plant, not only through the leaves, but also through 
the rind. 

Hales endeavoured to give a quantitative expression to the con- 
ception of the circulation of the blood in animals. He showed that 
just as there is a ' sap-pressure ' that can be measured, so there is 
a ' blood-pressure ' that can be measured. Moreover he perceived 
that this pressure in the vessels varies according to circum- 
stances. It is different in the arteries and the veins; different 
during contraction of the heart from what it is during its dilation ; 
different with a failing and with an active heart ; different in large 
and in small animals. All these differences Hales measured. He 
measured, too, the rate of flow in the capillaries of the frog. These 
experiments and conclusions of Hales initiated the quantitative 
phase of the science of animal physiology. 

In contrast to the secluded career of Hales is that of albrecht 
VON HALLER (1708-77), a Swiss of noble birth and ample means 
who, after many active years in Dutch and German universities, 
retired to his native Berne. He exhibited literary and scientific 
activity almost unparalleled in range and volume. His great 
Elementa Physiologiae (1759-66) set forth his conceptions of the 
nature of living substance and of the action of the nervous system. 
These formed the main background of physiological thinking for 
a hundred years after his time, and are still integral partsof physio- 
logical teaching. 

Associating life with movement and muscular contraction, 
Haller concentrated on an investigation of the muscle-fibres. A 
muscle-fibre, he pointed out, has in itself a tendency to shorten 
with any stimulus, and afterward to expand again to its normal 
length. This capacity for contraction Haller called 'irritability'. 
He recognized irritability as an element in the movement of 
various organs, and notably of the heart and of the intestines. 
The salient features of irritability are {a) that a very slight stimu- 
lus produces a movement altogether out of proportion to the 
original disturbance, and (6) that it will continue to do this 
repeatedly, so long as the fibre remains alive. We now recognize 
irritability as a property of all living matter. 


The Mechanical World 

Besides its own inherent force of irritability, Haller showed 
that a muscle-fibre can develop another force which (a) comes to 
it from without, {b) is carried from the central nervous system by 
a nerve, and (c) is that by which muscles are normally called into 
action after the death of the organism as a whole. This is the 
'nerve force* which he thus distinguished from irritability. It 
provides one way of arousing irritability. 

Having dealt with movement, Haller turned to feeling. 
He showed that the tissues are not themselves capable of sensa- 
tion, but that tlie nerves are the channels or instruments of this 
process, and that all the nerves are gathered together into the 
brain. These views he supported by experiments involving 
lesions or stimulation of the nerves and of different parts of the 
brain. He ascribed special importance to the outer part or cortex, 
but the central parts of the brain he regarded as the essential seat 
of the living principle, the soul. Although his view on the nature 
of the soul lacks clarity, he separates such conceptions sharply 
from those which he is able to deduce from actual experience. His 
work has, throughout, a modern ring, and he may reasonably be 
regarded as the father of modem physiology. 

(ii) Foundations of Bionomics, 

Light was thrown on the vital activities of plants by the chemist 
JOSEPH PRIESTLEY (p. 288). In his Experiments and Observations 
on Different Kinds of Air (1774) he demonstrated that plants 
immersed in water give off the gas which we term ' Oxygen*. He 
observed, too, that this gas is necessary for the support of animal 
life. His contemporary the French chemist, Lavoisier (p. 289), 
made quantitative examinations of the changes during breathing 
(1774, p. 289). These displayed the true nature of animal respira- 
tion, and proved that carbon dioxide and water are the normal 
products of the act of breathing. 

In the meantime jan ingenhousz (1730-99) was introducing 
the highly important concept of the balance of animal and vege- 
table life. He was a Dutch engineer who worked in London with 
Hunter, and in 1779 published his Experiments upon Vegetables ^ 
discovering their great power of purifying the common air in the 
sunshine and of injuring it in the shade and at night. It contains 


Physical Interpretation oj the Living Organism 

a demonstration that the green parts of plants, when exposed to 
light, fix the free carbon dioxide of the atmosphere. He showed 
that plants have no such power in darkness, but that they give 
off, on the contrary, a little carbon dioxide. This most significant 
discovery is the foundation of our wliole conception of the 
economy of the world of living things. Animal life is ultimately 
dependent on plant life. Plants build up their substance from the 
carbon dioxide of the atmosphere together with the products of 
decomposition of dead animals and plants. Thus a balance is 
kept between the animal and the plant world. The balance can 
be observed in the isolated world of an aquarium. 

The biological contribution of John hunter (1728-93), whose 
life was closely contemporary with his pupil Ingenhousz, is 
peculiarly elusive and difficult to present. His older contemporary 
Linnaeus and his young contemporary Cuvier were both occupied 
in classifying organisms. To do this they sought always dif- 
ferences. It was similarities, however, th^t attracted Hunter. 
He experimented on and anatomized over 500 species. He 
designed to trace systematically through all these the different 
phases of life, as exhibited by their organs, their structure, and 
their activities. But his main work was his museum. A spirit 
informs it which is as different as possible from the ‘magpie in- 
stinct ‘ which has been the motive of many great collections. Here 
every object has its place and its reason for being included. 
Hunter created the modern idea of a museum by his conception 
of a collection to illustrate the varieties of structure and function 
right through the organic series. 

Hunter was ever seeking the general principles that’ underlie 
the dissimilarities in organic forms. The most general of all is 
that mysterious thing called life. Life is never exhibited by itself, 
but is seen in the various activities of living things. As a surgeon 
Hunter naturally stressed, among these, the power of healing and 
repair. This power is peculiar to living things, and cannot be 
paralleled in the non-living world. He considered that, whatever 
life may be, it is something held most tenaciously by the least 
organized being. It must therefore be independent of structure 
and must be somehow an attribute of a substance which all 
organic forms contain. These ideas lead to the conception of 


The Mechanical World 

protoplasm, the substance, simple in appearance, yet inconceivably 
complex in ultimate structure and composition, without which 
life is never found. Hunter did not use the word 'protoplasm', 
which was invented (in 1846) fifty years after his death. But he 
was reaching out toward the conception of a common material 
basis of life (pp. 358-61). 

The orderly observations of vital phenomena by naturalists 
such as Hunter, Linnaeus, and Cuvier were given an entirely 
new direction by the chemical workers of the next generation. 
Respiration had already been made chemically intelligible by 
Priestley, Lavoisier, and Ingenhousz. Many other processes of the 
living organism were now chemically interpreted by Liebig and 
his school. 

JUSTUS VON LIEBIG (1802-73), professor of chemistry at Giessen, 
was an exceedingly stimulating teacher who had an immense 
following and did much to introduce laboratory teaching. He 
greatly improved the methods of organic analysis and, notably, 
he introduced a method for determining the amount of urea in a 
solution. This substance is found in blood and urine of mammals, 
and was the first organic compound to be prepared from what 
were then regarded as inorganic materials. It is of very great 
physiological importance, for it is regularly formed in the animal 
body in the process of breaking down the nitrogenous substances, 
known as 'proteins’ (p. 360), characteristically found in associa- 
tion with all living substances. 

With his colleague, Friedrich wohler (1800-82), who had 
already synthetized urea (1828), Liebig showed that a complex 
organic group of atoms — a 'radicle' as it is now called — is capable 
of forming an unchanging constituent which can be traced through 
a long series of compounds. A radicle may behave throughout as 
though it were an element (1832). The discovery is of primary 
importance for our conception of the chemical changes in the 
living body. 

From 1838 onwards Liebig devoted himself to attempting a 
chemical elucidation of living processes. In the course of his 
investigations he did pioneer work along many lines that have 
since become well recognized. Thus he classified articles of food 
with reference to the functions that they fulfilled in the animal 


Physical Interpretation oj the Living Orgariism 

economy (fats, carbohydrates, proteins), and he taught the true 
doctrine, then little recognized, that all animal heat is the result 
of combustion, and is not 'innate*. 

Very important was Liebig’s teaching that plants derive the 
constituents of their substance, their carbon and nitrogen, from 
the carbon dioxide and ammonia in the atmosphere, and that 
these compounds are returned by the plants to the atmosphere in 
the process of putrefaction. This development of the work of 
Ingenhousz made possible a conception of a sort of ‘circulation* 
in Nature. That which is broken down is constantly built up, to 
be later broken down again. Thus the wheel of life turns on, the 
motor power being energy from without, derived ultimately from 
the heat of the sun. 

By far the major part of existing living matter is contained in 
green plants. These also provide the ultimate source of aliment 
for the entire animal kingdom. The economic significance of the 
sources from which the substance of plants is replenished cannot, 
therefore, be exaggerated. A most important source is carbo- 
hydrate, especially in the form of starch, the formation of which 
is associated with the green matter itself. 

We now know that starch is built up in the plant from the 
carbon dioxide absorbed from the atmosphere (p, 349) ; that starch 
formation is a function of the living plant-cell, intimately con- 
nected with the green substance ; and that the process is active 
only in the presence of light. (The name ‘Chlorophyll*, Greek = 
‘leaf green*, was coined in 1817.) Steps toward the modern posi- 
tion were made by the French botanical experimenter henri 
DUTROCHET (1776-1847). A key to the working of the living 
organism is the process by which the gases of the atmosphere 
come into contact with the tissues. In animals the general charac- 
ter of this is fairly evident, especially in such as breathe actively. 
Plants, however, were long in giving up their secret. Dutrochet 
showed (1832) that little openings on the surface of leaves — 
‘stomata* (Greek, plural of stoma, ‘mouth*) as he called them — 
communicate with spaces in the substance of the leaf, but it was 
sixty years before the stomata were generally recognized as the 
normal channel of gaseous interchange. Dutrochet also knew from 
Ingenhousz that the plant as a whole gave off oxygen and absorbed 



A a 

The Mechanical World 

carbon dioxide, and he showed that only those cells that contain 
green matter are capable of absorbing the carbon dioxide (1837). 

From carbon dioxide assimilation and carbohydrate formation 
we turn to a consideration of the origin and fate of nitrogenous 
substances in living things. Davy, Liebig, and others were well 
aware of the importance of nitrogen in the substance of plants. 
Liebig showed that nitrogen is taken into the plant by the 
roots in the form of ammonia compounds and nitrates. He made 
the general process of nutrition intelligible by a wide generaliza- 
tion of the utmost importance. Rejecting the old idea that plants 
grow by the absorption of humus, he claimed that carbon dioxide, 
ammonia, and water contain in themselves all the necessary 
elements for the production of vegetable matter and that these 
substances are also the ultimate products of their processes of 
putrefaction and decay (1840). 

JULIUS SACHS (1832-97) of Wurzburg was immersed from 
1857 onward in problems of plant nutrition. He demonstrated 
that the green matter of plants, chlorophyll, is not diffused in 
tissues but contained in certain special bodies — * chloroplasts ' 
as they were later (1883) named. He showed also that sunlight 
plays the decisive part in determining the activity of chloroplasts 
in absorption of carbon dioxide. Further, chlorophyll is formed 
in them only in the light. Moreover, in different kinds of light 
the process of carbon dioxide assimilation goes on with different 
degrees of activity. The views and discoveries of Sachs were 
brought together in his treatise on botanical physiology (1865). 

The French mining engineer, jean baptiste boussingault 
(1802-87), applied himself persistently, and, in the end, success- 
fully to the nitrogen problem. During the fifties he succeeded in 
proving that plants absorb their nitrogen not from the nitrogen 
of the atmosphere but from the nitrates of the soil. He showed 
further that plants can grow in soil devoid of organic or carbon- 
containing matter, provided that nitrate be present, and that 
therefore the carbon in plants must be derived from the carbon 
dioxide of the atmosphere. 

Thus was built up a definite economic picture of the world 
of life, plants drawing their substance from the inorganic world, 
animals drawing their substance from plants, and the decom- 


Physical Interpretation oj the Living Organism 

position of both going back into the inorganic world to be re- 
absorbed by plants. 

(hi) Cell Theory. 

While chemists were interpreting in their own terms the pro- 
cesses by which living things build up the substance of their 
bodies, microscopists were investigating the details of those bodies 
that were invisible to the naked eye. The mystery of the unex- 
plored lay still over the world of microscopic beings with their 
bizarre forms and entrancing strangeness. By some they were 
fancifully endowed with complex organs that they do not possess, 
but the 'minima naturae' were more generally regarded as the 
'simplest' and 'most primitive' of beings wherein the secrets of 
life might most hopefully be sought. 

Such inquiries were prosecuted especially with those minute 
creatures — 'animalcula' was the old name for them — that ap- 
peared, seemingly ' spontaneously in infusions of various kinds. 
The term Infusoria soon, however, came to include certain other 
minute organisms that present superficial resemblances to the 
animalcula of infusions (1764). The limits and definition of the 
Infusoria were long disputed. 

As so often, the discussion was barren until directed along lines 
which corresponded to a concrete and intelligible theory. It came 
gradually to be realized that all non-microscopic and certain 
microscopic organisms are aggregates, each unit (cell) of which 
has some degree of individual life. Not until this position was 
reached could the Infusoria be properly definable and the term 
restricted to unicellular forms to the exclusion of ceU aggreg'^tes 
(1841). Again, as so often in scientific history, this position was 
repeatedly approached and even temporarily occupied before it 
was actually won. Such a pioneer attempt was that of the wildly 
speculative Naturphilosoph, lorenz oken (1779-1851), who in 
1805 compared Infusoria to the 'mucous vesicles (cells) of which 
all larger organisms are composed', spoke of 'the infusorial mass 
or Urschleim (protoplasm) of which larger organisms fashion 
themselves', and claimed that such organisms are equivalent to 
' agglomerations of Infusoria '. 

The conception that ‘cells' of various forms and functions, but 


The Mechanical World 

variants of a common plan with a greater or less degree of in- 
dependent life, form the basis of larger organisms came slowly to 
be accepted doctrine. The progress occupied the first half of the 
nineteenth century. The nomenclature of the earlier part of this 
period is naturally confused. The term 'cellula* dates back to 
Hooke (1664), who, however, applied it only to the cell-walls of 
plant-cells. The word ' cell ' is frequently used by late eighteenth- 
and early nineteenth-century writers to describe the microscopic 
divisions perceptible in most tissues with suitable treatment. 
The central body of the ' cell ' substance, its controller, is the 
nucleus. This term was first applied to the important structure 
now known by that name in 1823. Robert Brown (p. 331) in 
1831 realized that the nucleus was a regular feature of plant-cells 
and he normalized the use of the word. 

The great Czech naturalist Johannes Evangelista purkinje 
(1787-1869) in 1835 drew attention to the close analogy of the 
packed masses of cells in certain parts of animals with those in 
plants. FELIX DUJARDIN (1801-62) of Toulouse, a most pene- 
trating observer, entered in that year upon a critical examination 
of microscopic forms. Two conceptions of primary importance 
emerged from his researches. First, he clearly distinguished uni- 
cellular organisms as such, and adequately delimited the In- 
fusoria. Secondly, he discerned that life is always associated 
with a substance of mucilaginous consistence with certain very 
definite optical, chemical, and physical characteristics. Purkinje, 
who worked on comparable lines, gave to it the name protoplasm 
(1839; Greek = first formed). It became recognized that the 
living parts of all cells were composed of protoplasm. 

The first adequate presentation of the knowledge of the cell 
as a body of doctrine (1839) was made by theodor schwann 
(1810-82), a pupil of Johannes Miiller. He extended the discus- 
sion to the ovum or egg which is the beginning of the animal or 
plant body. In some animals, as the hen, the egg is very large, 
being distended with food substance — the yolk — and surrounded 
by a larger and protective substance — the white or albumen. In 
other eggs, as the frog's, the amount of yolk and albumen is much 
less. In yet others yolk and albumen are reduced to a minimum, 
as in the microscopic eggs of mammals then recently discovered 


Physical Interpretation oj the Living Organism 

(1828) by von Baer (p. 332). Schwann discerned that all these 
are essentially cells and exhibit the characteristic elements of 
cells — nucleus, protoplasm, cell membrane, &c. 

The development of the egg into the young animal (or plant) 
proceeds by division of the egg cell. This process of 'segmentation' 
is particularly evident in the earliest stages of development, and 
had been casually noted in a variety of organisms by several 
early naturalists. Schwann treated the process as a normal part 
of embryonic development. He showed that the continued divi- 
sion of the egg or 'germ-cell' gives rise to the organs and tissues, 
and he distinguished on a cellular basis five classes of tissues: 

[oL) Tissues in which the cells are independent, isolated, and 
separate. Such is the blood. 

(6) Tissues in which the cells are independent but pressed 
together. Such is the skin. 

(c) Tissues in which the cells have well-developed walls that 
have coalesced to a greater or less degree. Such are car- 
tilage, teeth, and bones. 

(d) Tissues in which the cells are elongated into fibres. Such 
are tendons, ligaments, and fibrous tissue. 

(e) Tissues ‘generated by the coalescence of the walls and 
cavities of cells '. Here he included muscles and nerves. 

Schwann now passed to a general statement of his belief as to 
the cellular origin and structure of animals and plants. His con- 
clusion may be expressed thus: 

[а) The entire animal or plant is composed either of cells or of 
substance thrown off by cells. 

(б) The cells have a life that is to some extent their own. 

(c) This individual life of all the cells is subject to that of the 
organism as a whole. 

This general attitude is still valid. 

The synthesis of the ideas of protoplasm, unicellular organisms 
or 'protozoa', and egg or germ-cell was made by max schultze 
(1825-74). He devoted himself to a study of tissues — 'histology' 
— in a wide range of animals. In 1861 he gave the definition of a 
cell as 'a lump of nucleated protoplasm', and in 1863 defined 
protoplasm as 'the physical basis of life'. He showed that proto- 
plasm presents essential physiological and structural similarities 


The Mechanical World' 

in plants and animals, in lower and higher forms, in all tissues 
wherever encountered. 

Great influence on the biology of the second half of the nine- 
teenth century was exercised by the liberal Berlin professor 
RUDOLF VIRCHOW (1821-1902). His main contributions are set 
forth in his Cellular Pathology (1858), in which he analyses diseased 
tissue from the point of view of cell-formation and cell-structure, 
and enunciates the now familiar idea that the body may be 
regarded 'as a state in which every cell is a citizen. Disease is a 
civil war, a conflict of citizens brought about by external forces. ' 
Further: ‘Where a cell arises, there a cell must have been before, 
even as an animal can come from nothing but an animal, a plant 
from nothing but a plant. Thus in the whole series of living things 
there rules an eternal law of continuous development, nor can any 
developed tissue be traced back to anything but a cell.' 

Virchow crystallized the matter in his famous aphorism, Omnis 
cellula e cellula ('Every cell from a cell’), to be placed beside 
Omne vivum ex ovo ('Every living thing from an egg’) of Harvey, 
and Omne vivum e vivo ('Every living thing from a living thing’) 
of Pasteur. These are three of the widest generalizations to 
which biology has attained. They were all reached within the 
ten years around the middle of the nineteenth century, for 
though Harvey’s was stated much earlier, he had not the evi- 
dence on which to base it. 

(iv) Protoplasm, 

From a time when it was first recognized that a similar sub- 
stance ‘protoplasm’ underlies all vital phenomena there has been 
much interest in its chemical and physical composition. Strictly 
the subject is insoluble since protoplasm can only be adequately 
investigated when it has ceased to be the basis of life. We may 
learn what protoplasm takes in and what it throws out. We 
may gain some idea of its local reactions to ingested or applied 
substances. But living protoplasm is beyond the reach of the 
chemist’s activities. It is protoplasmic products and dead proto- 
plasm that have been the subject of most of his researches. 

Dead protoplasm consists of a very complex mixture of numer- 
ous substances. Of these the bulkiest is water. The others are 


Physical Interpretation oj the Living Organism 

largely made up of the complex nitrogenous groups known as 
proteins and their derivatives, of the lipoids or fats, and of the 
carbohydrates or starchy substances. The general significance of 
these three types was first made definite by Justus von Liebig 
about 1840 (p. 352). 

Living protoplasm is liquid. Nevertheless, an elementary ac- 
quaintance with its behaviour shows that it exhibits a considerable 
degree of 'viscosity', that is it has some of the properties of a 
sticky or of a jelly-like substance. Modern views of the intimate 
structure or composition of living protoplasm have become closely 
linked with a comparison of its behaviour with that of other sub- 
stances in the colloid ('glue-like') state. The study of the colloid 
state, one of the many areas in which the old sciences of chemistry 
and physics have become merged, was initiated by thomas 
GRAHAM (1805-69) in 1850 while Master of the Mint in London. 
The term was already in use, but he applied it to a particular 
state of matter. He divided soluble substances in general into the 
two great classes, colloids and crystalloids. He observed that 
certain substances (a) pass very slowly into solution, (b) do not 
crystallize, and (c) cannot diffuse or diffuse very slowly through 
organic membranes. Of these substances glue is the type, hence 
the name colloid. In this class are starch (compare starch paste), 
white of egg, gelatine (the basis of most table jellies). Opposed to 
these in all three respects are the crystalloids. 

Graham was aware that certain substances — silica for instance 
— could exist as either colloid or crystalloid. He recognized, too, 
that instability was a characteristic of colloids. Moreover, he 
perceived that most colloids are of organic origin. He foresaw 
certain modem views of the nature of vital activity in his con- 
ception that the surface energy of colloids 'may be looked upon 
as the probable primary source of the force appearing in the 
phenomena of vitality'. 

The knowledge of the essential nature of colloids was but little 
extended until the twentieth century. Investigators of our own 
generation have given a physical interpretation to the differences 
between the colloid and crystalloid states. 

Among the colloids, biologically the most important is the vast 
and varied class known as proteins. They are absolutely necessary 


The Mechanical World 

to the building up of protoplasm. Dead protoplasm largely con- 
sists of them. They are not only essential for growth and repair 
of living substance, but they can be used by the living organism 
as a source of energy and of heat, though the carbohydrates and 
fats share this function with them. Chemically the proteins are 
all built up of very large molecules. 

The modern chemistry of the proteins is based on the work of 
the great German chemist emil fischer (1852-1919) from 1882 
onwards. Fischer demonstrated that proteins are built up of 
linkages or condensations of numbers of molecules of the substances 
known as amino-acids. The members of this very peculiar class 
are characterized by the presence in each molecule of one or more 
NH2 {'amino’) groups and one or more COOH ('carboxyl’) 
groups. The former gives them basic qualities, the latter acid. 
According as one or the other predominates, the amino-acid acts 
as a base or as an acid. 

A favourite theory of the nature of protoplasm regards it as a 
mixture of amino-acids. These can become immeasurably com- 
plex by associating with each other in varyingly intimate ways. 
A modem mechanist view of life pictures all vital activity as a 
continuous change and interchange of the conditions and relations 
of amino-acids. These, it is held, act through local changes in the 
degree of viscosity. Many other phenomena of the living cell have 
been interpreted as due to changes in degree of viscosity. 

Another aspect of protoplasmic activity is that of enzyme 
action. The word 'enzyme’ (Greek ‘in yeast’) was introduced by 
Willy Kiihne (1878) to distinguish a class of organic substance 
which activates chemical change. Such an enzyme can act on an 
indefinite amount of material without losing its activating power. 
The living body produces a large number of enzymes. These are 
remarkably specific in their action. 

Within the protoplasm, though not of it, are numerous 
materials, the so-called 'food substances’, which are often of 
relatively simple composition. Under this heading are to be in- 
cluded sugars and their derivatives, fats, and the 'reserve’ 
proteins. The problem of the nature of protoplasm thus resolves 
itself into that of the nature of the matrix in which a vast variety 
of controlled reactions are taking place, and the ways in which 


Physical Interpretation oj the Living Organism 

the matrix can influence these reactions. The chemical processes 
at any moment within a single cell are of many and varied types. 
In spite of the smallness of cellular dimensions, these must some- 
how be spatially separated from one another. 

(v) Physiological Synthesis. 

With the parallel development of a knowledge of the vital 
processes as a continuous elaboration and breaking down of living 
substance, of the living body as a structure composed of cells, 
and of the physical basis of life as protoplasm, there developed 
new views of the organism as a physico-chemical mechanism. 
Mechanist views have never lacked critics, and it is significant 
that the most effective critic of mid-nineteenth-century mechan- 
ism, JOHANNES MULLER (i8oi— 58), was himself an experimental 
physiologist of genius who is largely responsible for the picture 
of the body as a machine. In Muller's Handbook of Physiology 
(1834-40) the results alike of microscopic and of comparative 
anatomy, of physics and of chemistry were, for the first time, 
systematically brought to bear on physiological problems. His 
researches on the chemistry of the animal body touch on those of 
Liebig at many points. His most important physiological investi- 
gations, however, dealt with the action and mechanism of the 
senses, and were important starting-points for modem research. 

The doctrine specially associated with Muller's name is the 
' principle of specific nerve energies '. This teaches that the general 
character of the sensation, following the stimulation of a sensory 
nerve, depends not on the mode of stimulation, but on the nature 
of the sense organ with which the nerve is linked. Thus mechani- 
cal stimulation of the nerve of vision produces luminous impres- 
sions, and no other ; stimulation of the nerve of hearing gives 
rise only to an auditory impulse, and so on. This doctrine is of 
such importance that it is well to consider some of its implica- 

What do we know of the world in which we live ? Only what 
our senses tell us. But how do our senses convey anything to us ? 
That no man can answer. All we know is that certain external 
events somehow initiate specific disturbances in certain nerves, 
that these nerves convey the disturbances to the brain or central 


The Mechanical World 

nervous system, and that a sensation then arises. We can dimly 
picture a mechanism by which the external event may elicit a 
specific nerve-impulse, and we know a little about the nature of 
the impulse and how it travels up the nerve. But how that 
impulse becomes a sensation, which is what we experience, and 
how experience gives rise to something which so alters a nerve or 
series of nerves that it induces action — of these things we are not 
only completely ignorant but it is difficult to believe that we can 
ever be other than ignorant. Indeed, there are reasons to believe 
that here is a veil which never can be rent by mortal man. 

But consider further. External events are known to us only 
through our senses. Nevertheless from one and the same event 
we may receive completely different sensations. Thus, an electric 
stimulation of the optic nerve will give rise to a visual sensation ; 
the same stimulation of the olfactory nerve yields a sensation of 
smell.; of the auditory nerve a sensation of sound. Further, dif- 
ferent events may give rise to the same order of sensation. Thus 
it matters not whether the optic nerve be stimulated by electri- 
city, by heat, or mechanically, the sensation aroused will be 
visual. If our optic nerve were grafted to our auditory organ and 
our auditory nerve to our optic organ we should find ourselves 
transported to a world so strange that we cannot form the re- 
motest conception of it. (Such an operation may actually be 
practicable in certain organisms.) To beings with senses different 
from ours the world would be utterly different. 

The law of specific nerve energies is thus fundamental for our 
view as to the range of validity of scientific method, and indeed of 
experience as a whole. That law is a standing criticism of the 
‘common-sense’ view that the world is as we see it, and that its 
contents, and particularly the living things in it, can be com- 
pletely understood by us. 

Muller was a convinced vitalist. He laid emphasis on the exis- 
tence of something in the vital process that was, and must remain, 
insusceptible of mechanical explamation or physical measurement. 
This doctrine, however, occasionally misled him. Thus he held 
it impossible to measure the velocity of the nervous impulse. Yet 
that velocity was measured by his own pupil, Helmholtz, some 
ten years later. Vitalistic views are useful to the philosopher, but 


Physical Interpretation oj the Living Organism 

the working man of science had best, with Claude Bernard, forget 
them while he is at his appointed task. 

The French physiologist Claude Bernard (1813-78), one of 
the greatest of all biological thinkers and experimenters, was the 
most effective contributor to the presentation of a concert of all 
the bodily processes as a chemico-physical mechanism. Perhaps 
his greatest discovery was that the liver builds up, from the 
nutriment brought to it by the blood, certain highly complex 
substances which it stores against future need, and that these 
substances, and notably that known as glycogen^ it subsequently 
modifies for distribution to the body according to its requirements. 

It was already recognized that the source of bodily energy is 
the breaking down of nitrogenous substances, of which the final 
degradation product is urea (p. 352). Bernard, by his work on 
glycogen, demonstrated that the body not only can break down 
but also can build up complex chemical substances. This it does 
according to the requirements of its various parts. 

Bernard thus destroyed the conception, then still dominant, 
that the body could be regarded as a bundle of organs, each with 
its appropriate and separate functions. He introduced a con- 
ception that the various forms of functional activity are inter- 
related and subordinate to the physiological needs of the body as 
a whole. 

No less important, as bearing on this conception, was Bernard's 
work on digestion. Up to his time, an elementary knowledge of 
the facts of digestion in the stomach constituted the whole of 
digestive physiology. Bernard showed that this digestion is ' only 
a preparatory act' and that numerous other processes are in- 
volved. Thus the juice of the 'pancreas' or sweetbread, poured 
into the intestine near the lower opening of the stomach, emulsi- 
fies the fatty food substances as they leave the stomach and splits 
them into fatty acids and glycerin. He showed further that the 
pancreatic juice has the power to convert insoluble starch into 
soluble sugar for distribution to the body in the blood, and that 
it has a solvent action on such proteins as have not been dissolved 
in. the stomach. 

A third great synthetic achievement of Bernard was his exposi- 
tion of the manner of regulation of the blood-supply to the 


The Mechanical World 

different parts of the body. This we now call the 'vaso-motor 
mechanism'. In 1840 the existence of muscle-fibres in the coats 
of the smaller arteries was discovered. Bernard showed that these 
small vessels contract and expand, thereby regulating the amount 
of blood supplied to the part to which they are distributed. This 
variation in calibre of the blood-vessels is, he showed, associated 
with a complex nervous apparatus. The reactions of the apparatus 
depend upon a variety of circumstances in a variety of other 
organs. Thus he provided another illustration of the close and 
complex interdependence of the various functions of the body 
upon each other. 

Bernard's clear conception of the reciprocal relations of the 
organic functions led him to a very valuable generalization. He 
perceived that the characteristic of living things, indeed the test 
of life, is the preservation of internal conditions despite external 
change. ‘All the vital mechanisms', he held, ‘varied as they are, 
have only one object, that of preserving constant the conditions 
of life in the internal environment.' This phrase is the seal on 
Bernard's belief that the living organism is something sni generis, 
something quite different from everything in nature that is not 
living. The organism has an object, and it uses a mechanism for 
attaining that object. Is this conception infinitely removed from 
that of Aristotle ? 

What is the internal environment of an organism ? Bernard was 
thinking chiefly of the blood. But if we think of a part in terms 
of cells we see the environment of the cell made up of four main 

(a) The neighbouring cells and cell products. 

(b) The substances that are brought to it by the blood. 

(c) The substances that it throws off and that are removed 
from it by the blood. 

(d) The nervous impulses that come to it. 

The whole vast mass of physiological research since Bernard's 
time may be regarded as a commentary on these four factors of 
the internal environment. 

(vi) Supremacy of Nervous System. 

It will be impossible to follow further all the factors of 


Physical Interpretation oj the Living Organism 

internal environment, but there is one group upon which it is well 
to enlarge since the whole standpoint with regard to it has altered 
fundamentally since the time of Bernard. It is the consideration 
of the nervous system and its relation to the body as a whole. 

By the time of Haller (pp. 349~5o), the naked-eye anatomy of 
the nervous system had become quite familiar. A new physiological 
phase was opened by luigi galvani (1737-98) of Bologna, who 
showed (1791) that if a nerve be subjected to a certain method of 
stimulation, the muscle to which it leads will contract. The 
electric nature of Galvani's method was revealed by Alessandro 
VOLTA (1745-1827) of Pavia. In the fifth decade of the nineteenth 
century the Berlin professor, emil du bois-reymond (1818-96), 
pupil and successor of Johannes Muller, showed that a nervous 
impulse is always accompanied by the passage along the nerve of 
a change of electrical state. He and other investigators demon- 
strated, moreover, that chemical changes in the muscle accom- 
pany contraction. These chemical changes are initiated — * lit up 
we might say — by the nervous impulse. 

In the meantime sir Charles bell (1774-1842) had been at 
work on the double spinal roots from which most of the nerves 
of the body arise. He showed that of these roots, one conveys 
only sensory elements, while the other conveys only motor ele- 
ments. Thus the investigation of the action of individual nerves 
became possible. 

In the first half of the nineteenth century there appeared many 
comparative studies on the nervous system. Cuvier based his 
classificatory system in part upon the nervous reactions (p. 330). 
He had himself explored the nervous system of Molluscs, Starfish, 
and Crustaceans. His influence may be traced in many works on 
the anatomy of the vertebrate nervous system prepared in the 
first half of the nineteenth century, but it was not until the ap- 
pearance of T. H. Huxley’s Manual of the Anatomy of the In- 
vertebrated Animals (1877) that full stress came to be laid on the 
ascendancy of the nervous system in all members of the animal 

Despite the lead of Huxley, the nervous physiology of inverte- 
brates remained neglected. But the internal structure of the 
nervous system of mammals has been investigated with very 


The Mechanical World 

great detail. It has been found to be almost inconceivably 
complex. The investigations have been greatly helped by the 
introduction of new technique, at which we may now glance. 

The early anatomists, from Vesalius onward, recognized that 
the central nervous system consists of two main parts — the grey, 
and the white matter. It was perceived that in the brain the 
grey matter is mostly on the surface, while in the spinal cord it is 
mainly central in position. 

Soon after the foundation of histology as a special science it 
was observed that white matter consists of masses of enormous 
numbers of fibres while grey matter contains also numerous cells. 
These facts were known to Purkinje (1835, p. 356) and were 
formally set forth by Jacob henle (1809-85). It was, however, 
more than forty years before the Swiss Albrecht kolliker 
proved that all nerve-fibres are nothing more than enormously 
elongated processes given off from nerve-cells with which they 
retain continuity (1889). These nerve-cells are to be found either 
in the central nervous system itself or in the various ganglia. 

In 1873 the Pavia professor, camillo golgi (1844-1926), intro- 
duced a method of depositing metallic salts within various cell 
structures. These deposits are very evident under the microscope, 
and Golgi succeeded in applying this method to the central ner- 
vous system. He showed that the cells in that system tend to 
resemble irregular polygons from the angles of which project pro- 
cesses, axons, the essential parts of the nerve-fibres which ulti- 
mately end in a complicated system of branches, dendrites. The 
dendrites form twig-like 'arborizations' round other dendrites 
linked to other cells. Ultimately the system ends in terminal 
cells associated with sense organs, glands, or muscles. 

The method of Golgi has been developed especially by ramon 
Y CAJAL (1852-95) of Madrid, almost the only important scien- 
tific investigator that Spain has hitherto produced. His re- 
searches stamped upon biology the conception of an immensely 
complex series of systems for the transport of nervous impulses. 
These systems, if intact and working well, determine the activities, 
the reactions, the whole life of the organism. Most significant 
work has been done during the last half-century in the light of 
this conception. 


'Physical Interpretation oj the Living Organism 

While the various nervous tracts were thus being traced, much 
work was in progress in the localization of the functions of the 
different parts of the nervous system. 

In i86i the French surgeon, Paul broca (1824-80), demon- 
strated in a post-mortem room at Paris a relationship between 
loss of speech and injury to a definite area of the cortex. Broca 
made many contributions to the knowledge of the brains of men 
and of apes. 

Others soon continued his work in the experimental field. Thus 
in 1870 a very versatile naturalist, gustav fritsch (1838-91), 
and a student of insanity, eduard hitzig (1838-1907), working 
together at Berlin, found that stimulation of certain parts of the 
cortex regularly produced contraction of certain muscles. The 
Englishman david ferrier (1843-1928), followed this up by 
demonstrating that other areas of the cortex, which do not evoke 
muscular activity, are nevertheless functionally differentiated 

In the half-century that has since elapsed the surface of the 
brain has been mapped in great detail. Special areas have been 
associated with movements of different parts and different organs. 
Others are related to various forms of sensory discrimination such 
as sight, sense of position, weight, taste, and the like. Yet others 
are involved in the use of language, both in written and spoken 

Influential in determining modern views of the action of the 
nervous system have been researches on the nature of 'reflex 
action’, that is, non- voluntary movement in response to a sensory 
stimulus. The conception may be traced in physiological writings 
from Descartes onwards. The term 'reflex action’ was invented 
(1833) by the English physiologist marshall hall (1790-1857). 
The study of reflexes has resulted in the localization of functions 
in the grey matter of the spinal cord much as with the grey matter 
of the cortex. 

Since Hall’s time there has been vast extension of the concep- 
tion of reflexes. In addition to the simple nervous arc there 
are also more complex arcs which depend for their action on an 
elaborate mechanism. Beside ‘spasmodic’ events, as sneezing, 
coughing, scratching, &c., many of the ordinary acts of life, 


The Mechanical World 

standing, walking, breathing, &c., are expressible as reflexes. The 
attempt has also been made by Pavlov (1849-1936) and others to 
press even the 'instincts' into the same category, and the cortex 
has been shown to have the power of establishing new reflexes. 
The school that has been thus occupied seeks to explain all the 
reactions, and indeed the whole life, of the higher organisms on a 
purely objective basis without reference to volitional elements. 

If the simple reflexes of animal bodies are tested, it will be found 
that they clearly serve certain ends. Lightly touch the foot of a 
sleeping child and it will withdraw it. Tickle the ear of a cat and 
it will shake it. Exhibit savoury food to a hungry man and his 
digestive process will at once get to work, his mouth will 'water'. 
These instances might be multiplied a hundredfold. Such reflexes 
are admirably adapted to their ends. Many will continue in an 
animal in which the brain has been removed, provided that the 
spinal cord be still intact. Nevertheless, in the higher animals, 
and especially in man, the reflexes are controllable to a greater or 
less extent by the will. 

But to leave the question at that would give a false idea of the 
extremely complex functions performed by the central nervous 
system. Thus, the spinal cord which, to the naked eye, is a 
longitudinal and little differentiated nervous mass, is, in fact, a 
collection of nerve-centres which have historically, both in the 
individual and in the race, been formed by the union of a series of 
separate segments. Each segment in this system governs certain 
functions or movements of the body, and the activity of each 
segment is related in various ways to the activity of the other 
segments. There is thus a very complex process of 'integration' 
which runs right through the nervous system. 

The growing knowledge of the bodily functions of chemical and 
physical nature gradually revealed that these activities are far 
more largely under nervous control and discipline than was for- 
merly conceived. Thus, the main factor in the activity of any part 
is its blood-supply, but the blood-supply is determined, as Bernard 
showed (p. 364), by the state of contraction of the vessels of supply 
which are in their turn under nervous control. Similar relations 
prevail for the state of nutrition of muscles, for the action of the 
sweat glands of the skin, for the mechanism of childbirth, and for 


Physical Interpretation of the Living Organism 

a thousand bodily states. The regulation and control of all these 
events, processes, and states by the nervous system has since 
come to be called nervous integration. 

(vii) Mind as Condition of Life. 

During the.nineteenth century there was an enormous extension 
of scientific interest in the analytical study of animal function 
through physical experiment. The exponents of this science of 
physiology applied themselves mainly to the higher animals. They 
devoted themselves to an examination of the parts or functions 
in the adult or developed state. The results were portentous in 
bulk, complexity, and interest, yet they went a very little way to 
help us in considering the organism as a whole. 

The animal body is, as it were, a vast and complex maze. The 
physiologist enters it, and he wanders there as long as he will. But 
his close and detailed report on its paths and walls helps but little 
toward the exposition of the design as a whole, for the physiologist, 
in his special studies, is well nigh bound to consider isolated func- 
tions wall by wall, path by path. He selects respiration, nutrition, 
muscular movement, the action of the nervous system, or the 
like. But the performance of each of the functions of each of 
these systems is inextricably linked with the performance of the 
functions of all the other systems. 

We are always looking for metaphors in which to express our 
idea of life, for our language is inadequate for all its complexities. 
Life is a labyrinth. But a labyrinth is a static thing, and life, is 
not static. Life is a machine. But machines do not repair them- 
selves, nor do they reproduce themselves. Life is a laboratory, a 
workshop. But it is a workshop in which a thousand processes 
go on within a single microscopic cell, all crossing and intercrossing 
and influencing each other, and it is a workshop which is con- 
stantly multiplying itself and producing its like. 

Life is a dance. There was a ‘dance of death', and there is a 
dance of Hfe. It is but a metaphor. When we speak of the ultimate 
things we can, maybe, speak only in metaphors. Life is a dance, 
a very elaborate and complex dance! The physiologist cannot 
consider the dance as a whole. That is beyond his experimental 
power. Rather he isolates a particular comer or a particular 

B b 369 


The Mechanical World 

figure. His conception of the dance, as thus derived, is imperfect 
in itself and, moreover, in obtaining it he has disturbed the very 
pattern of the dance. The shortcoming of his method becomes 
fairly evident when he seeks to relate his corner to another in 
a far distant part of the dance. 

Moreover, even should he seek to treat the organism as a whole, 
he is still almost bound to consider it as an Tndividuar complete 
and separate in itself, shut off from its environment and its 
history, bom, as was Minerva, armed and fully equipped from 
the head of Jove. But in fact living beings are not so. There is 
every degree of independence of their fellows among organisms. 
' Individuality ' comes into prominence only in the more differen- 
tiated groups. The term is almost inapplicable to plants, in which 
physiology is, in effect, of a community, and that is a study not 
far, in its conceptions, from that of bionomics. The very idea of 
the 'individual* involves a historical record which the science of 
physiology has hitherto almost ignored. 

Physiology alone is of its nature incapable of presenting any 
picture of the mode of action of the organism as a whole, though 
modem doctrines of the workings of the nervous system have 
given some explanation of certain forms of animal behaviour. Yet 
the functions of the nervous system, like those of other systems, 
are relative to the other functions of the body. Not only is respira- 
tion, for example, regulated by the nervous system, but the 
nervous system itself is regulated by the character of the respira- 
tion. Raise the amount of carbon dioxide in the blood, and the 
respiratory movements are first stimulated and finally diminished 
via action on the respiratory centres. It would be possible to 
show that the same is true of any system or part of a system 
in relation to any other. What picture, then, can physiological 
processes give us of the interrelated complex of activities that we 
call an organism? 

The physiologist has found that his science can be best prose- 
cuted on the higher animals. Why? Because the functions of 
these creatures are best differentiated. If he wishes to study 
movement, respiration, nutrition, nervous action, he finds in the 
higher animals separate organs devoted to these processes. Such 
organs he cannot so easily, or cannot at all, find in the lower 


Physical Interpretation of the Living Organism 

organisms. In the lowest of all, the Protozoa, every process is 
carried on in a minute single cell. 

But the most distinctly and clearly developed characteristics of 
the highest animals are their mental powers. To discuss these in 
the mechanistic nomenclature adopted by physiology is merely 
contradiction in terms. The one thing that we really know is our 
own thoughts, and external things — including the science of physio- 
logy — we know only in relation to these. How then can external 
things be said in any sense 'to explain* our thoughts ? It is more 
intelligible to invert the process and to say that phenomena — 
including those of physiology — are parts of our thinking, than to 
say that our thinking can be built up of phenomena. 

But if we emphasize the conception of science as dealing with 
phenomena — 'things which appear* — we reach a modus vivendi 
both for a conception of mind, and for the findings of science. 
Having agreed that science shall deal only with phenomena, we 
expressly exclude our own mind, which is not an appearance at 
all, but that to which appearances happen. Science must keep to 
the phenomenal level. On that level she may prosecute physio- 
logical study. But no amount of that study will truly represent 
an entity in which any element of mind exists. Is that element of 
mind found in other organisms than myself ? Unless the solipsist 
view be taken, this question must be answered in the affirmative. 
The man who answers it in the affirmative is a vitalist. 

8. Evolution, 

(i) The Word. 

The leading contributions of the nineteenth century to the 
conception of a mechanical world are the twin doctrines of Energy 
and Evolution. As with most important scientific ideas, the enun- 
ciation of neither can be dated exactly or placed to one man*s 
credit. To the doctrine of Energy it is convenient to attach the 
name of Joule, and the date 1842 (pp. 324-5). The doctrine of 
Evolution has become so closely linked with the name of Darwin 
that 'Darwinism* is often taken as a synonym of this doctrine 
which is dated to 1859, publication of the Origin of 

species. The term* 'Evolution* should, however, be retained for 
the philosophical view that the world attained its present form 


The Mechanical World 

not by a single creative act, but by a slow process over long ages. 
This was held by a number of ancient thinkers such as Plato 
(pp. 32 7), and by several unorthodox medieval thinkers, such as 
Averroes (p. 139). Of this view, the doctrine of Evolution of 
Organic Forms, or Darwinism proper, is a special case. 

The Latin word evolvere means to unroll, to roll forth, to revolve. 
In classical usage its noun evolutio acquired the special meaning 
of the unrolling of a scroll in order to read it, * the opening of the 
records ' as we might say. In the Vulgate version of the Scriptures, 
evolvere is used either in its literal sense or, most often, to designate 
passage of time as marked by the revolving heavens. Derivatives 
of evolvere had little apf)lication in the Middle Ages, since scrolls 
had been replaced by books with leaves, and no form of it occurs 
in the Authorized Version of the English Bible (1611). The word 
Evolution was given currency in modern literature by the group of 
seventeenth-century philosophers* known as the ‘Cambridge Neo- 
platonists'. They employed it to describe the unrolling, as of a 
scroll, of vast records of Time (cf. Revelation vi, 14 ; Isaiah xxxiv, 
4). ‘The whole Evolution of ages, from everlasting to everlasting, 
is represented to God at once', wrote (1667) founder Henry 
More (1614-87), paraphrasing ‘a thousand years in Thy sight are 
but as yesterday when it is past' {Psalm xc, 4). 

Search of the writings of many philosophers of the eighteenth 
century, notably those of Leibnitz (1646-1714), Diderot (1713- 
84), and Kant (1724-1804), reveals uses of the word evolution 
extended from that of the Cambridge Neoplatonists, and even 
adumbrations of the modern philosophical sense considered under 
heading {e) below. During the same century the word ‘ Evolution ' 
was developed on lines comparable to those of the Cambridge 
Neoplatonists by the ‘Naturphilosophen', and notably by Oken 
(P* 355); ill connexion with their doctrine of ‘ideas'. In this sense 
it was reimported into nineteenth-century English, probably 
by Samuel Taylor Coleridge (1772-1834). ‘The sensible world', 
he wrote, ‘is but the evolution of Truth, Love and Life or their 
opposites in Man' (1820). 

In the course of its varied and adventurous career the word 
‘ Evolution ' thus acquired many different meanings and shades of 
meaning. It entered into the technical vocabulary of biological 



science — where we are chiefly concerned with it — in at least five 
clearly distinguishable senses. 

{a) Evolution naturally and conveniently designated the pro- 
cess, mainly an unfolding, of the parts of a bud opening into a 
flower ; or again of the imago of an insect, such as a butterfly, in 
its final transformation from the pupa. 

(d) There were two rival theories as to how living things de- 
velop. One held that the germ contained the living organism in a 
substantially complete state, folded on itself. This had to unfold 
in order to pass from the embryonic stage. The other held that 
the germ was at first uniform, and that the form of the embryo 
was later generated in it. The philosophical biologist Bonnet 
(P- 333) gave wide currency to the former view under the name 
Evolution (1762), while the latter came to be known as Epigenesis. 
It is usually said that it is the epigenetic view that has prevailed. 
In the literal sense, but not in certain other senses, this is the 
case (p. 356). 

(c) There has always been a philosophical problem of the rela- 
tion of Being to Becoming. We need not follow this discussion 
in its vast divarications. St. Augustine posed the problem 
for the next millennium and a half: 'In the beginning God 
made Heaven and Earth, that is the seeds of Heaven and 
Earth, for the material of Heaven and Earth was yet in 
confusion; but since it was inevitable that from these seeds 
Heaven and Earth would be, therefore the material is thus 
called' {De genesi contra Manichaeos). These are the seminales 
rationales of the great medieval Christian thinkers who stressed 
being rather than becoming. These seminales iu the mind of God 
were for them the ultimate reality. Bonnet is, in this sense at 
least, a belated medieval, insisting that every being already is, 
and only seems to become. Seventeenth-century thinkers, startled 
by the changes newly revealed by the telescope in the heavens, 
and by the extraordinarily complex processes discerned by means 
of the microscope in the development of individuals on earth, 
directed attention to becoming. This was expressed by the scien- 
tific dilettante Matthew Hale (1609-76), for example, who writes 
of an 'ideal principle in the evolution whereof Humane Nature 
must consist'. Several eighteenth-century authors treat in a 


The Mechanical World 

similar manner of the 'evolution of ideas', including 'ideas' in 
the technical sense of the N aturphilosophie, 

{d) Great confusion has been caused by an early and still 
current misapplication of this last use of the word in biology. 
The process of development of the organism [not its unfolding) 
became called its ' evolution ' ! Thus Erasmus Darwin, grandfather 
of Charles, wrote of ' the gradual evolution of the young animal or 
plant from the egg or seed' {Botanic Garden, 1791), meaning its 
epigenetic development, and not its evolution in the sense of 
Bonnet. This confusing usage has persisted to our time. 

(e) Finally the word is used for a process (or the result of a 
process) by which, in long stretches of time, organic types develop 
(or have developed) from other types. More or less definite expres- 
sions of this view can be traced very far back, but no earlier use 
has been found of the word ' Evolution ' to designate it than that 
of Lyell (1797-18.75) in his Principles. There he discusses in detail 
the biological theories of Lamarck, and notably the view of that 
naturalist that ' certain organisms of the ocean existed first, until 
some of them by gradual evolution, were improved into those in- 
habiting the land' (1831). 

The word ' Evolution ' has been awarded numerous other techni- 
cal meanings in departments other than biology, as for instance 
in mathematics, and in military tactics, where it is not our quarry. 
It is necessary, however, to remind the reader that the biological 
meanings of the word all interdigitate, and that this fact is not 
without significance in the development of the philosophical con- 
ception of evolution. The word, in fact, carries with it all the 
trailing clouds of a confused and intricate past. 

(ii) Eighteenth-Century Evolutionists. 

Among naturalists, the idea of the transformation of species was 
more or less overtly expressed by Hooke (1635-1703), Ray (1627- 
1705), Goethe (1748-1832), Oken (1779-1851), and many others. 
That it was much in the air is shown by the repeated insistence by 
Linnaeus, Haller, Bonnet, and many orthodox biological thinkers 
that species are not transformed from other species but exist in 
the form in which they were first created. (The difficulties that 
arose from the geological record and the way in which they were 



met are reviewed on p. 338.) The whole direction of biological 
activity in the period of Linnaean dominance was against dis- 
cussion of variation or transformation, and in favour of the treat- 
ment of the world of life as something static. Nevertheless, a few 
eighteenth-century naturalists were able to break away from 
this view. We discuss two of these. 

The first naturalist to give both form and substance to a con- 
ception of evolution of living things was Georges louis leclerc, 
COMTE DE BUFFON (1707-88). He was an attractive writer, and 
perhaps the ablest scientific popularizer that has ever lived. 
His great Natural History (1749-1804), in forty-four volumes 
which took fifty-five years to publish, sought to cover the whole 
area of natural knowledge, and was the first modem work of its 
kind. He himself regarded it as a sort of commentary on Newton's 
conception of a mechanical world. A new element in Buffon's 
work was its inclusion of living Nature which Newton had dis- 

Buffon paid little attention to minor differences between 
organisms on which biological classificatory systems must neces- 
sarily be based. For that reason the Linnaean system did not 
appeal to him. He was interested rather in features that can be 
traced through very long series of organic forms. As regards the 
fixity of species he expressed himself variously, but he settled 
gradually into opposition to that view. Particularly he noted 
that animals possess parts which have no function as, for example, 
the lateral toes of the pig which, though perfectly formed, can 
never come into action. To explain these, he conceived that a 
species may alter in type from time to time, but retain marks of 
its previous form, as the pig retains its disused toes. Then, moving 
a little further, he concluded that some species are degenerate 
forms of others. Thus the ape is a degraded man, the ass a de- 
graded horse, and so on. (We have already discussed his views of 
the history of the earth, and its relation to organic forms, on 
pp. 278-9.) 

The ideas of Buffon were examined by Erasmus darwin (1731- 
1802), grandfather of Charles Darwin. He, like Buffon, was 
anxious to show that living phenomena fitted in with those of 
the inorganic and mechanical world. With this in view, he sought 


The Mechanical World 

some way of showing how living things had naturally acquired 
their manifest adaptations to their environment. His solution of 
this problem is buried in the verbiage of several of his bulky 
works. In the best of these, his Zoonomia; or the Laws of Organic 
Life (I794--6), he sums up the general nature of the difficulties 
among which Buffon had been groping. For his solution he 
gathers together precisely those classes of facts that were most to 
impress his grandson. 

‘When we revolve writes Erasmus Darwin, ‘first the changes 
which we see naturally produced in animals after their birth, as in the 
butterfly with painted wings from the crawling caterpillar, or the 
[air-breathing] frog from the [water-breathing] tadpole; secondly 
the changes by artificial cultivation, as in horses exercised for 
strength and swiftness, or dogs for strength, courage, or acuteness 
of smell, or swiftness ; thirdly, the changes produced by climate, the 
sheep of warm climates being covered with hair instead of wool, 
and the hares and partridges which are long buried in the snow 
becoming white during the winter months ; fourthly, the changes 
produced before birth by crossing or mutilation', fifthly, the simi’- 
larity of structure in all the warm-blooded animals, including man- 
kind, one is led to conclude that they have alike been produced 
from a similar living filament. (Very greatly abbreviated.) 

Erasmus Darwin held that similar changes in nature produce 
species in the course of time. These changes, he held, were passed 
on to the offspring. The process is epigrammatically pictured in 
his conspicuously bad poem The Temple of Nature: 

Organic life beneath the shoreless waves 
Was born and nurs'd in ocean's pearly caves; 

First forms minute, unseen by spheric glass. 

Move on the mud, or pierce the watery mass ; 

These, as successive generations bloom, 

New powers acquire and larger limbs assume ; 

Whence countless groups of vegetation spring. 

And breathing realms of fin and feet and wing. 

The mechanism by which such changes come about is, he 
believed, the transmission of character acquired sometimes at least 
as* an act of will. ' All animals undergo perpetual transformations ; 

* This ‘filament' is a spermatozoon which he regarded, following Buffon, 
as a sort of biological unit. 



which are in part produced by their own exertions . . . and many 
of these acquired forms or propensities are transmitted to their 
posterity* {Zoonomia). 

(iii) *Transformism.* 

JEAN BAPTISTE DE MONET DE LAMARCK (1744-1829), unquestion- 
ably the greatest systematist of his age, was unfortunate in the 
simultaneous possession of too arid a style and too fertile an 
imagination. Many of his views were so fanciful that he was 
lightly esteemed by most of his contemporaries. Cuvier, who ad- 
hered to the fixity of species, formed a low opinion of his abilities. 
Charles Darwin, among his successors, held him almost in con- 
tempt. The interest of the theory by which Lamarck is remem- 
bered was not fully realized until after his death. It was discussed 
in great detail by Lyell (1831). 

Lamarck held that no frontiers can ultimately be found between 
species. It seemed to him, therefore, intrinsically improbable that 
they are permanently fixed. In reaching this conclusion he also 
laid stress on the domesticated animals, which vary greatly from 
their wild originals. Who, seeing for the first time a greyhound, 
a spaniel, and bulldog, would not think of them as different 
species ? Yet all have a common ancestor. Their different charac- 
ters have been produced by man*s selective breeding. In Nature, 
too, variations comparable to these in kind are occasionally found 
within the same species. The agent that produces them is, accord- 
ing to Lamarck, the environment. Species, he thought, maintain 
their constancy only so long as their environment remains un- 

Lamarck, having decided on the importance of variation in the 
production of new species, had to consider its mechanism. How 
do changes of environment give rise to variation and so to pro- 
duction of species ? In answer, he enunciated the Taw of use and 
disuse *, inseparably connected with his name. He supposed that 
changes of environment lead to special demands on certain organs. 
These, being specially exercised, become specially developed. 
Such development, or some degree of it, is transmitted to the 
offspring. Thus a deer-like animal, finding herbage scanty, took 
to feeding on leaves of trees. It needed a longer neck to reach the 


The Mechanical World 

leaves. In the course of generations, during which the poor crea- 
tures were always straining their necks to reach their food, long 
necks became an ever more accentuated feature of their anatomy. 
Thus emerged a beast recognizable as a giraffe. Conversely, 
useless organs, such as the eyes of animals that live in darkness, 
being unexercised, gradually became functionless and finally 
disappeared. The character of a longer neck or of defective eyes was 
acquired by the individual in its lifetime and transmitted, in some 
degree at least, to its descendants. 

The great assumption is that acquired characters are inherited. 
Whether and in what sense acquired characters can be inherited 
is a matter of current discussion, but it is certain that in the 
sense suggested by Lamarck they are not inherited. Nevertheless 
Lamarck's work was of value in directing attention to one of the 
most important problems in the whole range of biological thought. 
Unfortunately some of his early supporters set forth evolutionary 
schemes that were fantastic to the last degree. This resulted in 
biological speculation falling into disrepute for the first half of the 
nineteenth century. 

Yet there was one writer of the time, whose work bore upon the 
subject, against whom the charge of reckless speculation could 
most certainly not be made. The Rev. T. R. malthus (1766-1834) 
was a cautious and somewhat formal writer on mathematical and 
economic subjects. He produced anonymously in 1798 his Essay 
on Population. At that time political theory was a matter of 
acute controversy in connexion with the French Revolution. 
Such topics as the 'rights of man', 'natural justice', and the like 
were in the public mind. The most flourishing school of thought 
in England was the ' utilitarian ', which was the direct ancestor of 
that liberal philosophy on which Britain rose to industrial and 
imperial greatness during the nineteenth century. Adam Smith 
(1723-90), Joseph Priestley (1733-1804), and Jeremy Bentham 
(1748-1832) were the chief early spokesmen in England of this 
great movement. Many believed that a day was dawning when, 
amidst universal peace, all men would enjoy complete liberty 
combined with complete equality. Malthus, who followed in 
general the line of utilitarian thought, brought out the difficulties 
that must arise in such a state from over-population, by his famous 



(but fallacious) principle that populations increase in geometric, 
but subsistence at best only in arithmetic ratio. He argued that 
a stage must be reached at which increase in population will be 
limited by sheer want. Thus he held that 'checks' on population 
are a necessity in order to avoid vice and misery. 

Darwin read the Essay of Malthus in 1838, and the Principles 
of Lyell in 1831. The one suggested to him the idea of the Struggle 
for Existence and the Survival of the Fittest, the other the 
general doctrine of Evolution. In the first half of the nineteenth 
century both these ideas were discussed by a nun^ber of writers, 
and notably by several English amateur naturalists accessible to 
Darwin. None put the two ideas together, or at least none put 
them together adequately. Darwin derived nothing or next to 
nothing from such predecessors. 

(iv) 'The Origin of Species.* 

It is the great achievement of Charles darwin (1809-82) that 
he persuaded the scientific world, once and for all, that many 
diverse organic forms are of common descent, that species are 
inconstant and in some cases impossible of definition, and that 
some mechanism must be sought to explain their evolution. In 
search of this mechanism, he directed attention to the occurrence 
of variation, to its persistence, and to the question of its origin 
and its fate. 

In 1859 appeared Darwin's classic Origin of Species. He had 
opened a note-book on the subject in 1837, made a first draft of 
it in 1842, a second in 1844, and in 1858 published, simultaneously 
with ALFRED RUSSEL WALLACE (1823-1913), a preliminary sketch 
of his views. It is an interesting fact that Wallace, like Darwin, 
seems to have caught his idea immediately from Malthus. 

The Origin is one of the world's great books, and has proved 
significant for almost every human activity. It is unnecessary to 
discuss its greatness or its importance. But despite the conviction 
that it carried, and despite the fact that for the half-century after 
its publication its ideas provided the main stimulus for biological 
research, its arguments are frequently defective. 

Darwin's basic claim is that organs and instincts have been 
'perfected by the accumulation of innumerable slight variations, 


The Mechanical World 

each good for the individual'. For this, he says, it is necessary to 
admit only three propositions, (a) ‘That gradations in the per- 
fection of any organ or instinct, either do now exist or could have 
existed, each good of its kind.' (^) ‘That all organs and instincts 
are, in ever so slight a degree, variable.' (c) ‘That there is a 
struggle for existence leading to the preservation of each profitable 
deviation of structure or instinct.' But this assumes that the 
‘profitable deviations' are inherited. Thus not three but four 
propositions are needed. 

Again, after discussing our knowledge of the distribution of 
species in time and space — ^which carries irresistible conviction of 
organic evolution as an historical process — he turns to discuss 
conditions under which a variation is perpetuated. 

‘ Man does not produce variability [in domestic animals] ; he 
only exposes beings to new conditions, and then nature acts on 
the organisation, and causes variability. But man can select varia- 
tions, and accumulate them in any desired manner. He thus 
adapts animals and plants for his own benefit. He can influence 
the character of a breed by selecting, in each successive generation, 
individual differences so slight as to be quite inappreciable by an 
uneducated eye. That many of the breeds produced by man have 
to a large extent the character of natural species, is shown by the 
doubts whether many are variations or aboriginal species. 

‘ In the preservation of favoured individuals and races, during 
the Struggle for Existence, we see the most powerful means of 
selection. More individuals are born than can survive. A grain 
in the balance will determine which shall live and which die — 
which variety or species shall increase in number, and which shall 
decrease, or finally become extinct. 

‘There will in most cases be a struggle between the males for 
possession of the females. The most vigorous individuals will 
generally leave most progeny. But success will often depend on 
special weapons or means of defence, or on the charms of the males ; 
and the slightest advantage will lead to victory.* 

There are here, as we can now see, certain fallacies and 
erroneous assumptions. 

(a) All domestic breeds have not been produced by selecting 
very slight individual differences. Some domestic breeds have 
certainly been produced by breeding from individuals which pre- 
sented great deviations from the normal. 



(b) That a natural variation should confer an advantage is not 
enough to secure its perpetuation. The advantage must be 
effective, and it must be transmissible. Now it is difficult to believe 
that the earlier stages of some developments are effective as, for 
example, a wing so little developed as to give no power of flight or 
of gliding. 

(c) Darwin assumes that species differ from their nearer rela- 
tives in having some special advantages that enable them to 
adapt themselves to slightly different conditions. Closely allied 
species are, however, often found living in identical areas and 
under identical conditions. There are very few cases indeed in 
which the characters by which such species differ from their fellow 
species can be shown to be advantageous, and there are some cases 
in which they can, perhaps, be shown not to be advantageous. 

Darwin’s presentation of Natural Selection as an effective agent 
is probably at its weakest in dealing with the problem of disuse. 
Here he assumes the inheritance of acquired characters in a form 
hardly differing from that of the despised Lamarck. 

‘Disuse, aided sometimes by natural selection, will often tend 
to reduce an organ, when it has become useless under changed 
conditions of life ; and we can clearly understand on this view the 
meaning of rudimentary organs. But disuse and selection will 
generally act on each creature, when it has come to maturity and 
has to play its full part in the struggle for existence, and will thus 
have little power of acting on an organ during early life; hence 
the organ will not be much reduced or rendered rudimentary at 
this early age. The calf, for instance, has inherited teeth, which 
never cut through the gums of the upper jaw, from an early pro- 
genitor having well-developed teeth ; and we may believe that the 
teeth in the mature animal were reduced, during successive genera- 
tions, by disuse or by the tongue and palate having been better 
fitted by natural selection to browse without their aid ; whereas in 
the calf, the teeth have been left untouched by selection or disuse, 
and on the principle of inheritance at corresponding ages have been 
inherited from a remote period to the present day.* 

The full title of Darwin's book was The Origin of Species by 
means of Natural Selection, or the Preservation of Favoured Races 
in the Struggle for Life. Darwin himself compared the action of 
natural selection to that of a man building a house from stones of 


The Mechanical World 

all shapes. The shapes of these stones, he says, would be due to 
definite causes, but the uses to which the stones were put in the 
building would not be explicable by those causes. The conception 
reveals the general weakness of Darwinistic thought which treats 
natural selection as though it were an active and directive agent. 
For when a man builds a house, there is the intervention of a 
definite purpose, directed towards a fixed end and governed by 
a clearly conceived idea. The builder, in the proper sense of the 
word, selects. But the acts of selection — mental events in the 
builder's mind — have no relation to the 'causes' which produced 
the stones. They cannot be compared with the action of Natural 
Selection. If a metaphor be sought for the action of Natural 
Selection, a better one might be the arrangement of stones on a 
sandy shore. Large stones are found high up on the beach. The 
stones become smaller as we descend toward the sea. On approach- 
ing the brink, we come upon a zone of sand. This arrangement is 
due to the forces of winds, waves, and tides acting, according to 
their nature, and according to the nature of the rocks of which 
the cliffs are built, over a long period of time. Provided that it be 
kept well in mind that it is a metaphor, and provided that no 
teleological view is implied, there can be no harm (and not very 
much good) in calling this a 'selective action' of the forces of 
wind, waves, and tides upon the disintegrated rocks. 

Darwin repudiated teleology, but in his title, almost as though 
wishing to emphasize it, he repeats the teleological metaphor and 
speaks of the Preservation of Favoured Races, But how do we 
know that races are favoured ? By their preservation ! And what 
is preservation ? A favour ! And what is a favour ? Preservation ! 

So, too, with the phrase Survival of the Fittest, In the sense in 
which the Darwinians used the word, fittest was often ^nd naively 
confused with physical or even athletic fitness, and to it an ethical 
corollary was sometimes forcibly adjusted. But the only kind of 
fitness implied in the Darwinian phrase was fitness for survival. 
It is doubtless a good thing, on an ethical level, to be brave as a 
lion, and a bad thing, on an ethical level, to be timid as a rabbit. 
But, on a biological level, either quality may indicate fitness. 
Lions survive because of their courage in seeking their prey. 
Rabbits survive because of their cowardice in fleeing from those 



that prey upon them. Courage and cowardice are alike tests of 
fitness. Those that survive are fit, and those that are fit survive ; 
and survival is the test of fitness, and fitness the test of survival! 

Thus these phrases are, on analysis, devoid of ultimate meaning. 
This is very far from saying that no meaning can be extracted from 
the history of their use. Darwin was an investigator of the very 
first rank, but he was inexpert in the exact use of language and 
had little philosophical insight. His biological discovery, though 
of the highest scientific importance, was not quite of the nature 
that many of his, followers thought it to be. 

(v) Doctrine of Descent of Man, 

There is one species whose origin raised acute controversy. 
Ancient and modern anatomists had drawn attention to the like- 
ness of the anatomy of man to that of the apes. Darwin at first 
expressed no opinion on this point. Several of his supporters, 
notably t. h. huxley (1825-95), devoted attention to it. The 
formal expression of Darwin's views was reserved till 1871, when 
at the opening of The Descent of Man he wrote: ‘Huxley has 
conclusively shown that in every visible character man differs less 
from the higher apes than those do from the lower members of the 
same order of Primates.* This was very different from a demon- 
stration of any intermediate form between man and the higher 
man-like apes. Nevertheless, evidence of this sort was gradually 

In 1856, three years before the publication of the Origin, the 
long bones and part of the skull of a man-like being had been 
unearthed in the small ravine of Neanderthal in Rhenish Prussia. 
They were all at first misinterpreted as pathological. Huxley 
ultimately recognized them as those of a human being, but the 
most ape-like yet found. He held that man is ‘more nearly allied 
to the higher apes than the latter are to the lower *. The species to 
which these bones belong is now entitled Homo Neander^alensis,^ 
The remains of about a hundred individuals of this species are now 

Since the discovery of Neanderthal man, a number of other 

* A Neanderthal skull had been found at Gibraltar as early as 1848, but 
had not been brought to scientific notice. 


The Mechanical World 

species of fossil man have been discovered. On the other hand, 
several fossil species of apes approaching nearer than living forms 
to the human stem have also been found. The ape-man series is 
now probably more complete than that of most comparable mam- 
malian groups. About two hundred fossil individuals are known, 
distributed over eleven or more species of quaternary and late 
tertiary measures. 

Even before Darwin, and still more after him, evolutionary 
doctrine was applied to human habits, language, social organiza- 
tion, and psychology. Thus arose a science of Anthropology, 
which owes a deep debt to the French investigator, Jacques 
BOUCHER DE PERTHES (1788-1868). As early as 1830 de Perthes 
discovered in the gravels of the Somme certain flints which he 
believed bore evidence of very ancient human workmanship. In 
1846 he demonstrated the existence of such flints in company with 
the remains of elephant, rhinoceros, and other tropical or extinct 
forms. In his great Antiquites celtiques et antediluviennes (1847- 
64), he established the existence of man from human products in 
Pleistocene and early Quaternary times. In 1863 de Perthes 
clinched this view by discovering near Abbeville, in a Pleistocene 
deposit, a human jaw associated with worked flints. 

These conclusions were accepted, though with caution, by Lyell 
in his Antiquity of Man (1863). Since that time the study of the 
works and arts of Stone- Age man has developed parallel with the 
study of his physical structure. The succession of the cultures, 
crafts, and art of Palaeolithic Man and their emergence into those 
of Modern Man and notably into the culture known as Neolithic 
have now become familiar. It has been equated with geological 
and geographical change. 

The subject of Organic Evolution has been pursued along many 
paths which pass the frontiers of biology and indeed of the 
sciences in the limited sense, and enter into many departments 
where we cannot here follow. Evolution illumines the whole 
history of life, the life of Man in all its manifold variety as well 
as the lives of organisms in all their manifold variety. 

(vi) Reception of the Doctrine of Evolution, 

In 1852 — seven years before the publication of the Origin — the 



philosopher, Herbert spencer (1820-1903), expounded doctrines 
of Evolution in a work where that word was used to describe a 
general process of production of higher from lower forms. He 
devoted the remainder of his long life to a highly elaborate exposi- 
tion of what he regarded as the implications of evolution in every 
department of the inorganic and the organic world, in the structure 
of human society, and in the human mind. He eagerly adopted 
Darwinian principles as soon as the opportunity arose. Since his 
political philosophy of extreme 'individualism' fitted well the 
feeling of the age, his works were very widely read. They were 
translated into many languages, occidental and oriental, and thus 
did more, perhaps, than those of any other man to spread evolu- 
tionary views. The phrase ' Survival of the Fittest ' was coined by 
him (1864). 

That the evolutionary philosophical system of Spencer is an 
object of derision is one of the few points on which all philosophers 
seem now to agree. There are few living who can claim to have 
studied all his works. That the many who have done so are dead 
is a cause for reflection rather on their number than their state. 
But despite his extreme dryness as a writer, Spencer was a very 
great phrase-maker. A surprising number of his dicta have 
obtained currency. A selection of passages from one section of 
one chapter of his first independent work Social Statics (1850) will 
suffice to indicate not only his general attitude, which altered but 
little in later years, but also the philosophical atmosphere of the 
scientific public to which the Origin was delivered, nine years 

‘ Progress is not an accident but a necessity. It is part of nature.’ 
’ All perfection is a fitness to the condition of existence. ’ ‘ Evil tends 
perpetually to disappear.' ‘Nature’s rules have no exceptions.’ 
‘In virtue of an essential principle of life, non-adaptation of an 
organisiA to its conditions is ever being rectified. Whatever pos- 
sesses vitality obeys this law. We see it illustrated in the acclima- 
tisation of plants, in the altered habits of domestic animals, in the 
varying characteristics of our own race. . . . Such changes are 
towards fitness for surrounding conditions.* ‘Civilisation instead of 
being artificial is a part of nature ; all of a piece with the development 
of the embryo or the unfolding of a flower. . . . Man needed one 
moral constitution to fit him for his original state ; he needs another 

c c 385 


The Mechanical World 

to fit him for his present state ; and he has been, is, and will long 
continue to be, in process of adaptation. By civilisation \ve signify 
the adaptation that has already taken place. In virtue of this 
process man will eventually become completely suited to his mode 
of life.' 

The Origin came thus to a world well prepared. It had been 
drafted as early as 1842, and Darwin himself had used the phrase 
* Natural Selection' in a letter as far back as 1837. The central 
idea of the work was far from being new or even modern. Never- 
theless, it created a revolution in biology, and indeed in almost 
every department of thought. It was the first work by a cautious, 
penetrating, highly competent, and experienced investigator that 
set forth a large and carefully sifted body of evidence on the 
subject of Evolution. Darwin himself was not very fond of using 
this word, but usually refers to it, in his modest way, as ' the 
species question His great book, however, was the first that 
suggested a simple and apparently universally acting biological 
mechanism producing changes of form. The struggle of living 
forms, presented as natural selection by the survival of the fittest, 
as set forth by him, proved an extremely stimulating sug- 

The story of the rise of Darwinism has been so well and so often 
told that it is unnecessary to repeat it. It is probably the most 
familiar incident in the history of science. Among the opponents 
of Darwin were Owen, who occupied a very important scientific 
position and was the leading comparative anatomist in Europe, 
and Agassiz of Harvard, a very accomplished naturalist and the 
leading comparative anatomist in America. Both were still be- 
mused by Natur philosophic, as was also von Baer (p. 332), now in 
extreme old age. All opposed to evolution the 'idea* or 'type* of 
Goethe and Cuvier, a metaphysical conception and, of its nature, 
insusceptible of demonstration. 

In Germany, then swept by 'liberal' ideas, Darwinism made 
rapid progress and gave rise to something that was very near a 
religion. The ablest continental critic of Darwinism was the Swiss 
professor at Wurzburg, albrecht kolliker (1817--1905). With- 
out denying the inconstancy of specific forms, and while fuUy 
accepting evolution within the limits of certain wider groups, he 



indicates several real weaknesses in the Darwinian position, 
namely : 

{a) Absence of any experience of the formation of a species. 

(&) Absence of any evidence that unions of different varieties 
(i.e. of incipient species on Darwin’s view) are relatively 
more sterile than unions of the same variety. 

(c) Extreme rarity of true intermediate forms between known 
species, whether living or fossil. 

Kolliker and other critics claimed that the 'chance’ element in 
Darwin’s scheme was but a veiled teleology. Natural selection 
had been elevated to the rank of a ‘ cause ’ leading to an ‘ effect ’ 
and science has to deal not with causes but with conditions. In 
Kolliker ’s view, Darwin was dealing with the ‘might’ and ‘may 
be’ and not with any theory that could be tested by experience. 
Here Kolliker was right. Evolution is perhaps unique among 
major scientific theories in that the appeal for its acceptance is 
not that there is evidence for it, but that any other proposed 
interpretation of the data is whoUy incredible. 

In France the reception of Darwinism was on the whole hostile 
and its advance slow. The influence of Cuvier was still paramount. 
The ultimate victory was complete, though several very able biolo- 
gists, such as Bernard (p. 363), remained unconvinced to the end. 
The movement led to a revival of interest in Lamarck, and 
transformisme, as evolution was called, received in France a 
Lamarckian tinge. 

The battle of evolution is now a stricken field, and the whole of 
modern biology has been called ‘a commentary on the Origin of 
Species ’. Biologists are now at one in the view that living forms 
correspond to a hmited number of common stocks, and tolerable 
agreement has been reached as to the evolutionary history of these 
stocks. It was not many decades, however, before doubt began 
to dawn as to the mechanism of evolution. Even during Darwin’s 
active period, Gregor Mendel (1822-84) was at his unnoticed work 
(1857-69), the rediscovery of which (1900) introduced a particulate 
view of inheritance, a view of which Darwin and the generation 
after him knew nothing. 



Without as within the realm of biology, the leading feature of 
later nineteenth-century thought was its occupation with the con- 
ception of evolution. By unphilosophic minds and by the public 
generally evolution was, erroneously, elevated from a process into 
a ‘ cause ’ and from a law into a force. Further, by constant associa- 
tion with the conceptions of Natural Selection and Survival of 
the fittest. Evolution was frequently confused with them. The 
varied uses of these stock phrases provide good illustrations of the 
control of ideas by words. 

It fell out that the rise of evolutionary theory coincided with a 
period of industrial expansion and also with a period of social 
change to which the much abused term ‘progress’ may reasonably 
be attached. Naturalists discerned in the vast ranges of geological 
time a process of development of living forms to which the term 
‘progress’ might also reasonably be attached. The conditions of 
human life in England of the mid-nineteenth century were, on the 
whole, much better than those of the pre-industrial age. The 
adaptations of the living forms of our world to their environment 
are, on the whole, much better than those of earlier geological 
ages. The two processes were often equated and, for various 
reasons, a belief in ‘ evolutionary progress ’ conquered the imagina- 
tion of the generation. At first the fact was missed, even by 
many naturalists, that adaptation to environment might lead to 
loss of ‘ higher ’ qualities. Darwin himself placed opposite the title- 
page of the Origin a passage from Bacon’s Advancement of Learn- 
ing ‘ Let no man think that a man can search too far ... in God’s 
word or God’s works, divinity or philosophy [that is science] ; 
but rather let men endeavour an endless progress in both.’ But 
the poet who wrote : 

I dipt into the future, far as human eyes could see 

Saw the vision of the world, and all the wonder that would be; 

Till the war-drum throbbed no longer, and the battle-flags were 

In the Parliament of man, the Federation of the world. 

(Locksley Hall, 1832.) 

had to write, sixty years later: 



Is there evil but on earth ? or pain in every peopled sphere ? 

Well, be grateful for the sounding watchword ‘ Evolution * here. 

Evolution ever climbing after some ideal good. 

And Reversion ever dragging Evolution in the mud. 

{Locksley Hall, Sixty Years After, 1886.) 

The fallacies of the nineteenth-century evolutionists were from 
the first clearly discerned by professed philosophers. But in those 
days and in this country, professed philosophers dwelt securely 
and apart in scientifically constructed ivory towers, erected in 
and protected by ancient universities. There they spoke (to each 
other) in the idiom of Plato. Such missives as they sent down to 
mortals (if they sent any) were incomprehensible to that consider- 
able majority that did not understand the idiom. Thus the falla- 
cies of Spencer and of the more optimistic Darwinians attained 
the widest vogue. Thus misunderstandings of Darwin*s method 
and limitations were given a degree of notoriety that amounted 
to general acceptance. 

It would be wrong to end this book with the impression of any 
desire to belittle a very great naturalist. Himself a modest man, 
he rated low — and rightly — ^his own philosophic powers. This 
estimate of himself is additional evidence of his greatness, and of 
the soundness of his judgement. He never permitted himself to 
be drawn into any discussion of the wider implications of his views. 
Despite and perhaps because of his helplessness in the niceties of 
language he has many claims to be regarded as a great writer as 
well as a great naturalist. His services to science were enormous, 
and among them his greatest was to have laid bare the process of 
formation of organic types. Any other view of the origin of species 
than the evolutionary is incredible. That his 'explanation' of 
organic evolution turns out to be rather a redescription, is a 
charge against his philosophic but not against his scientific powers. 
Such redescription is the normal process of advance of scientific 

Thus we part with our story at the dawn of modem classical 
science. The task of science in the age following Newton was to 
describe the world in mechanical terms in the hope of reaching 
a unitary view. The age closed with a considerable advance to- 
wards a unitary conception of Force and with a suggestion for a 



unitary conception of Matter, while in the world of life continuity, 
at least, had been demonstrated. These successes found their most 
characteristic celebration in the Doctrine of Energy, in the Atomic 
View of Matter, and in the Theory of Evolution of Organic Forms. 

Despite such triumphs there yet remained in the narrative 
inconsistencies so evident and breaks so definite that they could 
be ignored only by the most optimistic or the least philosophical. 
Thus, for example, the Doctrine of Ether remained highly meta- 
physical, and there were unbridged gulfs between Matter and 
Force on the one hand and between the Living and the Not-living 
on the other. Nevertheless there were those who naively presented 
a supposedly complete picture ot a world built up of changeless, 
spherical atoms, often compared to billiard balls — ^hard, impene- 
trable, inelastic, devoid of all secondary qualities — ^between which 
was only the mysterious Ether with a wealth of endowments which 
seemed to come from more worlds than one : — 

The gift which is not to be given 

By all the blended powers of earth and heaven. 

These billiard balls were compelled, for a reason as impenetrable 
as themselves, to perform an everlasting dance. They were con- 
stantly changing partners under the orders of a protean dance- 
director in his various characters of ‘Heat', ‘Chemical Affinity', 
‘Electricity', &c., and the more he changed the more he remained 
the same. His masterpiece was ‘Living Matter' which had itself 
somehow created its own dance-director called ‘Natural Selection'. 
He was sometimes nicknamed ‘Survival of the Fittest' — and had 
develojDed various other characters. Under him there opened the 
dreary prospect of the dance becoming ever more complex, for was 
not life the passage from the less to the more highly organized ? 

This depressing picture made little appeal to the professed 
philosophers. They saw that the whole structure of science had 
been built — and necessarily built — on certain metaphysical 
fotmdations. These, for the science of that age, were the un- 
questioned data of the Newtonian world system. But during the 
later nineteenth century it became apparent that even were the 
scientific narrative sufficiently consistent and continuous it could 
not be integrated into a comprehensive system unless and until 



its metaphysical data were clearly displayed and recognized for 
what they were. 

During the nineteenth century science was immensely successful 
in many and revolutionary directions. It had improved the 
human lot. It had provided an intellectual stimulus that was 
far more effective than those of some other and more fatigued 
disciplines. It had rendered many current philosophical and theo- 
logical positions completely untenable. It had — despite modern 
misunderstanding — introduced a humaner spirit into human re- 
lations. It provided a new basis for education, and had made 
certain of the older bases more than a little ridiculous. Most of 
all, it had inseminated a hopeful and at least partially justified 
view of the possibility of human progress. Nevertheless, the 
method has its limits which were, in fact, more readily recognized 
by working scientific men than by some who assumed the task 
of interpreting them. 

Science, of its nature, is incapable of accomplishing or even of 
attempting the task of resolving all the various discrepancies of 
thought into one whole. For this reason, among others, a history 
of science is, in the strict sense of the word, hardly possible. 
Science cannot deal with the whole at all, but only with abstrac- 
tions, with ' Departments of Scientific Inquiry ' as we are accus- 
tomed to call them. But though it must perforce work in depart- 
ments, it is by no means pledged to keep the boundaries of those 
departments fixed; it is committed to no doctrine of status quo 
for the frontiers on its maps. In changing those frontiers science 
must, at need, go> back to its beginnings and question its own 
primary data: it must revise its metaphysic. In doing so it may 
well presuppose a philosophy different from the classical material 
istic plan. The world of science may well come to be regarded as 
an evolutionary scheme in which will emerge patterns of value, 
precisely that type of pattern in fact that was so stoutly repudiated 
by the materialist philosophers of a previous generation. 

The generation of philosophers that could ignore the great 
scientific conclusions is now at rest and is not likely to be dis- 
turbed. It seems probable that Science itself is now reaching a 
stage in which an adequate scientific equipment will involve some 
regard to the world as an interconnected whole, in other words, 



in which Science and Philosophy will dwell less apart. This does 
not mean that Science will abandon its method of abstraction — 
for then it would cease to be Science — nor does it mean that 
Science will seek a refuge in that tomb which has become the 
peaceful abode of an older philosophy based on ratiocination. But 
it does mean that the frontiers of scientific abstractions may be 
rendered more fluid and that the philosophical method may have 
a share in determining the nature of the change. Notably it seems 
probable that the conceptions of the separation of mind from mind 
and of mind from matter may need modification. There are many 
indications that the tendencies of science since the later nineteenth 
century have been working in these directions. 



Adams, John Couch (1819-92), 269 
Adelard of Bath (c. 1090-c. 1150), 

Agassiz, Alexander (1835-1910), 
342. 386 

Agassiz, Jean Louis Rodolphe 
(1807-73), 331, 332 
Agricola, Georg (1490-1555). I 75 
Al-Battani (d. 929), 135, 148 
Albertus Magnus f 1206-80), 154, 


Albiruni (973-1048), 137 
Albucasis (d. c. 1013), 138, 148, 149, 

Alcmaeon of Croton (c. 500 b.c.)> 


Alcuin (735-804), 128 

Aldo Manuzio (1449-1515), 169 

Alembert, Jean le Rond d’ (1717- 

83). 275 

Alexander of Aphrodisias (c. a.d. 
200), 52 

Alexander of Hales (d. 1245), 153-4 
Alfarabi (d. c. 951), 137, 148, 149 
Alfargani (d. c. 850), 135, 148, 149 
Alfonso the Wise (1223-84), 159 
Alhazen (965-1038), 136, 149, 156, 

Alkindi (813-80), 136, 148, 149 
Al-Kwarizmi (c. 830), 135, 147, 148 
Alpetragius (c. 1180), 138, 149 
Alphanus (d. 1085), 143 
Ammonius Saccas (died a.d. 245), 

Ampere, Andr^ Marie (1775-1836), 
308-9, 311. 313-14 
Anaxagoras of Clazomenae (488-428 
B.C.), 26-7, 54 

Anaximander of Miletus (611-547 
B.C.), 11-12 

Anaximenes of Miletus (born c. 570 
B.C.), 12 

Andronicus of Rhodes (ist century 
A.D.), 52 

Androsthenes (4th century b.c.), 50 
Apollonius of Citium (c. 100 b.c.), 80 
Apollonius of Perga (fl. 220 b.c.), 56, 
69-70, 77, 148 

Arago, Dominique Fran9ois (1786- 
1853), 277, 308, 309, 314 
Aratus of Soli (c. 260 b.c.), 54, 116 

Archimedes of Syracuse (287-212 
B.C.), 63-9, 114, 148, 170, 214, 

Argelander, Friedrich Wilhelm 
August (1799-1875), 270 
Aristarchus of Samos (c. 310-230 
B-C.), 59-60, 69, 1 16, 180 
Aristotle (384-322 b.c.), 34, 39-50, 
92, 127, 149, 150, 151, 162-3, 169, 
182, 193, 195, 216, 237, 245, 249, 
328, 330, 333, 337, 347, 364 
Arnald of Villanova (c. 1240-1311), 


Arzachel (c. 1080), 138 
Asclepiades of Bithynia (died c. 40 
B.C.), 106 

Augustine, St. ( 354 - 430 ). 105, 124-5, 
128, 154, 373 

Autolycus of Pitane (c. 360-c. 300 
B.C.), 51 

Auzout, Adrien (d. 1691), 258 n. i 
Averroes (1126^8), 139-41, 146, 
150, 154, 162 
Avicebron (1021-58), 146 
Avicenna (980-1037), i34> 148, 170, 


Avienus (c> a.d. 380), 116 
Avogadro, Amedeo (1776-1856), 


Bacon, Francis (1561-1626), 226-30, 
251, 388 

Bacon, Roger (1214-94), 148, 156-8, 

Baer, Karl Ernst von (1792-1876), 
332, 357. 386 

Banks, Sir Joseph (1745-1820), 329, 

Bartholomew the Englishman (c. 
1260), 154 

Beaufort, Sir Francis (1774-1857), 


Bede (673-735), 128 
Bell, Sir Charles (1774-1842), 61, 
332, 365 

Bentham, Jeremy (1748-1832), 378 
Bergman, Tobem Olaf (1735-84), 
285, 291-2 

Bernard, Claude (1813-78), 332, 
363-5, 387 

Bernard, Sylvester (c. 1150), 153 



Berthollet, Claude Louis (1748- 
1822), 285, 291-2 

Berzelius, Jons Jakob (1779-1848), 


Bessarion, Johannes (1389-1472), 

Bessel, Friedrich Wilhelm (1784- 
1846), 212, 269 

Black, Joseph (1728-99), 285-7, 

Boccaccio, Giovanni(i3i3-75), 164-5 
Bock, Jerome (1498-1554), 176 
Bode, Johann Ehlert (1747-1826), 

Boerhaave, Hermann (1668-1738), 
285, 347, 348 

Boethius (a.d. 480-524), 1 12-13, 1^2 
Bois-Raymond, Emil du (1818-96), 

Bonnet, Charles (1720-93), 333, 373, 


Borelli, Giovanni Alfonso (1608-79), 
239--40. 241. 250 

Botticelli, Sandro (1444-15 10), 172 
Boussingault, Jean-Baptiste (1802- 

87). 354 

Boyle, Robert (1627-91), 229, 233-5, 
250, 265, 283, 291, 297 
Bradley, James (1693-1762), 261 
Brahe, Tycho (1546-1601), 183-4, 
204, 212, 251 

Broca, Paul (1824-80), 367 
Brongniart, Alexandre (1770-1847), 

Brown, Robert (1773-1858), 331, 356 
Brunfels, Otto (1489-1534), 176 
Bruno, Giordano (1547-1600), 171, 
182, 185-9, 209, 211, 212, 219, 
249, 250 

Buffon, Georges Louis Leclerc, 
Comte de (1707-88), 278-9, 343, 


Bunsen, Robert Wilhelm (1811-99), 

Cajal, Ramon y (1852-95), 366 
Callipus of Cyzicus (4th century 
B.C.), 38 

Cannizzaro, Stanislao (1826-1910), 


Canton, John (1718-72), 277 
Cardan, Jerome (1501-76), 175 
Carnot, Sadi (1796-1831), 324, 326 
Cassini, Cesar Francois (1714-84), 



Cassini, Giovanni Domenico (1625- 
1712), 259, 272, 273 
Cassini, Jacques (1677-1756), 272 
Cassini, Jacques Dominique (1748- 
1845), 274 

Cassiodorus (490-585), 128 
Cavendish, Charles (1703-83), 298 
Cavendish, Henry (1731-1810), 287- 
8, 298, 303, 304 
Celsus [c. A.D. 30), 107, 169 
Charles, Jacques Alexander Cesar 
(1746-1823), 292 

Chastelet , Marquise du ( 1 706-49) ,254 
Chaucer, Geoffrey (1340-1400), 151 
Cicero (106-43 b.c.), 118 
Cleanthesof Assus (c. 250 b.c.), 54, 1 16 
Cleomedes (ist century a.d.), 80-2 
Cleostratus of Tenedos (6th century 
B.C.), 12 

Coleridge, Samuel Taylor (1772- 

1834). 372 [143 

Constantine the African (1017-87), 
Cook, James (1728-79); 274, 340 
Copernicus, Nicolas (1473-1543), 
179-82, 185-6, 212, 249, 256 
Coulomb, Charles Augustus (1736- 
1806), 304 

Crateuas {c. 80 b.c.), 78-9 
Cuvier, Georges Leopold Chretien 
Fr^d^ric Dagobert (1769-1832), 
279-80, 329-30, 336-8, 351, 365, 

377. 386 

Dalton, John (1766-1844), 275, 


Dante Alighieri (1265-1321), 165 
D’Anville, Jean-Baptiste Bourgui- 
gnon (1697-1783), 273-4 
Darwin, Charles Robert (18051-82), 
276, 279, 281, 283, 329, 339, 340, 
371, 377, 379-83, 386-^ 

Darwin, Erasmus (1731-1802), 374, 

Davy, Sir Humphry (1778-1829), 
295-6, 301, 304. 330, 354 
De Candolle, Augustin Pyramus 
(1778-1841), 330, 331 
De la Beche, Sir Thomas (1796- 
1855), 282-3 

De la Condamine, Charles Marie 
(1701-74), 272 

De la Perouse, J. F. de Galaup, 
Comte de (1741-89), 274 
Democedes of Cnidus (born c. 540 
B.C.), 14 


Democritus (c. 470-c. 400 b.c.), 15, 
33. 42. -47. 54 

D’Entrecasteaux, Joseph Antoine 
Bruni (i739-93). 274 
Descartes, Ren^ (1596-1650), 191-3, 
194, 210, 214, 220, 221-6, 227, 
231, 237-9, 241, 250, 313, 347 
Dicaearchus (c. 355-c. 285 b.c.), 51-2 
Diderot, Denis (1713-84), 372 
Diophantus (c. a.d. 180), 83 
Dioscorides (ist century), 89-90, 
128, 169, 170, 176 
Doppler, Christian (1803-53), 271 
Du Fay, C. F. (1698-1739), 303 
Dujardin, Felix (1801-62), 356 
Diirer, Albrecht (1471-1528), 173-4, 


Dutrochet, Henri (1776-1847), 353-4 

Empedocles of Agrigentum {c. 500- 
c. 430 B.C.), 24-6 

Epicurus of Samos (342-270 b.c.). 

15. 47. 54. 95 

Erasistratus of Chios {c. 280 B.c.), 

61-3. 90 

Eratosthenes [c, 194 B.c.), 56, 

68, 70-6, 102, 271 

Euclid {c. 330-c. 260 B.C.), 57-9, §0. 
147, 149, 170 

Eudoxus of Cnidus (409-356 b.c.), 
37-8, 47, 67, 1 16 

Eudoxus of Cyzicus (2nd or ist cen- 
tury B.C.), 100 

Eugenius of Palermo (fl. 1160), 149 
Euler, Leonhard (1707-83), 58, 265 

Fabiola (4th century a.d.), hi 
Fahrenheit, Gabriel Daniel (1686- 
1736), 298 

Faraday, Michael (1791-1867), 303, 
308, 310-16, 324 

Ferdinand II, Grand Duke of 
Tuscany (fl, 1641), 298 
Fernel, Jean (1497-1558). 

Ferrier, David (1843-1928), 367 
Fischer, Emil (1852-1919). 360 
Fischer, Ernst Gottfried (1754- 
1831), 291 

Fitzroy, Robert (1805-65), 276 
Fizeau, Hippolyte Louis (1819-96), 


Flamsteed, John (1646-1719), 259-60 
Fontenelle, Le Bovier de (1657- 
1757), 251 

Foucault, Jean Leon (1819-68), 

Fracastor, Jerome (1483-1543), 179 
Franklin, Benjamin (1706-90), 303, 


Fraunhofer, Joseph (1787-1826), 269 
Fresnel, Auguste Jean (1782-1827), 

Fritsch, Gustav (1838-91), 367 
Fuchs, Leonard (1501-66), 176-7 

Galen of Pergamum (a.d. 131-201), 
80, 90-3, 1 19, 149, 170, 174, 177 
Galileo Galilei (1564-1642), 167, 

171, 190, 195-221, 223, 231, 236, 
237, 249, 250, 251, 262, 264, 266, 
276, 298 

Galvani, Luigi (1737-98), 304. 365 
Gascoigne, William ( 1612-44) , 258 n. i 
Gassendi, Pierre (1592-1655), 235, 

Gauss, Karl Friedrich (1777-1855), 

Gay-Lussac, Joseph Louis (1778- 
1850), 275, 292, 293 
Geber (c. 850), 132, 148 
Geoffrey, Etienne Fran9ois (1672-- 
1731). 285, 291 

Geoffroy St. Hilaire, Etienne (1772- 
1844), 331 

Gerard of Cremona (1114-87), 143, 
148, 149 

Gerbert (d. 1003), 129, 141 
Gilbert, William (1546-1603), 188, 
219. 277, 313, 343 

Goethe, Johann Wolfgang von 
(1749-1832), 331. 335-6. 374, 386 
Golgi, Camillo (1844-1926), 366 
Gonzalez, Domenigo (fl. 1140), 148 
Graham, George (1673-1751), 272-3 


Graham, Thomas (1806-69), 359 
Grew, Nehemiah (1641-1712), 243, 

250. 331 

Grosseteste, Robert {c. 1175-1253), 


Guericke, Otto von (1602-86), 233 

Hadley, George (1685-1768), 275 
Hale, Matthew (1609-76), 373 
Hales, Stephen (1677-1761), 284, 
286, 348-9 

Hall, Marshall (1790-1857), 367 
Haller, Albrecht von (1708-77), 
34^50. 365. 374 

Halley, Edmond (1656-1742), 253, 
260-1, 263, 267, 275, 276, 277 



Harrison, John (1692-1776), 273 
Harvey, William (1578-1657), 214, 
220, 225, 226, 237-8, 243, 244, 

Hasdai ben Shaprut (d. c. 990), 138 
Hecataeus of Miletus (born c. 540 
B.C.), 12-13 

Helmholtz, Hermann (1821-94), 
325, 362 

Henderson, Thomas (1798-1844), 

Henle, Jacob (1809-85), 366 
Hensen, Victor (1835-1924), 342 
Heracleides of Pontus (c. 388-315 
B.C.), 38 

Heracleitus of Ephesus (c. 540-475 
B.C.), I 4 > 32. 40 

Herman the Cripple (1013-54), 142 
Hero of Alexandria {c. a.d. ioo), 

Herodotus of Halicarnassus {c. 484- 
425 B.C.), 16-17, 

Herophilus Of Chalcedon (fi. c. 300 
B.C.), 61-3 

Herschel, Frederick William (1738- 
1822), 262-4, 270 

Hildegard of Bingen, St. (1099- 
1180), 153 

Hipparchus of Nicaea {c. 1 90-1 20 
B.C.), 60, 76-8, 84, 160 
Hippocrates of Chios (born c. 430 
B.C.), 30, 57, 67, 254 
Hippocrates of Cos (born c. 460 
B.C.), 27-9, 33, 149, 170 
Hitzig, Eduard (1838-1907), 367 
Hobbes, Thomas (1588-1679), 210 
Hoffmann, Friedrich (1660-1742), 

Honain ibn Ishaq (809-77), 131 
Hooke, Robert (1635-1703), 233, 
243. 250, 251, 297, 304, 356, 374 
Hooker, Joseph Dalton (1817-1911), 
331, 340-1, 345 

Hugh of St. Victor (1095-1141), 153 
Humboldt, Friedrich Heinrich Alex- 
ander von (1769-1859), 277, 282, 

Hunter, John (1728-93), 304, 351-2 
Hutton, James (1726-^7), 280 
Huxley, Thomas Henry (1825-95), 

365, 383 

Huygens, Christian (1629-95), 193- 
4, 195, 208, 251, 257-9, 265, 272, 
29X, 297, 316-17 
Hypatia ( a . d . 379-415)1 83, 124 


Ingenhousz, Johannes (i73C>-79), 
304, 350-1. 353 

Isaac Judaeus (855-955), 134, 143, 

Isidore (560-636), 128 

John Holywood (d. 1256), 159, 161 
John Mesue (d. 857), 131, 170 
John of Peckham {c. 1220-92), 156 
John of Seville (fl. 1139-55), 148 
John Scot Erigena {c. 850), 164 
Joule, James Prescott (1818-89), 


Julius Caesar (102-44 b.c.), 101-2, 
103, 115-16 

Jung, Joachim (1587-1657), 234 

Kant, Immanuel (1724-1804), 333- 
4. 372 

Kelvin, William Thomson, Lord 
(1824-1907), 316, 325-7 
Kepler, Johannes (1571-1630), 184, 
191, 194, 195, 200-6, 212, 216, 
224, 250, 256, 276 
Kirby, W. (1759-1850), 329 
Kirchhoff, Gustav Robert (1824-87), 

Knight, Thomas Andrew (1759- 
1838), 329 

Kolliker, Albrecht (1817-1905), 332, 
366, 386-7 

Kiihne, Willy (1837-1900), 360 

Lagrange, Joseph Louis (1736- 
1813), 266-8 

Lamarck, Jean Baptiste Pierre 
Antoine de Monet de (1744-1829), 
280, 281, 374, 377-8, 387 [266-8 
Laplace, Pierre Simon (1749-1827), 
Lavoisier, Antoine Laurent (1743- 
94), 289-90, 295, 300, 347, 350 
Leeuwenhoek, Antony van (1632- 
1723), 243-5, 250 

Le Verrier, Urbain Jean Joseph 
(1811-77), 269 

Leibnitz, Gottfried Wilhelm (1646- 
1716), 67, 265, 291, 372 
Leonardo da Vinci (1452-15 19), 167, 
172-3, 179 [160-1 

Leonardo of Pisa {c. iiyo-c. 1245), 
Leucippus of Miletus (fl. c. 475 b.c.), 

Levi ben Gerson (1288-1344), x6o 
Liebig, Justus von (1803-73), 296, 
352-4. 359. 361 
Lind, James (1736-1812), 274 


Linnaeus, Karl (1707-78). 327-9, 
338> 351. 374 

Locke, John (1632-1704), 210. 229, 

Lucretius (c. 95-55 b.c.), 54. 95-7. 
120, 169, 179, 293 

Lyell, Charles (1797-1875), 281-2, 
329> 332, 343. 374. 377. 379. 384 

Maimonides (1135-1204), 146 
Malpighi, Marcello (1628-94), 239, 
242-5, 250 

Malthus, Thomas Robert (1766- 

1834), 378-9 

Malus, Etienne Louis (1775-1812), 

Manilius ( ? ist century b.c.), 169 
Mariotte, Edme (d. 1684), 242-3 [8 
Martianus Capella (c. a.d. 500), 127- 
‘Mary the Jewess’ (c. 100 a.d.), 93 
Maupertuis, Pierre Louis Moreau de 
(1698-1759), 272, 273 
Maury, Matthew Fontaine (1806- 
73). 275-6 

Maxwell, James Clerk (1831-79), 
316, 323 

Menaechmus (4th century b.c.), 38— 
9. 70 

Mendel, Gregor (1822-84), 387 
Mendeleef, Dmitri (1834-1907), 296 
Mersenne, Marin (1588-1648), 210 
Messahala (770-820), 135, 148, 149 
Meyer, Lothar (1830-95), 296 
Michael the Scot (c. 1175-c. 1235), 


Milton, John (1608-74), 180, 207 
Mondino da Luzzi (127^1328), 158, 


Morienus Romanus (fl. 12th century), 


Moses Farachi (d. 1285), 149 
Muller, Johannes (1801-58), 331, 

332, 356, 361-3, 365 

Muller, Johannes, see Regiomon- 

Murchison, Roderick (1792-1871), 
283, 329 

Murray, John (1841-1914), 341 

Napier, John (1550-1617), 190-1 
Nearchus (4th century b.c,), 50. 
Newton, Sir Isaac (1642-1727), 
199-200, 219, 225, 248-57, 260, 
264, 265, 271, 272, 276, 283, 291, 
298, 304. 316, 375 

Nicolas of Cusa (1401-64), 140, 171, 

Oersted, Hans Christian (1777- 
1851), 307-8, 310 

Oken, Lorenz (1779-1851), 355. 374 
Owen, Richard (1804-92), 331, 332, 
339, 386 

Paracelsus (1493-1541), 174-5, 240 
Pascal, Blaise (1623-62), 193 
Pavlov, Ivan Petro vitch ( 1 849-1 936) , 

Pedanius Dioscorides of Anazarba 
(ist century A.D. ), 89-90, 128, 169, 
170, 176 

Perrault, Claude (1613-88), 257 
Perthes, Jacques Boucher de (1788- 
1868), 384 

Peter of Abano (1250-1318), 163-4, 


Petrarch, Francesco (1304-74), 164 
Phillips, John (1800-74), 287 
Philolaus of Tarentum [c. 480-400 
B.C.), 21-2, 180 

Piazze, Giuseppe (1746-1826), 268 
Picard, Jean (1620-82), 257, 271-2, 


Plato (427-347 B.C.), 32-7, 192 
Pliny, the Elder (a.d. 23-79), 97-8, 
103, 107-9, 1 14, 117-20, 128, 168-9 
Plotinus (a.d. 204-70), 123 
Pollaiuolo, Antonio (1428-98), 172 
Polybius (204-122 B.C.), 100 
Pomponius Mela (c. a.d. 40), 102-3 
Posidonius of Apamea (135-50 
B.C.), 54 

Poulett Scrope, George Julius (1797— 
1876), 283 

Power, Henry (1623-68), 218 
Priestley, Joseph (1733-1804), 288, 

303, 350, 378 

Proust, Joseph Louis (1755-1826), 
291, 292, 293 

Prout, William (1785-1850), 295 
Ptolemy of Alexandria (fi. a.d. 170), 
78, 80, 83-9, 148, 149, 170, 171, 
255-6, 265 

Purbach, Georg (1423-61), 148, 171 
Purkinje, Johannes Evangelista 
(1787-1869), 356, 366 
Pythagoras (born c, 582 b.c.), 17-23, 

P3rtheas of Marseilles (c. 360-c. 290 
B.C.), 52 



Rabanus Maurus (776-856), 128 
Ramsden, Jesse (1732-1800), 273, 

Ray, John (1627-1705), 328, 374 
Redi, Francesco (1621-97), 245-6 
Regiomontanus (1436-76), 169, 171- 
2, 179, 217 

Remak, Robert (1815-65), 332 
Rey, Jean (fl. 1632), 298 
Rhazes (865-925), 133, 148, 149, 


Richter, J. B. (1762-1807), 291 
Robert of Chester (c, ii 10-60), 148, 


Roemer, Olaus (1644-1701), 259 
Roger of Salerno (c. 1220), 158 
Roland of Parma {c, 1250), 158 
Ross, Sir James (1800-62), 340-1 
Roy, William (1726-90), 274 
Rufus of Ephesus (c. a.d. 100), 82- 

Ruhmkorff, Heinrich Daniel (1803- 

_ 77). 315 

Rumford, Benjamin Thompson, 
Count (1753-1814), 300-2 
Rutherford, Daniel (1749-1819), 


Rutilius Namatianus (fl. a.d. 417), 

Sabine, Edward (1788-1883), 277 
Sachs, Julius (1832-97), 354 
Santorio, Santorio (1561-1636), 214, 
220, 236-7. 238 

Saussure, Horace B^n^dicte de 
(1740-99), 275, 282 
Scheele, Carl Wilhelm (1742-86), 
288, 295 

Schultze, Max (1825-74), 357-8 
Schwann, Theodor (1810-82), 356-7 
Sedgwick, Adam (1785-1873), 283 
Seneca (3 b.c.-a.d. 65), 98-9, 120 
Smith, Adam (1723-90), 378 
ISmith, William (1769-1839), 280, 
281, 346 

Snell, Willibrord (1591-1626), 194- 

Socrates (470-399 b.c.), 31. 

Spencer, Herbert (1820-1903), 385- 


Spinoza, Benedict (1632-77), 215, 

Sprat, Thomas (1635-1713), 229 
Stahl, Georg Ernst (1660-1734), 241, 
288, 347 


Steno, Niels (1648-86), 239, 278 
Stevin, Simon (1548-1620), 190 
Strabo of Amasia (bom c. 63 b.c.), 
80, loo-i, 103, 169 
Strato of Lampsacns {c. 300 b.c.), 

Swammerdam, Jan (1637-80), 243, 

Sylvia of Aquitaine {c. a.d. 380), 104 
Sylvius, Franciscus (1614-72), 240- 


Tacitus (c. A.D. 55-120), 103-4 
Thales of Miletus {c. 624-565 B.c.), 
8-1 1 

Theophrastus of Eresus (372-287 
B.c.), 51, 78, 92, 109, 169 
Thomas Aquinas, St. (1227-74), 
154, 162, 182 

Thomson, Charles Wyville (1830- 
82), 341 

Torricelli, Evangelista (160S-47), 
197, 232 

Vallisnieri, Antonio (1661-1730), 

Van Helmont, Jan Baptist (1577- 
1644), 171, 231, 240, 242, 284 
Van Leeuwenhoek, Antony (1632- 
i723)» 243, 245, 250 
Varro (116-27 b.c.), 97, 169 
Verrocchio, Andrea del (1435-99), 

Vesalius, Andreas (1514-64), 90, 
167, 177-9, 212, 220, 366 
Vidte, Fran9ois (1540-1603), 189 
Vincent of Beauvais (1190-1264), 


Vipsanius Agrippa (died 12 b.c.), 86 , 

Virchow, Rudolf (1821-1902), 358 
Vitruvius (c. a.d. 10), 114, 116, 118, 
Viviani,Vicenzo( 1622-1703), i98[i69 

Volta, Alessandro (1745-1827), 305- 

7. 365 

Voltaire (1694-1778), 254, 291 

Wallace, Alfred Russel (1823-1913), 
344 . 379 

Wallis, John (1616-1703), 193, 251, 
251, 258 n. 3. 

Watt, James (1736-1819), 299-300, 

Wells, Charles (1757-1817), 275 


Werner, Abraham Gottlob (1759- 
1817), 279, 283 
White, Gilbert (1720-93), 329 
WilUam of Moerbeke (d. 1286), 154, 

Williamson, William Crawford 
(1816-95), 332, 346 
Witelo (fl. 1270), 156 

Wohler, Friedrich (1800-82), 352 
Wollaston, William Hyde (1766- 
1828), 269 

Wren, Christopher (1632-1723), 258 
n. 3 

Young, Thomas (1773-1829), 318 
20, 325 

Zosimus (c. 300 A.D.), 93 


great BRITAIN