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NA TURE 


[October 16, 1902 


614 


The Search for a Planet beyond Neptune. —Herr 
T. Grjgull, of Miinster, Germany, describes in the October 
number of the Bulletin de la Society A stronomujue de France Ins 
new contribution to the research which has for its object the 
discovery of another planet, beyond the orbit of Neptune. 

In a previous paper ( Bulletin , January, 1902, p. 31), 11 err 
Origull explained the hypothesis on which his calculations are 
based, and the elements of the hypothetical planet as deduced 
from the observations of the aphelia of three comets. In the 
present contribution, the elements given below have been calcu¬ 
lated from the observed aphelia of twenty comets which appeared, 
and were observed and recorded, between the years 1490 and 
1898. After giving due weight to the various cometary observa¬ 
tions, the author has calculated these elements for the possibly 
existing planet:— 

Epoch 1902. 

* 357°'S4 ± i°'867 

DisS. from sun = 50'6i R, 

Time of revolution = 360 years. 

SI = 90° (???). 

ev — ?. 

A New Minor Pi.Anet.— In No. 3819 of the Astronomische 
Nachrichten, Prof. Max Wolf announces, along with other 
minor planetary observations, the discovery of another new 
minor planet, 1902 T. 

Comet 1902 A .—A number of observations of this comet 
have been made. 

A photograph taken on September 27 by Prof. Kononowitsch, 
Odessa, with three hours' exposure, shows a straight double tail 
extending in a southerly direction to a distance of 3 1 . 

Prof. Nijland has published, in the Astronomische Nackrichtin 
(No. 3817), a further ephemeris, from which the following extract 
is taken :— 


1902. 

app. a. 
h. m. s. 

npp. i. 

brightness. 

Oct. 16 

... 18 16 24 ... 

+ 16 3°'5 


17 

9 55 •• 

14 91 


18 

4 7 ••• 

II 58 9 

* 3 ’° 

19 

... 17 58 52 •• 

9 -59 ’i 


20 

54 6 ... 

8 8-9 


21 

49 43 

6 27 3 


22 

45 41 ... 

4 S3' 6 

... io’9 

23 

... 17 41 56 .... 

+ 3 26 '9 



The brightness o r the comet on September|6 ifftaken as unity, 
and it was then estimated at 7'5m. 


THE BRITISH ASSOCIATION AT BELFAST. 
SECTION A. 

SUBSECTION OK ASTRONOMY AND COSMICAI. PHYSICS. 

Opening Address by Arthur Schuster, F.R.S., 
F.R.A.S., Chairman of Subsection. 

Our proceedings to day constitute an innovation and require 
a few words of explanation. When, a few years ago, some 
astronomers felt that our Association bestowed an insufficient 
share of attention on their subject, an easy remedy suggested 
itself in the foimation of a special subsection devoted to that 
subject. Such a subsection was accordingly organised at Brad¬ 
ford and Glasgow, but for reasons, which are perhaps not 
altogether to be regretted, the experiment was only partially 
successful. In the meantime the work of Section A became 
heavier and heavier, and, as it seemed necessary to find some 
way of relieving its meetings, it was decided to hand over to 
the already established subsection of Astronomy other subjects, 
such as Meteorology, Terrestrial Magnetism, Seismology, and, 
in fact, anything that the majority of physicists is only too glad 
to ignore. 

When the Council of the British Association asked me to act 
as President of such an enlarged subsection, I was very doubtful 
whether I ought to accept the honour. In the first place, I felt 
incompetent, owing to my almost complete ignorance of most 
branches of astronomy, and in the second place I do not ap- 
rove of the formation of subsections dealing with important 
ranches of Physics. If I eventually consented, it was partly 
because I lacked the strength of mind to refuse an honour of 

NO. 1/20, VOL. 66] 


this kind, but partly because I was glad to have an opportunity 
of raising the whole question of the organisation of our meet¬ 
ings. The ground for such a discussion has, however, to a 
great extent disappeared, because, when the Organising Com¬ 
mittee of Section A met in the spring, there appeared amongst 
those present a sudden revival of interest in the subjects 
assigned to the subsection and it was decided that the main 
section should not meet at all to-day so as to allow its members 
to help us in our discussions. The parent section has, there¬ 
fore, voluntarily submitted itself 10 absorption by its neglected 
offspring, which now has to show that Cosmical Physics obeys 
the laws of Terrestrial Physics and that good absorbers are also 
good radiators. 

Gratifying as this reunion must be to us, it fails to realise one 
of the original objects for which we have been called into 
existence, because instead of lightening your work it has added 
to it by imposing upon you the burden of having to listen to a 
second Presidential Address. I will try to make this additional 
burden as light as possible by concentrating my general remarks 
into a few sentences and then introducing the business of the 
section by means of a contribution to its scientific work, which 
I otherwise should have made in the ordinary course of the 
meeting. 

To make our meeting as fruitful as possible, we should make 
the fullest use of the opportunities it gives us of personal con-* 
tact and interchange of ideas. This is not accomplished by 
dividing into separate camps as soon as we have come together* 
but rather by finding some common ground for our debates. We 
should not try to minister to the separate needs of the specialist 
in electricity, or in meteorology or in astronomy, but should im¬ 
press upon each of these specialists that they must bring before 
us the results of their investigations in so far as they bear on the 
more general questions in which we all are, or ought to be, 
interested. If it is necessary to lighten the work of the section 
this should be done by excluding all papers which are of interest 
only to specialists, or by establishing subsections for such papers. 
Letusdivide—if divide we must—according to the character of the 
contribution, rather than according to the subject it happens to 
deal with. The difficult and, perhaps, unpopular censorship- 
which such a course would involve would probably be temporary 
only, as the character of the papers which are desired for the 
main section would soon become known, and the increased 
attraction and usefulness of our discussions would, I am con¬ 
vinced, in a few years compensate for the initial trouble. We 
all require, occasionally, to be reminded that the detail work 
which is necessary, and on which most of us are engaged, is 
only of importance or interest if it helps us forward towards 
the >olution of the great problems of Nature. 

Addressing myself more particularly to Astronomers, I should 
like to say that we shall always welcome them as members of 
Section A, and that the benefit we shall derive from their con¬ 
tributions will be great in proportion as they will consider 
themselves to be citizens of the general empire of that section 
rather than inhabitants of an independently governed State. 

There is one minor reform, or perhaps I ought to call it a 
protest against one of the traditions of the Association, which I 
feel called upon to urge on you. Discussion is our principal 
aim, and we are always trying to find suitable subjects for dis¬ 
cussion ; yet we are prevented by the rules of the Association 
from discussing the Presidential address and the reports of Com¬ 
mittees. Those who framed such a rule must have had some 
unfortunate idea that the dignity of the chair might be en¬ 
dangered if some criticism happened to be expressed in the 
discussion of the Chairman’s address, or that the value of the 
report of a Committee might be endangered by some adverse 
comment coming from outside. But it seems to me that a 
scientific society or association, and especially one framed on a 
democratic constitution, ought not to take such a narrow and 
unscientific view. I can remember several Presidential addresses 
which might, and probably would, have given rise to most in¬ 
structive debates had the rule not existed. Reports of Com¬ 
mittees if not suitable for discussion should not be read at all ; 
but if read they should be open to discussion. 

I hope that to-day you will not feel yourself bound by ancient 
custom, but in order that, at any rate, the more scientific portion 
of my contribution to our proceedings should not be stained by 
the suspicion of immaculate conception, I will now ask the duly- 
constituted President of our section to take his proper place. 

The question I wish to bring to your notice to-day is an old 
one : if two events happen simultaneously or one follows the 


© 1902 Nature Publishing Group 











October 16, 1902] 


NA TURE 


615 


other at a short interval of time, does this give us any reason to 
suppose that these two events are connected with each other, 
both being due to the same cause, or one being the cause of the 
other? Everyone admits that the simple concurrence of events 
proves nothing, but if the same combination recurs sufficiently 
often we may reasonably conclude that there is a real connection. 
The question to be decided in each case is what is “ sufficient” 
and what is “ reasonable.” Here we must draw a distinction 
between experiment and observation. We often think it suffi¬ 
cient to repeat an experiment three or four times to establish a 
certain fact, but with meteorological observations the case is 
different, and it would, e.g. y prove very little if on four successive 
full moons the rainfall had been exceptionally high or excep¬ 
tionally low. The cause of the difference lies in the fact that in 
an experiment we can control to a great extent all the circum¬ 
stances on which the result depends, and we are generally right 
in assuming that an experiment which gives a certain result on 
three successive days will do so always. But even this some¬ 
times depends on the fact that the apparatus is not disturbed, 
and that the housemaid has not come in to dust the room. 
Here lies the difference. What is possible in a laboratory, though 
perhaps difficult, is not possible in the upper regions of the 
atmosphere, where some unseen hand has not made a clean sweep 
of some important condition. 

When we cannot control accessory circumstances we must 
eliminate them by properly combining the observations and in¬ 
creasing their number. The advantage does not lie altogether on 
the side of experiment, because the very identity of condition 
under which the experiment is performed gives rise to systematic 
errors, which Natu-ie eliminates for us in the observational 
sciences. In the latter also the great variety in the combinations 
which offer themselves allow us to apply the calculus of proba¬ 
bility, so that in any conclusion we draw we can form an idea of 
the chance that we are wrong. Astronomers are in the habit of 
giving the value the “probable error” in the publication of 
their observations. Meteorologists have not adopted this 
custom, and yet their science lends itself more readily than 
any other to the evaluation of the deviations from the mean 
result, on which the determination of the probable error 
depends. We look forward to the time when weather forecasts 
will be accompanied by a statement of the odds that the pre¬ 
diction will be fulfilled. 

The calculation of the probability that any relationship we 
may trace in different phenomena indicates a real connection 
seems to me to be vital to the true progress of Meteorology, and 
although I have on previous occasions (Cambridge Phil. Trans ., 
vol. xviii. p. 107) already drawn attention to this matter I should 
like once more to lay stress on it. 

The particular case I wish to discuss (though the methods are 
not restricted to this case) is that in which one of the two series 
•of events between which relationship is to be established has a 
definite period, and it is desired to investigate the evidence of 
an equal period in the other series. 

Connections between the moon and earthquakes, or between 
sunspots and rainfall if proved to exist, would form examples of 
such relationships. The question to be decided in these cases 
would be, is there a lunar period of earthquakes, or art 
eleven years’ sunspot period of rainfall. 

Everyone familiar with Fourier’s analysis knows that there is a 
lunar or sunspot, or any other period in any set of events 
from volcanic eruptions down to the birth-rate of mice; what 
we want to find out is whether the periodicity indicates a 
real connection or not. Let us put the.problem into its simplest 
form. Take it balls, and by some mechanism allow them to 
drop so that each falls into one of m compartments. If finally 
they are equally distributed each compartment would hold njm 
balls. If this is not the case we may wish to find out whether 
the observed inequality is sufficient to indicate any preference 
for one compartment or how far it is compatible with equality of 
chance for each. If we were able to repeat the experiment as 
often as we like we should have no difficulty in deciding between 
the two cases, because in the long run the average number 
received by each compartment would indicate more and more 
closely the extent of bias which the dropping mechanism 
might possess. But we are supposed to be confined to a single 
trial, and draw our conclusions as far as we can from it. 

It would be easy to calculate the probability that the number 
of balls in any one compartment should exceed a given number, 
but in order to make this investigation applicable to the general 
problem of periodicities we must proceed in a different manner. 

NO. 1720, vol. 66] 


If the compartments are numbered, it does not matter in which 
order, and a curve be drawn in the usual manner representing 
the connection between the compartments and.the number of 
balls in each, we may, by Fourier’s analysis, express the result 
by means of periodic functions. The amplitude of each period 

can be shown on the average to be ^ N /ir«. It is often more 

convenient to take the square of the amplitude—call it the in- 
tensity—as a test, and we may then say that (the “ expectancy ” 
of the intensity is 4«//«-. The probability that the intensity of 
any period should be k times its average or expectancy is e~ k 
We may apply this result to test the reality of a number of 
coincidences in periods which have been suspected. A lunar 
effect on earthquakes is in itself not improbable, as we may 
imagine the final catastrophe to be started by some tidpl de¬ 
formation of the earth's crust. The occurrence of more than 7000 
earthquakes in Japan has been carefully tabulated by’Mr, Knott 
according to lunar hours, who found the Fourier coefficient for 
the lunar day and its three first sub-multiples to be IO'3, ! 7 ' 9 , 
lo - 9, 3*97 ; the expectancy on the hypothesis of chance distri¬ 
bution for these coefficients I find to be K) *3, 157, io' 6, 5 02. 
The comparison of their numbers disproves the supposed con¬ 
nection ; on the other hand, the investigations of Mr. Davison 
on solar influence have led to a result much in favour of such 
influence, the amplitude found being in one series of observ¬ 
ations equal to five times, and in the other to fifteen times the 
expectancy. The probability that so large an amplitude is due 
to accident in the first case is one in 300 millions, and in the 
second the probability of chance coincidence would' be repre¬ 
sented by a fraction, which would contain a number of over 7° 
figures in the denominator. We may, therefore, take it to be estab¬ 
lished that the frequency of earthquakes depends on the time of 
year, being greater in winter than in summer. With not quite 
the same amount of certainty, but still with considerable prob¬ 
ability, it has also been shown that earthquake shocks show a 
preference for the hours between 9 a m. and noon. 

A great advantage of the scientific treatment of periodical 
occurrences lies in the fact that we may determine a priori how 
many events it is necessary to take into account in order to prove 
an effect of given magnitude. Let us agree, for instance, that 
we are satisfied with a probability of a million to one as giving 
us reasonable security against a chance coincidence. Let there 
be a periodic effect of such a nature that the ratio of the occur¬ 
rence at the time of maximum to that at the time of minimum 
shall on the average be as I + A to I-A, then the number of 
observations necessary to establish such an effect is given by the 
equation « = 200/A' 2 . If there are 2 per cent, more occurrences 
at the time of maximum than at the time of minimum \= 01, 
and n is equal to two million. If the effect is 5 percent., the 
number of events required to establish it is 80,000. 

To illustrate these results further, I take as a second example 
a suggested connection between the occurrence of thunderstorms 
and the relative position of sun and moon. Among the various 
statistical investigations which have been made on this point, 
that of Mr. MacDowall lends itself most easily to treatment by 
the theory of probability. One hundred and eighty-two thunder¬ 
storms observed at Greenwich during a period of fourteen years 
have been plotted by Mr, MacDowall as distributed through the 
different phases of the moon, and seem to show a striking con¬ 
nection. I have calculated the principal Fourier coefficient 
from the data supplied, and find that it indicates a lunar 
periodicity giving for the ratio of the number of thunderstorms 
near new moon to that near full moon the fraction 8'17 to 
4'83. 

This apparently indicates a very strong effect, but the 
inequality is only twice as great as that we should expect if 
thunderstorms were distributed quite at random over the month, 
and the probability of a true connection is only about 20 
to 1. No decisive conclusions can be founded on this, the 
number of thunderstorms taken into account being far too small. 
We might dismiss as equally inconclusive most of the other 
researches published on the subject were it not for a remarkable 
agreement among them, that a larger number of storms occur 
near new moon than near full moon 

I have put together in the following table the results of ail 
investigations that are known to me ; following the example of 
Koeppen, I hatfe placed in parallel columns the number of 
thunderstorms which have occurred during the fortnight in¬ 
cluding new moon, and the first quarter and the fortnight 
including the other two phases. 


© 1902 Nature Publishing Group 




616 


NA TURE 


[October 16, 1902 


Place of observation and 
author. 

Time of 
observations. 

Percentage of thunder¬ 
storms during the fortnight 
including 

New moon . Full moon 
and and 

first quarter, last quarter. 

Karlsruhe (Eisenlohr) 

1801 31 

50-8 

49 2 

Gotha (Luedicke) 

1867-75 

72-5 

275 

Vigevano (Schiaparelli) ... 

1827-64 

46 

54 

Germany (Kdppen) 

1879-83 

56 

44 

Glatz (Richter) ... 

1877-84 

62 

38 

United States (Ilazen) ... 

1884 

5&'5 

43 5 

Prag (Griiss) 

1840-59 

5 ' 

49 

»» it • • ■ ••• 

Gottingen (Meyer) 

1860-79 

52-5 

47 '5 

1857 -80 

54 

46 

Kremsmunster (Wagner).. 

1862-87 

53-8 

462 

Aix la Chapelle (Polis) ... 

>833-92 

54 '4 

45 <5 

Sweden (Eckholm) 

1880-95 

53 8 

46-2 

Batavia (v.d. Stock) 

1887-95 

5 ,- 9 

48'! 

Greenwich (McDowall) ... 

1888-91 

54 

46 

Average 

— 

54 9 

45 ' 1 


It will be seen that out of fourteen comparisons, thirteen show 
higher numbers in the first column, there being also, except in 
two cases, a general agreement : as regards the magnitude of the 
effect. Two of the stations given in the table, Gottingen and 
Gotha, are perhaps geographically too near together to be treated 
as independent stations, and we may, therefore, say that there are 
thirteen cases of agreement, against which there is only one 
published investigation (Schiaparelli) in which the maximum 
effect is near full moon. 

The probability that out of thirteen cases in which there are 
two alternatives, selected at random, twelve should agree and 
one disagree is one in twelve hundred. If the details of the 
investigations summarised in the above table are examined, 
considerable differences are found, the maximum taking place 
sometimes before new moon and sometimes a week later. There 
is, however, evidently sufficient pnma facie evidence to render an 
exhaustive investigation desirable. The most remarkable of all 
coincidences between thunderstorms and the position of the moon 
remains to be quoted. A. Richter has arranged the thunder¬ 
storms observed at Glatz, in Silesia, according to lunar hours, 
and finds that in each of seven successive years the maximum 
lakes place within the four hours beginning with upper 
culmination. If this coincidence is a freak of chance, the 
probability of its recurrence is only one in three hundred 
thousand. The seven years which were subjected to calculation 
ended in 1884. What has happened since? Eighteen years 
have now elapsed, and a further discussion wish increased 
material would have definitely settled the question, but nothing 
has been done, or, at any rate, published. To me it seems 
quite unintelligible how a matter of this kind can be left in this 
unsatisfactory state. Meteorological observations have been 
allowed to accumulate for years, one might be tempted to say 
for centuries, yet w'hen a question of extraordinary interest arises 
we are obliged to remain satisfied with partial discussion of 
insufficient data. 

The cases I have so far discussed were confined to periodical 
recurrences of single detached and independent events, the 
condition, under which the mathematical results hold true, 
being that every event is entirely independent of every other 
one. But many phenomena, which it is desirable to examine 
for periodic regularities, are not of this nature. The barometric 
pressure, for instance, varies from day to day in such a manner 
that the deviations from the mean on successive days are not 
independent. If the barometer on any particular day stands 
half an inch above its average it is much more likely that on 
the following day it should deviate from the mean by the same 
amount in the same direction than that it should stand half an 
inch below its mean value. This renders it necessary to 
modify the method of reduction, but the theory of probability is 
still capable of supplying a safe and certain test of the reality of 
any supposed periodic influence. I can only briefly indicate the 
mathematical theorem on which the test is founded. The 
calculation of Fourier’s coefficients depends on the calculation 

NO. 1720, VOL. 66] 


of a certain time integral. This time integral will for truly 
homogeneous periodicities oscillate about a mean value, which 
increases proportionately to the interval, while for-variations 
showing no preference for any given period, the increase is only 
proportional to the square root of the time. 

Investigations of periodicities are much facilitated by a certain 
preliminary treatment of the observations suggested by an 
optical analogy. The curve, which marks the changes of such 
variables as the barometric pressure, presents characteristics 
similar to those marking the curve of disturbance along a ray of 
white light. The exact outline of the luminous disturbance is 
unknown to us, but we obtain valuable information from its 
prismatic analysis, which enables us to draw curves connecting 
the period and intensity of vibration. For luminous solids we 
thus get a curve of zero Intensity for infinitely short or infinitely 
long radiations, but having a maximum for a period depending 
on temperature. Gases, which show preference for more or less 
homogeneous vibrations, will give a serrated outline of the 
intensity curve. 

I believe meteorologists would find it useful to draw similar 
curves connecting intensity and period for all variations which 
vary round a mean value such as barometric, thermometric 
or magnetic variations. These curves will, I believe, in all 
cases add much to our knowledge ; but they are absolutely 
essential if systematic searches are to be made for homogeneous 
periods. The absence of any knowledge of the intensity of 
periodic variation renders it, eg , impossible to judge of the 
reality of the lunar effect which Eckholm and Arrhenius believe 
to have traced in the variations of electric potential on the 
surface of the earth. The problem of separating any homo¬ 
geneous variation, such as might be due to lunar or sunspot 
effects, is identical with the problem of separating the bright 
lines of the chromosphere from the continuous overlapping 
spectrum of the sun. This separation is accomplished by 
applying spectroscopes of great resolving powers. In the 
Fourier analysis, resolving power corresponds to the interval of 
lime which is taken into account, hence to discover period¬ 
icities of small amplitude we must extend tire time interval of 
the observations. 

I believe that the curve which connects the intensity with 
the period will play an important role in meteorology. It is a 
curve which ought to have a name, and for want of a better 
one I have suggested that of periodograph. To take once more 
barometric variations as an example, it is easy to see that just 
as in the case of white light the periodograph would be zero for 
very short, and probably also for very long, periods. There 
must be some period for which intensity of variation is a 
maximum. Where is that maximum ? And does it vary 
according to locality? The answer to these questions might 
give us valuable information on the difference of climate. 
Once the periodograph has been obtained, the question oftesiing 
the reality of any special periodicity is an extremely simple 
one. If h be the height of the periodograph, the probability 
that, during the time interval chosen, the square of the Fourier 
coefficient should exceed kh is e~'\ If we wish this quantity 
to be less than a million, k must be about 11 ; so that in order 
to be reasonably certain that any periodicity indicates the 
existence of a truly homogeneous variation, the square of the 
Fourier coefficient found should not be less than 11 times the 
corresponding ordinate of a periodograph 

I have calculated in detail the periodograph of the changes 
of magnetic declination, at Greenwich, taking as basis the 
observations published for the 25 years 1871-95. It was not r 
perhaps, a very good example to choose, on account of the 
complications introduced by the secular variation, but my object 
was to test the very persistent assertions that have been made as 
to the reality of periodic changes of 26 days or thereabout?. 
The first suggestion of such a period cathe from Hornstein, of 
Prague, who ascribed the cause of the period to the time of 
revolution of the sun round its axis, fie only discussed the 
records for one year’s observations, but the evidence he offered 
was sufficient to impress Clerk Maxwell with its genuineness. 
Since Hornstein’s first attempts, a great many rough and some 
very elaborate efforts have been made by himself and others to 
prove a similar period in various meteorological variations. The 
period found by different computors differed, but there is a 
good deal of latitude allowed if the rotation of the sun really 
has an effect on terrestrial phenomena, because the angular 
velocity of the visible solar surface varies with the latitude. 
Hornstein himself and some of his followers deduced a period 


© 1902 Nature Publishing Group 




















October i6, 1902J 


NA TURE 


617 


not differing much from 26 days, while Prof. Frank Bigelow, 
using a large quantity of material, finds 26*68 days, and Eckholm 
and Arrhenius return to 26 days, or, as they put it more ac¬ 
curately, to 25 929 days. The two latter investigators do not, 
however, adopt the idea that this periodicity is due to the 
rotation of the sun. None of these periods can stand the test 
of accurate investigation. 

As the result ot my calculations, I can definitely state that 
the magnetic declination at Greenwich shows no period between 
25*5 and 27*5 days having an amplitude as great as 6" of arc. 
The influence of solar rotation on magnetic variation may there¬ 
fore be considered to be definitely disproved. 

The intensity of the periodograph increases rapidly with the 
period, and minute variations are, therefore, more easily de¬ 
tected in short than in longer periods. Six seconds of arc forms 
about the limit of amplitude, which can be detected in 25 years 
of observations, when the period is about 26 days; and from 
what has been said above, the amplitude which can be detected 
will be seen to vary inversely with the square root of the time 
interval.- For periods of about 14 days, an amplitude of 3" 
of arc is still distinguishable with the material I have used ; 
and such an amplitude is actually found for a period which has 
half 1 he synodic month as its time. The chance that this ap- 
parent variation is due to an accidental coincidence is one in 
two thousand; and I cannot, therefore, assert its definite 
existence beyond all possibility of cavil. But it is surely signifi¬ 
cant that of all the periods possible between 12'3 and 13*7 days, 
that gives the highest amplitude which coincides with half the 
synodic revolution of the moon. That it is at all possible to 
detect variations of 3" of arc in the observations which are taken 
to 6", with a probability of error of only one in two thousand, 
is, I think, a proof of the value of the method and the careful¬ 
ness of the observations. The periodograph has another valuable 
use. It not only gives us the time necessary to establish true 
periodicities of given amplitude, but it also gives us an outside 
limit of the time beyond which an accumulation of material 
is of no further advantage. That limit is reached when the time 
is sufficient to discover the smallest amplitude which the in¬ 
struments, owing to their imperfections, allow us to detect. 

I am only concerned to-day with a purely statistical inquiry, 
and not with the explanation of any suggested relationship. To 
prevent misunderstandings, however, I may state that I consider 
the possibility of a direct magnetic or electric action of the moon 
excluded ; as regards the latter, the diurnal variations of electric 
potential would be so much affected by a lunar electrification 
sufficiently strong to influence the outbreak of thunderstorms 
that it could not have escaped discovery. We must not, how¬ 
ever, be dogmatic in asserting the impossibility of indirect 
action. The unexpected discovery of radio-activity has opened 
out an entirely new field, and we cannot dismiss without re¬ 
newed careful inquiry the evidence of lunar action which I have 
given, [rs reality can be decided by observation only. 
No--not by observation only—but by observation supple¬ 
mented by intelligent discussion ; and this brings me to my 
concluding appeal, which I wish to urge upon you with all the 
legitimate weight of strong conviction and all the illegitimate 
influence of presidential infallibility. 

The subjects with which our subsection is concerned deal 
with facts which are revealed to us by observation more 
frequently than by experiment. There is in consequence a very 
real danger that the importance of observation misleads us into 
mistaking the means for the end, as if observation alone could 
add anything to our knowledge. Observation is like the food 
supplied to the brain, and knowledge only comes through the 
digestion of the food. An observation made for its own sake 
and not for some definite scientific object is a useless observ¬ 
ation. Science is not a museum for the storage of disconnected 
facts and the amusement of the collecting enthusiast. I dislike 
the name “ observatory 55 for the astronomical workshop, for 
the same reason that I should dislike my body to be called a 
food receptacle. Your observing dome would be useless with¬ 
out your computing room and your study. What you want is 
an Astronomical Laboratory, a Meteorological or Magnetic 
Laboratory, attaching to the word “ laboratory ” its true 
meaning, which is a workshop in which eyes and hands and 
brains unite in producing a combined result. 

The problems which confront the astronomer being more 
definite than those of Meteorology, Astronomy has grown under 
the stimulus of a healthy tradiiion. Hence it is generally 
recognised, at any rate in the principal observatories, that the 

NO. 1720, VOL. 66] 


advance of knowledge is the chief function of the observer. 
Nevertheless, the President of the Astronomical Department of 
Section A last year {Prof. II. II. Turner) has found it neces¬ 
sary, in his admirable address, to warn against the danger there 
is that the astronomer should allow himself to be swallowed up 
in a routine work and mere drudgery. The descent is easy : 
You begin by being a scientific man, you become an observer, 
then a machine, and finally—if all goes well—you design a 
new eyepiece. 

If such a danger exists in Astronomy, what shall we say about 
Meteorology ? That science is bred on routine, and drudgery is 
often its highest ambition. The heavens may fall in, but the 
wet bulb must be read. Observations are essential, but though 
you may never he able to observe enough, I think you can 
observe too much. I do not forget the advances which Meteor¬ 
ology has made in recent years, but if you look at these advances, 

I think you will find that most of them do not depend on the 
accumulation of a vast quantity of material. The progress in 
some cases has come through theory, as in the applications of 
Thermodynamics or through special experiments as by kite and 
balloon observations, and when it has come through the ordinary 
channels of ob-ervation, only a comparatively short period of 
time has been ultilised. It would not be a great exaggeration 
to say that Meteorology has advanced in spite of the observations 
and not because of them. 

What can we do to mend matters? If we wish to prepare the 
way for the gradual substitution of a better system, we should 
have some one responsible for the continuation of the present 
one. For this purpose it should be recognised that the head of 
the Meteorological Office is something more than a Secretary to 
a Board of Directors; also that he is appointed to conduct 
Meteorological research and not to sign weather forecasts. The 
endowment of Meteorology should mean a good deal more than 
the endowment of the Telegraph Office which transmits the 
observations. Terrestrial . Magnetism and Atmospheric Elec¬ 
tricity are looked after at present by institutions already over¬ 
worked in other directions and should be handed over to an en- 
Igrged Department of Meteorology. Seismology in this- 
country now depends on the private enterprise and enthusiasm 
of a single man, and as long as Prof. Milne is willing to continue 
his work, we cannot do better than leave it with him, but some 
permanent provision will ultimately have to be made. 

An improved organisation such as I have sketched out would 
do good, but could only very slowly overcome the accumulated 
inertia of ages. I should prefer a more radical treatment. 
Organisation is good, but sometimes disorganisation is better. 

Most earnestly do I believe that the subjects of meteorology 
and terrestrial magnetism, and possibly also of atmospheric 
electricity, could be most quickly advanced at the present 
moment if all observations were stopped for five years, and all 
the energy of all observers and computors concentrated on the 
discussion of the results obtained and the preparation of an- 
improved scheme of observation for the future. When we have 
made up our minds what to do with the observations, when we 
have actually done it ; when we know where our present in¬ 
struments require refining or supplementing, and especially 
when we have found out whether we have not spent much time 
and trouble on unnecessary detail, then the time will have 
ariived lor us to draw up an economical, sufficient and efficient 
scheme of observations. At present we are disinclined to dis¬ 
continue observations, though recognised as useless, for fear of 
causing a break. We make ourselves slaves to so-called “con¬ 
tinuity,” which is important, but, may be, and I believe is 
being, too dearly purchased. 

There are no doubt some, though probably not very many, 
observations which it is necessary to carry on continuously over 
long periods of time. But at present we are groping in the 
dark, and go on observing everything, and always in the hope 
that some time the observations might prove useful. Our 
whole point of view in this respect wants altering. We should 
fix on our problem first and then provide the observations which 
are necessary for the solution of the problem. Let us restrict, 
in the first instance, the secular observations to the smallest 
number, and concentrate our attention, for short periods of time, 
on some special question. Let us have, for instance, two or 
three years of thunderstorm observations, all countries joining 
I in concentrating their energies to the elucidation of all the 
various fenures of their phenomena. When that is accom¬ 
plished, it will probably be found that thunderstorms may be left 
to shift for themselves for a wnile, and attention might be 


© 1902 Nature Publishing Group 






oi8 


NATURE 


[October io, 1902 


directed to some other matter. The whole question of lunar 
influence on meteorological phenomena might be settled in a 
comparatively short space of time if the civilised countries of 
the world could agree to record all observations during a few 
years according to lunar instead of solar coordinates. Other 
problems will readily suggest themselves to you, and several 
might possibly be dealt with simultaneously. 

The great reform I have in view is this :—Before you observe, 
make sure that your observations will be useful and will help to 
answer a definite question. 

I hope that, though my frankly outspoken criticisms may not 
command universal assent, you will agree that there is some 
foundation for them, and, if so, the time is obviously not well 
chosen when observational science can be separated from its 
mathematical and experimental sisters. We hope that cosmical 
physics may remain an integral portion of Section A, and, 
though we acknowledge our weaknesses, we claim to have also 
something to teach. 

I hope that our proceedings this week may show that we can 
put aside observational detail and throw some light on the great 
and important problems with which our science is concerned. 


that the velocity varies with temperature in the way anticipated 
from the viscosity term in the expression given by Prof, Osborne 
Reynolds in his classical paper on critical velocity. By apply¬ 
ing in the case of mercury the method used in determining the 
specific heat of water, he has also found that the specific heat of 
mercury decreases at a rate which itself decreases slightly with 
increase of temperature. Lord Kelvin sent a short communica¬ 
tion in which he suggested that the temperature of an animal 
surrounded by a saturated atmosphere hotter than itself was 
kept down by evaporation within the lungs. 

Dr. J. Larmor, in a paper on the application of the method of 
entropy to radiant energy, showed that by defining the entropy 
of a given space containing radiant energy distributed in any 
arbitrary way, as the logarithm of the probability of the exis t * 
ence of that particular distribution, the law of distribution of the 
energy with wave-length, which was recently deduced by Planck 
by considering a space filled with electrical resonators, could 
equally well be established. According to it, the amount of 
energy between wave-lengths A and \ -f dx radiated by a perfectly 
black body at absolute temperature t is proportional to 


MATHEMATICS AND PHYSICS AT THE 1 ' 
BRITISH ASSOCIATION 
A LTIIOUGH the number of communications made to the 
Section at Belfast was less than at Glasgow last year, there 
was no decrease in the interest of the meetingsi The inclusion 
of cosmical physics in the subjects dealt with by the department 
for astronomy materially increased the attendance at the meet¬ 
ings of that department. 

In the mathematical department, Miss Ilardeastle described 
the ground covered by the second part of her report on the present 
state of the theory of point groups, and stated that a further 
communication would be necessary to bring the report up to 
the present time. In the absence of the author, Prof. Forsyth 
gave a short account of Mr. E. T, Whittaker’s solutions o^ the 
partial differential equations of mathematical physics. Mr. 
Whittaker finds that an expression of the type 


27 ? 

I fiz 4- ix cos u + iy sin u, u) Ju 
J U 

is the most general solution of the potential equation of Laplace, 
where /is an arbitrary function of the arguments 

z + ix cos u + iy sin u and u, and i = \ - i. 


It follows that Legendre’s, Bessel’s and other well-known solu¬ 
tions of the equation are special forms of Mr. Whittaker’s. 
In the same way, the general solution of the equation of wave 
motion is of the type 


7.7? rr 

I I f{x sin u cos v -by sin u sin v + z cos u -b - t u , v) du dv> 

J oJ 0 k 

where/is an arbitrary function. Mr. Whittaker points out that 
this solution may be analysed into plane waves, and therefore 
supports the conclusion arrived at by Dr. Johnstone Sroney in 
1897, that all disturbances in the ether can be resolved into 
trains of plane waves. 

In the department.of physics, Lord Rayleigh brought forward 
the question of the accurate conservation of weight in chemical 
reactions. He considered the discrepancies found by experi¬ 
menters too large to allow the law of conservation to be 
accepted as proved, and hoped that the experiments at 
present being carried out by Landolt and Heydweiller would 
soon lead to a definite conclusion. Prof. Morton described the 
experiments he and Mr. Hawthorne had carried out on the 
motion of a detached thread of liquid in a capillary tube. He 
concludes from them that there is some force of the nature of 
an attraction between the liquid and the material of the tube, 
which must be taken into account to explain completely the 
phenomena observed. He further detailed how he had, in 
conjunction with Mr. Vinycomb, repeated and extended the 
work of Raps on the mode of vibration of stretched strings, and 
investigated the effect of the rigidity of the support on the 
motion of the string. 

Dr. Barnes, of Montreal, on continuing his experiments on 
the critical velocity of flow of water through tubes, has found 

NO. 1720, VOL. 66] 


A-' 1 

X( r 

e - I 

where a is a constant. 

Mr. Petavel gave an account of the work he had done 
towards the production of a standard of light. He considered 
that the incandescent surface of a metal of the platinum group 
heated electrically furnished the best source, and proposed to fix 
the temperature of that source by the equality of the radiation 
transmitted by suitable thicknesses of two media, the absorption 
of one of which (water) increased, and of the other (black fluor¬ 
spar) decreased, with increase of temperature of the source. 
Dr. C. S. Myers called attention to a variation of pitch of 
Galton and other high-frequency whistles when the wind 
pressure was changed, which he had not been able to explain. 

Lord Rayleigh prefaced a description of his own experiments 
to determine whether double refraction was produced in isotropic 
transparent bodies by their motion through the ether, by an 
account of those of Michelson and Morley. The latter led to 
the conclusion that light travelled with the same velocity, 
whether the direction of transmission was coincident with, 
across or opposed to that of the motion of the body. Lord 
Rayleigh’s arrangement would have enabled a change of velocity 
of io~ 10 of the velocity cf light to be detected, but no change 
was observed when the light was transmitted through water or 
carbon bisulphide. The experiments on solids are not yet con¬ 
cluded. 

Dr. Johnstone Stoney forwarded a note in which he showed 
that by substituting for Huyghen’s wave surface a wave film of 
finite thickness, within which the phases of the disturbances 
were given proper values, the disturbance propagated*to a point 
outside the wave surface could be accurately calculated. In a 
second note, Dr. Stoney showed how his method of resolving the 
light traversing any isotropic medium into trains of plane waves 
might be applied to explain several optical phenomena which 
have not hitherto yielded to other methods. 

Prof. E. Wilson described his experiments on the use of a 
magnetic detector in space telegraphy. His detector consists of 
an iron ring magnetised to instability by a current through a 
coil wound on the ring. The electric waves falling on the ring 
slightly disturb its magnetic state, and the disturbance is in¬ 
dicated by the sound produced in a telephone in series with a 
second coil wound on the ring. He finds such a detector very 
convenient and satisfactory in working. 

Prof. Minchin has found that a coherer consisting of a carbon 
rod lightly supported in aluminium stirrups in an evacuated 
glass tube decoheres better than any other form he has tried, 
and is now engaged in applying the arrangement to long-distance 
transmission. 

Dr. Marchant showed that the graphical method of determin¬ 
ing the discharge of a condenser through a variable inductance 
gave results which agreed very closely with the calculated dis¬ 
charge in those cases in which the calculation could be carried 
out. 

Mr. Butler-Burke gave a short account of his work on the 
phosphorescence produced in partially exhausted tubes by the 
passage of an alternating current round them. He concludes 
that it is due to the formation of groups consisting of a- large 
number of molecules of gas within the tube. 


© 1902 Nature Publishing Group