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262 



SCIENCE. 



[Vol. XX. No. 509 



fluid when sent, and that evening sections were cut and mounted 
after short treatment with picro-carmine. Without examination 
two slides were sent to Sir Robert (we were busy on small-pox), 
who returned them with the remark, "Only muscular fibre.'' 

Dr. Bookey looked at me and I gazed upon him, we then sub- 
jected the slide to examination with T \ water-immersion Powell 
and Leland and No. 3 eye-piece, all apparatus being Powell and 
Leland. I have seen reticulation since, but in a tumor purely 
epitheleomatous; it was simply wonderful. The cells were per- 
fectly differentiated, and the reticulation was so regular that 
we at once forgave Sir Eobert for his hasty conclusion. 

We hope to continue our investigations on amoeboid organisms; 
but, as the process is so long, my colleague persuaded me to send 
you these remarks. A. Cowley Malley. 

Munslow, England. 



The Fundamental Hypotheses of Abstract Dynamics. 

I have been prevented from making earlier reference to Mr. 
Dixon's letter in Science of Sept. 9, p. 149, criticising my address 
on the above topic. Science, Aug. 5, p. 71. The letter was espe- 
cially interesting to me as I had not seen his paper, " On the 
Logical Foundations of Applied Mathematical Sciences," com- 
municated to the Mathematical Society of London some few 
months ago. 

Mr. Dixon, taking the relativity of direction into account, 
seems to me to have proved that the Laws of Motion may be re- 
garded as forming a definition of force. My argument to show 
that if they be so regarded, they are not in general consistent with 
one another, involved the specification of accelerations by refer- 
ence to a single point, and thus assumed the possibility of deter- 
mining directions absolutely. While valid, therefore, as against 
the writers to whom I referred, who make the same assumption, 
it has not the more general validity which I supposed. 

That 1 have regarded force as a non-relative conception, while 
Mr. Dixon has thus shown that it may be regarded as relative, 
would seem at first sight to place us in antagonism. It does not, 
however; for I have merely discussed certain points in connec- 
tion with the laws of motion, employing the ordinary conception 
of force, and making no inquiry as to the assumptions involved 
in it, while Mr. Dixon proves that this conception must involve 
certain assumptions, and seeks to determine what they are. 

Mr. Dixon points out that it is the law of the conservation of 
mechanical energy only which is deducible from the assumption 
that stresses are functions of the distance between the particles 
on which they act, and that this law would not include the gen- 
eral law of the conservation of energy until all energy was shown 
to be mechanical. That is quite true; but it does not seem to af- 
fect my contention, that, since we are now so sure of the conser- 
vation of all forms of energy that the law of the conservation of 
mechanical energy is frequently assumed as itself axiomatic, the 
laws of motion, if they are to be retained as dynamical axioms, 
should be supplemented in such a way that this law would be de- 
ducible from them. Nor does the fact that the law of the con- 
servation of energy is usually expressed at present in a form 
which is probably temporary seem to me to make this any the 
less desirable. The conception of potential energy may lose its 
utility as we gain clearer insight into dynamical phenomena. 
When that time comes we may have to modify our fundamental 
hypotheses to suit the clearer views which will have been gained ; 
but in the meantime it seems none the less desirable that we 
should have axioms sufficient for the deduction of the law of 
c uservation in its present form. 

There is, as Mr. Dixon supposes, an omission in the sentence of 
my paper which he found unintelligible. If commas be inserted 
after the words sum and masses, it will be found to state that, if 
m 1 and w s be the masses of two particles, and a the relative ac- 
celeration produced by a stress between them, this stress may be 
shown to be proportional to 

a m x w a -f- (Wj -f m 2 ). 
It follows that, if one of the particles be of infinite mass, the 
stress is proportional to the mass of the other multiplied by the 
relative acceleration. When I conclude from this that "if, in 



applying the second law of motion, a particle of infinite mass be 
chosen as point of reference, all the forces acting on a system of 
particles, may be regarded as exerted upon them by the particle 
of infinite mass," these forces are supposed to be exerted in ac- 
cordance with the third law of motion, which asserts action and 
reaction to be equal and opposite, but not to be in the line joining 
the particles acting on one another. I do not myself regard this 
fiction as of any importance. I mentioned it in passing because 
I wished to refer subsequently to Newcomb's assertion that the 
law of the conservation of energy assumes it. 

Mr. Dixon considers it inconvenient to include in one law of 
stress two statements resting on such very different evidence as 
that forces may be considered to be attractions or repulsions and 
that their magnitudes depend solely on the distances between the 
particles on which they act. I need hardly say, however, that I 
see no objection to enunciating the two statements in separate 
sentences. For educational purposes, indeed, it would certainly 
be well to enunciate what I have called the law of stress, piece- 
meal, as is invariably done in the case of what I have called the 
law of force. J. G. MacGregor. 

Dalhousle College, Halifax, N. S., Oct. 4. 



The Libyan Alphabet. 
I gladly accept Dr. Brinton's offer (Science, Sept. 80) ; only, if 
his object is truth rather than the scoring of a point, he will 
place in the editor's hands, not the Grammaire tamachek, which 
would be useless for the purpose, but the Grammaire Icabyle, 
which alone contains the full forms of the three Berber alpha- 
bets, but which Dr. Brinton appears never to have seen. Even 
the Grammaire tamachek, now that he has got hold of it, he 
seems incapable of understanding. The other day he mistook 
diacritical marks for accents, and now he tells us that Hanoteau 
connects the Libyan and Semitic systems " solely" because both 
are read from right to left, even charging me with disingenuous- 
ness for suppressing this fact. The charge might stand, had I 
made the assertion, which is as wide of the mark as is Dr. Brin- 
ton's appeal to Hanoteau, on the question of accent. The very 
Berber name asekkil (pi. isekkilen) of the letters is equated by 
Hanoteau (p. 5) with the Arabic shakl and the Hebrew sakal, 
"forme, figure, dont les Grecs ont fait aiyXal,'' hence the French 
sigle. I am not defending these equations, but merely give them 
to show how ignorant Dr. Brinton still is of the contents of the 
Grammaire tamachek, which he had the temerity to insinuate I 
had never seen (Science, Aug. 19). May I ask Dr. Brinton who 
are the " French scholars " that regard the initial t as radical in 
the word M/mar, and that accent the word differently from Barth, 
for this also appears to be again insinuated ? The recent death 
of M. E. Renan reminds me that that illustrious " French 
scholar " is also arrayed against Dr. Brinton, holding that the 
Punic origin of the Libyan alphabet is an established fact (His- 
toire des langues semitiques, 2d ed., p. 194. et seq.). Dr. Brin- 
ton is to be envied his possession of " plenty of documents in tift- 
nar." Such documents are excessively rare in Europe, and even 
amongst the Tuaregs themselves, who, apart from rock inscrip- 
tions, have never made any extensive use of this old and defec- 
tive script. Considering the weakness of his position, Dr. Brin- 
ton shows as much want of tact as of bad taste in charging his 
opponent with lack of candor. A. H. Keane. 

79 Broadhurst Gardens, Soulh Hampstead, N. W. 



Is There a Sense of Direction ? 

IK his article on the "Sense of Direction," in Science of Oct. 7, 
Dr. Work says, "It is very well known that an unguided horse 
returning to familiar haunts will do so over the same route by 
which he left them, rather than in a direct line by sense of direc- 
tion." An incident which came under my observation some six 
years ago directly contradicts this theory. My father had pur- 
chased a very intelligent mare about a month before, and on this 
occasion I hitched her single to a carriage, and drove to a town 
about fourteen miles distant. As the direction was almost due 
north-west, the road ran alternately west and north, there being 
about eight corners to turn. Although the mare might have been