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 -^^ 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 Robert 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. 



MuDslow, Eugland. 



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 I 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 VIr. 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 sufiicient for the deduction of the law of 

 c nservation 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, and m^ 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 viim,^ -i- (TJii -f wij,). 

 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 as.'sertion 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 dififerent 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. MacGregok. 



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



The Libyan Alphabet. 

 I GLADLY accept Dr. Brinton's oflfer {Science, Sept. 30) ; only, if 

 his object is truth rather than the scoring of a point, he will 

 place in the editor's hands, not the Orammaire tamachek, which 

 would be useless for the purpose, but the Orammaire kdbyle, 

 which alone contains the full forms of the three Berber alpha- 

 bets, but which Dr. Brinton appears never to have seen. Even 

 the Orammaire 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 sdkal, 

 " 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 

 Orammaire taviachek, 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 wordii/iiiar, 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 documenis in tifi- 

 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, South Hampstead, N. W. 



Is There a Sense of Direction ? 

 In 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 



