June 1 8, 1874] 



NA TURE 



123 



The llluslrated London News is quoted, and the Hamp- 

 shire Teles^rapli. is made to paraphrase the Pliilosophical 

 Magazine. 



Reprint of Boddaerfs Tirble aes Planches Enlumincez 

 d'Histoirc Natiaelle. Edited by W. B. Tegetmeier, 

 F.Z.S. 



Mr. Tegetmeier has done a service to ornithology by 

 increasing the faciUties for precise avian nomenclature, in 

 reprinting, with an accuracy in typography which does 

 him much credit, a catalogue compiled by Dr. Boddaert, 

 printed in 17S3, which contains the names of a large 

 number of birds, given on the then novel binomial system 

 of Linnrcus. The original work is extremely scarce, only 

 two copies being known in the United Kingdom ; and as 

 so much stress has to be laid on priority in naming, a 

 book published so soon after the tenth edition of the 

 " Systema Natura;" ought to be available to all working 

 ornithologists. 



LETTERS TO THE EDLTOR 



[The Editor does not hold himself responsible for opinions expressed 

 by his eorrespotuleiits. A'o notice is taken of anonymous 

 communieationsi] 



Molecular Motion 



In Prof. Maxwell's communication. Nature, vol. viii. , p. 537, on 

 this subject, heassumesthat if ;/j represent thenumber of molecules 

 of a particular kind in a given element of space with a velocity 

 given in direction and magnitude, which we will call t'j ; and 

 if n.i represent the particles of another kind in the same element 

 with the velocity r„, thtn the number of encounters of these 

 particles is proportional to «j x »», and if out of these we 

 select the particular encounters whiclr give vise to a given set 

 of resultant velocities -\' and v.f, then we may assume that if 

 the number of particles in the element which originally had the 

 velocities v^ and v.^ be called n^ and n.l, then 



«i Hj = «,' n.l 

 This reasoning does not seem convincing. Assuming that in an 

 element of space the average number of particles having a given 

 velocity is the same, so that n^ and ;/., are ;;{V functions of r', and 

 i'.j, then Ml'. Maxwell's statement might be admitted ; but if the 

 number of particles in a given element is a function of its velo- 

 city in direction and magnitude, then although the average of the 

 numbers in each direction is maintained, it does not follow that 

 the average numbers of particles having the velocities f, and c, 

 are directly restored from the particles having the velocities 

 I'y and T.l. All that can be assumed is, that the average num- 

 ber of particles in a given element of space is maintained from 

 the particles in that and the rem.aining elements. Just as in the 

 case of an equilibrium of trade, the aver.ige course of exchange 

 with respect to a given country is at par ; but we cinnot there- 

 fore safely assume that the same is the case relatively to any 

 other individual country. 



There are several other points in Mr. Maxwell's communi- 

 cation which seem to me to require fortification, but the subject 

 has already assumed so technical a form that it would peiliaps 

 be uninteresting to your readers to point them out. My im- 

 pression is that the whole subject is still somewhat beyond the 

 grasp of strict mathematical reasoning, and is still open to expe- 

 rimental investigation. F. Guthrie 



Graaff Reinet College, Feb. 7 



[This question is treated at length in my paper On the dyna- 

 mical theory of gases (I'hi). Trans., 1S66). It is there shown 

 that if the average course of exchange is in a cycle from A to B, 

 B to C, C to A, an equal reason may bo given why it should be 

 in the opposite cycle A to C, C to I?, I! to A., and tlius it is 

 shown that the exchange is at par between each pair of stales 

 separately. For a far more elaborate theoretical treatment of 

 the subject Prof Guthrie is referred to ihe papers of Prof. Ludwig 

 Eollzmann in the Vienna Tr.ansactions since 1S68. I fear we 

 must delay the experimental investigation for some time, till we 

 are able to count the molecules in a given space, to observe their 

 velocities, and to repeat these operations millions of times in a 

 second.— J. Clerk Maxwili..] 



The Germans and Physical Axioms 



Although the d priori origin of the fundamental principles 

 of Mechanics has been lucidly demonstrated by the reasoning of 

 Herbert Spencer, it is presumable that his antagonists, who evi- 

 dently pay great deference to authority, will not be convinced of 

 its truth except by the opposition of acknowledged authorities. 

 Kant, in Germany, one of the first and most assiduous students 

 of Newton's Prineifia, from which he derived the nebular 

 hypothesis subsequently developed by Laplace, thus delivers 

 himself respecting the matter under discussion : — 



"The science of Natural Philosophy (Physics) contains in 

 itself synthetical judgments,) priori as principles. For instance, 

 the proposition, ' in all changes of the material world, the quan- 

 tity of matter remains unchanged ; ' or, that ' in all communica- 

 tion of motion, action and reaction must always be equal.' In 

 both of these, not only is the necessity, and therefore their origin 

 ci priori elcar. . . . And so it is with regard to tlie other proposi- 

 tions of the pure part of Natural Philosophy." — "Critique of 

 Pure Reason," Bohn's edition, page 11 of Introduction : — 



This is explicit and incontiovertible. Yet those with whom 

 precedents are omnipotent may argue that, since Kant was pre- 

 eminent as a metaphysician rather than as a physicist, his 

 deliverances must fall before the contrariety of such a man as 

 Prof. Tait. Read then, the dcclar.ation of Ilelmholz : — 



" [n mathematics the general propositions which, under the 

 name of axioms, stand at the head ot the reasoning, are so few 

 in number, so comprehensive, and so immediately obvious, that 

 no proof whatever is needed for them. Let me remind you that 

 the whole of algebra and arithmetic is developed out of the 

 three axioms — 



' Things which are equal to the same things are equal to 



one another.' 

 ' If equals be added to equals, the wholes are equal. ' 

 'If unequals be added to equals, the wholes are unequal.' 



"And the axioms of geometry and meehanies are not more 

 numerous. The sciences we have named are developed out of 

 these few axioms by a continual process of deduction Irom them 

 in more and n.ore complicated cases." — Lectiire " On the Rela- 

 tion of Natural .Science to Gener.al Science." 



Of course neither of these attestations is elucidatory, but they 

 suffice to show that in Germany, at least, the axiomatic nature 

 of physical principles is beyond controversy. 



Waterbury, Conn., U.S. Chas. G. Root 



The Long Peruvian Skull 



A KIND correspondent has called my attention to a communi- 

 cation from Dr. Daniel Wilson, of Toronto, in Nature, vol. x. 

 p. 46, to which my friend considers it incumbent upon me to 

 reply. The communication in cjuestioii has now reached me, 

 although so late, but I can hardly regard it as requrring any 

 answer, since I am quite satisfied my Irieud Dr. Wilson in it 

 answers himself. As to his logical arguments, based upon Prof. 

 Wyman's suggestion, that in Dr. Wilson's estimation the skulls 

 are natural because they are symmetrical, no one can doubt that 

 Dr. Wilson is lully acquainted with the want of symmetry in a 

 large number of crania of all races. Of this it was scarcely 

 needful for Dr. Wilson to reassure us. 



Put in reply to the real question at issue, had the ancient 

 Peruvians dolichocephalic or long skulls, as well as brachyce- 

 phalic, or short skulls ? This question I must regard as fully 

 solved, and I look upon it that craniologists consider this race to 

 be brachycephalic. How is it, then, that Dr. Wilson, who has 

 paid great attention to the study of craniology, maintains that 

 there were among the ancient Peruvians two distinct types, a 

 dolichocephalic and a brachycephalic section ? A reference 

 to his "Prehistoric Man," the two editions of which lie be- 

 fore me on the table, will suffice to indicate the source 

 of error. I will refer to the figures which are une- 

 quivocal. In the first edition of this work, Dr. Wilson 

 gives, Fig. 59, p. 240, vol. ii., the wood-cut of a Peruvian doli- 

 chocephalic skull, as an instance of ihe long skull \y\-Q natural 

 to the ancient Peruvians. At p. 242 he gives, "Fig. 60. — A 

 Peruvian Child's hkul', Normal." '1 his is tliewoodcut repeated 

 in Nature, vol. x. p. 48, Fie;. 3. Seeing that both these skulls 

 bore unequivocal marks of artificial distortion, years ago I ac- 

 quainted Dr. Wilson with this fact, when I understood him to 

 reply that the printer had not put the proper figures in the right 

 places. When thesecond edition of "Prehistoric Man "reached me 

 I looked to see if the right cuts had got put into their proper places, 



