54 



NA TURE 



[May 1 8, 1905 



names also are incorrectly printed, and the references 

 given at the end of the chapter on mine illumination 

 mostly refer to ventilation. On p. 6Si the student 

 is taught to load a hole " with nitroglycerine by 

 pouring from a tin cup upon the fuse with its cap 

 and covering the mass with water." Evidently the 

 Coal Mines Regulation Act has no analogue in a 

 countrv where, as the authors point out, " each new 

 camp, 'untrammelled by tradition to keep it in the rut 

 of prejudice, displays its genius for organisation and 

 absorbs the latest devices, tried and true." 

 The Practical Plwloi;rapher. (Library Series.) 

 Edited by Rev. F. C^ Lambert. No. i6, Pictorial 

 Composition. Pp. xx + 64. No. 17, Animal Photo- 

 graphy. Pp. xxiv + 64. (London: Hodder and 

 Stougiiton, 1905.) Price is. net. 

 In the first of these books the editor gives an interest- 

 ing account of the pictorial work of Bernard Alfieri, 

 illustrating it with six excellent reproductions of this 

 well-known worker's studies. .Among the other 

 sections of the book, which are written by various 

 authors, those on the principles of composition, by 

 Arthur Burchett, and some notes on composition in 

 landscape, by Horace Mummery, will be found of great 

 practical value. In these the pen and ink sketches 

 showing the several methods of producing balance 

 in pictures call for special attention. Other articles, 

 such as that on the arrangement of the foreground, 

 are well worth perusing. Numerous well reprodi ced 

 illustrations, serving as examples of good and bad 

 composition, accompany the text. The second of the 

 above books appeals to another class of photographers, 

 for, with the exception of the editor's article on the 

 pictorial work of Viscount Maitland, it is devoted to 

 the photography of animals. Like the former bock, 

 numerous authors have contributed to the text, and 

 a very wide range of points of view is included. It is 

 written on the same practical lines, and is accompanied 

 bv tiftv-five well selected illustrations. Both volumes 

 will add to the value of this useful library series. 



Determination des Especcs minerales. By L. M. 



Granderye. Pp. 184. (Paris : Gauthier-Villars, 



n.d.) Price 2.50 francs. 

 In this little book, which is a publication of the 

 " Encvclop^die scientifique des Aide-Memoire," the 

 author has apparently attempted to devise a royal 

 road for the determination of a mineral species. For 

 this purpose he has compiled a number of lists of 

 the more common minerals arranged according to 

 physical characters, viz. crystal-system, colour, struc- 

 ture, density, &c., and has supplemented these with 

 some instructions on blowpipe analysis and chemical 

 examination in the dry way. Such lists are certainly 

 of great value for determination purposes, but, as 

 regards the more common minerals, at any rate, it 

 would be a mistake to encourage the student to rely 

 upon anv methodical scheme of determination to the 

 neglect of an acquisition of a thorough knowledge of 

 the characters of the individual species. For many 

 minerals, especially with imperfectly crystallised speci- 

 mens, we fear these tables would prove an uncertain 

 guide in the absence of any observations of the 

 optical characters or of chemical examination in the 

 wet wav. In Brush and Penfield's standard work on 

 determinative mineralogy it is true that no account 

 is taken of the optical characters, but sufficient im- 

 portance is given to chemical tests in the wet way. 

 The tables are not altogether free from errors 

 and misprints ; thus a saline taste is attributed to 

 sodalite, rhodonite is described as a carbonate, and 

 the den.sity of wolframite is given as 5.5 on one page 

 and 7.5 on another. The book concludes with a list 

 of 600 minerals with their principal characters, viz. 

 density, hardness, &c. 



NO. 1855, VOL. 72] 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 

 The Dynamical Theory of Gases and of Radiation. 

 I AM glad to have elicited the very clear statement of 

 his view which Mr. Jeans gives in Nature of April 27. 

 In general outline it corresponds pretty closely with that 

 expressed by O. Reynolds in a IJritish Association dis- 

 cussion at Aberdeen (Nature, vol. xxxii. p. 534, 1885). 

 The various modes of molecular motion are divided into 

 two sharply separated groups. Within one group in- 

 cluding the translatory modes, equipartition of energy is 

 supposed to establish itself within a small fraction of a 

 second ; but between the modes of this group and those 

 of vibration included in the other group, equipartition may 

 require, Mr. Jeans thinks, millions of years. Even if 

 minutes were substituted for years, we must admit, I 

 think, that the law of equipartition is reconciled .with all 

 that is absolutely proved by our experiments upon specific 

 heat, which are, indeed, somewhat rough in all cases, 

 and especially imperfect in so far as they relate to what 

 may happen over long intervals of time. 



.As I have already suggested, it is when we extend the 

 application of the law of equipartition to the modes of 

 a;thereal vibration that the difficulties thicken, and this 

 extension we are bound to make. The first question is as 

 to the consequences of the law, considered to he applicable, 

 after which, if necessary, we may inquire whether any 

 of these consequences can be evaded by supposing the 

 equipartition to require a long time for its complete 

 establishment. As regards the first question, two things 

 are at once evident. The energy in any particular mode 

 must be proportional to $, the absolute temperature. And 

 the number of modes corresponding to any finite space 

 occupied by the radiation, is infinite. ."Mthough this is 

 enough to show that the law of equipartition cannot apply 

 in its integrity, it will be of interest to follow out its 

 consequences a little further. Some of them were dis- 

 cussed in a former paper,' the argument of which will 

 now be repeated with an extension designed to determine 

 the coefficient as well as the law of radiation. 



.As an introduction, we consider the motion of a 

 stretched string of length I, vibrating transversely in one 

 plane. If a be the velocity of propagation, f the number 

 of subdivisions in any mode of vibration, the frequency / is 

 given bv 



y = a?/2Z (i) 



.\ passage from any mode to the next in order involves 

 a change of unity in the value of (, or of 2lfla. Hence 

 if e denote the kinetic energy of a single mode, the law 

 of equipartition requires that the kinetic energy correspond- 

 ing 10 the interval df shall be 



2lc!(i.df (2) 



In terms of X the wave-length, (2) becoines 



2lel\\d\ (3) 



This is for the whole length of the string. The longi- 

 tudinal density of the kinetic energy is accordingly 



2elX-.dX (4) 



In each mode the potential energy is (on the average) 

 equal to the kinetic, so that if we wish to reckon the 

 whole energy, (4) must be doubled. Another doubling 

 ensues when we abandon the restriction to one plane of 

 vibration ; and finally for the total energy corresponding 

 to the interval from X to X + dX we have 



?,e!X-.dX (5') 



When we proceed to three dimensions, and consider the 

 vibrations within a cube of side I, subdivisions may occur 

 in three directions. In place of (i) 



/ = a;2!.s'(l' + l' + n .... (6) 



where |, ^, ^ may assume any integral values. The next 

 step is to ascertain what is the number of modes which 

 corresponds to an assigned variation of /. 



If the integral values of |, ?;, ^ be regarded as thf 

 1 " Remarks upon the Law of Complete Radiation," Phii. Mag., xlix. 

 P- 539 June, 1900. 



