NATURE 



289 



THURSDAY, JANUARY 25, igcxs. 



THE OLD AND THE NEW KINETIC 



THEORY. 



The Kinetic Theory of Gases. By Dr. Oskar Emil 



iMeyer. Translated from the Second Revised Edition 



by Robert E. Baynes, M.A. Pp. xvi + 472. (London : 



Longmans, Green and Co., 1899.) 

 Treatise on the Kinetic Theory of Gases. By S. H. 



lUirbury, M.A., F.R.S. Pp. vi + 158. (Cambridge: 



At the University Press, 1899.) 

 T T is difficult for a reader at the present time to imagine 

 ^ himself back in the seventies before the first edition 

 <■( Meyer's " Kinetische Gastheorie " appeared. After the 

 outlines of the kinetic theory of gases had been sketched 

 out by Clausius and Maxwell, much was needed to bring 

 the theory into closer accord with the requirements alike 

 of the mathematician and of the experimentalist. The 

 Ijack numbers of the Wiener Sitzmiiishcrichte testify to 

 the keen interest taken in the subject at the period to 

 which we are alluding, and in connection with dififusion 

 and other allied phenomena mainly depending on the 

 free paths of the molecules of gases, a prominent place 

 must be given to the writings of Oskar Emil Meyer. It 

 was Meyer, for example, who taught us that in the 

 diffusion of two gases whose molecules have unequal 

 powers of penetrating into one another, a counter-current 

 must set in to compensate for the differences of pressure 

 which would otherwise be produced by the transference 

 of molecules in the direction of the more penetrable gas 

 — a theory which has met with wide acceptance. 



Mr. Baynes, in preparing the English version of a new 

 edition of Meyer's treatise, has given English readers a 

 book calculated to meet the wants of a large and varied 

 class of persons interested in the kinetic theory. Mathe- 

 maticians wiU naturally turn their attention to the 112 

 pages of " Mathematical Appendices," and will there 

 obtain an introduction to theories for the further develop- 

 ment of which they will probably pass on to the 

 writings of Boltzinann, Tait, Watson, Natanson and 

 others ; while the removal of this mathematical matter 

 to a separate section renders the book specially suited 

 to students of physics and chemistry who are interested 

 with experimental conclusions rather than with abstract 

 reasoning. It was for such readers that Meyer's first 

 edition was written in 1877, and there can be no doubt 

 that the book, presenting, as it does, the subject in the 

 aspect of a physical reality and not as a mere collection 

 of formulae which may or may not accord with results 

 of experiments, has done much to popularise the kinetic 

 theory of gases, and thus indirectly to help to make its 

 name at least familiar even to elementary pass-degree 

 candidates. Now that we have an English edition 

 students can have no excuse for not carrying their know- 

 ledge of the subject rather further ; for a better intro- 

 ductory treatise could hardly be written, and there is 

 little in Meyer's treatment that could present difficulties 

 tven to the veriest beginner. After an introductory 

 < hapter on the foundations of the theory, the relations 

 between pressure and energj: are dealt with very fully. 

 ■ Maxwell's Law" is illustrated by a curve showing the 

 NO. 1578, VOL. 61I 



distribution of speed, a diagram showing shots on a 

 target distributed according to the error-law, and a 

 statistical table showing the relative proportions of 

 molecules whose speeds lie between different limits, re- 

 minding one of the statistical reports required by the 

 Civil Service examiners. The two last illustrations well 

 exhibit the fact that the probability of a molecule having 

 its speed i&xo'is infinitely small, and that there is a certain 

 speed whose frequency is a maximum, notwithstanding 

 that the most probable value of the velocity component 

 in any direction is zero. In the chapter on " Ideal and 

 actual gases," we have an account of Van der Waalb' 

 and allied hypotheses ; while under the heading " Mole- 

 cular and atomic energy" the specific heat ratios of 

 gases and their dependence on the number of degrees 

 of freedom of a molecule for heat-motions are discussed. 

 The second part deals with molecular free paths and 

 the phenomena depending on them. It contains an ex- 

 haustive account of all that has been done in explaining 

 viscosity, diffusion, and heat-conduction by the kinetic 

 theory, the part on viscosity alone extending over seventy- 

 six pages. The third part, which is much shorter than 

 the two preceding ones, aeals with "direct properties of 

 molecules," including determinations of the size, number, 

 and speed of molecules and the magnitudes of inter- 

 molecular forces. This concludes the physical portion 

 of the book. In the mathematical appendices, the calcu- 

 lations are in many cases based both on Clausius' hypo-- 

 thesis of equal speeds, and also on Maxwell's distribution, 

 and while the former method is at the present day of 

 purely academic interest, its inclusion may be serviceable 

 to beginners. Mr. Baynes has supplied an index besides 

 adding to the already copious references to original 

 memoirs, which are an important feature of the treatise. 

 While a number of new theories have been inserted, and 

 on the other hand many recent developments have been 

 excluded, the author has perhaps wisely made the general 

 scope and plan of the book the same as m the first 

 edition. As he remarks in his preface, 



" with the present limitation to the old range it has cost 

 very much trouble and very much time to work up the 

 literature of the subject, which has grown mightily in 

 these more than twenty years." 



While Prof. Meyer and Mr. Baynes are contented to 

 accept " Maxwell s Law" as a working hypothesis, Mr. 

 Burburyhas taken up the far more difficult task of work- 

 ing out the distribution of a system of molecules under 

 conditions to which the ordinary proofs of the Boltzmann- 

 Maxwell distribution are inapplicable, viz. when finite 

 intermolecular forces exist, or when the volume of the 

 molecules is not infinitely small compared with the total 

 volume of the gas. The appearance during recent years 

 of several papers from Mr. Burbury's pen has acquainted 

 us with the general character of his labours, which in- 

 volve practically the foundation of a new kinetic theory, 

 and we are glad to read the general conclusions in the 

 form of a handy treatise. In investigating the distribu- 

 tion of molecular co-ordinates and momenta, Burbury 

 points out that we may take two different fundamental 

 assumptions for our starting-point, namely, " Condition 

 A," that the chance of any molecule having velocity . 

 components within given limits is independent of the 



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