74 



NA TURE 



[November 23, 1899 



representative point just falls outside this region the 

 conditions required for the occurrence of an explosion 

 admit of a simple geometric interpretation. 



In the second volume, Book iii. deals with change of 

 state, dissociation, and the triple point ; much of the 

 latter matter will be familiar to those who have read the 

 author's "Thermodynamic Potential." Book iv. deals 

 with the critical point, the principle of James Thomson, 

 Van der Waals's and allied formulae, and the principle of 

 corresponding states, specific heats of fluids, and adia- 

 batic expansion of vapours. Book v. treats of dissociation 

 in mixtures of perfect gases. In the third volume. Book 

 vi. deals with the thermodynamic potentials of a homo- 

 geneous mixture, solution, osmotic pressure, the hypo- 

 theses of Van 't Hoff and Arrhenius, and the law of 

 Guldberg and Waage. Book vii. contains a full investi- 

 gation of the general problem of solution, the chapter 

 dealing with double salts being of much interest, 

 especially the graphical representations. In the fourth 

 volume Book viii. is devoted to the consideration of 

 double mixtures, including the thermodynamic theory 

 of distillation, while an account of Willard Gibbs's theory 

 of the statics of heterogeneous systems in Book ix. con- 

 cludes the treatise. In this last book the law of phases 

 is established, and the diflferent degrees of variance of a 

 system are considered separately, actual instances of the 

 systems in question being cited. A separate chapter is 

 devoted to the properties of univariant and bivariant 

 systems. As Duhem points out, the whole of this theory 

 is based on " classical " thermodynamics where " friction " 

 is left out of account, as is also capillary action. 



The treatise, taken as a whole, shows what vast pro- 

 gress has been made in expressing the laws of mixture, 

 combination, dissociation, and chemical transformation 

 generally, in terms of a single potential function of 

 generalised coordinates, and thus placing chemistry 

 and chemical physics on a similar footing to dynamics. 

 The essentially mathematical treatment is not the 

 least valuable feature of Duhem's work. Thermo- 

 dynamics is quite as capable of being regarded from a 

 purely mathematical standpoint as dynamics or hydro- 

 dynamics, but hitherto its mathematical aspect has not 

 been exhibited so prominently as it ought to be. The 

 inclusion of descriptions of details of experiments would 

 have broken the continuity of the theory, and such 

 details can be far better studied in the original papers to 

 which abundant references are given in footnotes. Indeed, 

 the present work appears to be in many respects a 

 model of what such a treatise ought to be. In any 

 special problem certain hypotheses are first made ; these 

 should be clearly pointed out, and attention specially 

 drawn to them. From these hypotheses certain conclu- 

 sions are drawn by mathematical reasoning, and lastly we 

 have references to the evidence derived from experiment 

 as to the accordance of these conclusions with observed 

 facts. So long as a substance is regarded as a purely 

 mathematical abstraction, it may be defined by any 

 hypotheses whatever as to the form of its thermo- 

 dynamic functions, and a Thermodynamics based on 

 hypotheses convenient for purposes of calculation would 

 possess the same interest to mathematicians -as a Hydro- 

 dynamics which ignores viscosity and capillarity or a 

 NO. 1569, VOL. 61] 



Geometry of any particular non-Euclidian space. But it 

 would appear that the conclusions do largely represent, 

 either exactly or as approximations, the results of ex •- 

 periment ; and the subject thus assumes a physical 

 reality. 



It is difficult in writing on such a subject as the present 

 to avoid, quite unintentionally, "smuggling" doubtful 

 assumptions into the midst of an argument without de- 

 claring their nature. As we all know the late Clerk 

 Maxwell was much addicted to this practice, the gaps in 

 his reasoning having afforded fruitful material for later 

 investigators. When we consider the variety of sources 

 from which the subject-matter of the present treatise has 

 been compiled, we can only congratulate the author on the 

 measure of success he has achieved in admitting only 

 perfectly rigorous deductions based on explicitly stated 

 hypotheses. 



We cannot close this work without some reflections as to 

 the relative progress that has been accomplished by the 

 two schools in explaining the properties of matter, the one 

 by meansof the thermodynamical potential, and the other 

 by the application of dynamical principles to the indi- 

 vidual molecules of bodies. Molecular dynamics has 

 given us equations representing, under certain conditions, 

 the fact that ^Q/T is a perfect differential ; but there is 

 still a something we have not got to the bottom of in 

 every kinetic theory of matter, as applied to thermo- 

 dynamics. We have as yet discovered no dynamical 

 theorem of sufficient generality corresponding to the 

 uniqueness of temperature, or establishing the fact 

 that under the most general possible conditions the 

 entropy of a system tends to a maximum. The ques- 

 tion — Can the irreversible phenomena of thermo- 

 dynamics of a body of finite size be accounted for by 

 applying the equations of a conservative and re- 

 versible dynamical system, to its individual molecules 

 without making some special assumptions ? — has never 

 been completely answered. To deduce the second 

 law from the equations of the kinetic theory im- 

 poses restrictions on the systems to w'hich the con- 

 clusion applies where no such restrictions exist in the 

 law itself. Even the very question of applying statistical 

 methods at all to systems of molecules endowed with the 

 property of perpetual motion requires careful considera- 

 tion, since our statistical theories are so largely based on 

 our experience of every-day phenomena — events by their 

 very nature irreversible. One may thus be led to wonder 

 whether Prof. Duhem's " friction " may possibly involve 

 the existence of some molecular property which prevents 

 molecular motions from being represented by the equations 

 of what in the author's own nomenclature may be styled 

 "classical" dynamics, and which introduces irrevers- 

 ibility into the motions even of individual molecules. 



From a mathematical point of view the theory of the 

 thermodynamic potential has attained far greater perfec- 

 tion than any theories based on molecular hypotheses 

 that have been suggested up to the present ; whatever 

 the future may bring forth is another question. While 

 thermodynamics originated in this country from the 

 discoveries of Joule, it now hardly receives so much 

 attention from Englishmen as it deserves. Prof. 

 Duhem's treatise, by showing the wide range of pheno- 



