386 



SCIENCE 



[N. S. Vol. XXV. No. 63G 



the multi-atomic case is given, under a certain 

 hypothesis, viz., that when the gas has assumed 

 a stationary condition, for every group of 

 molecules with a state of motion A there is 

 another with the opposite state of motion 

 A (-). 



Chapter VII. — Ueber die Grosse von Ge- 

 bieten in einer n-fachen Mannigfaltigkeit. 

 Here is found a short mathematical discussion 

 leading to results which are of importance in 

 connection with their bearing on the kinetic 

 theory of gases. 



Chapter VIII. — Ueber die Entropie eines 

 Gases. — In his treatment of the kinetic theory 

 of gases Boltzmann was led to the considera- 

 tion of a certain function, S, depending on 

 the motion of the molecules, which in conse- 

 quence of their collisions can only decrease. 

 The author points out that for a stationary 

 state the function — H and the entropy stand 

 in close connection. He then proceeds to 

 show how in processes which progress infinitely 

 slowly this function behaves in the same way 

 as the entropy function. 



Chapter IX. — Sur la theorie moleculaire des 

 dissolutions diluees. On account of the sim- 

 plicity of the laws of osmotic pressure and 

 allied phenomena. Professor Lorentz has at- 

 tempted with considerable success to derive 

 thera directly from kinetic theory without the 

 aid of thermodynamics. The results of his 

 investigations in this direction are the subject 

 matter of this chapter. 



Chapter X. — Bemerkungen zum Virialthe- 

 orem. This chapter is an article which ap- 

 peared in the Boltzmann-Festschrift, 1904, p. 

 Y21. A method is described, very similar to 

 the ' Virial ' method of Clausius, which leads 

 to the same results in the kinetic theory of 

 gases. Application of the ' Virial ' theorem is 

 made to the case of the motion of an electron 

 in the field of an electric doublet. 



Chapter XI. — Ueber den zweiten Hauptsatz 

 der Thermodynamik und dessen Beziehung zu 

 den Molekulartheorien. This, the last chapter 

 of the book, is by far the most extensive, com- 

 prehending the last one hundred pages. The 

 author claims to give here nothing essentially 

 new, apart from the method of presentation. 

 The clearness with which the subject is 



treated, however, must appeal strongly to all 

 readers. 



Professor Lorentz begins at the beginning, 

 and treats concisely, yet comprehensively, the 

 fundamental principles of the subject, and 

 arrives shortly at the expression of the second 

 law through the entropy function. The dis- 

 cussion is limited practically throughout to 

 the case of reversible processes. The thermo- 

 dynamic relations of a general system of 

 bodies are expressed through generalized par- 

 ameters. The laws in connection with en- 

 tropy, free energy and thermodynamic poten- 

 tial are derived, particular stress being laid 

 upon the importance of the free energy prin- 

 ciple in the solution of problems. Applica- 

 tions of this principle in the case of a perfect 

 gas, and of liquid mixtures, are given in con- 

 siderable detail; and the case of osmotic pres- 

 sure is also worked out through this principle. 



The general conditions for equilibrium 

 among any number of different phases of a 

 system are derived by the method of free 

 energy, also by the method of thermodynamic 

 potential. Attention is called to the impor- 

 tance of graphical methods in the treatment 

 of various problems of phase relations. 



Perhaps the most interesting part of this 

 last chapter is the section dealing with prob- 

 lems of equilibrium by means of molecular 

 theory. After some general remarks concern- 

 ing the beautiful results obtained by treating 

 the subject by the two methods, the thermo- 

 dynamic and the molecular, the author makes 

 the following cogent comment : " Bei dieser 

 Sachlage kann mann, wie mir scheint, kaum 

 daran zweifeln, dass die beiden Betrachtungs- 

 weisen, die thermodynamische und die moleku- 

 lartheoretische, gleich berechtigt sind und dass 

 wirkliche Wiederspriiche zwischen den beiden 

 auf die Dauer nicht bestehen konnen; einer 

 Meinung, in der wir durch die Tatsache 

 bestarkt werden, dass mann wenigstens einen 

 Teil der Folgerungen, die sich aus den thermo- 

 dynamischen Satzen ergeben, audi molekular- 

 theoretisch, mit Hilfe gewisser Vorstellungen 

 iiber den Mechanismus der Erscheinungen 

 begrunden kann." A few examples showing 

 the coincident results derived from the two 

 methods are then given. 



