367 



(loc. cit.). The equation of state at which I have arrived in this 

 manner is no longer incompatible with the requirements of Nernst's 

 theorem ^). 



2. Let 1 gr. of tlie associating substance contain .t', gr. of single 

 molecules, a\ gr. of double molecules, etc. in general./?,, gr. of^i-fold 



molecules'), so that ^.r„=rl. The .v,] grammes contain ^-^ gram- 



71 M 



mols {M being the molar weight of the simple substance), èo that 



1 ,Vu 



there will be altogether — -2" — gram-mols per gramme. If «iV/ be the 



At n I o 



mean molar weight, « being the mean degree of association, the 



number of grammols per gramme will be — , so that 



aM 



---^- (1) 



a n 



We now assume, that for M grms. of an arbitrary unchanging 

 mixture of molecules of mean degree of association a, the equation 

 of state has the form used by van der Waals : 



P = -^--,. ....... (2) 



V —Ox V 



where Rx does not represent the gas-constant R corresponding to a 



R 

 gram-mol, but R^ =z — '). Moreover ax and bx are functions of the 

 « 



quantities .r,j, hx being also a function of v, whereas both ax and b^ 

 might in general be functions of the temperature; but on various 

 grounds, which were fully discussed by van der Waals "), we shall 

 not inti-oduce the last-mentioned supposition. 



We shall also for the sake of simplicity following van dkr Waals ^) 

 leave out a dependence of b o«i the quantities Xn, i. e. we assume 



1) According to E Aries (Paris C. R. 164 (1917) p. 593) this theorem 

 would be implied by the ordinary theorems of thermodynamics. This statement i? 

 incorrect, however, and is obviously due to the author unconsciously introducing 

 suppositions which involve the theorem. As an instance he adheres to the identity 

 of adiabatics and isentropics down to the absolute zero, although at that tempe- 

 rature dQ—TdS = does not necessarilly imply dS = 0. He also introduces in 

 some well known relations such as Helmholtz's theorem transformations which 

 are not in general mathematically allowable and therefore presuppose a special 

 course of the thermodynamical functions at r = n. 



3) n is supposed to assume all possible integral values from 1 to oo. 



•^) See page 366, footnote 1. 



i) These Proceedings, XIU (1), p. 109; XIII (2) p. 1213. 



5) These Proceedings, XIII (1), p. 121, 



