59 



+ i)'"' -"'*=¥'"' ^"* 



Had we expressed everything in the real RTk, pk a,nd vk, we 

 shoidd have got : 



27:r^\ 8 



or also : 



27 : X.r'\ 8 A, 



e + - \{ti—^)— — ~m = sm, . . . (10a) 



11 J ^ >^2 



in which [i = h : vk = b : rbk- 



Hence the new reduced quantities e, m, n, and /? of equation (10) 

 are to the original ones in the following simple relations: 



m'= X^7n = m Xi^'k- T'k) \ q|\ 



n' = y^r.n^z n X {vk '■ v'k) ] 



Substitution of (iJ) in (10^/), of course, im mediately leads to (10), 

 and vice vei'sa. 



Van der Waat.s has retained e' = f, ul' = m, and therefore his 

 new reduced equation of state will in this respect only hold by 

 approximation, though the dilTerence will be exceedingly slight. But 

 as VAN DER Waals does not put n' == -/^r . n (or ii! = n : 7»), but 

 n' = 71 : VrS ill which r' does not represent Vk : bk, but Vk ■ bg, while 

 bg and bk can differ 4 or 57o , the difference with the reduced 

 equation of state (10) will be much greater for the quantity n -. '/,', 

 because in (10) the specific element [embodied in the quantity r 

 (A, and X^ left out of consideration), which quantity r can be difTerent 

 for different classes of bodies] has been entirely removed. 



U a and b are still functions of the temperature, the term 3 : ?i"' in 

 (10) will have evidently to be replaced by 3/(?7i') : ?z", or /5' by l^'fim'). 



As according to (6) X^{/ — 1) : 3 == 9 : r\ also : 



and we may also write instead of n'^zn-.y,.- 



n' = n : \X 't 



now perfectly accurate. 



In a following (concluding) pa])er some remarks will be made 

 about the dependence of a or b on the temperature, and some general 

 considerations will be given about the nature of the function b =zf{v). 



Fontanivent sur Clarens, March 1913. 



