Finite Volume of Molecules on Equation of State. 201 

 From the relations S = K log W + C 



and 



BS 



(SIX- 



we can easily verify that 



K<9 . Y-n/3 



W 



V 



V-2b 



-^log^(R==»K) 



(3) 



As a first approximation, when b is small compared to v, 

 1STTC/9 

 we obtain p= (Boyle-Charles-Avogadro Law), and 



as a second approximation we obtain 



p= j (van der Waals correction). 



We also note that 



»V = NK0 . i -^— -, where x= & 

 1 — e x r±u 



(4) 



To account for the influence of internal forces, we multiply, 

 following the lead of Dieterici, the above expression (3) by 



g-NKfl^ a having the same significance as before. 



From this equation of state, we can easily verify the 

 following results for the critical point : 



9, 



Critical volume, V c 



ze 



7^1 



6 = 3*166 6, 



K=™ =3-513. 



The corresponding values of V c from the van der Waals and 

 the Dieterici equations are (3b, 2b) respectively, and of 



K are I - = 



(Q 2 \ 



~ = 2"66 ? — =3 6951 respectively. 



As a matter of fact, for the simpler gases, the value of 

 '* K ' obtained in this paper agrees better with the experi- 



mental results than the Dieterici value 



we have for 



oxygen* K = 3346, for nitrogen f K=3*53, for argon J 



* Mathias and K. Onnes, Proc. Amst. Feb. 1911. 



t Berthelot, Bull, de la Soc. France de Phys. 167 (1901). 



% Mathias, Onnes, and Crommelin, Proc. Amst. 1913, p. 960, vol. xv 



