342 Dr. G. Bakker on the 



It is very probable that this relation exists up to the 

 critical temperature. Indeed, the theory of capillarity of 

 van der AVaals gives in the immediate neighbourhood of the 

 critical temperature 



H=H (1-^ 

 and Pl -p 2 =2!3p k (l-$)i, 

 where H and /3 are constants. Hence 



— - = *(1-S). 



PI-P-2 



Generally I put, therefore, 



H=«(l-d)(p 1 - ft ), (8) 



k being a constant. 



In his paper, " Remarques snr le Theoreme des etats 

 correspondants " {Annates de Toulouse, v.), Mathias gives 

 empirical formulae for the densities of the liquid and the 

 saturated vapour. For the density of the vapour he gives : 



p 2 = A(l-a- 1-124 Vl^ + 0-579 2 ), 



where A is a constant. 

 For C0 2 , for instance, 



p 2 = 1-295 (1-3- 1-13 Vl-^ + 0-579 2 ). 



For C0 2 in the liquid state, he gives, further, 



p 1 = l-064(S-0-569 + 1-655 s/1— &). 



The difference of the two densities is therefore given by 

 the formula 



p 1 —p 2 — 0l $+j3 ^1— £— 7. 



where a, /3, and 7 are positive constants. 

 For C0 2 we have : 



« = 2-36 and 7 = 2'32, 



but in reality ex. and 7 must have the same value, pi and p 2 

 having the same value at the critical temperature. 

 I put, therefore, 



Pi-P2 = *(S-l) + /3 VI— &. 

 Substituting this expression in the formula (8), we find 



H=*(l -■&)*(£- VlT-S) (9) 



