tome New Equations derived therefrom. 27 



b here is the volume of N molecules exerting the same 

 pressure at the volume (V c + &) as N molecules of a perfect 

 gas at the volume Y c (which of the actual gas only contains 

 N 2 molecules). 



In accordance with (1) we find for N x 



and !• . . . (6) 



and the volume of these N x molecules is 



*=vSv*=§ 6 0) 



(5) and (7) give 



Y c = 2b='S/3 (8) 



Substituting v and /3 in equation (4) we find 



r.R.T e= g.R.Tc R.T C R.T C 



V c -£- 2b-%b 2b Y c ' 



From (6) we deduce that the density at the critical state is 

 for all substances § of the theoretical one, or § of the density 

 of a perfect gas exerting at the same volume a pressure 

 equal to the critical pressure at the critical temperature. 



This in combination with (8) may well lead us to suppose 

 that the gaseous laws again hold good for the critical state. 

 We shall see presently that this actually is the case. 



In an entirely similar manner we deduce from (B) 



dp__ n 2c_ r.R.T c 



dv~^ V c 3 ~(V c -/3) 2 ' 



cfp_ () 6c _ 2v.R.T c 



dv* ~°' v c 4 ""(V c -/3) 3, 



whence V c =3/3, (Sa) 



a value in accordance with {&). 



We have already seen that equation (A) is not identical 

 with van der Waals' equation. 



It will also be seen that the usual solution of the latter by 

 multiplying and arranging according to powers of V c cannot 

 atford correct values of P c and P lc . For doing so, we con- 

 sider^- the density (or the pressure) to be the inverse value 



of V (the volume) which for an actual gas can never be, 

 so long as b has a positive and definite value. 



