66 Mr. J. Kam on Molecular Attraction and 



becomes /3i = #./3 ; so that the combined effect of these last 

 two increases compensates the decrease of c. 

 This might be expressed as follows : — 



E.T_^.R.Tj R.T X 



n = 



ff v — x.ft v _o 



X 



T 

 and it will be seen, since tt<^, that a gas reaches a total 



pressure IT at a lower temperature sooner than at a higher 

 temperature. The same changes of volume cause larger 

 changes of pressure at lower than at higher temperatures. 



Another objection lies in the solution of the equation of 

 van der Waals for the critical state. If we convert it into 

 the form 



a _ R . T, 

 7)+ (<H/3)2- <j> 



making t> = <£ + /3, and solve for the critical state, we find 



2a R . T c 



d<f> ' f^ + /9) 3 fr 

 £g= 0. 



6a 2R . T, 



(i.) 

 (ii.) 



wh ence 



</>* = 2/5. 



Since c/> here is certainly a volume but not a density, we 

 may not calculate the values of the critical data by sub- 

 stituting </> c = 2/3 in (i.) or (ii.). Yet if we do so, we obtain 

 those values as found by van der Waals. The operation is 

 the same though in inverse order as the one of multiplying 

 and arranging according to powers of <£ c , and the same error 

 is made. 



Substituting e. g. in (i.), we find 



2a R.T C 

 27/S 3 ~ 4/3 2 



and 27 Q -p T 



a = -jT-.p.H. l c , 



a 1 a _ 1 



Pc ~~ 27@ 2 " 3 ^?~ 3^' 



T- -1 _iL 

 c ~ 27*R./3' 



which for a, p c , pi C , and T c are the values found by van der 

 Waals. 



