336 Dr. R. D, Kleeman on Relations let ween the 

 General Considerations. 



We will now deduce some further results of a general 

 nature from the law of attraction between molecules quoted 

 at the beginning of the paper. 



It can be easily shown that the theory of corresponding 

 states follows from the law quoted. It will first be proved 

 in the case of a liquid in contact with its saturated vapour. 

 The equation for the internal latent heat of evaporation 

 deduced from the law* is 



L=A 1 $- 3 (2 v /™ 1 ) 2 -A/-£(2 V^) 2 , 



nv 



wh 



ere 



A]=, Kt'iO' a * = * i (*!*t.)' 



and x a , Xb denote the distances of separation of the mole- 

 cules in the liquid and gaseous state respectively. The form 

 of Aj and A 2 , it should be noticed, depends only on the 



form of the expression <£ 2 (-7>7jt ) occurring in the law of 



\X C 1 c / 



attraction. "We have seen that an infinite number of formulae 

 for the latent heat can be obtained which correspond to 

 different forms of </> 2 , and there exists, therefore, a series of 

 equations of the form 



• 4/3 4/3 



4/3 4/3 



=A 1 "^- 3 (2v/,» I ) 2 -A 2 "^ 7 - 3 (S Vm0 2 = ... , 

 or 



where — = - , and — = — . 



&c Pc x c pc 



It will be readily seen that if we express the quantities p u 

 p 2 , and T in terms of their critical values in the same way 

 as before, the equations will contain w,, ?? 2 , and n 3 , only. 

 Since it must be possible to express n^ and n 2 in terms of ??, 3 , 

 therefore if n 2 for a number of substances has equal values, 

 w-t and n 2 will each have equal values. This proves the theory 

 of corresponding states from the general law of attraction 

 for the quantities p u /o 2 , and T. 



* Phil. Mag. May 1910, pp. 793-794. 



