§ 19 OF ARTS AND SCIENCES. 427 



facts as we possess is that the truth must lie between them. 



It was pointed out in § 10 that, in expansion, the free 

 path would increase with the distance moj'e than one 

 might expect, b}' an amount which could be calculated, 

 for instance, in the case of spherical atoms. 



The impact, which is necessarily central in the most 

 condensed state, would often be oblique in a state less con- 

 densed. The effect of thus increasing the length of the 

 free path would be to diminish the visible expansion and 

 also its rate of change. The same is true of the rapidl}^ 

 increasing vapor tension, and these considerations, together 

 with those given in the last section, are sufficient to ac- 

 count for a much greater ditference than actually exists 

 between the theoretical and empirical formulae. 



The latter is undoubtedly, as Mendelejeff claims, ?i first 

 opproximation to the expression of the facts; the former, 

 to their exact theoretical solution. The close ai^reement of 

 the formulae must be considered as a mutual confirmation. 



§ 19. In the same April Journal of the Chemical So- 

 ciety will be found an article by Thorpe and Rlicker On a 

 Relation between the Critical Teinperatuj-es of Bodies 

 and their Thermal Expatisions as Liquids. 



The formula of Van der Waals is first considered, name- 

 ly, that at corresponding temperatures, 



I dV, 



V, dt 



X 7^, = C, I. 



in which the first factor is evidently the same as our e. 

 This formula, by the way, may be derived from § 13. 

 In (6) we have 



/' V 



f: - ^1 = -8,5 ^ i^^^i-^) 



I ) \ I J '^7; P 



where, neglecting the last factor, which is nearly equal to 

 I, we see that if we know the ratio of Z", to T, which is 



