Law of Molecular Force. 123 



inversely as v when t is constant ; so that we may put 



In his " Troisieme Memoire sur la Theorie Mecanique de la 

 Chaleur,"* Dupre obtains an equation which may be written 



AT d4>M)_ AT fjfi 



1 v + ty "&v v + yjr 



yjr is a constant for each substance, which he calls its covolume. 

 The amount of experimental data in existence did not admit 

 of any adequate testing of this type of equation. 



These forms all belong to a period prior to the publication 

 of Olausius^s theorem of the virial ; and they were constructed 

 and studied almost entirely for thermodynamical purposes. 

 But since the kinetic theory has been strengthened by that 

 theorem, much encouragement has been given to regard the 

 characteristic equation rather from the molecular point of 

 view. Van der Waals, whose work I know only through a 

 resume' (Wiedemann's Beiblatter, i. p. 10), starting from the 

 equation of the virial, and applying Laplace's theory of mo- 

 lecular force in evaluating the virial, arrives at an equation 

 similar both to Dupre'' s and to Hirn's ; except that the R in 

 Hirn's formula is made to vary inversely as the square of the 

 volume, or the f(t) of Dupre's is reduced to a constant. His 

 method of evaluating the virial of the internal forces is as 

 follows : — 



All round the surface of a body we can imagine a layer, of 

 thickness L, isolated, where L is the distance at which the 

 action of two molecules on one another becomes negligible : 

 then if we disregard for the moment the forces which act be- 

 tween the remainder of the body and the layer, and the mutual 

 actions of the molecules of the layer, we see that the virial of 

 the remaining molecular forces vanishes, because for every 

 force acting on a given molecule which has a component X, 

 there is another force whose component in the same direction 

 is — X ; hence the only parts of the whole virial 



-^(Xz + Yy + Zz) 



which it is necessary to take account of are those arising from 

 the actions of the inner molecules on the outside layer and the 

 part arising from the actions amongst themselves of the mo- 

 lecules of the layer. But this last part is negligible in com- 

 parison with the virial of all the forces at play in the whole 

 body ; so that the virial of all the mutual attractions of the 



* Ann. de Ch. et de Ph. 4 serie, iv. (1865). 



