148 Physical Properties [CH. vi 



by equations (340) and (341), 



on introducing the temperature from equation (265), 



= ^ T 



Hence, as far as first powers of 



(344), 



o / 



and this agrees with equation (294). 



168. The approximation has been extended* to the second order of small 

 quantities, by taking account of the further correction mentioned in 164, 

 which arises from the possibility of two of the shells, which there are supposed 

 to surround the molecules, intersecting one another. The corrected equation 

 is found to be 



(345). 



169. If we now suppose that forces of cohesion act of the kind specified 

 in 135, these forces will have a contribution to make to the virial. To the 

 first order of small quantities, we may, in calculating 22n/>(r), ignore the 

 effect of the forces of cohesion on the distribution of density of the gas. 

 The value of 22r< (r) is therefore obviously proportional simply to p 2 . 

 Allowing for this addition to the virial, equation (343) becomes 



where c is the c of 134, and is independent of the temperature. Or again 

 this last equation may be written 



agreeing with Van der Waals' equation (281), since the b in that equation is 

 the same as the present -0'. 



170. It is obvious that the calculation of the effect of the forces of 

 cohesion to a second approximation, would be extremely tedious, and I am 

 not aware that it has ever been attempted. Indeed a comparison of the 

 general equation of the virial (equation (335)), with the general equation 

 giving the pressure (equation (303)) seems to suggest that the virial is hardly 

 suited to the calculation of pressures to any accuracy other than that of a 

 first approximation. 



* Boltzmann, Vorlesungen iiber Gastheorie, u. 51. 



