_ 2ttN 2 r 



3v } a 



798 Mr. R. H. Fowler on the 



proper field of attractive force <j>(r) by making Q->oo and 

 <€->0 in a suitable manner. *The virial argument starts 

 from the formula * 



v 



for the number of pairs of molecules in the gas whose centres 

 are at a distance between r and r 4- dr. Then for the contri- 

 bution %2i%rf(f) to the virial we have 



^trf(r)= 2 ^"r^r)e-^>^dr. . (21) 



We split this integral up into the two ranges (o - — e, cr) 

 and (<r, go). In the former we can replace r 3 by a 3 since 



n co 



-eventually e -> 0. On evaluating I f(x)dx we get 



Jr 



l%trf(r)^^^^^ qe- 2 ^^dr 



00 r*4>(r)e 2jm dr. 



The first integral can be evaluated ; it is 



If therefore we make Q->co and e->0 in such a way 

 that Qe->co we may replace the first integral by 1/2/, 

 which must be its value appropriate to elastic spheres. We 

 can write the second integral in the form 



- Crm'(r)e 2jn{r) dr 

 Jo 

 with our previous conventions for H(r). This can be 

 integrated by parts in the form 



" [J^)-!]" + j£ rV lB(r) -l)dr, 

 and the integrated part vanishes at both limits. Hence 



&trf{r)= ?^^- ^f r'(e 2 ^-l)dr. 



3 fyu 2jv J v J 



The complete virial equation is 



pv=mT + ^rf(r), 

 * Jeans, he. cit. p. 132. 



