Kinetic Theory of Gases. 795 



(13) we obtain the following integral equation for %(~), 

 namely, 



• • • (W 



Further corrections for the size of molecules beyond the 

 first-order correction result in a series of similar terms v\ 

 v d , ..., on the right-hand side. 



This is an integral equation of an unusual type. A formal 

 proof that it has a unique solution would not (apparently) be 

 particularly difficult. The relevant point at the moment is 

 that the form of (14) shows that the first approximation to 

 the solution (y small, ^ large) must be of the form 



S=f -(*-/>#+ (;). • • ■ (i5) 



and therefore that in calculating B we should ignore all 

 boundary variations of v(f), and replace v(f) by v in equation 

 (12). 



§(8). Continuing the calculations of § 6 in view of the 

 discussion of § 7, we find that, to the required order, 



= 2ttv \ *vr(f) elf + 2itv \ v ( 



Jo Jo 



(/)#• . . • (16) 



Using the definition of 57(c) we obtain after reduction 

 (integration by parts) 



-f' &-*)(/** -l)md»} . . . (17) 

 From equation (17) it follows at once that 



X(0)=:i X (.)=^fV(> w -l) < &r. • (18) 



l l Jo 



One would expect a priori ^(so ) to vanish. The fact that 

 it does not do so is due to the artificial nature of the assumed 

 infinity conditions. And in fact it does not matter, for 

 %(oo ) means the work done by the attractions when the 

 molecule is brought from positive infinity (in the gas) to a 



