large sphere of attraction), then Bif'ty a|)proaciies ^) '/« -'' — ."r?i, hence 

 ai approaches to x - X - '"ï^' = oo. Now x^'^ lies between J— ?i' = ± 1 



at high temperatures and (0) at low temperatures, so that at high 

 temperatures will lie between =1= 0° and 90^, and at low 

 temperatures between (90°) and 90°. And the limiting value of y^ 

 is near oo, i.e. T^ near 0, so that the available range of temperature 

 is very large in this case. That aj now becomes infinite, is not 

 astonisiiing, for to obtain a piiite value, F[r) should decrease much 

 more rapidly with /• than is the case on our assumption (8) — viz. 

 in inverse ratio to r'. This assumption, however, only holds for not 

 too large values of a -. s. 



^ XVII. Calculation of (aj^. 



Now we must carry out the second integration in (7"). This 

 applies, therefore, to all the molecules that can come in collision, 

 as now remains smaller than the limiting angle <9„. It should be 

 carried out in tu.:o stages, viz. from x (= cos 6) = p to x = .r,, and 

 from .r ^ 1 (<9 = 0) to x=^i). For in the general integral with 

 respect to r (see ^ XVI), viz. 



ƒ; 



dr 



r\/p^r^.—a' (p^— cos' d) 



/)' — cos"^ 6 = p^ — .t^ will be positive in the first case, negative on 

 the other hand in the second case. Accordingly the first stage gives 

 rise to a Bgtg, the second to a log. The first stage, integrated with 

 respect to r, yields : 





al/j ^ 



Bgtg —Bgtg 



because />' [1 ^ j is = x^' (see § XVI). Hence we have : 



1 r r dx X r dx „ Vx^—x^n 



1^1— n' 1 



^Q^Q is namely = BgUj - = Bg cos n = -|- tt — w, hence Bg^tg = 



= ijx^—an. 



