﻿562 Dr. S. R. Milner on the 



exponential can possibly do, even in the most unfavourable 

 ease which occurs when all the ions have the same sign ; 

 consequently, a p /nr p is always smaller than ajri, and the 

 application of the theorem remains valid throughout. 



Integrating successively by (21) until only the integration 

 in r remains to be performed, we get 



r - 4 W r * m ' 1 - 1 I" S-ft- 9 - 3 ^- 1 - 



Tm '■ 



e 



6.9.. .3(^-1) . 9...3(m-l) , n 1 3(w-n 



This can be written in the form 





m-irt ,^\0 



r m n>n~l) 



3" l "T(m) 



where 



AW=a 1 ^ ir +o 2l p r + + a '»-f>^r 



__ i r(p-« 



4 



To integrate it, substitute x— »7rr OT 3 and write 



■ s (l) AW ^ = rx^T) a • • * (22) 



and t.=(4«r)— *, [v. (19)]. 



Then, writing zero instead of the negligible e for the lower 

 limit, we get 



p ^=rwJ * « ** • • • (23) 



Expanding the exponential e~ in series, we get 



P(,n) = tfey p ~' T (- i "' ! " 1 -/ 3 - i '"'" 1 " i + H a '"~ 1_J )<*•* 



= rfey{ r( '" ) - /Sr( " l -* )f fi r(m - |) }' 



and on substituting the value of /3 given in (22) this 

 becomes 

 »y_j f, ,,« 2 r(m) r(m-§) q»/ TQn) \» !>»-§) 1 J 



