﻿736 Mr. G. Breit on the Elective 



But it may easily be shown that * 



and 



jQo'(j-O) _ _2 



QoO'.O) " 7T 



Q.O'.o) _ ir- 



Hence 



This solves the electrostatic problem proposed. 



Computation of the Function M(#) . 



In order to find the function M(a?), a choice must be 

 made of the variable x. Here r will be chosen as this 

 variable. 



It was assumed that the e.m.f. varies as r 2 . This means 

 that 



or, differentiating, 



fr 2 



M(r)dr = L r - 2 ; 

 Jo a 



V 



M(V).= 2L- 2 (18) 



# These formulas can be derived from using the following facts : — 



(a) Q ( 2 ) = ilog^±l. 



z — l 



(t>) — = 2 (2n+i)P„(*)Q»(y). 



(e) The recurrence formulas 



(2n+l)«P;W = (n+l^+iM+nP^rfe). 



Using (c) in (6), the expression for Q 2m in terms of Q can be derived 

 by writing the identity 



y-z~ y-z ~ 



Then from (a) expressions for Q 2m are obtained. On differentiating 

 these expressions and passing the limit in the result of the differentiation 

 as well as the original, the result follows at once. 



