COXDORCET. So 5 



to (2) which shall be identically true, whatever v and e may be. 

 We have only to replace the left-hand member of (1) by 



^(^ + l)-(v + ey<f>(q), 



and we can then deduce 



q_±l ^ 



=^v{v + ef" + (v - e) \ve {v + ey' + ? ^^e^ [v + e)^"* 

 5 4 1 2a - 1 1 



1.2^^ [£ [£— 1 



This is identically true ; if we suppose v-{-e=l, we have the 

 equation (2). 



665. We resume the consideration of the equation (2). 



Suppose V greater than e ; then we shall find that <j) (q) =1 

 when q is infinite. For it may be shewn that the series in powers 

 of ve which occurs in (2) arises from expanding 



in powers of ve as far as the term which involves vV. Thus when 

 q is infinite, we have 



^(^g^) = v + {v-e) 1-2 + 2 (1 -^^^)"4- 



Now 1 — 4<ve= (v+ ef — ^ve= (v —ey. Therefore when q is 

 infinite 



/ \ { V — e , V + 6 ] 



— v+{v — e)<— 777 \ + o^ \C 



^ ^ [ 2(v-e) 2{v- e)} 



= V + e = 1. 



The assumption that v is greater than e is introduced when 

 we put v — e for (1 — 4re)i 



23—2 



