160 



Mr. C. S. Whitehead on the Effect of a 



}■■ 



&>) %=( w + !) 



(iX M «X — „,_i 



^ 



rf0 



d0 



d0 



1 ^. ^.A rf X~ ^Z_ H _i 



(12) 



(13) 



J 



From these equations we obtain 



X» + X_„-i _ b n tyn{\b) 

 Z_»_i a n yfr n (Xay 



(■>i + l)X„ — nX-,,-1 _ h n (j>n(\b) 

 — nZ_«_i a n (b n (\a)' 



. b*{(n + l)0 w (\a)^r n (\&) + w0„(\&)^r„(Xa)}Z_ H -i 



= a w (2n+l)^ B (Xa)^ m (Xa)X_ w _i. . (14) 



Let Xa and \& be so large that — > -^ may be neglected. 



Act A.0 



i|r w (\r) satisfies 



Assume 



and let 



dr 



^ n ~ »»+i' 



\ 2 + ?Ji 2 = 0, 



^ 

 A 



l+2m^- 



^7* 





W = 0. 



Let 





Substituting, we find in the usual manner, 



where 



_ n{n+l) (n — l)n(n + l)(n + 2) 

 2mr 1.2. (2mr) 2 



m = + 1\. 



Hence, when — is small, 

 Ar 



ci\r e~ 



^A\r)=—^ x or— pr 



