100 Prof. W. E. Story on Partial 



Also, by (2), 



to? „arf° 



and, by (3), 



M x) fcf asp® 



= N 



^??3 



(7« = 1, 2, 3, . . „ *), 



09 



» *„» 



_ = ^_^ = N °|^-^ ) (r=l,2,3,...,*-l). . 



(?) 



From (7), (2), (3), and (5) follows 



*P.\ *P7\ W.* W. 



B.l'l 0<^2 0.^3 0^ K _! 



= N[(^^.,^ + .^ + ... + ,^) 



L\ 3/Jj d" 2 0^3 o ? V-i 7 



CO 



d«i d" 2 On 3 O'^.i on 



-N 



7 M1 



(8) 



Furthermore, considering jt? ( tf ,l) as derived from p^ by sub- 

 stituting the values of a? 1? x 2 , #3, . . ., ,v k _ 1 in terms of the n's 

 from (2), we have, by (8), 



dn r NLdx r \ dXi Ox 2 0# 3 



to M 



+ OS . 



' K-l 



<K 



-,)] 



y (9) 





as also by (7). 



By condition d, we have 



p# = for * = or ^ = (s = 1, 2, 3, ■ . ., *). (10) 



