114 Prof. W. E. Story on Partial 



case. So far as they correspond, we designate the formula} 

 l»v the same numbers as in the general method, with an 

 accent attached. 



By (28) and (23) we have 





p 1 = x i e , y/ 2 = .r 2 e ~> • • • v' v 



wiiere 



Ml =ln P, for arissl, u 2 =\n P 2 For .r,= l. . (23') 



Put iei =\ +z, .*,*j-s . . . (33') 



and 



u l - l/ ., = 0) (34') 



Then 



(g+-)^i+ (5^)^=0, . . . (30') 



u t = ( g-sjdm, <fc/ 2 =-^+ c ) c/w . . (64) 



50 that 



</ 

 Put 



Ml = 2 a* 1 ) c«, w 2 = 2 a (2) a*, . . . (41') 





2,/V" (42') 



Then, by (64), 





SO 



that 



(i) 1 ,tf~ 1 m^ 



(2) l (f—l 



«?=-2 e i--— e >-i> J (52') 



and, in particular 3 



Also, by (23') and (41'), because z = 7) corresponds to a\ -1 



