'26 CHAPTER X. 



* i 



^o^oi + "10*0 +^ 

 1=1 



F 02 ) 



respectively. By choice of the ^ f , we can make the terms in brackets 

 all zero; those of the first sum by choice of A n , . . ., Aiki, those 

 of the second by choice of A 1Q , A 21 , . . ., A^kit those of the third 

 by choice of A 20 , A 31 , ...,^.3^1. A like result holds for the remain- 

 ing Y 0s (s = 1, . . ., a). 



S replaces Z 01 , Z Q %, ... by respectively 



k 1 





Since Ki L =|= 0, the coefficients of A,- may be made to vanish by 

 choice of the 2?i,-. Hence, /S takes the form $ 2 : 



0, 1, ...,*- 1) 



i,.(^.+^-i) (j-^.-.A) 

 L i (Zii >l +j+Z i ^+:j- 1 ) 



w -%..., 



0, 1, . . ., J - 1) 



If the constants qp(^i), ^(Ki) y %(Kt), are all zero, no further 

 reduction is necessary. If any two are not zero, as <p and ^, suppose 

 for definiteness that <% ^ a 2 , and introduce in place of YU, . . ., Y ia ^ 

 the new indices 



