Non-generating Force exerting Cumulative Influence. 167 



where the term in the (r + l)th row and (s-r-l)th column 

 is « r+s -f«| r _ S | , unless r = s, in which case the term is 



l — s\n/fi) 2 + *28- 



This equation determines one limit of each of the ranges 

 of n associated with fi, /i/2, . . . fi/r .... For the other limit 

 A_ r = — A r in (ii.)> and the particular solutions are 



x = X B r sin rnt } 



1 



CO CO 



x = t^B r sin rnt— X C r cos rnt, 

 1 o 



where 



{l-(^) 2 -« 2 }B 1 + ( ai -a 3 )B 2 + (« 9 -«4)B 8 +(* 8 -«5)B4+ ... =0, 



(« 1 -a 3 )Bi+{l-(2V/A) 8 -a4}B 2 +(« 1 -a 5 )B 3 +(a s -a 6 )B 4 + ..=0, 

 (a 2 -« 4 )B 1 + («i-« s )B 2 +{l-(3^) 2 -a 6 }B3+(a 1 -a 7 )B 4 +...=0, 

 (^-« 5 )B 1 ^(a 2 -« 6 )B 2 +(« 1 -a 7 )B 3 +{l-(-i^) 2 -«J B 4+.. =0, 



Co 4 aiC 1 + a 2 3 + t z 3 C 3 + ... 

 2«iC + {l-(n//i) 2 + « 2 }C 1 + (« 1 -r«3)C 2 + (a 2 + «4)C 3 + ... 

 ^ 2 C + («i-f a 3 )C 1 +{l-(2n/^) 2 +a,}C 2 +(« 1 + a 5 )C 3 4 . 



Hence, 

 1_ G) " a2 ai ~* 3 



a 2 -a 4 



a 2 — a 4 





«3~ a 5 



«i — a 5 





«2""" a 6 



(?V- 



*6 



«1- a 7 



-or- 



«8 



= 2».B lf 

 = 2n.2Bj 



= 0,(3) 



where the term in the rth row and 5th column is a | r _, | — « y+s , 

 if =£s ; if r = s the term is 1 — s 2 (/?//i6) 2 - ao*. This equation 

 determines the other limits. 



