290 Prof. Thomson on the Mutual Attraction or Repulsion 



P.Qt 





b b 



and therefore 



Ps^t Ps-^Qt+^ _ Ps-2^t+2 P\qt^B-x ,,^f 



c—fs-^Qt c—fs-i^fft+i C-'fs-2—9t+2 C-/i-^<+,-i 



and 



Similarly, we find 



PsP't Ps-^lP't+l _ 



and 







m+'f 



=z'-vqt+s. 



c-ffs-9't 



Now — = — , and — and — are each independent of u and 

 u V u V 



V ; hence the following notation may be adopted conveniently : 



p 



I W__ ; 



s„ 



^"=K^ ^»^q: 



• (13). 



Then, taking n to denote ^ +5 in the preceding equations, we have 



Pn-t qt _ _ P'n-tzl^t__ _ Jf!L ; 



C—fn-t—fft C—fn-t-l—g't Sn-i' 



Pn-tp't J^ . qn-tq 't ^ _ J!l 



C-fn-t-fr P» ' C^Sfn-t-^ On 



Hence we have 



(14), 



im which we conclude that 



