A SYSTEM OF PARTICLES. 253 



hence it is evident that, omitting all the terms of the summation 

 except those respectively which involve the highest power of s, we 

 have, as the sum with respect to %, nothing more than the integral 

 with respect to z ; and, by the integral Calculus, we know that 



,• fh _ n.(?i ~2)...2 1 



,,. .. , J^ (m +!).(«- 1)...3" ,„ , o,^ 

 {x' + y' + X-) ' ' ^ ' {x- + y) • 



Pursuing an analogous process for y, we obtain 



r dy ^ (w - !).(?< - 3)...l r rfy 



J„.o , ., ..^2±i n.(n-2)...2 ' J {x' + y') x'-' 



hence /^/ 



(W - 1).{U - 3)...l 1 TT 



n.{n - 2). ..2 x"-' ' 2 



(?/ - 3).(m- 5)...1 1 ,r_ 

 M.(« - 2).. .2 ' x"-' ' 2' 



n.(n - 2). ..2 (w - l)...l 



/ - _L «, ^^^' (m + 1)...3 w.(m-2)...2 2a;"-' 



1 1 TT 



" w + 1 *a;"+'" 2 



^ , r /• y' n.(n-2)...2 {n - 3). ..l ir 



JyJ'„ „ , „,'^~ (« + 1)...3 "m . (« - 2)...2'2x°-' 



■ {n + !).(// - \)' X'-' ■ 2' 



K K 2 



