348 RKPOUT— 1872. 



Now let us define a symbol, 



then, when v^ becomes v^ + 2m^ir . . . ., u^ becomes 



and therefore 3^{v^ + 2'm^ir, v^+2m^ir, +....)= 



Section 10. — Let us now recall the values of S^ ^ (section 8) defined by the 

 equation Sy^c~^c'^c' p^'c' c • '"'' ^^^ ^®* ^^ assume 



K^^A. i+^A.2+^^K.z+ ■ ■ • -'-A. 



71' 



and let us ascertain the values of itj^u^u^ .... when v^v^ .... become v^ + S^i, 

 v.^+B^i,. . . . Thus itj becomes 



J(3^i, A + Ki,2^+ • ■ • ■^y.n-J + ^(Ki. A + Ki, A+ . . . .^\JJi= 

 \ + Ki. i(>-.2,G, ,K',„ , + r,S A, iK;. 2 + »-32,G,, ,K;, 3 + . . . . )i 



+ .... 

 =^^.+(r,\\G^,,'^\,i^i.,+r.WK,^'.,2^i.,+ ■■■■) 



SO Wj becomes u^-{-io\i, u^, u^+w\i,+ .... 

 We will now investigate the value of 



_^g w-r 1. 2T- 2. 'A1(m^ + 2(^jI, M^+2w^t, ), 



Now E(Mj+2w'i, ttj+2w'jr. . . .)=E(Mj, m^Mj. . . .) 



But 



