76 



Mr. Jarrett on Algebraic Notation. 



-1 ^T-l 



= 1 + (.r- 1) ^'v. 1 + {x- \y . s\Sr;-' . 1 + &c. 



= i+s',(.r-i)».5'vs,;-...s,^;--'.i 



+ {x- 1)'^' . S'vS,;-' . . . s,;,: -'x'-r' 



= 1 + .9', (X- 1)' . S/'^'- - . s,; . . . s,,_;,-. . 1 



+ {x- 1)'+' . 5,"-' V • • • Sr^'X'-r^ (Art. 19.) . . . .(l). 

 Now S^;- s,;. . S. ^ . 1 = S,; 5,;. . r, = s,; a,^- ' (r, + 1) 



and similarly, 5,; . . . Sr,_;-' • 1 = \r + s-2 . —^ . 



s — 1 1 



Whence S,"+' -' . S,; . . . S,_J.-^ • ^ = l!L- ,s • 



Also AV-S../.^,;.. x--.-' = S,:S,:^:c^-\S,;.^^-'..l 



= .S,; 5,;. . x^- ' . (r, + 1 - r,), (Art. 1 6) 

 = 5/ j:'- .-' . .9,;+ • -'■ (r, +r, - 1 + 1 - r,) 



= S.I'xT' . «,; + '-'■. . r, = S./x--.-' . Ar' ■ (»-+ 2 - r,) 



= Vx^.-'. |r + 2-r. .i^; 



md similarly, S,^' . . . S.y^xT' = S^^a;'"-' . [r + t - l - r, . -^ ; 



whence S,""' . V . . . S,,'.-. . x-"."' = S/-'a;'-' . |«-r . - ; 



t 11 



