Mr. Jarrett on Algebraic Notation. 77 



and, substituting in (l), we get 



(s ^7 1^ 



^t~t 



= 1 + S'^in .i^-Jl\ (x- iy^\ S,"-'\t+ I -s. ~ 



ii c 



Ex. 2. x'-^i +-^M-»-^~^' + (l-3^r'.S%| « + ^-s . — 



' ' — ' li. 



r~" — 1 



For, _,_! = S",.T-<'-", 



x-" = 1 + (.r-'-l) 5'\a;-:+', 

 by multiplication and transposition, 



= 1 + (1-x) S\x-'' 



+ {I -x)'*\ S'-.S,^'- . . . S.y.x-'., 

 by successive substitution. 



But S\S,;...S, '•-..l =|n + s-i .1 



L ^ 



and S\ S^; . . . S,;,-. ji;-'-. = .r - ' . S"'- S/^ . . . S,y . x-"-->' 



= X-' S%in+t-r . 



il 



S% [n + t-7- . ^ 



.-. x-" = l + S',^n + s-^.^l-^ + (l-xy*\S",[n + t-s.~ 



[s_ ■ t 



