298 
Miscellanea 
V/Si must of course be given the same sign as fi^. Accordingly we have : 
Square, multiply by n^/N and sum and we have ; 
JV N 
It remains to find : 
^J^'hlM = s [n, Y ( - Vft X - 1 )IN] = qu - rV/S: . 
N 
Thus it follows from (iii) that a2 = (912 - r \/Wi)l{^2 - ft - 1)- 
We now proceed to find \//3 : 
Multij^ly by )i^\l/nlX and sum : 
S (n Y^) — 
0= -^30, or C3o=\/ft. 
Multiply by /iV and sum : 
0= -g3i^^-~S or C3i = /32. 
Multi^jly by Wj-x/^o/-^^ and sum : 
^-\/ft32-VA=C32 02-/3l-l), 
7= = C32 (P2 - Pi - i J) 
C32 — 
Accordingly: >/'3 = ^r^- ^-^ ^'^'^"^^ ^j^2-/32>^i - Vft>/^o, 
V/3i 
or y o = A — j= A ^ H A + -— 
Vft(ft-/3i-l) /32-/3i-l V/3i02-ft-l 
We have next to determine K3 : 
>S'(?i,jJ>3) 
= (7i3 ;= qi2-\ r 
V/3i(ft-/3i-l) 
Let VIS write : f 12 = ?i2 - V ^1 , f 13 = ?i3 - A'', 
<^2 = /32-/3i-l, <^3=(ft-ft/32-/3i)/VA. 
03 
Thus K3=ei3-— 612. 
02 
We have next to find X3 : 
= a - (^3-/3i/32 ^i) ft (ft-ftH ft-ft)ft ft-2ft /32 + ft^ 
'^^ /3i(ft-ft-l) ft2-ft-l ft-ft-l 
« «2 « ( ft-ftft-ft )^ 
-'^^"^■^"'^'"ft(ft-ft-l) 
= 04-03^02 f04 = ft-ft'-ft- : 
