168 
PROFESS OE CAYLEY’S SECOND MEMOIR ON THE 
*(3,2) =*( — 9 + a)=*(3(% — 3)+* — 1 + 1) Referringto 
= 3L+2M+0 (third equation) 
*(3, 1, 1) =*(> 2 +2mw+i% 2 -^-i%+27-f«) 
=H+2I+D'+J' (fourth equation) 
viz. * _1 H =fm 2 — fm +4% —fa 
* _1 . 21 = 2wm — 6m — 8w+24 
* -, .D' = — §w+ 6 
* _1 J' = n— 3 
fm 2 + 2?7m + — L 2 -m — 1 £ j n + 2 7 — f a. 
*(2, 3) =*(2*1, 3) (fifth equation) 
*( 2, 2, 1) =*(2*1, 2, l)+*(w-3) 
=*(2*1, 2, 1) + J' (sixth equation) 
*(2, 1, 1, 1)=*(2*I, 1, 1, l)+*.i(»-3)(w-4) 
=*(2*1, 1, 1, 1)+D' (seventh equation) 
*( 1, 4) =*(1*1, 4)+* 
=*(1*1, 4)+0 (eighth equation) 
*(T, 1, 3)+ *(2, 3) +*2(4, 1) 
=*(1*T, 1, 3)+*(M, 3) +*(»-3) 
+*(2*1, 3) 
+ *(2m + 2w— 6) 
=*(1*1, 1, 3)+2*(2*l, 3) +2R + 3J' .... (ninth equation) 
*(1,2,2) =*(1*1, 2, 2)+*{3(w— 3)+*— 1} 
=*(1*1, 2, 2)+3L+2M) (tenth equation) 
*( 1 , 1 , 1 , 2 )+*( 2 , 2 , 1 ) 
=*(1*1, 1, 1, 2)+*(2*l, 2, l)+*{f(w— 3)(%— 4)+^+2 3 m— 4} 
+*(2il, 2, l)+*( w _3) 
=z(lzi, 1 , 1 , 2)+2*(2*l, 1 , 2) 
+D'+H + 2I+J' (eleventh equation) 
