448 PROFESS Oil CAYLEY ON 
THE TRANSFORMATION 
and we find 
s m~ a § ivin g 
S- 
b M 
=Aw 4 , 
S — —0 
° M u ” 
s ^ 3 
b M 
= 0, 
v‘ 2 
S~=A'm 2 
s" 2 
b M 
=A'w 2 , 
S^=A"«+BV „ 
S ^M 
-AV+B"«r 5 . 
But for w=l the corresponding values of v, 
M are 
v=l, -1, -1, - 
-1, -1, 
-1, 
H=5. 1. 1. 
1, 1, 
1; 
whence A— A'=10, A"+B"=0, or say the value of is =A"m(1— w 8 )- 
The value of A" is found very easily by the ^-formulse, viz. neglecting higher powers 
of q, we have 
u=qi^/ 2, v 0 =q$^/% j^=5; v 5 —q^2, j^=l; hence 
= ^(v^) 5 =A ,, 2\/2 ; that is A"=20, and the equations are 
S M= 10 > S M=°> 
8^=10*% 8^=0, S M =10< S m =20m(1-<); 
whence 
Fy.l=20i^(l-M 8 ) 
-10m 4 (Sv„-v) 
— 10 u\ S-y^u, — vSv^y + « 2 Sy 0 — v 3 ) 
— 10 (SvgV^v^ — vSv 0 v 1 v 2 v 3 + v^SvqV^ — v 3 Sv 0 v 1 + o 4 Su 0 — v B ), 
where Sw 0 , &c. are the coefficients of the equation 
v 6 + 4zV 5 u 5 -f- bvHF — 5 v 2 u * — 4 vu —u 6 = 0, 
viz. Sv 0 , v 0 v 19 v 0 v,v 2 , v 0 v x v 3 v 3 , v 0 v l v 2 v 3 v i 
are —4 u 5 , +5 m 2 , 0 , — 5 u* , 4m; 
20 u (1—0 
10 « 6 4 (— Au 5 — v) 
10w 2 ( _5 m 2 u-4mV- v 3 ) 
10 (4 u +5 u 4 v — 5vV— 4vV— O 
or the equation is 
F»-h= 
