194 
MESSRS. A. E. H. LOVE AND F. B. PIDDUCK 
Since x 0 , which is — a ( 0 -/ 0 - 0) 10 9Z/cV, vanishes at all points of the locus 
*-B, = P, (s-S 1 ) + (B i /2 ] )(s-S 1 ) 2 + (B a /2 1 3 ) (s-S, 
the expression 
945F!(2?’) — 945crF 1 <1) (2r) + 420<x 2 F 1 (2) (2r) — 105cr 3 F 1 (3) (2r) + 15o- 4 F 1 (4) (2r) — cr 5 F 1 (o) (2r), 
in which 
F, (2 r) = A 0 + A 1 (2r-2R 1 ) + A 2 (2r-2R 1 ) 2 + ..., 
must become identically zero on substitution of 
for r —R x and of 
(B^ + B 2 <5 2 +B 3 d 3 + ...) 
2 1 {l+(B 1 + l)<S+B 8 3 a +B 8 3 8 +...} 
for rr. Now the powers of cr/Sj and (r — ~R 1 )/% 1 can all be expanded in powers of S, 
and then the coefficients of the powers of $ in the expansion of 
can be ecpiated severally to zero. The equations thus arising give the values of 
A 6 , A 7 , ... , successively. Suppressing the algebra, which is rather long, we may write 
down the results in the following form :— 
The equation for A 6 is 
The equation for A 7 is 
2B 1 ^4wt I = 2B 1 2 (945 ^-945 +420 
Z{ \ 2/! 2/j Zi 
+ 2B, (B x +1) 
(B 1 + l) 2 (420 
!LAi_i05 5 -^ + 15 — 
v 6 -v 5 1 % 
z - 1 - 
5! 
945 2^ + 840 3^ _ 3:5 4__A 4 + 60 5_ 
^- 315 ^ + 90 ^- 10 ^ 
+ B 2 ^945 ^ —1050 + 525 ^^-150 ilA- 4 +25 
V • wj "1 —1' ■—1 
+ 
