502 
ON A FORMULA FOR THE INTERSECTIONS OF A LINE AND CONIC, 
[371 
which are, in fact, Mr Spottiswoode’s linear equations, and which lead, as before, to the 
value 
a*—v, er. 
But this value of 6 is obtained in a different manner by expressing (x, y, z) as 
linear functions of P, Q, R ; viz. putting as usual K = abc — af 2 — b(f — c/i 2 + 2fgh, the 
linear equations thus become 
AP + HQ + GR+^UQ- n B) = 0, 
HP + BQ + FR + - (fK - £P) = 0, 
GP+FQ + OR + ~ (r/P~ (Q) = 0, 
or eliminating (P, Q, R), we have 
A 
, H + 1{ §, G- 1 ^ 
H--g, B 
, F + 
Ki 
<? + -/’ F-’f, C 
= 0, 
that is 
ABC-AIF 
B G*- 
K*rf 
~w 
- G (h* 
KR? 
6 2 
or, reducing, 
that is 
as before. 
+ { F+K i) 
K#) 
+ 
1 
Cbl ^ 
Urrt 
(»-*') 
(*- f)=°; 
AF 2 - BG 2 - 
- C№ + 2FGH+ ~ (A, v, if = 0, 
P+(A,.„lt, ,, ?) 2 = 0, 
I reproduce, as follows, a fundamental formula of Aronhold’s Memoir, 
function 
V{-(M, ...£w, v, wf\ 
log 
(ft, y lt Z$X, y, z) 
ux + vy + wz 
Consider the 
where x 1 , y lt z x (corresponding to x, y, z in the former part of this paper) are deter 
mined by the conditions 
(ft, ...$>!, y lt zf = 0, 
ux x + vy x + iv z x = 0,