1891-92.] Hon. Lord McLaren on the Ellipse-Glissette. 
89 
On the Eliminant of the Equations of the Ellipse-Glissette. 
By the Hon. Lord M‘Laren. 
(Read June 6, 1892.) 
The problem consists in the elimination of 6 from two equations 
which (after expressing cos^^ in terms of sin^^) may be written 
-Csin0cos^-Bsin20 + aiCos0 + /8isin0 + yi = O : . . . (1) 
C sin ^ cos ^ + B sin^^ + ag cos 0 + ^2 ^ + 72 ^ • • • * 
whence, 
{ci-^ + cos 6 4" (^2 /^ 2 ) ^ d- y 2 + y 2 = 9 : 
or 
Acos 6' + />tsin ^ + v = 0 : ... (3) 
As only two of the equations can be used, the elimination will be 
effected by means of (2) and (3), using the relation cos^^ + sin2^= 
where necessary, to suppress the term of cos^. 
The original equations include five terms, and it is proposed to 
find the determinant of the 5th order j the first step to which is the 
formation of a determinant of the 8th order. 
Putting X for cos 0, and Y for sin 6, we have 
Y3 X^Y XY2 XY Y2 X Y 1 
C B 
B . C 
- A . fji 
C B 
fji — A 
A 
a 
V 
P 
— a 
— V 
y 
A 
7 
V 
A 
a 
V 
(2 
(3 
(4 
(5 
(i 
{e 
{d 
(« 
B/i + XC B^ + Aa A/3 . A(B + y) . (/) 
fJiB + CA /x/3 Ci^ - fia t^y ~ CA . fxa - Cv {g) 
aA — /?//, + Bi/ /^X + ag — Cv CA — y/4 (B + y)A Cv— a/>t(6) 
