1898-99.] Lord M‘Laren on Glissette Elimination Problem. 379 
Symmetrical Solution of the Ellipse-Glissette Elimina- 
tion Problem. By The Hon. Lord M‘Laren. 
The publication of Mr Xanson’s paper on the glissette elimination 
problem ( Proc . Roy. Soc., vol. xxii. p. 158) has led me to make a 
further investigation of this interesting point, with the result that 
the general eliminant is expressed in the form of a single sym- 
metrical bordered determinant. I shall first give the solution for 
the case where the tracing-point is on the axis of the ellipse, and 
then extend it to the general case. 
I. Case of the Tracing-point on the Elliptic Axis. 
The equations for the centre of the generating ellipse as tracing- 
point are — 
For a point in the line of the major axis, if r be the distance of 
the tracing-point from the centre, we have 
whence, by squaring each side, 
(a 2 - r 2 ) cos 2 # + # 2 sin 2 # + 2 rx cos 0 -x 2 = 0 . . . (1) 
5 2 cos 2 # + (a 2 — r 2 ) sin 2 # + 2 ry sin 0 - y 1 = 0 . . . (2) 
By addition, 2rx cos # + 2ry sin # + a 2 - r 2 + b 2 - x 2 - y 2 (3) 
To abridge, these may be written, 
(Read January 23, 1899.) 
X — J(a 2 c,o& 2 6 + # 2 sin 2 #) ; Y = J(b 2 o,os 2 0 + a 2 sm 2 6). 
x — r cos # = (< 2 2 cos 2 # + # 2 sin 2 #) ) 
y - r sin # = ^(^cos 2 # + « 2 sin 2 #) J 
A cos 2 # + C sin 2 # + a cos # — x 2 = 0 
C cos 2 # + A sin 2 # + (3 sin # — y 2 = 0 
a cos # + /?sin# + y= 0 
where y = A + C — P — y 2 = a 2 — r 2 + b ' 2 — P — if. 
We have also, 
cos 2 # + sin 2 # —1 = 0 
( 4 ) 
