1897-98.] Mr Hanson on the Pllipse-Glissette Problem. 161 
and a conjugate point at the origin. In this case the curves A, <E> 
are 
x 2 y 2 = 0 , x 2 - y 2 = 0 , 
and the contact of the glissette with A is at the conjugate point. 
If the disc be circular the glissette is 
4 (r 2 + a P)\r 2 - a 2 ){r 2 - /3 2 ) + (a + p)\x 2 - y 2 ) 2 = 0 
and this gives the four circles 
r 2 + a/3 = ± a ^(x±y) 
as it ought to do. The curve A is 
(r’ + a/^o, 
and is real or imaginary according as the tracing point is outside or 
inside the director circle of the disc. When real it represents two 
coincident circles through four of the intersections of the four 
circles which form the glissette. 
If the tracing point be on the director circle, we have /? = 0, 
a 2 = 4 (a 2 + b 2 ), and writing p = d cos 8, q = d sin 8, x — r cos 0 } 
y — r sin 0, equation (6) takes the form 
r\ia 2 + 4 b 2 - r 2 ){a 4 sin 2 (8 - 20) + 5 4 cos \8 - 20)} 
= 4(a 2 + b 2 ) 2 {a 2 sin 8 sin (8 - 20) + b 2 cos 8 cos (8 - 20)} 2 . 
The form of this equation shows that the four lines represented by 
A = 0 in this case are imaginary. 
