1891-92.] Dr Muir on a ProUem of Elimination. 
25 
Note on a Problem of Elimination connected with 
Glissettes of an Ellipse or Hyperbola. By Thomas 
Muir, LL.D. 
The problem occurs in a paper of Professor Tait’s (“ Glissettes of 
an Ellipse and of a Hyperbola,” Proc. Roy. Soc. Edin.., xvii. pp. 
2-4). An ellipse whose semi-axes are a and h is considered as 
moving so as always to be in contact with both axes of coordinates, 
and the glissette in question is the curve traced out during this 
motion by a point whose coordinates with respect to the axes of the 
ellipse are p and q. Professor Tait states, and it is readily seen, 
that if the current coordinates of the point be x and y, and 0 be the 
variable angle made by one of the axes of the ellipse with the axis 
of X, we have the equations 
{x-pGO?~0-\-q^m6Y = a^ .... ( 1)1 
(y-psin0 - g'cos^)2 = a^sin2^-l-52cos2^ .... (2) j 
and that to obtain the ir-and-y equation of the glissette it remains to 
eliminate 0 between these two equations. 
Before attempting the elimination I first satisfied myself that the 
resultant uiust be, as affirmed by Professor Cayley, of the 
degree. 
From (1) and (2) by addition there is obtained 
2(qx - py)^m0 = 2(ypx-^ qy) o? - - q^ - x"^ - y^ . (S), 
and, on squaring both sides of this, and putting for shortness’ sake 
(Read January 19, 1891.) 
x = cos^ O + sin ^0 -\-p cos ^ - g sin ^ 
or 
