The problem in question is to determine the equation of the curve traced out by any point of an elliptic or hyperbolic disc which touches two fixed rectangular axes. Mechanically constructed figures of different forms of the curve have been given by Tait, who also showed that the same glissette can be traced either by means of an ellipse or a hyperbola. If p, q are the coordinates of the tracing point referred to the axes of the disc as axes of coordinates, the glissette is clearly the θ eliminant of

and Cayley stated that it would be found to be of order 8 in x, y. The actual elimination was first performed by Muir, who obtained in the first instance an equation of order 10. On dividing by an extraneous quadratic factor a lengthy equation of order 8 was obtained; and subsequently Lord M'Laren verified the accuracy of the terms of highest order in this equation.