Last summer, while engaged with some quaternion investigations connected with Dr Plarr's problem (the locus-boundary of the points of contact of an ellipsoid with three rectangular planes) I was led to construct the glissettes of an ellipse. I then showed to the Society a series of these curious curves, drawn in my laboratory by Mr Shand, who had constructed for the purpose a very true elliptic disc of sheet brass. I did not, at the time, think it necessary to print my paper; but, after the close of the session, I made the curious remark that precisely the same curves can be drawn each as a glissette of its own special hyperbola. This double mode of sliding generation of the same curve seems to possess interest. It is somewhat puzzling at first, since the ellipse turns completely round, while the hyperbola can only oscillate. But a little consideration shows the cause of the coincidence.