In “Tait and Steele's Dynamics of a Particle,” chap, iv., a number of geometrical constructions are given, some possibly for the first time, connected with the motion of projectiles in parabolic paths in vacuo. I have recently been led to remark that most of these propositions still hold when we substitute, for the uniform action of gravity in parallel lines, the action of gravity supposed to be directed to the earth's centre, and to vary inversely as the square of the distance from that point. My excuse for bringing so simple a matter before the Society is; that the propositions are in themselves curious and elegant, and that I am not aware of their having been before mentioned. A very few examples will suffice to indicate the change of form required by the more general assumed conditions.