The method of treating tangents to confocal conicoids, of which I propose to give an account, is discussed in the number for December 1867 of the Nouvelles Annales de Mathématiques. The writer of the paper referred to is M. Ph. Gilbert, Professor at the University of Louvain. The results arrived at are in nearly every case already well known, but the method of reaching them is somewhat novel, and I have thought that it might interest the members of this society if I were to give a statement of the chief methods and results of Gilbert's paper. In one or two cases I have altered the proofs, and I have added two or three propositions that seemed to follow naturally from the equations dealt with. Gilbert deals only with central conicoids; but I have put in an equation for the paraboloids that corresponds to Gilbert's fundamental one.