1. Poncelet’s well-known theorem states that if two conies S and S′ in a plane are such that an n-gon exists whose vertices lie on S′ and whose sides touch S, then an infinite number of such polygons exist. When this is the case, a relation holds between the invariants of the two conies. The explicit determination of this relation is due to Cayley, whose result is quoted by Salmon in a footnote on p. 342 of his Conic Sections (reprint of 1929). With a slight change of notation, Cayley’s result takes the following form.