The recent discussion in the Gazette on the subject of asymptotes to algebraic curves has tempted me to offer a short account of a method of treatment which I have found useful in my teaching, in forming clear conceptions of the nature, not only of the contact of a curve with its asymptotes, but also of such singularities at infinity as the curve possesses. Incidentally the method affords an expeditious means of determining conies of closest contact at infinity—a subject upon which most text-books are discreetly silent—including parabolic asymptotes as a particular case.