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In a paper “On thec - andp -Discriminants of Ordinary Integrable Differential Equations of the First Order,” published in vol. 19 of the ‘Proceedings of the London Mathematical Society,' the factors which occur in thec -discriminant of an equation of the formf (x, y, c ) = 0, wheref (x, y, c ) is a rational integral function ofx, y, c , are determined analytically. It is shown that if E = 0 be the equation of the envelope locus of the curvesf (x, y, c ) = 0; if N = 0 be the equation of their node-locus; if C = 0 be the equation of their cusp-locus, then the factors of the discriminant are E, N2 , C3 .

V. On the locus of singular points and lines which occur in connection the theory of the locus of ultimate intersections of a system of surfaces