 Complete the following phrase:  Roberts discovered many properties of geodesic lines and lines of curvature on the ellipsoid, especially in relation to umbilics, and from 1845 published papers in the Journal de Mathématiques, the Proceedings of the Royal Irish Academy, Cambridge and Dublin Mathematical Journal, Nouvelles Annales de Mathématiques. In 1850 he wrote in the Journal de Mathématiques of the lines of curvature and asymptotic lines on a surface, at any point of which the sum of the principal curvatures is zero. The 