In the Appendix III. of his “Mechanics of Machinery,” Le Conte attacks the problem of rolling curves by an elegant analytical method in which the cartesian forms of the involute and the trochoids are derived from elementary differential equations. Weisbach(“Mechanics of Engineering and of Machinery,” Vol. III., chap. II.), while using mainly the geometrical method, discusses one application analytically (see §3 of this paper) in which polar forms are introduced. Many other writers, for example Barr (“Kinematics of Machinery,” chaps. III., IV.), deal wholly with the geometry of the subject.