192, resembling the **trochoidal** curves, which can be looped, investigated in § 29 for the motion of a cylinder under gravity, when surrounded by a vortex.

Further, on examining the small variation in i/i, it appears that in a slightly disturbed slow precession the motion of any point of the axis consists of a rapid circular vibration superposed on the steady precession, so that the resultant path has a **trochoidal** character.

The equations to the hypocycloid and its corresponding **trochoidal** curves are derived from the two preceding equations by changing the sign of b.

The epicychid when the radii of the circles are equal is the cardioid (q.v), and the corresponding **trochoidal** curves are limacons.