On a Dynamical Top, for exhibiting the phenomena of the motion of a system of invariable form about a fixed point, with some suggestions as to the Earth's motion

by James Clerk Maxwell

,

, and

.

Angular momenta may be compounded like forces or velocities, by the law of the “parallelogram,” and since these three are at right angles to each other, their resultant is

(1)

and this must be constant, both in magnitude and direction in space, since no external forces act on the body.

We shall call this axis of angular momentum the invariable axis. It is perpendicular to what has been called the invariable plane. Poinsôt calls it the axis of the couple of impulsion. The direction-cosines of this axis in the body are,