situated at that instant in its rotatory motion from pole to pole; this velocity accordingly diminishes as the mass withdraws from the equator, and becomes zero when it actually reaches the poles of rotation at N and S; and the energy of each mass in motion, since its linear velocity is thus constantly varying, will be itself a continuously varying quantity, increasing or diminishing accordingly as the mass is moving to or from the equatorial regions, attaining its maximum value at the equator and its minimum value at the poles. Now, since the masses thus moving are assumed to be a material and inherent portion of the spherical system, the source of the energy which is thus alternately supplied to and returned by them is the original energy of motion of the system; this original energy being assumed strictly limited in amount, the increase of the energy of each mass as it moves towards the equator will, therefore, be productive of a retardative effect on the revolution of the system as a whole. But, in a precisely similar manner, the energy thus gained by the mass would be fully returned on its movement towards the pole, and an accelerative effect would be produced corresponding to the original retardation. In the arrangement shown (Fig. 12), the moving masses are assumed to be situated at the extremities of diameters at right angles. With this symmetrical distribution, the transformation and return of energy would take place concurrently. Retardation is continually balanced by acceleration, and the motion of the sphere would, therefore, be approximately uniform about the central axis of rotation. It will be clear that the movements thus described of the masses will be very similar in nature to those of the pendulum masses in the experimental system previously discussed. The fact that the motion of the auxiliary masses over the surface of the sphere is assumed to be completely circular and not vibratory, as in the pendulum case, has no bearing on the general energy phenomena. These are readily seen to be identical in nature with those of the simpler system. In each case every movement of the masses implies either an expenditure of energy or a return, accordingly as the direction of that movement is to or from the regions of high velocity. [Illustration: FIG. 12]