kinds—periodic and secular. In the first kind, the perturbations are soon compensated, the oscillations being comparatively rapid. The latter are those in which the compensation is effected only after comparatively vast intervals of time. The former depend on the relative positions of the planets themselves; the latter, upon the positions of their orbits.
To illustrate the difference between periodic and secular inequalities, we may suppose the orbit of a planet to be represented by the margin of an oval or elliptical lake, whose surface is agitated by waves. The observer, standing on the margin, will observe the waves advancing upon the beach and then receding. Every advancing wave increases the length of the lake by a very minute quantity; but, then, it is shortened just as much by the receding of the wave. There is a complete compensation, then, in the period of each wave, and however long the observer watches, he will find that there is no advance made up the beach beyond a certain point. If we, however, conceive the lake to be affected by tides, there will not be a complete compensation in the case of each successive wave. If it is flood, then the recess does not fully compensate the advance of the wave; so that although there is a constant oscillation, backwards and forwards, there is a margin left for advance. Still, this advance is, after all, periodical; for, after flowing for six hours, the tide begins to ebb, and the full compensation is effected in other
