The earth being a mass of matter of a form nearly spherical, revolving with considerable velocity on an axis, its component parts are affected by a centrifugal force; in virtue of which, they have a tendency to fly off in a direction perpendicular to the axis. This tendency increases in the same proportion as the distance of any part from the axis increases, and consequently those parts of the earth which are near the equator, are more strongly affected by this influence than those near the pole. It has been already explained (145.) that the figure of the earth is affected by this cause, and that it has acquired a spheroidal form. The centrifugal force, acting in opposition to the earth’s attraction, diminishes its effects; and consequently, where this force is more efficient, a pendulum will vibrate more slowly. By these means the rate of vibration of a pendulum becomes an indication of the amount of the centrifugal force. But this latter varies in proportion to the distance of the place from the earth’s axis; and thus the rate of a pendulum indicates the relation of the distances of different parts of the earth’s surface from its axis. The figure of the earth may be thus ascertained, and that which theory assigns to it, it may be practically proved to have. This, however, is not the only method by which the figure of the earth may be determined. The meridians being sections of the earth through its axis, if their figure were exactly determined, that of the earth would be known. Measurements of arcs of meridians on a large scale have been executed, and are still being made in various parts of the earth, with a view to determine the curvature of a meridian at different latitudes. This method is independent of every hypothesis concerning the density and internal structure of the earth, and is considered by some to be susceptible of more accuracy than that which depends on the observations of pendulums. (221.) It has been stated that, when the arc of vibration of a pendulum is not very small, a variation in its length will produce a sensible effect on the time of vibration. To construct a pendulum such that the time of vibration may be independent of the extent of the swing, was a favourite speculation of geometers. This problem was solved by Huygens, who showed that the curve called a _cycloid_, previously discovered and described by Galileo, possessed the isochronal property; that is, that a body moving in it by the force of gravity, would vibrate in the same time, whatever be the length of the arc described.