In the chapter on Gravitation we have mentioned the fact that a body let fall near the surface of the earth drops through sixteen feet in the first second. This distance varies slightly at different parts of the earth. If the earth were a perfect sphere, then the attraction would be the same at every part, and the body would fall through the same distance everywhere. The earth is not round, so the distance which the body falls in one second differs slightly at different places. At the pole the radius of the earth is shorter than at the equator, and accordingly the attraction of the earth at the pole is greater than at the equator. Had we accurate measurements showing the distance a body would fall in one second both at the pole and at the equator, we should have the means of ascertaining the shape of the earth. It is, however, difficult to measure correctly the distance a body will fall in one second. We have, therefore, been obliged to resort to other means for determining the force of attraction of the earth at the equator and other accessible parts of its surface. The methods adopted are founded on the pendulum, which is, perhaps, the simplest and certainly one of the most useful of philosophical instruments. The ideal pendulum is a small and heavy weight suspended from a fixed point by a fine and flexible wire. If we draw the pendulum aside from its vertical position and then release it, the weight will swing to and fro. For its journey to and fro the pendulum requires a small period of time. It is very remarkable that this period does not depend appreciably on the length of the circular arc through which the pendulum swings. To verify this law we suspend another pendulum beside the first, both being of the same length. If we draw both pendulums aside and then release them, they swing together and return together. This might have been expected. But if we draw one pendulum a great deal to one side, and the other only a little, the two pendulums still swing sympathetically. This, perhaps, would not have been expected. Try it again, with even a still greater difference in the arc of vibration, and still we see the two weights occupy the same time for the swing. We can vary the experiment in another way. Let us change the weights on the pendulums, so that they are of unequal size, though both of iron. Shall we find any difference in the periods of vibration? We try again: the period is the same as before; swing them through different arcs, large or small, the period is still the same. But it may be said that this is due to the fact that both weights are of the same material. Try it again, using a leaden weight instead of one of the iron weights; the result is identical. Even with a ball of wood the period of oscillation is the same as that of the ball of iron, and this is true no matter what be the arc through which the vibration takes place.