Equatorial diameter, 7925.648 miles. Polar diameter, 7899.170 " Average diameter, 7912.409 " The difference between the greatest and the least is about twenty-six and one half miles, which is about one two hundred and ninety-ninth part of the greatest. This fraction is denominated the _ellipticity_ of the earth,--being the excess of the equatorial over the polar diameter. The operations, undertaken for the purpose of determining the figure of the earth, have been conducted with the most refined exactness. At any stage of the process, the length of the last side, as obtained by calculation, may be actually measured in the same manner as the base from which the series of triangles commenced. When thus measured, it is called the _base of verification_. In some surveys, the base of verification, when taken at a distance of four hundred miles from the starting point, has not differed more than one foot from the same line, as determined by calculation. Another method of arriving at the exact figure of the earth is, by observations with the _pendulum_. If a pendulum, like that of a clock, be suspended, and the number of its vibrations per hour be counted, they will be found to be different in different latitudes. A pendulum that vibrates thirty-six hundred times per hour, at the equator, will vibrate thirty-six hundred and five and two thirds times, at London, and a still greater number of times nearer the north pole. Now, the vibrations of the pendulum are produced by the force of gravity. Hence their comparative number at different places is a measure of the relative forces of gravity at those places. But when we know the relative forces of gravity at different places, we know their relative distances from the centre of the earth; because the nearer a place is to the centre of the earth, the greater is the force of gravity. Suppose, for example, we should count the number of vibrations of a pendulum at the equator, and then carry it to the north pole, and count the number of vibrations made there in the same time,--we should be able, from these two observations, to estimate the relative forces of gravity at these two points; and, having the relative forces of gravity, we can thence deduce their relative distances from the centre of the earth, and thus obtain the polar and equatorial diameters. Observations of this kind have been taken with the greatest accuracy, in many places on the surface of the earth, at various distances from each other, and they lead to the same conclusions respecting the figure of the earth, as those derived from measuring arcs of the meridian. It is pleasing thus to see a great truth, and one apparently beyond the pale of human investigation, reached by two routes entirely independent of each other. Nor, indeed, are these the only proofs which have been discovered of the spheroidal figure of the earth. In consequence of the accumulation of matter above