always be performed in the same time, the length of the pendulum must be altered. By numerous and careful experiments it is proved that a pendulum, which oscillates 86,400 times in a mean day at the equator, will do the same at every point of the earth’s surface, if its length be increased progressively to the pole, as the square of the sine of the latitude. From the mean of these it appears that the whole decrease of gravitation from the poles to the equator is 0·0051449, which, subtracted from 1/115·2, shows that the compression of the terrestrial spheroid is about 1/285·26. This value has been deduced by the late Mr. Baily, president of the Astronomical Society, who devoted much attention to this subject; at the same time, it may be observed that no two sets of pendulum experiments give the same result, probably from local attractions. The compression obtained by this method does not differ much from that given by the lunar inequalities, nor from the arcs in the direction of the meridian, and those perpendicular to it. The near coincidence of these three values, deduced by methods so entirely independent of each other, shows that the mutual tendencies of the centres of the celestial bodies to one another, and the attraction of the earth for bodies at its surface, result from the reciprocal attraction of all their particles. Another proof may be added. The nutation of the earth’s axis and the precession of the equinoxes (N. 146) are occasioned by the action of the sun and moon on the protuberant matter at the earth’s equator. And, although these inequalities do not give the absolute value of the terrestrial compression, they show that the fraction expressing it is comprised between the limits 1/279 and 1/573.