far as a point in Spitzbergen, near the Pole; and both officers went to many places near the equator; to the West India Islands, to South America, and to South Africa. In this manner it was found that the number of vibrations which a pendulum makes per diem is not the same in different parts of the earth. When near the Pole, the pendulum makes about 240 vibrations in a day more than when near the equator. It is easily seen that this is a consequence of the force of gravity being greater there. If gravity be very small indeed, the motion of the pendulum will be exceedingly sluggish. The greater is the force of gravity which acts upon a pendulum when out of its central position, the more briskly it pulls the pendulum down towards its central position, and the shorter time is occupied by every vibration, and the greater is the number of vibrations made in one day. Thus we have the means of measuring the gravity at different parts of the earth.
Now, the practical inference from the experiments is this: the proportion of the force of gravity at the Pole to the force of gravity (that is, attraction diminished by the centrifugal tendency) at the equator, is not as 230 to 229, as Newton stated, but is very nearly the proportion of 180 to 179. Now, here we have a remarkable departure from Newton's results. He proved that, if the earth were of equal density throughout, the proportion of the two axes would be as 229 to 230; and the proportion of gravity at the Pole and the equator would be as 230 to 229. We find from trigonometrical surveys, and observations with the Zenith Sector, as you may remember, that the proportion of the earth's axes is as 299 to 300; and we have now found, from experiments with the pendulum, that the proportion of gravity at the Pole
