The oscillations of the pendulum have afforded another method of ascertaining the form of the earth. Like all heavy bodies, its descent, and consequently its oscillations, are accelerated in proportion to the force of gravitation, which increases from the equator to the poles. In order, therefore, that the oscillations may be everywhere performed in the same time, the length of the pendulum must be increased progressively in going from the equator to the poles, according to a known law,[6] from whence the compression or flattening at the poles may be deduced. Experiments for that purpose have been made in a great number of places, but, as in the measurement of the arcs, no two sets give exactly the same results; the mean of the whole, however, differs very little from that given by the degrees of the meridian and the perturbations of the moon; and as the three methods are so entirely independent of each other, the figure and dimensions of the earth may be considered to be known. The sea has little effect on these experiments, both because its mean density is less than that of the earth, and that its mean depth of perhaps four miles is inconsiderable when compared with 4000 miles, the mean terrestrial radius.[7] The discrepancies in the results, from the comparison of the different sets of pendulum experiments, and also of degrees of the meridian, arise from local attraction, as well as from irregularities in the form of the earth. These attractions, arising from dense masses of rock in mountains, cause the plumb-line to deviate from the vertical, and when under ground they alter the oscillations of the pendulum. Colonel Sabine, who made experiments with the pendulum from the equator to within ten degrees of the north pole, discovered that the intensity is greatly augmented by volcanic islands. A variation to the amount of a tenth of a second in twenty-fours can be perfectly ascertained in the rate of the pendulum, but from some of these local attractions a variation of nearly ten seconds has occurred during the same period. The islands of St. Helena, Ascension, St. Thomas, the Isle of France, are some of those noted by Colonel Sabine. There are other remarkable instances of local disturbance, arising from the geological nature of the soil; for example, the intensity of gravitation is very small at Bordeaux, from whence it increases rapidly to Clermont-Ferrand, Milan, and Padua, where it attains a maximum (owing probably to dense masses of rock under ground), and from thence it extends to Parma. In consequence of this local attraction, the degrees of the meridian in that part of Italy seem to increase towards the equator through a small space, instead of decreasing, as if the earth were drawn out instead of flattened at the poles.