Page:Elementary Text-book of Physics (Anthony, 1897).djvu/95

§ 64] the most interesting problems connected with the physical aspect of grayitation is the determination of the constant of mass attraction. It has been attacked in several ways, each of which is worthy of consideration. The methods employed usually depend upon a determination of the mean density of the earth.

The first successful determination of the earth's density was based upon experiments made in 1774 by Maskelyne. He observed the deflection from the vertical of a plumb-line suspended near the mountain Schehallion in Scotland. He then determined the density of the mountain by the specific gravity of specimens of earth and rock from various parts of it, and calculated the ratio of the volume of the mountain to that of the earth. From these data the mean density of the earth was determined to be about 4.7.

The next results were obtained from the experiments of Cavendish, in 1798, with the torsion balance already described. The density, volume, and attraction of the leaden balls being known, the constant of mass attraction could be calculated, and also the density of the earth obtained. The value obtained by Cavendish for the latter was about 5.5.

Another method, employed by Carlini in 1824, depends upon the use of the pendulum. The time of the oscillation of a pendulum at the sea-level being known, the pendulum is carried to the top of some high mountain, and its time of oscillation again observed. The value of $$g$$ as deduced from this observation will, of course, be less than that obtained by the observation at the sea-level. It will not, however, be as much less as it would be if the change depended only on the increased distance from the centre of the earth. The discrepancy is due to the attraction of the mountain, which can, therefore, be calculated, and the calculations completed as in Maskelyne's experiment. The value obtained by Carlini by this method was about 4.8.

A fourth method, due to Airy, and employed by him in 1854, consists in observing the time of oscillation of a pendulum at the bottom of a deep mine. By § 57 it appears that the attraction of a spherical shell of earth the thickness of which is the depth of the