rod, on which a perpendicular beam of light is made to fall, indicates, by means of a graduated circle engraved upon it, the most minute horizontal deflections of the balance. Two leaden balls. K and K' are brought within a suitable distance of the balls a and b, exercise an attractive force upon, them, and cause an horizontal deflection of the balance, in a direction opposed to the torsion force of the cord, the value of which may be ascertained by measurement. From this value is computed the force of the attraction which the leaden masses K and K' exercise upon a and b. Since the masses of the four balls, their relative distances from each other, and the amount of the attraction exerted upon them by the earth (which is given by the absolute weight of the balls), are all measurable, the ratio of the mass of the earth to the masses of the balls K and K' can be calculated, and from this, by the process already given, the mean density of the earth.
The results obtained by this method have a considerable degree of trustworthiness, for clear determinations are obtained in which errors are possible only in a small degree. The method was used by Cavendish in 1798, whose calculations gave 5·48, by Reich in Freiberg in 1837, who obtained 5·44, and by Baily in 1842, who obtained 5·6747. Reich repeated his experiments with improved apparatus between 1847 and 1850, using tin balls instead of leaden ones, and twisted copper wires or double iron wires instead of cord, and obtained 5·5756, a value which is often written briefly as 5·58. Hutton calculated the specific gravity of the earth from Cavendish's observations at 5·32, and E. Schmidt at 5.52.
Determination by Means of the Two-Armed Balance.—The idea of using the balance as means of measuring the mean density of the earth originated with the physicist Jolly, who suggested its application to this purpose in describing some improvements he had made in the instrument to increase its sensitiveness. The application was made by H. Poynting, in Manchester, who adopted the following method: Instead of a scale, he attached a weight (b Fig. 4), of 452·92 grammes to the end of a rod six feet in length, to which he opposed a counter-weight in the scale at the other end of the balance; a ball, C, weighing 154·220·6 grammes was brought to a position perpendicularly under b, when the mutual attraction of the two bodies occasioned a disturbance of the balance to the amount of 0·01 of a milligramme. The weight of the two mutually attracting bodies and the amount of attraction exerted upon them by the earth being known, and the distance apart of their centers of gravity having been carefully measured, Poynting calculated the mean density of our planet at 5·69, with a probable error of 0·15.
The approximate agreement of the results obtained by these four methods authorizes us to conclude that the masses of the interior of the earth possess a great density. If we consider, with Alexander von
