Page:Elementary Text-book of Physics (Anthony, 1897).djvu/96

83 mine vanishes. The mean density of the earth may, therefore, be determined by the discrepancy between the values of $$g$$ at the bottom of the mine and at the surface.

Still another method, used by Jolly, consists in determining by means of a delicate balance the increase in weight of a small mass of lead when a large leaden block is brought beneath it. Jolly's results were very consistent, and give as the earth's density the value 5.69.

These methods have yielded results varying from that obtained by Airy, who stated the mean specific gravity to be 6.623, to that of Maskelyne, who obtained 4.7. The most elaborate experiments, by Cornu and Bailie, by the method of Cavendish, gave as the value 5.56. This is probably not far from the truth.

When the density of the earth is known, we may calculate from it the value of the constant of mass attraction, that is, the attraction between two unit masses at unit distance apart. Represent by $$D$$ the earth's mean density, by $$R$$ the earth's mean radius, and by $$k$$ the constant of attraction. The mass of the earth is expressed by $$\tfrac{4}{3}\pi R^3 D$$. Since by § 57 the attraction of a sphere is inversely as the square of the distance from its centre, the attraction of the earth on a gram at a point on its surface, or the weight of one gram, is expressed by $$g = \tfrac{4}{3}\pi \frac{R^3 D}{R^2}k$$. $$\pi R$$ is twice the length of the earth's quadrant, or 2 X 109 centimetres. The value of $$g$$ at latitude 40° is 980.11, and from the results of Cornu and Bailie we may set $$D$$ equal to 5.56. With these data we obtain $$k$$ equal to 0.000000066 dynes.