met. This difficulty is felt particularly in the Russian and Indian triangulations. While Colonel Chodsko found in the Caucasus a deflection of fifty-four seconds, and Schweitzer, in an open plain in the environs of Moscow, deflections of eight and nine seconds, the Himalayan chain appears to have had but an insignificant influence in place of the considerable one which the theory required—as if these mountains were composed of less dense rocks than the soil of the plain.
The operations referred to serve to indicate the form of the earth by the angles which the verticals of a series of stations—i. e., the direction of weight—make with the earth's axis. Another mode consists in measuring at numerous points the degree of the weight, and from this the distance to the center of the earth, the rate of oscillation of the pendulum being also noted. These oscillations are accelerated as the attractive power of the earth increases—that is, as the center is approached. We have seen that Richer remarked these variations of the pendulum in his voyage to Cayenne, and that Newton furnished the explanation of the phenomenon. At the commencement of the present century Biot, Sabine, Kater, Lütke, Foster, and others, made numerous experiments of this nature which have furnished a valuable verification of the results of geodesy, properly so called. But it must not be forgotten that the degree of weight may be changed by the same causes that change its direction. A local accumulation of very dense rocks may increase the terrestrial attraction, and light ones may diminish it. The de-leveling of the ocean of which we have spoken, by which the waters near continents are elevated while the mass of the ocean at large is lowered, results in making an ocean-valley, as it were, from which the islands, that are thus nearer the earth's center than the continents, project. This will explain the increased rate of oscillation of the pendulum observed in many islands, which is otherwise inexplicable.
The perturbations to which the direction as well as the degree of weight is subject have enabled us to determine the earth's mean density. The principle of the method is easily comprehended. Let us suppose that the deflection of the plummet has been measured near an isolated mountain whose volume and weight it is possible to estimate with some degree of precision. The amount of the deflection will furnish a means of calculating the relation of the mass of the mountain to that of the earth, and, the two masses being known, their relative densities can then be determined. The oscillations of the plummet at the summit and at the foot of the mountain afford the basis for a similar calculation. On carrying the plummet to the top some oscillations per day will be lost, the distance from the earth's center being increased; but the mountain's own attraction in part offsets the decrease in weight attributable to altitude, and herein we have the means of comparing its mass with that of the earth.
These methods were not neglected by Bouguer in his voyage to
