it—to the beginning of the nineteenth century. Alexander von Humboldt relates that he and Sir Humphry Davy were several times invited by Captain Symmes to join an expedition into the interior of the earth, which was represented as a hollow sphere having a large opening at the eighty-second parallel of north latitude. The idea of the existence of a hollow space within the earth was set at rest by the measurement of the average density of the planet, and the contrary view was advanced that the globe is a mass of great specific gravity. The constituency of this mass, whether it is fluid or solid, with only local bubble-like spaces, filled with fluid matter, has not been determined; but the calculations that have been made contradict the theory of a wholly fluid interior.
Several methods have been adopted for ascertaining the mean density of the earth, to the older of which a more accurate method has been added within a few years. An account of the methods hitherto adopted, and the results obtained by them, is here given.
Determination from the Deflection of the Plum-Line.—Newton first suggested that the specific gravity of the earth could be ascertained by means of the plumb-line, but he made no effort to apply his suggestion. The thought was a sequence of his law of gravitation, on which all the methods that have been employed have been based. That law declares that all bodies exert an attractive force upon each other in direct proportion to their masses and in inverse proportion to the square of the distance of their centers of gravity from each other. Accordingly, a body hanging by a line, which over a level surface would be drawn by the earth's attraction into a direction with reference to its point of suspension, the prolongation of the line of which would pass through the center of the earth—that is, would be perpendicular, or plumb—would be attracted and turned away from the perpendicular by a mass like a mountain in the neighborhood. If, now, the amount of this diversion and the size of the mass exercising the deflecting influence were known, then the mass of the earth, and from this in connection with the shape and size of the earth, its mean density, could be computed. The diversion of the plummet from its perpendicular direction is, however, too minute to make a direct measurement possible, and the following method has, therefore, been adopted: In Fig. 1, let K L be a part of the surface of the earth, and G an isolated mountain. A plumb-line at the point A, at the foot of the mountain, and one at B, several miles from it, would take such directions in case the earth were a perfect sphere that the prolongation of the lines would intersect each other at the center of the earth, and form the angle x, with the sides C Z and C Z″, Z and Z″ representing the zeniths at A and B. The zenith-distance v, of any suitable fixed star S, in the neighborhood of Z, may be easily obtained by direct measurement. Let also the zenith-distance of the same star at the point B, which is equivalent to the angle u, be determined. The lines
