Application of Gravity Surveys
We have noted previously that in the ancient and early modern periods, the earth was presupposed to be spherical in form. Determination of the figure of the earth consisted in the measurement of the radius by the astronomical-geodetic method invented by Eratosthenes. Since the earth was assumed to be spherical, gravity was inferred to be constant over the surface of the earth. This conclusion appeared to be confirmed by the determination of the length of the seconds pendulum at various stations in Europe by Picard and others. The observations of Richer in South America, the theoretical discussions of Newton and Huygens, and the measurements of degrees of latitude in Peru and Sweden demonstrated that the earth is an oblate spheroid.
Figure 33.—Gravity characteristics of the globe. Deductions as to the distribution of matter in the earth can be made from gravity measurements. This globe shows worldwide variations in gravity as they now appear from observations at sea (in submarines) as well as on land. It is based on data from the Institute of Geodesy at Ohio State University.
The theory of gravitation and the theory of central forces led to the result that the intensity of gravity is variable over the surface of the earth. Accordingly, determinations of the intensity of gravity became of value to the geodesist as a means of determining the figure of the earth. Newton, on the basis of the meager data available to him, calculated the ellipticity of the earth to be 1/230 (the ellipticity is defined by (a-b)/a, where a is the equatorial radius and b the polar radius). Observations of the intensity of gravity were made on the historic missions to Peru and Sweden. Bouguer and La Condamine found that at the equator at sea level the seconds pendulum was 1.26 Paris-lines shorter than at Paris. Maupertuis found that in northern Sweden a certain pendulum clock gained 59.1 seconds per day on its rate in Paris. Then Clairaut, from the assumption that the earth is a spheroid of equilibrium, derived a theorem from which the ellipticity of the earth can be derived from values of the intensity of gravity.
Figure 34.—An exhibit of gravity apparatus at the Smithsonian Institution. Suspended on the wall, from left to right, are the invariable pendulums of Mendenhall (1/2-second), Peirce (1873-1874), and Peirce (1881-1882); the double pendulum of Edward Kübel (see fig. [15], p. [319]), and the reversible pendulum of Peirce. On the display counter, from left to right, are the vacuum chamber, telescope and flash apparatus for the Mendenhall 1/4-second apparatus. Shown below these are the four pendulums used with the Mendenhall apparatus, the one on the right having a thermometer attached. At bottom, right, is the Gulf apparatus (cover removed) mentioned in the text, shown with one quartz pendulum.