Formulas and tables for the deflection of the vertical

Abstract

The use of the spheroid of revolution as representative of the figure of the Earth rests on the assumption of a regular distribution of matter. The fact that there is an irregular distribution is patent to everyone—there are hills, valleys, plains, mountains, and oceans. But underneath this visible irregularity there is a concealed regularity that the theory of isostasy tries to represent. According to this theory, or rather according to the Pratt‐Hayford formulation of it, if we go down into the Earth a certain distance, 60 to 120 km, upon every unit‐area of a certain size there‐stands an approximately equal amount of matter regardless of whether the surface be valley, plain, hill, mountain, or ocean. The Airy formulation of isostasy reaches the same approximate equality of superincumbent matter by another conception, which may be called the “roots‐of‐the‐mountains” theory. The theory of isostasy in one form or another represents approximately the conditions over a large portion of the land‐surface of the Earth and probably over a large portion of the oceanic surface. If this were not so, the theory would never have been accepted as it is. It was foreshadowed by Bouguer and Cavendish in the 18th century but was not explicitly formulated until the middle of the 19th century, when Pratt and Airy at about the same time put forward their various conceptions as to the equilibrium of the Earth's crust. The name itself was given by Dutton [see 1 of “References” at end of paper] in 1889.