The Southerly Deviation of Falling Bodies

In the work of previous writers on the subject of this paper the potential function used for that of the earth's gravitational field of force has, in general, not been more than a first approximation, i. e., a development, in the neighborhood of the initial point of the falling body, which includes terms of only the first order in the independent variables. The circle of reference (parallel of latitude) used has also, in general, been different from that used in experiments for the determination of the same quantity. From equations (1) and (2) which follow it appears that the southerly deviation is proportional to the square of the height h through which the body falls (at least for sufficiently small values of h) and that the constant of proportionality involves the first and also the second derivatives of the potential function fx .f Hence the truth of the following statement : I. The potential function to be used for that of the earth's gravitational field of force should be a second approximation, i. e., a development in the neighborhood of the initial point of the falling body, which includes terms of at least the second order in the independent variables. In experiments for the determination of the southerly deviation of falling bodies, a plumb-line P0R is supported at the point P0 (Fig. 5), from which the body falls, and the deviation is measured on the level (equipotential) surface which passes through the plumb-bob R, from the circle of latitude which passes through R. The direction of gravity at R is RP0, and that at P0 is the limiting direction which is approached by the line RP0 as the length PQ R approaches zero. Let us denote by t the limiting position of P0 R. It is easy to prove the following statement : II. In a field of force in which the lines of force are not rectilinear, plumb-