Newton and the acceleration of gravity (Q1074569)

In CUL Add. MS. 3958, f. 45, dating from his student days, Newton calculated the ratios of gravity at the earth's surface to the centrifugal forces arising from the earth's diurnal and annual motions, using measurements of the earth and the acceleration due to gravity taken from the Salusbury translation of Galileo's Dialogue. While Newton's intention may well have been to demonstrate that the centrifugal forces were not strong enough to throw bodies off the earth, this aim is not stated, as the author seems to imply, in the manuscript. In his commentary on the manuscript, he makes two original contributions to its interpretation. The first concerns the part played by the conical pendulum in Newton's determination of the ratios. For although measurements with a conical pendulum seem to be described in the manuscript, they would have been impracticable. In particular, the question is raised as to how Newton arrived at the result that an ordinary pendulum, of length equal to the vertical height of a conical pendulum, oscillated with the same period. The author suggests that he obtained the result by considering the limiting case of infinitesimal amplitude, and then applying Galileo's principle (which is not strictly true) that the period is independent of the amplitude. The conical pendulum was thus used as a theoretical device to define the centrifugal force, while the actual measurements were based on experiments with an ordinary pendulum. The author's second original contribution is a speculative reconstruction of the method of measuring time.