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a mathematical treatment was given by Darwin in 1905.

A common feature in the quantitative analysis of all these approaches was that the force law for gravitation differed from a pure inverse square law by the addition of very small terms proportional to higher negative powers of the distance between particles. Newcomb calculated the magnitude that such terms would have to have in order to account for the advance in the perihelion of Mercury, and concluded that, for an inverse cube term, the coefficient would have to be 16 x 10-8 times that for the inverse square term. Small as this may seem, it leads to forces that are significant over very small distances and contradicts the experimental findings of Henry Cavendish. In 1798, he used

18 Challis The Force of Gravity (1859). Quoted from Roseveare (1982).

Le Sage called them 'ultra-mundane corpuscles' (Whittaker (1951), p. 31).

The Analogy Between Lesage 's Theory of Gravitation and the Repulsion ofLight.

21 See Roseveare (1982), p. 113

experimental apparatus designed by John Michell22 to measure the mean density of the Earth. This involved the attraction of lead spheres over distances measured in inches, and if there were extra terms in the expression for the gravitational force of the type hypothesized by Clairaut, they would dominate at such distances and lead to far greater attraction than was measured by Cavendish. Newcomb thus ruled out modifying the inverse square law in this way.

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