the duplicate proportion,[41] or as the squares of their distances from the sun. In drawing this conclusion, he supposed the planets to move in orbits perfectly circular, and having the sun in their centre. Having thus obtained the law of the force by which the planets were drawn to the sun, his next object was to ascertain if such a force, emanating from the earth and directed to the moon, was sufficient, when diminished in the duplicate ratio of the distance, to retain her in her orbit. In performing this calculation, it was necessary to compare the space through which heavy bodies fall in a second at a given distance from the centre of the earth, viz. at its surface, with the space through which the moon, as it were, falls to the earth in a second of time while revolving in a circular orbit. Being at a distance from books when he made this computation, he adopted the common estimate of the earth’s diameter then in use among geographers and navigators, and supposed that each degree of latitude contained sixty English miles. In this way he found that the force which retains the moon in her orbit, as deduced from the force which occasions the fall of heavy bodies to the earth’s surface, was one-sixth greater than that which is actually observed in her circular orbit. This difference threw a doubt upon all his speculations; but, unwilling to abandon what seemed to be otherwise so plausible, he endeavoured to account for the difference of the two forces, by supposing that some other cause[42] must have been united with the force of gravity in producing so great a velocity of the moon in her circular orbit. As this new cause, however, was beyond the reach of observation, he discontinued all further inquiries into the subject, and concealed from his friends the speculations in which he had been employed.