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 endeavored to account for the difference of the two forces by supposing that some other cause must have been united with the force of gravity in producing so great 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. After his return to Cambridge in 1666 his attention was occupied with optical discoveries; but he had no sooner brought them to a close than his mind reverted to the great subject of the planetary motions. Upon the death of Oldenburg in August, 1678, Dr. Hooke was appointed secretary to the Royal Society; and as this learned body had requested the opinion of Newton about a system of physical astronomy, he addressed a letter to Dr. Hooke on November 28, 1679. In this letter he proposed a direct experiment for verifying the motion of the earth, viz., by observing whether or not bodies that fall from a considerable height descend in a vertical direction; for if the earth were at rest the body would describe exactly a vertical line; whereas if it revolved round its axis, the falling body must deviate from the vertical line toward the east. The Royal Society attached great value to the idea thus casually suggested, and Dr. Hooke was appointed to put it to the test of experiment. Being thus led to consider the subject more attentively, he wrote to Newton that wherever the direction of gravity was oblique to the axis on which the earth revolved, that is, in every part of the earth except the equator, falling bodies should approach to the equator, and the deviation from the vertical, in place of being exactly to the east, as Newton maintained, should be to the southeast of the point from which the body began to move.