In the middle of the year 1694, about the time when our author is said to be beginning to understand the Principia, we find him occupied with the difficult and profound subject of the lunar theory. In order to procure observations for verifying the equations which he had deduced from the theory of gravity, he paid a visit to Flamstead, at the Royal Observatory of Greenwich, on the 1st September, 1694, when he received from him a series of lunar observations. On the 7th of October he wrote to Flamstead that he had compared the observations with his theory, and had satisfied himself that by both together “the moon’s theory may be reduced to a good degree of exactness, perhaps to the exactness of two or three minutes.” He wrote him again on the 24th October, and the correspondence was continued till 1698, Newton making constant application for observations to compare with his theory of the planetary motions; while Flamstead, not sufficiently aware of the importance of the inquiry, received his requests as if they were idle intrusions in which the interests of science were but slightly concerned.[86] In reviewing the details which we have now given respecting the health and occupations of Newton from the beginning of 1692 till 1695, it is impossible to draw any other conclusion than that he possessed a sound mind, and was perfectly capable of carrying on his mathematical, his metaphysical, and his astronomical inquiries. His friend and admirer, Mr. Pepys, residing within fifty miles of Cambridge, had never heard of his being attacked with any illness till he inferred it from the letter to himself written in September, 1693. Mr. Millington, who lived in the same university, had been equally unacquainted with any such attack, and, after a personal interview with Newton, for the express purpose of ascertaining the state of his health, he assures Mr. Pepys “that he is very well,—that he fears he is under some small degree of melancholy, but that there is no reason to suspect that it hath at all touched his understanding.” During this period of bodily indisposition, his mind, though in a state of nervous irritability, and disturbed by want of rest, was capable of putting forth its highest powers. At the request of Dr. Wallis he drew up an example of one of his propositions on the quadrature of curves in second fluxions. He composed, at the desire of Dr. Bentley, his profound and beautiful letters on the existence of the Deity. He was requested by Locke to reconsider his opinions on the subject of innate ideas; and we find him grappling with the difficulties of the lunar theory.