Newton, however, though he could not but feel assured that the true law of gravitation was indicated in the result he had reached, with that singular reticence as to his labors and indifference to fame which were among the marked features of his character, not only did not publish his investigations but did not even in his correspondence with his friends allude to the subject. For more than thirteen years he does not appear to have made any further progress toward the solution of the problem of gravitation. Though his attention was doubtless at times directed to it, he was mainly occupied during this period with other scientific labors, particularly in investigating the phenomena of light, making many brilliant discoveries on this subject which, even if he had not subsequently discovered the law of gravitation, would have entitled him to a distinction among men of science scarcely inferior to that which is now awarded him.
In 1679, after Bouilland, Hooke, Wren, Halley and others had become well convinced of the true law of gravitation and yet were unable to furnish a demonstration of it, Newton was led to a renewed investigation of the subject. Hooke had for some time been investigating the motion of projectiles, and in a letter to Newton about this time asserted that a body acted on by an impulsive force and at the same time by an attractive force varying in intensity inversely as the square of the distance, would describe an ellipse. What proof Hooke had of the fact asserted does not appear. It may be regarded as certain that he was not able to give a mathematical demonstration of it. As he had become well convinced that the attraction of gravitation varied according to the law mentioned, it is altogether probable that the main if not the sole ground for his assertion, was the fact that the orbits of the planets are elliptical. However this may be, Newton at once appreciated the importance of the assertion if it could be demonstrated, and was led to attempt the solution of the problem suggested by Hooke's or rather the converse problem, namely, to determine the law of variation in intensity of a central force which would cause the body acted upon to describe an ellipse. By the aid of the calculus, which he had by this time considerably perfected, he finally succeeded, after long and laborious effort, in demonstrating in its most general form the truth of Hooke's assertion. The importance of the result cannot be over estimated. The enigma which the elliptical orbits of the planets had presented was solved, and not only the fact of the sun's attraction but the precise law of the variation in intensity of that attraction was at last established beyond the possibility of further doubt or questioning.
The demonstration of the universality of gravitation however was still incomplete. The sun indeed attracted the planets with a force varying inversely as the square of the distance, but was this a property
