A great step had been taken toward the solution of the problem of planetary motion, but a formidable difficulty yet remained to be overcome. The orbits of the planets were not circular, but elliptical, and the sun—the center of the attractive force—was not at the center of the ellipse, but at one of the foci. For the complete solution of the actual problem which the phenomena presented, a calculus was needed which neither Borelli nor Huyghens possessed, and the preeminent genius of Newton was illustrated, probably more by the invention of the needed calculus than by his successful application of it to the solution of the important problem in question.
The general fact having been established that the curvilinear motion of the heavenly bodies was explicable on the hypothesis of a central attractive force, it was soon surmised that the particular character of the planetary orbits—involving as it did a continual variation in the distance of each planet from the sun, as well as a continual variation in the velocity of the planet's motion—could be due to no other cause than a difference in the intensity of the sun's attractive force at different distances. The query was: What was the precise law of this variation in intensity, which would account for the phenomena? Was the attraction inversely as the distance? or, as the square of the distance? or, as the cube? or, was it such as admitted of any precise expression? Guided probably by the best known fact as to the distribution of light, of heat, indeed of any emanation radiating in all directions from a center, several individuals, independently as it would seem, adopted the conclusion which was afterwards demonstrated to be correct, namely: That the attractive force of matter for matter varied inversely as the square of the distance, that is, at double the distance the attraction is one-fourth, at treble the distance one-ninth, and so on. The first to announce the true law of variation in the intensity of attraction was a French philosopher, Bouilland, or as his name ordinarily appears in the Latinized form, Bullialdus. About the same time. Sir Christopher Wren, the distinguished architect of St. Paul's, Dr. Hooke, for a long time secretary of the Royal Society, and the eminent mathematician astronomer, Halley, had arrived at the same conclusion. It was still however but a conjecture. In spite of the most earnest and persevering effort no one was able to furnish a demonstration.
As contributing to the discovery of the demonstration, the place of merit next to that of Newton, though of course far inferior, is doubtless due to Hooke. His labors were probably of aid to Newton by way of suggestion, without however affording any just ground for the charge which Hooke subsequently made that Newton was wearing the laurels to which he himself was justly entitled. As early as 1666 Hooke exhibited in the presence of the Royal Society an experiment
