484 POPULAR SCIENCE MONTHLY. 



A great step had been taken toward the solution of the problem of 

 planetary motion, but a formidable difficulty yet remained to be over- 

 come. 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 char- 

 acter 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 dis- 

 tribution 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 in- 

 tensity 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 Eoyal 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 doubt- 

 less due to Hooke. His labors were probably of aid to ISTevrton 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 Eoyal Society an experiment 



