488 POPULAR SCIENCE MONTHLY. 



I^ewton, 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 investi- 

 gating 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 cer- 

 tain 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 sug- 

 gested by Hookcy 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 enigina 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 



