222 A Short History of Astronomy [Cn. ix. 



distance between the two bodies. Kepler's laws of planetary 

 motion were in fact shewn to lead necessarily to the 

 conclusions that the sun exerts on a planet an attraction 

 inversely proportional to the square of the distance of the 

 planet from the sun, and that such an attraction affords a 

 sufficient explanation of the motion of the planet. 



Once more, however, Newton published nothing and 

 " threw his calculations by, being upon other studies." 

 *, 176. Nearly five years later the matter was again brought 

 to his notice, on this occasion by Edmund Halley (chap- 

 ter x., 199-205), whose friendship played henceforward 

 an important part in Newton's life, and whose unselfish 

 devotion to the great astronomer forms a pleasant contrast 

 to the quarrels and jealousies prevalent at that time 

 between so many scientific men. Halley, not knowing 

 of Newton's work in 1666, rediscovered, early in 1684, tne 

 law of the inverse square, as a consequence of Kepler's 

 Third Law, . and shortly afterwards discussed with Wren 

 and Hooke what was the curve in which a body would 

 move if acted on by an attraction varying according to 

 this law ; but none of them could answer the question.* 

 Later in the year Halley visited Newton at Cambridge 

 and learnt from him the answer. Newton had, character- 

 istically enough, lost his previous calculation, but was 

 able to work it out again and sent it to Halley a few 

 months afterwards. This time fortunately his attention 

 was not diverted to other topics ; he worked out at once a 

 number of other problems of motion, and devoted his usual 

 autumn course of University lectures to the subject. 

 Perhaps the most interesting of the new results was that 

 Kepler's Third Law, from which the law of the inverse 

 square had been deduced in 1666, only on the supposition 

 that the planets moved in circles, was equally consistent 

 with Newton's law when the paths of the planets were 

 taken to be ellipses. 



177. At the end of the year 1684 Halley went to 

 Cambridge again and urged Newton to publish his results. 

 In accordance with this request Newton wrote out, and sent 



* It is interesting to read that Wren offered a prize of 405. to 

 whichever of the other two should solve this the central problem of 

 the solar system. 



