PK ELUDE TO THE EPOCH OF NEWTON. 397 



in An Attempt to prove the Motion of the Earth from Observations, 

 published in 1674. In this, he distinctly states that the planets would 

 move in straight lines, if they were not deflected by central forces ; 

 and that the central attractive power increases in approaching the 

 centre in certain degrees, dependent on the distance. "Now what 

 these degrees are," he adds, " I have not yet experimentally verified ;" 

 but he ventures to promise to any one who succeeds in this under- 

 taking, a discovery of'the cause of the heavenly motions. He asserted, 

 in conversation, to Halley and Wren, that he had solved this problem, 

 but his solution was never produced. The proposition that the attrac- 

 tive force of the sun varies inversely as the square of the distance from 

 the centre, had already been divined, if not fully established. If the 

 orbits of the planets were circles, this proportion of the forces might 

 be deduced in the same manner as the propositions concerning circular 

 motion, which Huyghens published in 1673; yet it does not appeal- 

 that Huyghens made this application of his principles. Newton, how- 

 ever, had already made this step some years before this time. Accord- 

 ingly, he says in a letter to Halley, on Hooke's claim to this discovery, 23 

 " When Huygeuius put out his Iloroloyium Oscillatorium, a copy 

 being presented to me, in my letter of thanks I gave those rules in the 

 end thereof a particular commendation for their usefulness in computing 

 the forces of the moon from the earth, and the earth from the sun." 

 He says, moreover, " I am almost confident by circumstances, that 

 Sir Christopher Wren knew the duplicate proportion when I gave him 

 a visit ; and then Mr. Hooke, by his book Comcta, will prove the last 

 of us three that knew it." Hooke's Cometa was published in 1678. 

 These inferences were all connected with Kepler's law, that the times 

 are in the sesquiplicate ratio of the major axes of the orbits. But 

 Halley had also been led to the duplicate proportion by another train 

 of reasoning, namely, by considering the force of the sun as an emana- 

 tion, which must become more feeble in proportion to the increased 

 spherical surface over which it is diffused, and therefore in the inverse 

 proportion of the square of the distances. 24 In this view of the matter, 

 however, the difficulty was to determine what would be the motion of 

 a body acted on by such a force, when the orbit is not circular but 

 oblong. The investigation of this case was a problem which, we can 



23 Bioy. Brit., art. Hooke. 



'" Bulliakltis, iu 1045, had nsserted that the force by which the sun " prehendit 

 et harpagat,'' take? hold of and grapples the planets, nui^t be as the inverse square 

 of the distance. 



