54
THE HOOK’S MOTIONS.
square of the distance, would travel in an ellipticorbit, having the centre of force in one of the foci.I do not at present pause to explain this remark,which is indeed only introduced here to indicate thesequence of Newton’s researches. It is to be notedthat Hooke gave no proof of the truth of his remark;nor was tjiere anything in his letter to show that hehad established the relation. He was not, indeed,endowed with such mathematical abilities as wouldhave been needed (in his day) to master the problemin question. Newton, however, grappled with it atonce, and before long the idea suggested by Hookehad been mathematically demonstrated by Newton.Yet, even in ascribing the idea, to Hooke’s sug-gestion at this epoch, we must not forget thatNewton, in the very circumstance that he had dis-cussed the moon’s motion as possibly ruled by theearth’s attraction, had implicitly entertained the ideanow first explicitly enunciated by Hooke : for themoon does not move in a circle around the earth, butin an ellipse.
In studying this particular problem, Newton’s atten-tion was naturally drawn again to the long-abandonedtheory that the earth’s attraction governs the moon’smotions. But he was still unable to remove the dis-crepancy which had foiled him in 1665.
At length, however, in 1684, news reached him thatPicard* had measured a meridional arc with great