$ 174, i7s] The Motion of the Moon> and of the Planets 221 



substantially defective, is possible, but by no means certain ; 

 whatever the cause may have been, he laid the subject 

 aside for some years without publishing anything on it, and 

 devoted himself chiefly to optics and mathematics. 



174. Meanwhile the problem of the planetary motions 

 was one of the numerous subjects of discussion among the 

 remarkable group of men who were the leading spirits of 

 the Royul Society, founded in 1662. Robert Hooke (1635- 

 1703), who claimed credit for most of the scientific dis- 

 coveries of the time, suggested with some distinctness, not 

 later than 1674, that the motions of the planets might be 

 accounted for by attraction between them and the sun, and 

 referred also to the possibility of the earth's attraction on 

 bodies varying according to the law of the inverse square. 

 Christopher Wren (1632-1723), better known as an architect 

 than as a man of science, discussed some questions of this 

 sort with Newton in 1677, and appears also to have thought 

 of a law of attraction of this kind. A letter of Hooke's to 

 Newton, written at the end of 1679, dealing amongst other 

 things with the curve which a falling body would describe, 

 the rotation of the earth being taken into account, stimulated 

 Newton, who professed that at this time his " affection to 

 philosophy " was " worn out," to go on with his study of 

 the celestial motions. Picard's more accurate measurement 

 of the earth (chapter vni., 159) was now well known, and 

 Newton repeated his former calculation of the moon's 

 motion, using Picard's improved measurement, and found 

 the result more satisfactory than before. ' 



175. At the same time (1679) Newton made a further 

 discovery of the utmost importance by overcoming some of 

 the difficulties connected with motion in a path other than 

 a circle. 



He shewed that if a body moved round a central body, 

 in such a way that the line joining the two bodies sweeps 

 out equal areas in equal times, as in Kepler's Second Law 

 of planetary motion (chapter vii., 141), then the moving 

 body is acted on by an attraction directed exactly towards 

 the central body ; and further that if the path is an ellipse, 

 with the central body in one focus, as in Kepler's First Law 

 of planetary motion, then this attraction must vary in 

 different parts of the path as the inverse square of the 



