vii LAW AND PRINCIPLE 109 



this discovery not only were the facts then known as 

 to celestial forms and movements capable of explanation, 

 but also every case to which the principle has since 

 been applied. 



Nature and Nature's laws lay hid in night. 



God said, " Let Newton be ! " and all was light. Pope. 



There had been many surmises as to the nature of the 

 force which keeps the planets in their courses around 

 the sun and makes the moon describe its path around the 

 earth. It had been shown that the strength of the force 

 of attraction between two bodies does not diminish, as 

 Kepler supposed, in the simple ratio of the distance 

 separating them, that is, is halved when the distance 

 is doubled, but varies as the square of the distance. 

 When the distance is doubled, the force is thus reduced 

 to one- quarter, when trebled, to one-ninth, and so on. 

 The problem was to account for the movements of the 

 planets and their satellites in elliptical orbits upon the 

 assumption of a force varying in this way. 



In January, 1684, Sir Christopher Wren offered Hooke 

 and Halley " the present of a book of forty shillings " 

 if either of them could bring him a convincing demon- 

 stration within two months that such a force would 

 cause a planet to move in an ellipse. The demonstration 

 had not been given in August of the same year when 

 Halley went to Cambridge to consult Newton on the 

 subject. Without mentioning any of the speculations 

 of Wren, Hooke or himself, he asked at once : 



" What will be the curve described by the planets on the sup- 

 position that gravity diminishes as the square of the distance ?" 



Newton answered immediately, " An ellipse." 



" How do you know ? " asked Halley in amazement. 



" Why," replied Newton, " I have calculated it," and he 

 proceeded to search for the calculation, but unsuccessfully. 



