CH. XVIII. THE 'PRINCIPIA: 



153 



3 it would be about twice as far, or two millions of miles 

 distant ; and the square of 2 being 4 (2 x 2 = 4), the at- 

 traction of the sun at this point will be only one-fourth as 

 much as it was at the point i. At the point 7 the planet 

 would be about three times as far, or three millions of miles 

 from the sun, and as the square of 3 is 9 (3 x 3 = 9), the 

 attraction here will be only ^th of the attraction at the point 

 I. And so the calculation goes on ; if the planet went 12 

 millions of miles off, the attraction would be ^\^ what it was 

 at first, and at 92 millions of miles the attraction would be 

 ^tVt » SQ ^^^ when the planet is very far away the attraction 

 becomes very slight indeed, but it will never entirely cease. 

 In scientific language this law is expressed by the words. 

 The attraction varies inversely as the square of the distance. 

 When once this law was known, it explained in a most 

 beautiful and complete way not only the three laws of Kep- 

 ler, but all the complex movements of the heavenly bodies. 

 These Newton worked out with the greatest accuracy by 

 the help of his * Method of Fluxions,' which enabled him 

 to calculate all the varying rates at which the planets move 

 in consequence of their mutual attraction ; and he showed 

 that whenever we know clearly the position and mass of all 

 the bodies attracting a planet, the law of gravitation exactly 

 accounts for the direction in which it moves. 



If you will consider for a moment what a labour it must 

 be to calculate how much all the different planets pull each 

 other at different times — when they are near together and 

 when they are far off, when they are near each other and 

 near th sun, or near each other and far from the sun, in 

 fact in all the different positions you can imagine — you may 

 form some idea of the tremendous work he did. When he 

 published his great book, the ' Principia,' in 1687, there were 



