ISO SEVENTEENTH CENTURY. PT. in. 



tion 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 at- 

 traction here will only be -|-th of the attraction at the point i. 

 And so the calculation goes on ; if the planet went 1 2 

 millions of miles off, the attraction would be T -j- T what it 

 was at first, and at 9 2 millions of miles the attraction would 

 be -g-fVirj so tnat wnen tne 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 Kepler, but all the complex movements of the 

 heavenly bodies. These Newton worked out approximately 

 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 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 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 the 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 not more than eight people in the world who were able 

 to understand the full meaning of his calculations and 

 reasonings ; and though his theory of gravitation was well 



