10 Britain's Heritage of Science 



is the law of u action and reaction," which has played so 

 important a part in the history of science. 



Having accurately defined what is meant by change of 

 motion, Newton in his " Principia " establishes a number 

 of propositions relating to the motion of a body acted on 

 by a force directed to a fixed centre. The Copermcan 

 hypothesis that the earth and planets are in motion round 

 the sun, replacing the older view which believed the earth 

 to be the centre of the universe, was at that time generally 

 accepted by scientific men, and Kepler had formulated three 

 laws defining the orbits of the planets. Newton's pro- 

 positions, applied to Kepler's laws, proved that the movements 

 of the planets may be accounted for by imagining attracting 

 forces to act between the sun and the planets diminishing 

 in proportion to the squares of the distances. If this attrac- 

 tion be accepted, it is natural to identify it with the force 

 that keeps the moon in its orbit round the earth, and finally 

 with that which we observe directly when a body falls down 

 from a height. But it had to be proved that the intensity 

 of gravitation at the surface of the earth and that acting 

 on the moon were related to each other according to the 

 law deduced from the planetary motions; in other words, 

 as the distance between the centres of the earth and moon 

 is 60 times the earth's radius it had to be shown that 

 the gravitational force at the surface of the earth is 3,600 

 times as great as that which keeps the moon in its orbit. 

 The calculation is easily made if we know the length of the 

 earth's diameter, and this having been ascertained with 

 sufficient accuracy by Picard in France shortly before the 

 publication of the " Principia," Newton had the satisfaction 

 of finding an almost perfect agreement. His theory was 

 confirmed, and it was definitely proved that the motion of 

 the planetary system, as well as the behaviour of heavy 

 bodies on the surface of the earth, could all be deduced from 

 the general proposition that every particle of matter attracts 

 every other particle with a force which varies in the inverse 

 ratio of the square of the distance. 



Commentators on Newton's work frequently draw atten- 

 tion to the delay in publishing for ten years or more the 

 results of his calculations, because when they were first 



