THE RENAISSANCE 129 



that the force would be less at the distance of the 

 moon than at the surface of the earth in the ratio of 

 (60) 2 or 3600 to i. With the only estimate of the 

 earth's radius available in 1666, this calculation gives 

 a force too great to explain the moon's motion round 

 the earth, and Newton, always dissatisfied with the 

 slightest inaccuracy, put aside the enquiry. But in 

 1679 a redetermination of the size of the earth, giving 

 a markedly different value, led Newton once more to 

 take up the problem, and, in a state of excitement 

 which is said to have been so great that he could 

 hardly see his figures, he proved that the fall of 

 a stone to the earth and the majestic sweep of the 

 moon in her orbit may be ascribed to one and same 

 cause. 



Newton then proceeded to attack the general 

 problem of the motion of a body under a force directed 

 towards a fixed point, and showed that the sup- 

 position that every particle of matter attracts every 

 other particle in accordance with the law of inverse 

 squares was necessary and sufficient to explain Kepler's 

 planetary observations. The simple law of the heavens, 

 the universal rule of gravity, was thus revealed the 

 greatest achievement in the history of science. 



The mechanism by which the force is exerted re- 

 mained unexplained by Newton, and has hitherto 

 baffled all subsequent enquiry. As always, one of 

 the chief results of new scientific knowledge was to 

 define more accurately the limits of our ignorance. 

 Newton indeed described himself as a child gathering 

 pebbles of knowledge by the shore of the boundless 

 ocean of the unknown. The larger grows the sphere 

 of knowledge, the greater is its surface of contact 



9 



