172 DISCOVERY CH. 



Using the new value, Newton again took up the cal- 

 culation of the moon's deflection from a straight path, 

 on the assumption of the force controlling it being the 

 same as that which causes bodies to fall on the earth, 

 but diminished in strength on account of the distance 

 of the moon from the earth. The result now obtained 

 showed that the central force should cause the moon 

 to swerve from a straight line path by 53 thousandths 

 of an inch in a second, which is exactly the amount that 

 will produce the curved path described by the moon 

 around the earth. As the calculations which were thus 

 to extend the domain of gravity from the earth to the 

 universe were drawing to a close, it is related that Newton 

 was " so much agitated that he was obliged to desire a 

 friend to finish them." 



It must not be supposed for a moment that the 

 problem of testing the theory of gravitation by the 

 motion was so simple as it is here presented. In order 

 to establish the principle, Newton had to prove that as 

 regards gravitational attraction, a globe like the sun, 

 moon, or earth behaves as if the force due to the whole 

 of the mass resided at the centre alone. This conclusion 

 was only arrived at after infinite labour and by the 

 employment of a new mathematical method invented 

 by him. By this same method also he was able to prove 

 that the path of a body under the influence of attraction 

 depending upon a central force could be an ellipse or 

 any other related curve. The elliptical paths of the 

 moon around the earth, the earth and other planets 

 around the sun, and of all satellites around their primary 

 planets were explained by this discovery ; yet, as we 

 have seen, Newton was content with having found it, 

 and only through the intervention of Halley was the 

 world made aware of it. 



