PRESIDENTIAL ADDRESS, B.A., 1871. 157 



but the rewards of accurate measurement and 

 patient long-continued labour in the minute sifting 

 of numerical results. The popular idea of Newton's 

 grandest discovery is that the theory of gravitation 

 flashed into his mind, and so the discovery was 

 made. It was by a long train of mathematical 

 calculation, founded on results accumulated 

 through prodigious toil of practical astronomers, 

 that Newton first demonstrated the forces urging 

 the planets towards the Sun, determined the 

 magnitudes of those forces, and discovered that a 

 force following the same law of variation with 

 distance urges the Moon towards the Earth. Then 

 first, we may suppose, came to him the idea of the 

 universality of gravitation ; but when he attempted 

 to compare the magnitude of the force on the 

 Moon with the magnitude of the force of gravita- 

 tion of a heavy body of equal mass at the earth's 

 surface, he did not find the agreement which the 

 law he was discovering required. Not for years 

 after would he publish his discovery as made. It 

 is recounted that, being present at a meeting of the 

 Royal Society, he heard a paper read, describing 



