246 A Short History of Astronomy [On. ix., $ 195 



obtained by calculation. The calculation was made and 

 found to agree roughly with the actual motion of the 

 moon*. 



Moreover it may be fairly urged, in illustration of the 

 great importance of the process of verification, that 

 Newton's fundamental laws were not rigorously established 

 by him, but that the deficiencies in his proofs have 

 been to a great extent filled up by the elaborate pro- 

 cess of verification that has gone on since. For the 

 motions of the solar system, as deduced by Newton from 

 gravitation and the laws of motion, only agreed roughly 

 with observation ; many outstanding discrepancies were 

 left ; and though there was a strong presumption that 

 these were due to the necessary imperfections of Newton's 

 processes of calculation, an immense expenditure of labour 

 and ingenuity on the part of a series of mathematicians has 

 been required to remove these discrepancies one by one, 

 and as a matter of fact there remain even to-day a few 

 small ones which are unexplained (chapter xin., 290). 



