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 process 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 xiii., § 290).
