Writing of Principia Mathematica: Difference between revisions

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Between 1685 and 1686, Newton had a very extensive correspondence with [[John Flamsteed]], who was then the astronomer-royal. Many of the letters are lost but it is clear from one of Newton's, dated 19 September 1685, that he had received many useful communications from Flamsteed, especially regarding [[Saturn]], "whose orbit, as defined by [[Johannes Kepler|Kepler]]," Newton "found too little for the sesquialterate proportions." Newton refers to [[Kepler's laws of planetary motion|Kepler's third law]], that the orbital period is proportional to the distance from the sun to the power of 3/2 ("sesquialteral" comes from the Latin word for the ratio 3/2).

In the other letters writtewritten in 1685 and 1686, he asks Flamsteed for information about the orbits of the moons of [[Jupiter]] and Saturn, the rise and fall of the spring and neap tides at the solstices and the equinoxes, about the flattening of Jupiter at the poles (which, if certain, he says, would conduce much to the stating the reasons of the precession of the equinoxes), and about the universal application of Kepler's third law. "Your information for Jupiter and Saturn has eased me of several scruples. I was apt to suspect there might be some cause or other unknown to me which might disturb the {{sic|hide=y|sesqui|altera}} proportion. For the influences of the planets one upon another seemed not great enough, though I imagined Jupiter's influence greater than your numbers determine it. It would add to my satisfaction if you would be pleased to let me know the long diameters of the orbits of Jupiter and Saturn, assigned by yourself and Mr [[Edmond Halley|Halley]] in your new tables, that I may see how the {{sic|hide=y|sesqui|plicate}} proportion fills the heavens, together with another small proportion which must be allowed for." <ref>(Letter of mid-January (before 14th) 1684|1685 (Old Style), published as #537 in Vol.2 of ''The Correspondence of John Flamsteed'', ed. E.G. Forbes et al., 1997. (This reference was supplied after original compilation of the present article, and gives original spellings; but most spellings and punctuations in the text above have been modernised. The words 'sesquialtera' and 'sesquiplicate', now archaic, refer to the relation between a given number and the same multiplied by its own square root: or to the square root of its cube, which comes to the same thing: the 'one-and-a-half-th' power, as it were.)</ref>

Upon Newton's return from [[Lincolnshire]] in the beginning of April 1685, he seems to have devoted himself to the preparation of his work. In the spring he had determined the attractions of masses, and thus completed the law of universal gravitation. In the summer he had finished the second book of the ''Principia'', the first book being the treatise ''[[De motu corporum in gyrum]]'', which he had enlarged and completed. Except for correspondence with Flamsteed we hear nothing more of the preparation of the ''Principia'' until 21 April 1686, when Halley read to the [[Royal Society]] his ''Discourse concerning Gravity and its Properties'', in which he states "that his worthy countryman Mr Isaac Newton has an incomparable treatise of motion almost ready for the press," and that the law of the inverse square "is the principle on which Mr Newton has made out all the phenomena of the celestial motions so easily and naturally, that its truth is past dispute."