Writing of Principia Mathematica: Difference between revisions

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[[Isaac Newton]] composed ''[[Philosophiae Naturalis Principia Mathematica|Principia Mathematica]]'' during 1685 and 1686,<ref>For information on Newton's later life and post-''Principia'' work, see [[Isaac Newton's later life]].

</ref> and it was published in a first edition on July 5, July 1687 and began changing the world. Widely regarded as one of the most important works in both the [[Physics|science of physics]] and in [[Mathematics|applied mathematics]] during the [[Scientific revolution]], the work underlies much of the technological and scientific advances from the [[Industrial Revolution]] (usually dated from 1750) which its tools helped to create.

== Authoring ''Principia'' ==

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===Work begins===

[[Image:NewtonsPrincipia.jpg|thumb|250px|right|Newton's own copy of his Principia, with hand written corrections for the second edition.]]

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 [[September 19]] [[September 1685]], that he had received many useful communications from Flamsteed, especially regarding [[Saturn (planet)|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 written 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 April 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."

At the next meeting of the Society, on April 28, April 1686, "Dr Vincent presented to the Society a manuscript treatise entitled ''Philosophiae Naturalis Principia Mathematica'', and dedicated to the Society by Mr Isaac Newton." Although this manuscript contained only the first book, yet such was the confidence the Society placed in the author that an order was given "that a letter of thanks be written to Mr Newton; and that the printing of his book be referred to the consideration of the council; and that in the meantime the book be put into the hands of Mr Halley, to make a report thereof to the council."

Although there could be no doubt as to the intention of this report, no step was taken towards the publication of the work. At the next meeting of the Society, on 19 May 19, 1686, some dissatisfaction seems to have been expressed at the delay, as it was ordered "that Mr Newton's work should be printed forthwith in quarto, and that a letter should be written to him to signify the Society's resolutions, and to desire his opinion as to the print, volume, cuts and so forth." Three days afterwards Halley communicated the resolution to Newton, and stated to him that the printing was to be at the charge of the Society. At the next meeting of the council, on 2 June 2, 1686, it was again ordered "that Mr Newton's book be printed," but, instead of sanctioning the resolution of the general meeting to print it at their charge, they added "that Mr Halley undertake the business of looking after it, and printing it at his own charge, which he engaged to do."

In order to explain to Newton the cause of the delay, Halley in his letter of May 22, May 1686 alleges that it arose from "the president's attendance on the king, and the absence of the vice-president's, whom the good weather had drawn out of town"; but there is reason to believe that this was not the true cause, and that the unwillingness of the council to undertake the publication arose from the state of the finances of the Society. Halley certainly deserves the gratitude of posterity for undertaking the publication of the work at a very considerable financial risk to himself.

In the same letter Halley found it necessary to inform Newton of [[Robert Hooke|Hooke]]'s conduct when the manuscript of the Principia was presented to the Society. Sir [[John Hoskyns]] was in the chair when Dr Vincent presented the manuscript, and praised the novelty and dignity of the subject. Hooke was offended because Sir John did not mention what he had told him of his own discovery. Halley only communicated to Newton the fact "that Hooke had some pretensions to the invention of the rule for the decrease of gravity being reciprocally as the squares of the distances from the centre," acknowledging at the same time that, though Newton had the notion from him, "yet the demonstration of the curves generated thereby belonged wholly to Newton." "How much of this," Halley adds, "is so, you know best, so likewise what you have to do in this matter; only Mr Hooke seems to expect you should make some mention of him in the preface, which 'tis possible you may see reason to prefix. I must beg your pardon that 'tis I that send you this ungrateful account; but I thought it my duty to let you know it, so that you might act accordingly, being in myself fully satisfied that nothing but the greatest candour imaginable is to be expected from a person who has of all men the least need to borrow reputation."

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[[Image:Principia Page 1726.jpg|thumb|right|A page from the ''Principia'']]

In thus appealing to Newton's honesty, Halley obviously wished that Newton should acknowledge Hooke in some way. Indeed, he knew that before Newton had announced the inverse law, Hooke and [[Christopher Wren|Wren]] and himself had spoken of it and discussed it, and therefore justice demanded that Hooke especially should receive credit for having maintained it as a truth of which he was seeking the demonstration, even though none of them had given a demonstration of the law. On June 20, June 1686 Newton wrote to Halley the following letter:

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On June 20, June 1686, Halley wrote to Newton:

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On June 30, June 1686 the council resolved to license Newton's book, entitled ''Philosophiae Naturalis Principia Mathematica''.

On 14 July 14, 1686, Newton wrote to Halley approving of his proposal to introduce woodcuts among the letterpress, stating clearly the differences which he had from Hooke, and adding, "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley." After this letter of Newton's the printing of the ''Principia'' was begun. The second book, though ready for the press in the autumn of 1686, was not sent to the printers until March 1687. The third book was presented to the Society, on April 6, April and the whole work published about midsummer in that year, 5 July 5, 1687.<ref>[[Richard S. Westfall]], ''Never at Rest'', ISBN 0-521-27435-4 (paperback) Cambridge 1980..1998.</ref> It was dedicated to the Royal Society, and to it was prefixed a set of Latin hexameters addressed by Halley to the author. The work, as might have been expected, caused a great deal of excitement throughout Europe, and the whole of the impression was very soon sold. In 1691 a copy of the Principia was hard to obtain.

===Conflict between the University and James II===

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Upon receiving the mandamus [[John Pechell]], the master of [[Magdalene College]], who was vice-chancellor, sent a messenger to the Duke of Albemarle, the chancellor, to request him to get the mandamus recalled; and the registrary and the bedell waited upon Francis to offer him instant admission to the degree if only he would take the necessary oaths. A menacing letter was despatched by Sunderland&mdash;respectful explanations were returned, but the university showed no sign of compliance, nor suggested a compromise. The vice-chancellor and deputies from the senate were summoned to appear before the [[High commission court]] at Westminster. Newton was one of the eight deputies appointed by the senate for this purpose.

The deputies, before starting for London, held a meeting to prepare their case for the court. A compromise which was put forward by one of them was resisted by Newton. On April 21 April the deputation, with their case carefully prepared, appeared before the court. Lord Jeffreys presided at the board. The deputation appeared as a matter of course before the commissioners, and was dismissed. On April 27 April they gave their plea. On May 7 May it was discussed, and feebly defended by the vice-chancellor. The deputies maintained that in the late reign several royal mandates had been withdrawn, and that no degree had ever been conferred without the oaths having been previously taken. Jeffreys spoke with his accustomed insolence to the vice-chancellor, silenced the other deputies when they offered to speak, and ordered them out of court. When recalled the deputies were reprimanded, and Pechell was deprived of his office as vice-chancellor, and of his salary as master of Magdalene.

Newton returned to [[Trinity College, Cambridge|Trinity College]] to complete the ''Principia''. While thus occupied he had an extensive correspondence with Halley, a very great part of which is extant. The following letter from Halley, dated London, July 5, July 1687, announcing the completion of the Principia, is of particular interest:

"I have at length brought your book to an end, and hope it will please you. The last errata came just in time to be inserted. I will present from you the book you desire to the Royal Society, Mr Boyle, Mr Paget, Mr Flamsteed, and if there be any else in town that you design to gratify that way; and I have sent you to bestow on your friends in the University 20 copies, which I entreat you to accept. In the same parcel you will receive 40 more, which having no acquaintance in Cambridge, I must entreat you to put into the hands of one or more of your ablest booksellers to dispose of them. I intend the price of them, bound in calves' leather, and lettered, to be ''[OCR error]'' shillings here. Those I send you I value in [[Paper quire|quire]]s at 6 shillings, to take my money as they are sold, or at 5 sh. for ready, or else at some short time; for I am satisfied there is no dealing in books without interesting the booksellers; and I am contented to let them go halves with me, rather than have your excellent work smothered by their combinations. I hope you will not repent you of the pains you have taken in so laudable a piece, so much to your own and the nation's credit, but rather, after you shall have a little diverted yourself with other studies, that you will resume those contemplations wherein you had so great success, and attempt the perfection of the lunar theory, which will be of prodigious use in navigation, as well as of profound and public speculation. You will receive a box from me on Thursday next by the wagon, that starts from town tomorrow."

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===Illness in 1693===

In 1692 and 1693 Newton seems to have had a serious illness, the nature of which has given rise to very considerable dispute. In a letter dated the13 September 13, 1693, addressed to [[Samuel Pepys]], he writes: "Some time after Mr Millington had delivered your message, he pressed me to see you the next time I went to London. I was averse, but upon his pressing consented, before I considered what I did, for I am extremely troubled at the embroilment I am in, and have neither ate nor slept well this twelvemonth, nor have my former consistency of mind. I never designed to get any thing by your interest, nor by icing James's favour, but am now sensible that I must withdraw from your acquaintance, and see neither you nor the rest of my friends any more, if I may but have them quietly. I beg your pardon for saying I would see you again, and rest your most humble and obedient servant." And in a letter written to [[John Locke]] in reply to one of his about the second edition of his book, and dated the 15th of October 1693, Newton wrote: "The last, winter, by sleeping too often by my fire, I got an ill habit of sleeping; and a distemper, which this summer has been epidemical, put me farther out of order, so that when I wrote to you, I had not slept an hour a night for a fortnight together, and for five days together not a wink. I remember I wrote to you, but what I said of your book I remember not. If you please to send me a transcript of that passage, I will give you an account of it if I can."

The loss of sleep to a person of Newton's temperament, whose mind was never at rest, and at times so wholly engrossed in his scientific pursuits that he even neglected to take food, must necessarily have led to a very great deal of nervous excitability. It is not astonishing that rumours got abroad that there was a danger of his mind giving way, or, according to a report which was believed at the time, that it had actually done so. Pepys must have heard such rumours, as in a letter to his friend Millington, the tutor of [[Magdalene College, Cambridge|Magdalene College]] at Cambridge, dated September 26, September 1693, he wrote: "I must acknowledge myself not at the ease I would be glad to be at in reference to excellent Mr Newton; concerning whom (methinks) your answer labours under the same kind of restraint which (to tell you the truth) my asking did. For I was 10th at first dash to tell you that I had lately received a letter from him so surprising to me for the inconsistency of every part of it, as to be put into great disorder by it, from the concern I have for him, lest it should arise from that which of all mankind I should least dread from him and most lament for I mean a discomposure in head, or mind, or both. Let me, therefore, beg you, Sir, having now told you the true ground of the trouble I lately gave you, to let me know the very truth of the matter, as far at least as comes within your knowledge."

On September 20, September 1693, Millington wrote to Pepys that he had been to look for Newton some time before, but that "he was out of town, and since," he says, "I have not seen him, till upon the 28th I met him at Huntingdon, where, upon his own accord, and before I had time to ask him any question, he told me that he had written to you a very odd letter, at which he was much concerned; added, that it was in a distemper that much seized his head, and that kept him awake for above five nights together, which upon occasion he desired I would represent to you, and beg your pardon, he being very much ashamed he should be so rude to a person for whom he hath so great an honour. He is now very well, and though I fear he is under some small degree of melancholy, yet I think there is no reason to suspect it hath at all touched his understanding, and I hope never will; and so I am sure all ought to wish that love learning or the honour of our nation, which it is a sign how much it is looked after, when such a person as Mr Newton lies so neglected by those in power."

The illness of Newton was very much exaggerated by foreign contemporary writers. [[Christiaan Huygens]], in a letter dated 8 June 8, 1694, wrote to Leibniz, "I do not know if you are acquainted with the accident which has happened to the good Mr Newton, namely, that he has had an attack of [[phrenitis]], which lasted eighteen months, and of which they say his friends have cured him by means of remedies, and keeping him shut up." To which Leibniz, in a letter dated the 22nd of22 June, replied, "I am very glad that I received information of the cure of Mr Newton at the same time that I first heard of his illness, which doubtless must have been very alarming."

===Initial election to Parliament===

The active part which Newton had taken in defending the legal privileges of the university against the encroachments of the crown had probably at least equal weight with his scientific reputation when his friends chose him as a candidate for a seat in parliament as one of the representatives of the university. The other candidates were Sir Robert Sawyer and Mr Finch. Sir Robert headed the poll with 125 votes, Newton next with 122 and Mr Finch was last with 117 votes. Newton retained his seat only about a year, from January 1689 till the dissolution of the [[Coventry Parliament]] in February 1690. During this time Newton does not appear to have taken part in any of the debates in the House, but he was not neglectful of his duties as a member. On April 30, April 1689 he moved for leave to bring in a bill to settle the charters and privileges of the [[University of Cambridge]], just as Sir [[Thomas Clarges]] did for Oxford at the same time, and he wrote a series of letters to Dr Lovel, the vice-chancellor of the university, on points which affected the interests of the university and its members.

Some of the members of the university who had sworn allegiance to James had some difficulty in swearing allegiance to his successor. On February 12, February 1689, the day of the coronation of William and Mary, Newton intimated to the vice-chancellor that he would soon receive an order to proclaim them at Cambridge. He enclosed a form of the proclamation, and expressed a hearty "wish that the university would so compose themselves as to perform the solemnity with a reasonable decorum."

==See also==