In order to let you know ye case between Mr Hook & me I gave you an account of wt past between us in or Letters so far as I could remember. For tis long since they were writ & I do not know that I have seen ym since. I am almost confident by circumstances that Sr Chr. Wren knew ye duplicate proportion wn I gave him a visit, & then Mr Hook (by his book Cometa written afterward) will prove ye last of us three yt knew it. I intended in this Letter to let you understand ye case fully but it being a frivolous business, I shal content my self to give you ye heads of it in short: vizt yt I never extended ye duplicate proportion lower then to ye superficies of ye earth & before a certain demonstration I found ye last year have suspected it did not reach accurately enough down so low: & therefore in ye doctrine of projectiles never used it nor considered ye motions of ye heavens: & consequently Mr Hook could not from my Letters wch were about Projectiles & ye regions descending hence to ye center conclude me ignorant of ye Theory of ye Heavens. That what he told me of ye duplicate proportion was erroneous, namely that it reacht down from hence to ye center of ye earth. That it is not candid {illeg}|to| require me now to confess my self in print {illeg}|th|en ignorant of ye duplicate proportion in ye heavens for no other reason but because he had told it me in the case of projectiles & so upon mistaken grounds accused me of that ignorance. That in my answer to his first letter I refused his correspondence, told him I had laid Philosophy aside, sent him only ye experimt of Projectiles (rather shortly hinted then carefully described) in complemt to swi|e|eten my Answer, expected to heare no further from him, could scarce perswade my self to answer his second letter, did not answer his third, was upon other things, thought no further of philosophical matters then his letters put me upon it, & therefore may be allowed not to have had my thoughts of that kind about me so well at that time. That by the same reason he conclude{illeg}|s| me then ignorant of ye duplicate proportion he may as well conclude me ignorant of ye rest of that Theory I had read before in his books. That in one {illeg}|o|f my papers writ (I cannot say in what year but I am sure some time before I had any correspondence wth Mr Oldenburg & that's) above fifteen years ago, the proportion of ye forces of ye Planets from ye Sun reciprocally duplicate to their distances from him is exprest & ye proportion of or gravity to ye Moon's conatus recedendi a centro Terræ is calculated thô not accurately enough. That wn Hugenius put out his Horol. Oscil. a copy being presented to me; in my letter of thanks to him I gave those rules in ye end thereof a particular commendation for their usefulness in Philosophy, & added out of my aforesaid paper an instance of their usefulness in comparing ye forces of ye Moon from ye earth & earth from ye Sun in determining a Probleme about ye Moons phase & putting a limit to ye Sun's parallax. Which shews that I had then my eye upon comparing ye forces of ye Planets arising from their circular motion & understoo{d} it: so that a while after wn Mr Hook propounded ye Probleme solemnly in ye end of his Attempt to prove ye motion of ye earth, if I had not known ye duplicate proportion before I could not but have found it now. Between 10 & 11 years ago there was an Hypothesis \of mine/ registred in yor {illeg}|b|ooks, wherein I hinted a cause of gravity towards ye earth Sun & Planets wth ye dependance of ye celestial motions thereon: in wch ye proportion of ye decrease of gravity from ye superficies of ye Planet (thô for brevities sake not there exprest) can be no other then reciprocally duplicate of ye distance from ye center. And I hope I shall not be urge{d} to declare in print \that I understood not/ ye obvious mathematical conditions of my own Hypothesis. But grant I received it afterwards from Mr Hook, yet have I as great a right to it as to ye Ellipsis. For as Kepler knew ye Orb to be not circular but oval & guest it to be Elliptical, so Mr Hook without knowing what I have found out since his letters to me, can know no more but that ye proportion was duplicate quam proximè at great distances from ye center, & only guest it to be so accurately & guest amiss <55v> in extending yt proportion down to ye very center, whereas Kepler guest right at ye Ellipsis. And so Mr Hook found less of ye Proportion then Kepler of ye Ellipsis. There is so strong an objection against ye accurateness of this proportion, yt without my Demonstrations, to wch Mr Hook is yet a stranger, it cannot be beleived by a judicious Philosopher to be any where accurate. And so in stating this business I do pretend to have done as much for ye proportion as for ye Ellipsis & to have as much right to ye one from Mr Hook & all men as to ye other from Kepler. And therefor{illeg}|e| on this account also he must at least moderate his pretenses.

The Proof you sent me I like very well. I designed ye whole to consist of three books, the second was finished last summer being short & only wants transcribing & drawing the cuts fairly. Some new Propositions I have since thought on wch I can as well let alone. The third wants ye Theory of Comets. In Autumn last I spent two months in calculations to no purpose for want of a good method, wch made me afterwards return to ye first Book & enlarge it wth divers Propositions some relating to Comets others to other things found out last Winter. The third I now designe to suppress. Philosophy is such an impertinently litigious Lady that a man had as good be engaged in Law suits as come neare \as have to do with/ her{.} I found it so formerly & now I no sooner come near her again but she gives me warning. The two first books without the third will not so well beare ye title of Philosophiæ naturalis Principia Mathematica & therefore I had altered it to this De motu corporum libri duo: but upon second thoughts I retain ye former title. Twill help ye sale of ye book wch I ought not to diminish now tis yors. The Articles are wth ye largest to be called by that name. If you please you may change ye word to sections, th{illeg}|ô| it be not material. In ye first page I have struck out ye words uti posthac docebitur as referring to ye third book. Which is all at present from

Yor affectionate friend &

humble Servant

Is: Newton.

June 20. 1686.

Since my writing this letter I am told by one who had it from another lately present at one of yor meetings, how that Mr Hook should there make a great stir pretending I had all from him & desiring they would see that he had justice done him. This carriage towards me is very strange & undeserved, so that I cannot forbeare \in stating yt point of justice/ to tell you further, that he has published Borell's Hypothesis in his own name & the asserting of this to himself & completing it as his own, seems to me the ground of all ye stir he makes. Borel did something in it & wrote modestly, he has such a way done nothing & yet written in such a way as if he knew & had sufficiently hinted all but what remained to be determined by ye drudgery of calculations & observations, excusing himself from that labour by reason of his other business: whereas he should rather have excused himself by reason of his inability. For tis plain by his words he knew not how to go about it. Now is not this very fine? Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another {that} does nothing but pretend & grasp at all things must carry away all the invention <55ar> as well of those that were to follow him as of those that went before. Much after the same manner were his letters writ to me, telling me that gravity in descent from hence to ye center of ye earth was reciprocally in a duplicate ratio of ye altitude, that ye figure described by projectiles in this region would be an Ellipsis & that all ye motions of ye heavens were t{illeg}|h|us to be accounted for: & this he did in such a way as if he had found out all & knew it most certainly. And upon this information I must now acknowledge in print I had all from him & so did nothing my self but drudge {illeg} in calculating demonstrating & writing upon ye inventions of this great man. And yet after all, the first of those three things he told me is fals & very unphilosophical, the second is as fals & ye third was more then he knew or could affirm me ignorant of by any thing that past between us in or letters. Nor do I understand by \wt/ right he claims it as his own. For as Borell wrote long before him that by a tendency of ye Planets towards ye sun like that of gravity or magnetism the Planets would move in Ellipses, so Bullialdus wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center, & used that very argument for it by wch you, Sr, in the last Transactions have proved this ratio in gravity. Now if Mr Hook from this general Proposition in Bullialdus might learn ye proportion in gravity, why must this proportion here go for his invention? My letter to Hugenius \wch I mentioned above/ was directed to Mr Oldenburg who used to keep ye Originals. His papers came into Mr Hooks possession. Mr Hook knowing my hand might have ye curiosity to look into that letter & thence take ye notion of comparing ye forces of ye Planets arising from their circular motion & so what he wrote to me afterwards about ye rate of gravity, might be nothing but ye fruit of my own Garden. And its more then I can affirm yt ye duplicate proportion was not \exprest/ in that letter. However he knew it not (i|a|s I gather from his books) till five years after any Mathematician could have told it him. For when Hugenius had told how to find ye force in all cases of circular motion, he had told 'em how to do it in this as w{illeg}|e|ll as all others. And so ye honour of doing it |in| this way is due to Hugenius. For another five \years/ after to claim it as his own invention, is as if some Mechanick who had learnt ye Art of surveying from a Master should afterwards claim the surveying of this or that piece of ground for his own invention & keep a heavy quarter to be in print for 't. But wh{illeg}|at| if this surveyor be a bungler & give in an erroneous survey? M{illeg}r Hook has erred in the invention he pretends to & his error is ye cause of all the stirr he makes. For his extending ye duplicate proportion down to ye center (which I do not) made him correct me & tell me ye rest of his Theory as a new thing to me & now stand upon it that I had all from that his letter: notwithstanding that he had told it to all ye world before & I had seen it in his printed books all but ye proportion. And why should I record a man for an Invention who founds his claim upon an error therein & on that score gives me trouble? He imagins he obliged me by telling me his Theory, but I thought my self disobliged by being upon his own mistake corrected magisterially & taught a Theory wch every body knew & I had a truer notion of then himself. Should a man who thinks himself knowing, & loves to shew it in correcting & instructing others, come to you when you are busy, & notwithstanding your excuse, press discourses upon you & through his own mistakes pr{illeg} correct you & multiply discourses & then make this use of it, to boast that he taught you all he spake & oblige you to acknowledge it & cry out injury & injustice if you do not, I beleive you would think him a man of a strange unsociable temper. Mr Hooks letters in several respects abounded too much wth that humour wch Hevelius & others complain of & therefore he may do well \in time/ to consider whether after this new {pro}vocation I be much more bound {illeg} (in doing him that justice he claims) to make an hon{ourable} <55av> mention of him in {illeg}|p|rint, especially since this is ye third time that he has given me trouble in this kind.

For your further satisfaction in this business, I beg ye favour you would consult yor books for a paper of mine entitled, An Hypothesis explaining ye properties of light. Twas dated Decemb. 7th 1675 & registred in your Book about Ian or Feb following. Not far from ye beginning there is a Paragraph ending wth these words. And as ye Earth so perhaps may the Sun imbibe this spirit copiously to conserve his shining & keep ye Planets from receding further from him & they that will may also suppose that this spirit affords or carries thither the solary fewel & materiall principle if light: And that ye vast ethereal spaces between us & ye stars are for a sufficient repository for this food if ye Sun & Planets. But this if ye constitution if ethereal natures by ye by. In these & ye foregoing words you have ye common cause of gravity towards ye earth Sun & all the Planets, & that by this cause ye Planets are kept in their Orbs about ye Sun. And this is all ye Philosophy Mr Hook pretends I had from his letters some years after, the duplicate proportion only excepted. The preceding words contein ye cause of ye phænomena of gravity as we find it on ye surf{illeg}|a|ce of the earth without any regard to ye various distances from ye center: For at first I designed to write of nothing more. Afterwards, as my manuscript shews, I interlined ye words above cited relating to ye heavens, & in so short & transitory an interlined hint of things, the expression of ye proportion may well be excused. But if you consider ye nature of ye Hypothesis you'l find that \gravity decreases upward &/ can be no other from ye superficies of ye Planet then reciprocally duplicate of ye distance from the center, but downwards that proportion does not hold. This was but an Hypothesis & so to be looked upon only as one of my guesses which I did not rely on: but it sufficiently explains to you why in considering ye descent of a body down to ye center I used not ye duplicate proportion. In ye small ascent & descent of projectiles above ye earth ye variation of gravity is so inconsiderable yt Mathematicians neglect it. Hence ye vulgar Hypothesis with them is uniform gravity. And why might not I as a Mathematician use it frequently without thinking on ye philosophy of ye heavens or beleiving it to be philosophically true?

For Mr Edmund Halley.

< insertion from the right margin of f 55bv >

Mr Newton of
      June 20o 1686

< text from f 55av resumes >

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