Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/473

Rh NEWTON 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.&quot; Three days afterwards, namely, on May 22, 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 June 2, it was again ordered &quot;that Mr Newton s book be printed,&quot; but, instead of sanctioning the resolution of the general meeting to print it at their charge, they added &quot; that Mr Halley undertake the business of looking after it, and printing it at his own charge, which he engaged to do.&quot; In order to explain to Newton the cause of the delay, Halley in his letter of May 22 alleges cnat it arose from &quot;the president s attendance on the king, and the absence of the vice-presidents, whom the good weather had drawn out of town &quot;; 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 pecuniary risk to him self. Halley in his letter to Newton of May 22, found it necessary to inform him of 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 passed a high encomium on 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 &quot; 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,&quot; acknowledging at the same time that, though Newton had the notion from him, &quot; yet the demonstration of the curves generated thereby belonged wholly to Newton.&quot; &quot;How much of this,&quot; Halley adds, &quot; is so, you know best, so like wise 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.&quot; In thus appealing to Newton s candour, Halley obviously wished that some acknowledgment of Hooke should be made. He knew indeed, that before Newton had announced the inverse law Hooke and Wren and himself had spoken of it and discussed it, and therefore justice demanded that, though none of them had given a demonstration of the law, Hooke especially should receive credit for having maintained it as a truth of which he was seeking the demonstration. On June 20, 1686, Newton wrote to Halley the following letter : &quot;Sir, In order to let you know the case between Mr Hooke and me, I give you an account of what passed between us in our letters, so far as I could remember ; for tis long since they were writ, and I do not know that I have seen them since. I am almost confident by circumstances, that Sir Chr. Wren knew the duplicate proportion when I gave him a visit ; and then Mr Hooke (by his book Cometa written afterwards) will prove the last of us three that knew it. I intended in this letter to let you understand the case fully; but it being a frivolous business, I shall content myself to give you the heads of it in short, viz., that I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found the last year, have suspected it did not reach accurately enough down so low ; and therefore in the doctrine of projectiles never used it nor considered the motions of the heavens ; and consequently Mr Hooke could not from my letters, which were about projectiles and the regions descending hence to the centre, conclude me ignorant of the theory of the heavens. That what he told me of the duplicate proportion was erroneous, namely, that it reached down from hence to the centre of the earth. &quot; That it is not candid to require me now to confess myself, in print, then ignorant of the duplicate proportion in the heavens ; for no other reason, but because he had told it me in the case of projectiles, and 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 the experiment of projectiles (rather shortly hinted than carefully described), in compliment to sweeten my answer, expected to hear no further from him ; could scarce persuade myself to answer his second letter ; did not answer his third, was upon other things; thought no further of philosophical matters than his letter* put me upon it, and 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 concludes me then ignorant of the rest of the duplicate proportion, he may as well conclude me ignorant of the rest of that theory I had read before in his books. That in one of my papers writ (I cannot say in what year, but I am sure some time before I had any correspondence with Mr Oldenburg, and that s) above fifteen years ago, the proportion of the forces of the planets from the sun, reciprocally duplicate of their distances from him, is expressed, and the proportion of our gravity to the moon s conatus rccedendi a, centra terras is calculated, though not accurately enough. That when Hugenius put out his Horol. Oscil., a copy being presented to me, in my letter of thanks to him I gave those rules in the end thereof a particular commendation for their usefulness in Philosophy, and added out of my aforesaid paper an instance of their usefulness, in comparing the forces of the moon from the earth, and earth from the sun ; in determining a problem about the moon s phase, and putting a limit to the sun s parallax, which shews that I had then my eye upon comparing the forces of the planets arising from their circular motion, and understood it.; so that a while after, when Mr Hooke propounded the problem solemnly, in the end of his attempt to prove the motion of the earth, if I had not known the duplicate proportion before, I could not but have found it now. Between ten and eleven years ago there was an hypothesis of mine registered in your books, wherein I hinted a cause of gravity towards the earth, sun, and planets, with the dependence of the celestial motions thereon ; in which the proportion of the decrease of gravity from the superficies of the planet (though for brevity s sake not there expressed) can be no other than reciprocally duplicate of the distance from the centre. And I hope I shall not be urged to declare, in print, that I under stood not the obvious mathematical condition of my own hypo thesis. But grant I received it afterwards from Mr Hooke, yet have I as great a right to it as to the ellipsis. For as Kepler knew the orb to be not circular but oval, and guessed it to be elliptical, so Mr Hooke, without knowing what I have found out since his letters to me, can know no more, but that the proportion was duplicate quam proximo at great distances from the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre, whereas Kepler guessed right at the ellipsis. And so Mr Hooke found less of the proportion than Kepler of the ellipsis. &quot; There is so strong an objection against the accurateness of this proportion, that without my demonstrations, to which Mr Hooke is yet a stranger, it cannot be believed by a judicious philosopher to be any where accurate. And so, in stating this business, I do pretend to have done as much for the proportion as for the ellipsis, and to have as much right to the one from Mr Hooke and all men, as to the other from Kepler ; and therefore on this account also he must at least moderate his pretences. &quot; The proof you sent me I like very well. I designed the whole to consist of three books; the second was finished last summer being short, and only wants transcribing, and drawing the cuts fairly. Some new propositions I have since thought on, which I can a& well let alone. The third wants the theory of comets. In autumn last I spent two months in calculations to no purpose for want of a good method, which made me afterwards return to the first book, and enlarge it with divers propositions, some relating to comets, others to other things, found out last winter. The third I now design to suppress. Philosophy is such an impertinently litigious- lady, that a man has as good be engaged in lawsuits, as have to do- with her. I found it so formerly, and now I am no sooner come near her again, but she gives me warning. The two first books, without the third, will not so well bear the title of Philosophise, Naturalis Principia Mathematica ; and therefore I had altered it to this, DC Motu Corporum libri duo. &quot; But, upon second thoughts, I retain the former title. Twill help the sale of the book, which I ought not to diminish now tis yours. The articles are, with the largest, to be called by that name ; if you please you may change the word to sections, though it be not material. In the first page, I have struck out the words uti posthac docebitur, as referring to the third book; which is all at present, from your affectionate friend, and humble servant, &quot;Is. NEWTOX.&quot;