Letter to Edmund Halley about Newton's correspondence with Huygens on vis centrifuga Isaac Newton c. 806 words The Newton Project Falmer 2014 Newton Project, University of Sussex

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 27 July 1686, in English with a little Latin, c. 815 words, 3 pp. 3 pp.

in English with a little Latin

Published in H.W. Turnbull (ed), The Correspondence of Isaac Newton, vol. 2 (Cambridge: 1960), p. 446

 EL/N1/57, Royal Society Library, London, UK UKLondonRoyal Society Library EL/N1/57 27 July 1686 England English Latin Holograph Edmund Halley Unknown Cataloguer (1) Unknown Cataloguer (2) MathematicsCorrespondence Transcription by Daniele Cassisa Code audited by Michael Hawkins
57Newton 1657

Sr.Sir

Yesterday I unexpectedly struck upon a copy of yethe Letter I told you of to Hugenius. Tis in yethe hand of one Mr John Wickins who was then my chamber fellow & is now Parson of Stoak Edith neare Monmoth & so it is authentick. It begins thus being directed to Mr Oldenburg:

"Sr.Sir

I received your letters wthwith M. Hugens kind present, wchwhich I have viewed wthwith great satisfaction, finding it full of very subtile & useful speculations very worthy of yethe Author. I am glad that we are to expect another discourse of yethe Vis centrifuga, wchwhich speculation may prove of good use in natural Philosophy & Astronomy as well as Mechanicks. Thus for instance, if yethe reason why yethe same side of yethe moon is ever towards yethe earth be yethe greater conatus of yethe other side to recede from it, it will follow (upon supposition ofyethe earths motion about yethe Sun) that yethe greatest distance of yethe sun from yethe earth is to yethe greatest distance of yethe Moon from yethe earth, not greater then 10000 to 56 & therefore yethe parallax of yethe Sun not less then 5610000 of yethe Parallax of yethe Moon: because were yethe Sun's distance less in proportion to that of yethe Moon she would have a greater conatus from yethe Sun then from yethe earth. I thought also ytthat sometime that yethe Moons Libration might depend upon her conatus from yethe Sun & earth compared together till I apprehended a better cause."

Thus far this Letter concerning the vis centrifuga. The rest of it for yethe most part concerning colours, is printed in yethe Ph. Transactions of July 21 1673. Num. 96. Now from these words its evident ytthat I was at that time versed in the Theory of yethe force arising from circular motion, & had an eye upon yethe forces of yethe Planets, knowing how to compare them by the proportions of their periodical revolutions & distances from yethe center they move about, an instance of wchwhich you have here in yethe comparison of yethe forces of yethe Moon arising from her menstrual motion about yethe Earth & annual about yethe Sun. So then in this Theory I am plainly before Mr Hook. For he about a year after in his Attempt to prove yethe Motion of yethe Earth, declared expressly that yethe degrees by wchwhich gravity decreased he had not then experimentally verified, that is he knew not how to gather it from phænomena, & therefore he there recommends it to yethe prosecution of others. Now though I do not find yethe duplicate proportion exprest in this letter (as I hoped it might) yethet if you compare this passage of it here transcribed wthwith ytthat Hypothesis of mine registred by Mr Oldenburg in your Book, you will see ytthat I then understood it. For I there suppose that yethe descending spirit acts upon bodies here on yethe superficies of yethe earth wthwith force proportional to the superficies of their parts, wchwhich cannot be unless yethe diminution of its velocity in acting upon yethe first parts of any body it meets with be recompensed by the increase of its density arising from that retardation. Whether this be true is not material. It suffices that 'twasit was yethe Hypothesis. Now if this spirit descend from above wthwith uniform velocity, its density & consequently its force will be reciprocally proportionall to yethe square of its distance from yethe center. But if it descend with accelerated motion, its density will every where diminish as much as its velocity increases, & so its force (according to yethe Hypothesis) will be yethe same as before that is still reciprocally as yethe square of its distance from yethe center. In short as these things compared together shew that I was before Mr Hook in what he pretends to have been my Master so I learnt nothing by his letters but this that bodies fall not only to yethe east but also in orour latitude to yethe south. In yethe rest his correcting & informing me was to be complain'ded of. And thô his correcting my Spiral occasioned my finding yethe Theorem by wchwhich I afterward examined yethe Ellipsis; yet am I not beholden to him for any light into ytthat business but only for yethe diversion he gave me from my other studies to think on these things & for his dogmaticalnes in writing as if he had found yethe Ellip motion in yethe Ellipsis, wchwhich inclined me to try it after I saw by what method it was to be done. SrSir I am YorYour affectionate Friend & humble Servant Is. Newton. July 27th 1686. Mr Newton of July 27 1686 For Mr Edmund Halley to be left with Mr Hunt at Gresham College London 2