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Sr.

Yesterday I unexpectedly struck upon a copy of ye Letter I told you of to Hugenius. Tis in ye 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 Oldenbur{g:}

"Sr.

I received your letters wth M. Hugens kind present, wch I have viewed wth great satisfaction, finding it full {illeg}|of| very subtile {illeg}|&| useful speculations very worthy of ye Author. I am glad that {illeg}|w|e are to expect another discourse of ye Vis centrifuga, wch speculation {illeg}|m|ay p{illeg}|ro|ve of good use in natural Philosophy & Astronomy as well as Mechanicks. Thus for instance, if ye reason why ye same side of ye moon is ever towards ye earth {illeg}|b|e ye greater conatus of ye other side to recede from it, it will follow (upon supposition ofye earths motion about ye {illeg}|S|un) that ye greatest distance of ye sun from ye earth is to ye greatest distance of ye Moon from ye earth, not greater then 10000 to 56 & therefore ye parallax of ye Sun n{illeg}|o|t {illeg}|l|ess then $\frac{56}{10000}$ of ye Parallax of ye Moon: because were ye Sun's distance less in proportion to that of ye Moon she would have a greater conatus from ye Sun then from ye earth. I thought also yt sometime that ye Moons Libration might depend upon her conatus from ye Sun & earth compared together till I apprehended a better cause."

Thus far this Letter concernin{illeg}|g| the vis centrifuga. The rest of it for ye most part concerning colours, is printed in ye Ph. Transactions of July 21 1673. Num. 96. Now from these words its evident yt I was at that time versed in the T{illeg}|h|eory of ye force arising from circular motion, & had an eye upon ye forces of ye Planets, knowing how to compar{illeg}|e| them by the proportions of their periodical revolutions & distances from ye center they move about, an instance of wch you have here in ye comparison of ye forces of ye Moon arising from her menstrual motion about ye Earth & annual about ye Sun. So then in this Theory I am plainly before Mr Hook. For he about a year after in his Attempt {illeg}|t|o prove ye Motion of ye Earth, declared expressly that ye degrees by wch gravity d{illeg}|e|creased he had not then experimentally {illeg}|v|erifi{illeg}|e|d, that is he knew not how to gather it from phænomena, & therefore he there recommend{illeg}|s| it to ye prosecution of others.

Now though I do not find ye duplicate proportion exprest in this letter (as I hoped it might) yet if you compare this passage of it here transcrib{ed} wth yt Hypothesis of mine registred by{illeg} Mr Olden{illeg}|b|urg in your Book, you will see yt I then understood it. For I there suppose that ye descending spirit acts upon bodies here on ye superficies of ye earth wth force proportional to the superficies of their parts, wch cannot {illeg}|b|e unless ye diminution of its velocity in acting upon ye first parts of any body it <57v> meets with be recompensed by the increase of its density arising from that retardation. Whether this be true is not material. It suffices that 'twas ye Hypothesis. Now if this spirit descend \from above/ wth uniform velocity, its density & consequently its force will be reciprocally proportionall to ye s{illeg}|q|uare of its distance from ye 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 ye Hypothesis) will be ye same as before that is |still| reciprocally as ye square of its distance from ye 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 ye east but also in or latitud{e} to ye south. {illeg} In ye rest his correcting & informing me was to be complain'd of. And thô his correcting my Spiral occasioned my finding ye Theorem by wch I afterward examined ye Ellipsis; yet am I not beholden to him for any light into yt business but only for ye diversion he gave me from my other studies to think on these things & for his dogmaticalnes in writing as if he had found ye Ellip motion in ye Ellipsis, wch inclined me to try it after I saw by what method it was to be done. Sr I am

Yor affectionate Friend

& humble Servant

Is. Newton.

July 27th 1686.

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Mr Newton of July 27
1686

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For Mr Edmund Halley
to be left with Mr Hunt
at Gresham College

London

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