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{in} d. 28 jun. 73.

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LB. 6. 152.
(Pr. Trans: 96.)

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Mr Newton's Letter upon the \his/ receipt of Monsr Hugen'ss {sic} Book de Motu Pendulorum, together wth his \some/ considerations upon it; as also an Answer to \ye same/ M. Hugens's Letter of June 10. 1673; in wch Answer ye \he further explains his/ New Theory of Light and Colors, and particularly yt of Whiteness, etc.

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I received yor letters wth M. Hugens kind prsent, wch I have viewed wth great satisfaction, finding it full of very subtile & usefull speculations very worthy of ye Author. I am glad yt we are to expect another discours of ye vis centrifuga, which speculation may prove of good use in naturall Philosophy & Astronomy as well as mechanicks. Thus for instance if the reason why the same si{illeg}|d|e of ye Moon is ever towards ye earth be ye greater conatus of ye other side to recede from it; it will follow (upon supposition of ye Earths motion about ye S{illeg}|u|n) that ye greatest distance of ye sun from ye earth is to ye greatest distance of ye Moon from ye earth, not greater then 100000 to 55912 10000 to 56 & therefore the parallax of ye Sun not less then 5610000 of ye Parallax of ye Moon: Because were the sun's distance less in proportion to yt of ye Moon, she would have a greater conatus from ye sun then from ye earth. I thought also \sometime/ that ye moons libration might b|d|epend upon yt her conatus from ye {illeg} Sun & Earth compared together, till I apprehended a better cause.

In ye Demonstration of ye 8th Proposition, d|D|e descensu gravium, there seems to be an illegitimate supposition, namely yt ye flexures at B & C {illeg}|do| not hinder ye motion of ye descending body. For in reality they will hinder it, so yt a body wch descends from A shall not acquire so great velocity when arrived to D as one wch descends from E. If this supposition be made becaus a body descending by a curve line meets with no such opposition, & this Proposition is laid down in order to ye contemplation of motion in curve lines: then it should have been shown that though rectilinear flexures do hinder, yet ye infinitely little flexures which are in curves, though infinite in number, do not at all hinder the motion{.}

The rectifying curve lines by that way wch M. Hugens calls Evolution, I \have/ been sometimes considering also, & have met wth a way of resolving it wch seems more ready & free from ye trouble of calculatio then that of M. Hugens. If he please I will send it him. The Problem also is capable of being improved by being propounded thus more generally.

"Curvas invenire quotascunqꝫ quarum longitudines cum propositæ alicujus Curvæ longitudine, vel cum area ejus ad {illeg}|d|atam lineam applicata, comparari possunt.{"}

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[1]Mr Newtons Answer to ye foregoing letter further explaining his Theory of Light and Colors, and particularly yt of Whitenes; together wth his continued hopes of perfecting Telescopes by Reflections rather than Refractions.

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Concerning the bussiness of colours; in my saying that when M. Hugens \Monsr/ \M. Hugens/ hath shown how White may be produced out of two uncompounded colours, I will tell him why he can conclude nothing from that; my meaning was, that such a White, (were there any such,) would have different properties from the White, wch I had respect to, when I described my Theory, that is, from ye white of ye Sun's immediate light, of ye ordinary objects of or senses, & of all white Phænomena that have hitherto faln under my observation. And those different properties would evince it to be of a different constitution: Insomuch that such a production of white {illeg}would be so <47v> far from contradicting, that it would rather illustrate & confirm my Theory; because by ye difference of that from other whites it would appear that other whites are not compounded of onely two colours like that. And therefore if M. Hugens \Monsr N./ would prove any thing, it is requisite that he do not onely produce out of white two primitive [2]colours a white wch to ye naked eye shall appear like other whites, but also shall agree wth them in all other properties.

But to let you understand wherein such a white would differ from other whites & why from thence it would follow that other whites are otherwise compounded, I shall lay down this position

That a compounded colour can be resolved into no more simple colours
then those of wch it is compounded.

This seems to be self evident, & I have also tryed it severall ways, & particularly by this wch follows: Let α represent an p|o|blong piece Figure of white paper \about 12 or 14 of an inch broad &/ illuminated in a dark room with a mixture of two colours as little compounded cast upon it from two Prisms, suppose a deep blew & scarlet, wch are \must/ severally \be/ as uncompounded as th{illeg}|e|y can conveniently be made. Then at a convenient distance, suppose of six or eight yards, view it through a clear triangular glass or crystall Prism held parallel to ye paper {illeg}|&| you shall see the two colours parted from one another in the fashion of two images of ye paper as they are represented at β & γ where suppose β the scarlet & γ ye blew, without green or any other colour between them.

Now from the afforesaid Position I deduce these two conclusions: 1 That if there were found out a way to compound white of {illeg}|t|wo simple colours onely, that white would be again resolvable into no more then two. 2dly That if other whites (as that of the suns light &c) be resolvable into more then two simple colours (as I find by experiment that they are) then they must be compounded of more then two.

To make this plainer, suppose that A represents a white body illuminated by a direct beam of the sun transmitted through a small hole into a dark room, & α such another body illuminated by a mixture of two simple colours wch if possible [3]may make it also appear of a white colour exactly like A. Then at a convenient distance view these two whites through a Prism & A will be changed into a series of all colours, r|R|ed, y|Y|ellow, g|G|reen, Blew, Purple with all their intermediate degrees succeeding in order from B to C. But α, according to the afforesaid experiment, will onely yeild those two colours of wch '{illeg}|tw|as compounded, & those not conterminate like ye colours at BC but separate from one another, as at β & γ, by means of the different refrangibility of ye rays to wch they belong. And thus by comparing these two whites, they would appear to be of a different constitution & A to consist of more colours then α. So that what M. Hugens \Monsr N./ contends for, would rather advance my Theory by the access of a new kind of white then conclude against it. But I see no hopes of compounding such a white.

As for M. Hugens \Monsr N. his/ expression that I maintain my doctrine wth some concern I confess it was a little ungratefull to me to meet wth objections wch had been answered before, without having the least re{illeg}|a|son given me why those a{illeg}|n|swers were insufficient. The answers wch I speak of are in ye Transactions from pag 5093 to pag 5102. And particularly in pag 5095, to show that there are other simple colours besides blew & yellow, I instance in a simple or homogeneal green such as cannot be made by mixing blew & yellow or any other colours. And there also I show why, supposing that all colours might be produced out of two, yet it would not follow that those two are the onely originall colours. The reasons i|I|n desire you would compare with what hath <47ar> been now said of white. And so the necessity of all colours to produce white might have appeared by ye experiment pag 5097 where I say that if any colour at ye Lens be intercepted ye whiteness (wch is compounded of them all) will be changed into (ye result of) the other colours.

However, since there seems to have happened some misunderstanding between us, I shall indeavour to explain my self a little further in these things accor{illeg}|d|ing to the following method.


1. I call that Light homogeneal, similar or uniform whose rays are equally refrangible.

2. And that heterogeneal whose rays are unequally refrangible.

Note. There are but three affections of light in wch I have observed its rays to differ. viz: Refrangibility, Reflexibility & Colour, & those rays wch agree in refrangibility agree also in the other two & therefore may well be defined homogeneal: especially since men usually call those things homogeneal wch are so in all qualities that come under their knowl{illeg}|e|dg, though in other qualities that their knowledg extends not to there may possibly be some heterogeneity.

3. Those colours I call simple|, or| homogeneal, which are exhibited by homogeneal light.

4{.} And those compound or heterogeneal wch are exhibited by heterogeneal light.

5{.} Different colours I call not, onely the more eminent species, red, yellow, green, blew, purple, but all other gradations the minutest gradations: much after ye same manner that not onely the more eminent degrees in musick but all ye least gradations are esteemed different sounds.


1. The Sun's light consists of rays differing by indefinite degrees of refrangibility.

2. Rays wch differ in refrangibility, when parted from one another do proportionally differ in the colours wch they exhibit. These two Propositions are matter of fact.

3. There are as many simple or homogeneal colours as degrees of refrangibility. For to every degree of refrangibility belongs a different colour by Prop: 2. And that colour is simple by Def: 1, & 3.

4. Whiteness such as is \in all respects like/ that of the Sun's immediate light & of all ye usuall objects of or senses cannot be compounded of two simple colours alone. For such a composition must be made by rays that have onely two degrees of refrangibility by Def. 1, & 3.; & therefore it cannot be like that of the suns light by Prop. 1; Nor for ye same reason like that of ordinary white objects.

[4]5. That Whiteness in all respects like that of the Sun's immediate light may \cannot/ be compounded of simple colours, there are requisite \without/ an indefinite variety of them. For to such a composition there are requisite rays indued wth all ye indefinite degrees of refrangibility by Prop. 1. And those infer as many simple colours, by Def. 1 & 3. & Prop. 2 & 3{.}

To {illeg} \make these a little plainer/, I have added also the Propositions that follow.                                {follow.}

7|6|. The rays of light do not act on one another in passing through the same Medium. This appeares by several passages in ye Transactions pag. 5097, 5098, 5100, & 5101, & is capable of further proof.

7. The rays of light suffer not any change of their qualities from refraction{.}

8. Nor afterwards from the adjacent qu{illeg}|i|et Medium. These two Propositions are manifest de facto in homogeneal light, whose colour & refrangibility is not at all <47av> changeable either by refraction or by the \con/termination of a quiet Medium. And as for heterogeneal light, it is but an aggregate of severall sorts of homogeneal light no one sort of wch suffers any more alteration then if it were alone becaus the rays act not on one another by Prop. 6. And therefore the aggregate can suffer none. These two Propositions also might be further proved apart by Experiments, too long to be here described.

9. There can no homogeneal colours be educed out of light by refraction wch were not commixt in it before: Because by Prop 7, & 8, Refraction changeth not ye qualities of ye rays, but onely separates those wch have divers qualities, by means of their different Refrangibility{.}

10. The sun's light is an aggregate of an indefinite variety of homogeneal colours; by Prop 1, 3, & 9. And hence it is, that I call homogeneal colours also primitive {illeg}|o|r original. And thus much concerning colours.

M. Hugens \Monsr N./ has tho{illeg}|u|ght fit to insinuate yt ye aberration of rays (by their different refrangibility) is not so considerable a disadvantage in glasses as I seemed to make be willing to make men beleive when I propounded concave mirrors as ye onely hopes of perfecting Telescopes. But if he please to take his pen & compute the{illeg} errors of a Glass & Speculum that [5]collect rays at equall distances, {illeg}|h|e will find how much he is mistaken, & that I have not been extravagant, as he imagins, in preferring reflexions. And as for what he adds says of ye difficulty of ye praxis I know it is very difficult, & by those ways wch he attempted it I beleive it next to an impossibility \unpracticable/. But there is a way insinuated in ye Transactions pag. 3080 whereby {illeg} by wch it is not improbable but that as much may be done in large Telescopes, as I have thereby done in short ones, but yet not without more then ordinary diligence & curiosity.

Pray wth these Notes return my thanks to M. Hugens for his book.

By a former letter of yors I was a little dubious whether M. Slusius might not apprehend, by wt you w{illeg}|r|ote to him concerning me, yt I pretended to his Method of drawing tangents; untill I understood by M. Collins yt you signifyed to him yt you thought it here of a later date. For {illeg} it seems to me that he was acquainted wth it some yeares before he printed his Mesolabum & consequently before I understood it. But if it had been otherwise yet since he first imparted it to ye worl his friends & ye world, it ought deservedly to be accounted his. As for ye Methods they seem to be \are/ ye same, though I beleive derived from different principles. And|But| I know not whether his Principles afford it so generall as mine wch extend{illeg}|s| to Equations affected wth surd terms, wthout reducing them to another form. But if you please let this pass.

The incongruities you speak of, I pass by. But I must, as formerly, signify to you yt I intend to be no further sollicitous about matters of Philosophy. And therefore I hope you will not take it ill if you find me {ever {refusing}{refraining}} doing any thing more in yt kind, or rather yt you will favour me in my determination by preventing so far as you can conveniently any objections or other philosophicall letters that may concern me. For your profer about ye my Quarterly payments I thank you. But I would not have you trouble yor self to get them excused if you have not done it already. And now being tired with this long letter, I must in hast write my self

Yor humble Servant

I. Newton

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Cambridg. june {sic} 23. 73.

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H Relation

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[1] {No 6086}|Pr. 4.|

[2] {illeg}|N| 6 {8. 6.}{p. 6.}{n. 6.}

[3] N 6|7|

[4] Oooooo. 6091

[5] N 6 P 2 6092

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