Oeuvres complètes. Tome VII. Correspondance 1670-1675

N^o 1956.
Is. Newton à H. Oldenburg.
3 Juillet 1673.
Appendice I au No. 1955.

La lettre se trouve à Londres, Royal Society.
Elle a été imprimée par Horsley¹⁾.

Mr. Newton, june 23. 73²⁾.

I receiued y^r lettres w^th Monsr. Hugens his kind present, for w^ch I pray you return him my humble thanks. I haue view'd it w^th great satisfaction, finding

1) Dans son ouvrage:
Isaaci Newtoni opera quae exstant omnia. Commentariis illustrabat Samuel Horsley, LL. D.R. SS. Reverendo admodum in Christo Patri Roberto Episcopo Londinensi a Sacris. Londini: Excudebat Joannes Nichols. m dcc lxxix-m dcc lxxxv. 5 Tomes in-4^o.

2) La lettre qui suit a été considérée par Newton comme ayant été écrite à Huygens lui-même. C'est ce qui résulte de sa célèbre correspondance avec Halley, au sujet de la découverte de l'attraction universelle, publiée par Brewster dans l'Appendice au premier volume de ses Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, pp. 437 à 456, et reproduite par M.W.W. Rouse Ball dans sa monographie: An essay on Newton's ‘Principia’. London, Macmillan and C^o. and New York 1893, pp. 153-174.
Dans sa lettre à Halley, du 20 juin 1686, Newton dit:
‘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 (c'est-à-dire les lois de la force centrifuge, données par Huygens) 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 shows that I had than my eye upon 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.’
Dans le post-scriptum de cette même lettre Newton dit encore:
‘My letter to Hugenius, which I mentioned above, was directed to Mr. Oldenburg, who used to keep the originals’.
Enfin, dans sa lettre à Halley, datée du 27 juillet 1686, Newton écrit:
‘Sir, Yesterday I unexpectedly struck upon a copy of the letter I told you of, to Hugenius. 'T is in the hand of one Mr. John Wickins, who was then my chamber-fellow, and is now parson of Stoke Edith near Monmouth and so is authentic. It begins thus, being directed to M. Oldenburg.
Sir, I receiv'd your letters, with M. Hugen's kind present, which I have viewed with great satisfaction, finding it full of very subtile and useful speculations very worthy of the author. I am glad that we are to expect another discourse of the vis Centrifuga, which speculation may prove of good use in Natural Philosophy and Astronomy, as well as Mechanics. Thus, for instance if the reason, why the same side of the moon is ever towards the earth, be the greater conatus of the other side to recede from it, it will follow (upon supposition of the earth's motion about the sun), that the greatest distance of the sun from the earth is to the greatest distance of the moon from the earth, not greater than 10000 to 56; and therefore the parallax of the sun not less than 56/10000 of the parallax of the moon, because were the sun's distance less in proportion to that of the moon, she would have a greater conatus from the sun than from the earth. I thought also some time that the moon's libration might depend upon her conatus from the sun and earth compared together till I apprehended a better cause.’
Après cette citation, Newton continue:
‘Thus far this letter concerning the Vis Centrifuga. The rest of it for the most part concerning colours, is printed in the Phil. Trans. of July 21, 1673, N^o. 96. Now from these words it's evident, that I was at that time versed in the theory of the force arising from circular motion, and had an eye upon the forces of the planets, knowing how to compare them by the proportion of their periodical revolutions and distances from the centre they move about: an instance of which you have here in the comparison of the forces of the moon arising from her menstrual motion about the earth, and aunual about the sun. So then in this theory I am plainly before Mr. Hooke. For he about a year after, in his Attempt to prove the Motion of the Earth, declared expressly that the degrees, by which gravity decreased, he had not then experimentally verified, that is, he knew not how to gather it from phenomena, and therefore he there recommends it to the prosecution of others.
Now, though I do not find the duplicate proportion expressed in this letter (as I hoped it might), yet if you compare this passage of it here transcribed, with that hypothesis of mine, registered by Mr. Oldenburg in your book (voir Birch, History, III, p, 251), you will see that I then understood it. For I there suppose that the descending spirit acts upon bodies here on the superficies of the earth with force proportional to the superficies of their parts; which cannot be, unless the diminution of its velocity in acting upon the 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 't was the hypothesis. Now if this spirit descend from above with uniform velocity, its density and consequently its force, will be reciprocal proportional to the square of its distance to the centre. But if it descend with accelerated motion, its density will every-where diminish as much as its velocity increases; and so its force (according to the hypothesis) will be the same as before, that is still reciprocally as the square of its distance.
In short, as these things compared together shew, that I was before Mr. Hooke in what he pretends to have been my master,’ etc.
On voit que le principal argument de Newton en faveur de sa priorité vis-à-vis de Hooke consiste dans le passage de sa lettre à Huygens que nous venons d'imprimer en italiques.
On remarquera que ce passage manque dans notre texte, c'est-à-dire dans la copie qu'Oldenburg a transmise à Huygens. Il est difficile d'expliquer une omission aussi importante. Elle est absolument contraire aux habitudes d'Oldenburg. Toutes les copies de lettres qu'Oldenburg a transmises à Huygens ont été reconnues exactes. Ce n'est que dans de rares exceptions qu'Oldenburg omet une phrase, soit l'exorde on les compliments de la fin d'une lettre, soit quelque détail personnel, une fois une phrase qui aurait pu blesser Huygens (Voir la Lettre N^o. 1920, note 5). Or, le passage, omis ici par Oldenburg, paraît trop long pour pouvoir être sauté par inadvertance et n'a certainement rien de personnel; de plus Newton, au commencement de sa lettre d'envoi (l'Appendice N^o. 1957), recommande expressément de transmettre ses notes à Huygens.
Si, comme il est probable, on doit exclure la conjecture qu'Oldenburg ait omis le passage soit par inadvertance, soit de son propre gré, il faudrait admettre qu'il l'a supprimé par suite d'instructions reçues.
Quelle est la main qui a soustrait aux yeux de Huygens les réflexions de Newton sur la force centrifuge, suscitées à la lecture de l'Horologium Oscillatorium, et dont Newton a voulu faire part à l'auteur?
Sur l'authenticité tant de la lettre d'Oldenburg que de celle de Newton, transmise en copie à Halley, il ne peut rester aucun doute. La lettre originale de Newton est conservée dans les collections de la Société Royale, d'où elle a été reproduite pour la première fois par Horsley.
Nous mettons sous les yeux de nos lecteurs, dans les planches qui suivent cette page, les reproductions 1^o. de la première partie de la lettre d'Oldenburg à Huygens, où manque le passage de la lettre de Newton, ensuite celles de deux pages de la lettre originale de Newton à Oldenburg, savoir: 2^o. le commencement de la lettre destinée à être communiquée à Huygens, et 3^o. la fin de la lettre de Newton plus particulièrement destinée à Oldenburg lui-même, l'Appendice N^o. 1957. Nous devons à la libéralité de la Société Royale de Londres et aux soins bienveillants de M. Harrison, secrétaire assistant de cette Société, d'avoir pu nous procurer les photographies de ces deux pages de l'unique pièce de correspondance entre Newton et Huygens, dont, jusqu'ici, on ait connaissance.
L'en-tête de la lettre de Newton, le n^o. 2, est de la main d'Oldenburg. La plus grande partie de la première page a été biffée et un nouveau titre inscrit au commencement de la partie qui a paru dans les Phil. Trans. Ce dernier titre est identique à celui de ce journal. La dernière partie de la lettre, celle qui forme la Lettre N^o. 1957 de notre texte, est de nouveau biffée. Il paraîtrait qu'on ait voulu rendre illisibles les sept deruières lignes, exprimant les sentiments personnels de Newton et se rapportant au payement de sa cotisation comme membre de la Société Royale. Elles ont, toutefois, été imprimées par Edleston et Brewster.

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it full of very subtile and usefull speculations very worthy of y^e Author. I am glad, we are to exspect another discours of y^e Vis centrifuga, w^ch speculation may prove of good use in natural Philosophy and Astronomy, as well as Mechanicks.

In the Demonstration of prop. 8. de Descensu gravium, there seems to be an

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Illegitimat supposition, namly, That y^e flexures at B and C do not hinder y^e motion of y^e descending body³⁾. For in reality they will hinder it, so y^t a body, w^ch descends from A, shall not acquire so great velocity when arrived to D, as one w^ch descends from E. If this supposition be made, because a body descending by a curve line meets w^th no such opposition, and this Proposition is laid down in order to y^e contemplation of motion in curve lines; then it should have been shown, y^t though rectilinear flexures do hinder, yet the infinitly litle flexures w^ch are in curves, though infinit in number, do not at all hinder the motion.

3) Dans la proposition VIII de l'Horologium Oscillatorium, Huygens démontre que la vitesse acquise dans la chute le long d'une série de plans inclinés contigus est la même que celle due à la chute directe de la même hauteur. Dans sa démonstration il dit: ‘cum flexus ad B nihil obstare motus ponatur.’

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The rectifying curve lines by y^t way w^ch M. Hugens calls Evolution, I haue been sometimes considering also, and haue met w^th a way of resolving it w^ch seemes more ready and free from y^e trouble of calculation than y^t of M. Hugens. If he please, I will send it him^a). The Problem also is capable of being improved by being propounded thus more generally;

‘Curvas invenire quotascunque, quarum longitudines cum propositae alicujus curvae longitudine, vel cum area ad datam lineam applicatâ, comparari possunt.

⁴⁾ Concerning y^e busines of Colors, I have this to return, that in my saying, when M. Hugens had shown, how white may be produced out of two vncompounded colors, I would tell him, why he can conclude nothing from that; my meaning was, That such a white (were there any such) would haue different proporties from the white of y^e Sun's immediat light, of y^e ordinary objects of our Senses, and of all white phaenomena y^t haue hitherto falne vnder my observation. And those different properties would evince it to be of a different constitution; In somuch y^t such a production of white would be so far from contradicting, y^t it would rather illustrate and confirme my Theory; because by y^e difference of that from other whites it would appear, y^t other whites are not compounded of only two colors like that. And therefore, if M. Hugens would prove any thing, 't is

a) Sur cecy vous n'avez qu'a me faire savoir votre ordre [Oldenburg].

4) La partie qui suit a été publiée par Oldenburg dans les Phil. Trans. N^o. 96, du 21 juillet 1673 [V. st.]. On y a remplacé, par la lettre N, le nom de Huygens, de même que dans la pièce N^o. 1931.

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N^o. 1. Première page de la lettre de H. OLDENBURG à CHR. HUYGENS, N^o. 1955 de la Correspondance.

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N^o. 2. Première page de la lettre de Is. NEWTON à H. OLDENBURG, N^o. 1956 de la Correspondance.

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N^o. 3. Dernière page de la lettre de Is. NEWTON à II. OLDENBURG, N^os. 1956 et 1957 de la Correspondance.

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requisite y^t he do not only produce out of two Primitive colors a White, w^ch to y^e naked ey shall appear like other whites, but also shall agree w^th him in all other proporties.

But to let you vnderstand, wherein such a white would differ from other whites, and why from thence it would follow, y^t other whites are otherwise compounded, I shall lay down this position;

‘That a compounded colour can be resolved into no more simple colors than those of wich it is compounded’.

This seems to be self-evident; and I haue also tryed it several ways, and particularly



by this w^ch follows. Let α represent an oblong piece of white papier about ½ or ¼ of an inch broad, and illuminated in a dark room with a mixture of two colors cast vpon it from two Prismes, suppose a deep Blew and Scarlet, w^ch must severally be as vncompounded as they can conveniently be made. Then at a convenient distance, suppose of 6 or 8 yards, view it through a clear triangular glass or crystal Prism, held parallel to y^e paper and you shall see y^e two colors parted from one another in y^e fashion of two images of y^e paper, as they are represented at β and γ, where suppose β y^e scarlet, and γ y^e blew without green or any other colour between y^m.

Now from y^e afores^d Position I deduce these two conclusions: 1. That if there were found out a way to compound white of 2 simple colors only, y^t white would be again resolvable into no more than two. 2. That if other whites (as y^t of y^e Suns light etc) be resolvable into more than two simple colors (as I find by Experient that they are) then they must be compounded of more than two.

To make this plainer, suppose, y^t A represents a white body illuminated by a direct beam of y^e sun transmitted through a smal hole into a dark room, and α such an other body illuminated by a mixture of two simple colors, w^ch if possible, may make it also appear of a white color exactly like A. Then at a convenient distance view these two whites through a Prisme, and A will be changed into a series of all colors, Red, Yellow, Green, Blew, Purple, w^th their intermediat degrees succeeding in order from B to C. But α, according to y^e afores^d Experiment, will only yield those two colors of w^ch 'twas compounded, and those not conterminat like y^e colors at B C but separate from one another, as at β and γ by means of y^e different refrangibility of y^e rays to w^ch they belong. And thus by comparing these two whites, they would appear to be of a different constitution, and A to consist of more colors than α. So y^t what M. Hugens contends for, would rather advance my Theory by y^e access of a new kind of white, than conclude ag^st it. But I see no hopes of compounding such a white.

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As for M. Hugens expression, y^t I maintain my doctrine with some concern⁵⁾, I confess it was a litle vngratefull to me to meet w^th objections w^ch had been answer'd before, wi^thout having y^e least reason giuen me why those Answers were insufficient. The Answers, w^ch I speake of, are in the Transactions⁶⁾ from pag. 5093 to 5102; And particularly in p. 5095, to show y^t there are other simple colors besides Blew and Yellow, I instance in a simple or homogeneal Green, such as cannot be made by mixing Blew and Yellow or any other colors. And there also I show, why, supposing y^t all colors might be produced out of two, yet it would not follow, y^t those two are y^e only original colors. The reasons I desire you would compare w^th what hath been now said of White. And so y^e necessity of all colors to produce white might haue appear'd by y^e Experiment p. 5097. where I say, y^t if any color at y^e Lens be intercepted, y^e whitenes (w^ch is compounded of them all) will be changed into (y^e result of) other colors.

However, since there seems to haue happen'd some misvnderstanding between us, I shall endeavor to explaine myself a litle further in these things according to y^e following method.

5) Voir la Lettre N^o. 1945, qu'Oldenburg paraît avoir communiquée à Newton. Oldenburg n'a pas publié dans les Phil. Trans. cette observation de Huygens, ni sa résolution de ne plus disputer sur cette question.

6) Celles du 18 novembre 1673 [V. st.], N^o. 83, contenant l'article cité dans la Lettre N^o. 1914, note 2.

Definitions.

1. I call y^t Light homogeneal, similar or uniform, whose rays are equally refrangible.

2. And y^t heterogenial, whose rays are vnequally refrangible.

Note. There are but three affections of Light in w^ch I haue observed its rayes to differ, viz. Refrangibility, Reflexibility and Color; and those rays w^ch agree in refrangibility, agree also in y^e other two, and therefore may well be defined homogeneal; especially since men usually call those things homogeneal, w^ch are so in all qualities y^t come vnder their knowledge, though in other qualities, y^t there knowledge extends not to, there may possibly be some heterogeneity.

3. Those Colors I call simple, or homogeneal, w^ch are exhibited by homogeneal light.

4. And those compound or heterogeneal, w^ch are exhibited by heterogeneal light.

5. Different colors I call not only y^e more eminent species, viz. Yellow, Green, Blew, Purple, but all other y^e minutest gradations: much after y^e same manner y^t not only y^e more eminent degrees in musick, but all y^e least gradations are esteem'd different sounds.

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Propositions.

1. The suns Light consists of rays differing by indefinit degrees of refrangibility.

2. Rays w^ch differ in refrangibility when parted from one another, do proportionaly differ in y^e colors w^ch they exhibit. These 2 Propositions are matter of fact.

3. There are as many simple or homogeneal colors as degrees of refrangibility. For, to every degree of refrangibility belongs a different color by Prop. 2. And that color is simple, by Defin. 1 and 3.

4. Whitenes, in all respects like that of y^e Suns immediate light and of all y^e usual objects of our Senses, cannot be compounded of two simple colors alone. For, such a composition must be made by rays y^t have only two degrees of refrangibility, by Def. 1 and 3, and therefore it cannot be like y^t of y^e suns light, by Prop. 1, nor for y^e same reason like y^t of ordinary white objects.

5. Whitenes, in all respects like y^t of y^e Suns immediat light, cannot be compounded of simple colors, w^thout an indifinit variety of y^m. For, to such a composition there are requisit rays indued w^th all y^e indefinit degrees of refrangibility by Prop. 1. And those inferr as many simple colors, by Def. 1 and 3. and Prop. 2 and 3.

To make these a litle plainer, I haue added also y^e Propositions y^t follow.

6. The rays of light do not act on one another in passing through the same medium. This appears by several passages in y^e Transactions p. 5097. 5098. 5100. and 5101. and is capable of further proof.

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

8. Nor afterwards from y^e adjacent quiet medium.

These two propositions are manifest de facto in homogeneal light, whose color and refrangibility is not at all changeable either by refraction or by y^e contermination of a quiet medium. And as for heterogeneal light, it is but an aggregat of several sorts of homogeneal light, no one sort of w^ch suffers any more alteration, than if it were alone, because y^e rays act not on one another by Prop. 6. And therefore y^e 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 colors be educed out of light by refraction, w^ch were not commixt in it before; because, by prop. 7. & 8, Refraction changes not y^e qualities of y^e rays, but only separates those w^ch haue divers qualities, by means of their different refrangibility.

10. The Suns light is an aggregat of an indefinit variety of homogeneal colors, by prop. 1. 3. and 9. And hence it is y^t I call homogeneal colors also primitive or original. And thus much concerning colors⁷⁾.

7) Après ce chef-d'oeuvre, Huygens a dû reconnaître que l'objection qu'il avait faite dans les Lettres N^o. 1919 et 1945, se trouvait pleinement levée. Toutefois, il a continué de voir des difficultés dans l'explication de la cause des couleurs et c'est ce qui l'a toujours tenu éloigné de cette partie de l'Optique. En Angleterre, les savants n'ont été que lentement gagnés à la théorie de Newton. En 1674 parut la denxième édition des Lectiones Opticae et Geometricae de Barrow, dont la première avait été rédigée avec la collaboration de Newton. Barrow, dans la nouvelle édition, maintient sans aucune modification, sur la nature des couleurs, ses spéculations entièrement incompatibles avec les vues de Newton. Voir l'analyse de cette édition au Journal des Sçavants du 18 novembre 1675. Comparez aussi Brewster, Memoirs etc. Tome I, pag. 28.

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M. Hugens has thought fit to insinuate, that y^e aberration of rays (by their disserent refrangibility) is not so considerable a disadvantage in Glasses as I seem'd to be willing to make men belieue, when I propounded concave mirrors as y^e only hopes of perfecting Telescopes. But if he please to take his pen, and compute ye errors of a glas and speculum that collect rays at equal distances, he will find, how much he is mistaken, and y^t I haue not been extravagant, as he imagins, in preferring reflexions⁸⁾. And as for what he says os y^e difficulty of y^e praxis, I know it is very difficult, and by those ways w^ch he attempted it, I believe it vnpracticable. But there is a way insinuated in y^e Transactions p. 3080⁹⁾, by w^ch it is not improbable but y^t as much may be done in large Telescopes, as I haue thereby done in short ones, but yet not without more than ordinary diligence and curiosity¹⁰⁾.

8) Consultez la Lettre N^o. 1919, note 9.

9) Celles du 19 février 1672 [V. st.], N^o. 80. dans l'article cité dans la Lettre N^o. 1873, note 2.

10) Voir la suite, qu'Oldenburg n'a pas communiquée à Huygens, au N^o. 1957.