<51r>

Cambridge.
Feb. 29. 167$\frac{\text{5}}{\text{6}}$.

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A particular Answer of Mr Isaac Newton to Mr Linus his Letter, printed in Numb. 121. p.     , about ye an Experiment relating to ye New doctrine of Light and Colors: T{illeg}|h|is Answer sent \from Cambridge/ in a Letter to ye Publisher Febr. 29. 167$\frac{\text{5}}{\text{6}}$.

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Sr

By reading Mr Linus's letter when you shewed it to me at London, I retained only a general rem{illeg}|e|mbrance that Mr Linus denyed what I affirmed \& so could \lately/ say nothing in particular to it/; but having ye opportunity to read it again \in Numb. 121./ in|of| y{illeg}|e| Transactions, I perceive he would persuade you, that ye information you gave him about ye experiment is as inconsistent wth my {illeg}|p|rinted Letters, as wth Experience; & therefore, least any sil{illeg} who have not read those letters should take my silence herein \in this point/ for an acknowledgment, I thought it not amis, to send you something in answer to this th to this also{.}

He tells you \that, where{illeg}|as|{illeg} you/ assure him, First, yt ye Expt was made in clear days; {illeg}|se|condly, yt ye Prism was placed close to ye hole so that ye light had no room to diverge; & thirdly, yt ye Image was not parallel but Trans{illeg}|v|ers to ye axis of ye Prism:; If these assertions be compared wth my relation of ye experi{illeg}|m|ent in the \Phil./ Transactions N. 80 p. 3076. it will evidently appear, they {illeg}|c|annot be addmitted as being \directly/ contrary to what is there delivered. His reasons are these;

First, that I said, ye ends of ye long image seemed semicircular, wch, saies he, never happens in any of ye three cases above said. But I say it happens in them all, & \this is not to sed|t| me at odds with my self, but w{illeg}|it|h {the} experiment; for it/ is there described to happen in them all; & {I still say, it doth happen in them. Let others} try ye experiment, and judge.

{Further he saies, that the Prism is placed at a distance from the hole in the Scheme of the Experiment in N. 84. p 4091. But, what if it were so there? For, that is the Scheme of a demonstration, not of the experiment, and would have served for the demonstration, had the distance been put twenty times greater than it is. In the Schemes of the Experiment N. 80. p. 3086, and N. 82. p. 5016 it is represented close, and close enough in the Scheme, N. 83. p. 4061: But Mr. Linus though fit to wink at these, and pitch upon the Schemeof a Demonstration, and such a Scheme too as hath no hole at all represented in it. For the Scheme ✝[1] Numb. 84. p. 491 is this; in which the rays are not so far distant from one another at GL, but that the hole, had I exprest it, might have been put there, and yet have comprehended them. But if we should put the hole at x, their decussation; yet will it not be any thing to his purpose; the distance xG or xL being but about half the breadth of a side of the Prism ($\frac{1}{2}$ AC) which I conceive is not the twentieth part of the distance requisite in his conjecture.}

{3. He says, that more might be said out of my relation to shew, that the Image was not transvers, for if it had been transvers, I could not have been surprized (as I said I was) to see the length thereof so much exceed the breadth, it being a thing so obvious & easie to be explicated by the ordinary rules of Refraction. But on the contrary, it may rather be said, that if the Image had been parallel, I could not have been surprized to see the} <51v> the length thereof so much exceed the brea{illeg}|dth|, it being a thing {illeg} \so/ extreamly obvious as not to need any explication. For, {illeg}|wh|at Naturall, \(give me {livor} to argue,)/ that has but eyes in his head, knows not y{illeg}|e| sun shine from a bright cloud? And \For/ who, that had but common sence, and saw ye whole Prism or a good part of it illuminated, \so {illeg}tl{illeg}/ by that \or by the Sun's immediate/ light would not expect {illeg}|the| \light/ should have ye same long figure upon ye wall that it had when it came out of ye Prism? Mr Linus therefore, while he would strengthen his argument by representing me well skilled in Opticks, does but overthrow it. But whereas he saides, I could not have been surprized at ye length, had ye Image been parallell, it being a thing so obvious & easy to be explicated by the ordinary rules of refraction: Let any man take ye experiment intire, as I have there delivered it, that is, wth this condition, that ye refractions on both sides ye Prism were equal, & try if he can reconcile it with ye ordinary rules of refraction. On ye contrary, he may find ye impossibility of such a reconciliation demonstrated in my answer to P. Pardies N. 84, p. 4091.

In ye last place he objects, that my saying, in N{illeg}. 80 p. 3077, that ye incident Re{illeg}|f|ractions were in ye Experiment equal to the emergent, proves again that y{illeg}|e| long Image was parallel. And yet that very saying is a sufficient argument that I meant ye contrary; because it becomes wholly impertinent, if applied to a parallel Image; \but in the other case is a very nec{illeg}|e|ssary circumstance./ What is added therefore of P. Pardies might have been spared, especially since that Learned person understood my discourse to be meant of a transvers Image, & acquiesced {in my Answers.}

{This in Answer to Mr. Linus's Letter: And now to take away the like suspicions from his Friends, if my declaration of my meaning satisfie not, I shall note some further passages in my Letters, whereby they may see, how I was to be understood from the beginning, as to the aforesaid three circumstances.}

{For the Day; I express every where that the Experiment was tried in the Sun's light, and in N. 80. p. 3077, that the breadth of the Image by measure answered to the Sun's diameter: But because it is pretended, I was imposed upon, I would ask, what the Experiment as it is advanced to that which I called the Experimentum Crucis, can have to do with a cloudy day? For, if the Experimentum Crucis (which is that which I depend on) can have nothing to do with a cloudy day, then it is to no purpose to talk of a cloudy day in the first Experiment, which does but lead on to that. But if this satisfie not, let the Transactions N. 83. p. 4060, be consulted: For. there I tell you, how by applying a Lens to the Prism, the streight edges of the oblong Image became distincter than they would have been without the Lens: a circumstance which cannot happen in Mr. Linus's case of a bright cloud.}

{For the Position of the Prism; I tell you N. 80. p. 3076, that it was placed at the Sun's entrance into the Chamber, and in p. 3085. I bad to make a hole in the shut, and there place the Prism, and in the next page I say again, that the Prism ABC is to be set close by the hole F of the window EG; and accordingly represent it close in the Figure. Also in pag. 3077 I tell you, that the distance of the Image from the hole or prism was 22 foot; which is as much as to say, that the Prism (suppose that side of it next the hole) was as far from the Image as the hole it self was, and consequently that the Prism and Hole were contiguous. Also in p. 3078, where instead of the Window shut I made use of a hole in a loose board, I tell you expressly, that I placed the board close behind the Prism. All these passages are in my very first Letter about Colours; and who therefore would imagine, that any one that had read that Letter should so much as suspect, that I placed the Prism, I say not at so great a distance as Mr. Linus supposes, but at any distance worth considering?}

{Lastly, for the Position of the Image, it is represented transvers to the axis of the Prism in the figures N. 80. p. 3086. N. 83. p. 4061, and N. 85. p. 5016. And in N. 88. p. 5093, where I made use of two cross Prisms, I tell you expresly, that the Image was cross to both of them at an angle of 45 degrees. The calculations also N. 80. p. 3077. are not to be understood without supposing the Image cross. Nor are my notions about different Refrangibility otherwise intelligible: For in Mr. Linus's supposition, the rays that go to the two ends of the Image, are equally refracted. So the colours, the red, according to my description, falls at one end of the Image, and the blew at the other; which cannot happen but in a tranvers Image. The same position is also demonstrable from what I said in N. 80. p. 3076, about turning the long Image into a round one, by the contrary refraction of a second Prism, further explained in Num. 83. p. 4061. For this is not to be done in Mr. Linus surmise of a parallel Image, and therefore had Mr. Linus considered it, he could never have run into that surmise.}

{This I suppose is enough to manifest the three particulars; any one of which being evidenced, is sufficient to tak away the scruple. And therefore Mr. Linus Friends need not fear but that the further directions I sent them lately for trying the Experiment are the same with those I have follow'd from the beginning; nor trouble themselves about any thing but to try the Experiment right. But yet, because Mr. Gascoin has been pleased to insinuate his suspicion that I do differ from himself in those directions, I shall not scruple here to reduce them to particulars, and shew where each particular is to be found.}

{1. Then, he is to get a Prism with an angle about 60 or 65 degrees, N. 80. p. 3077, and p. 3086. If the angle be about 63 degrees, as that was which I made use of N. 80. p. 3077, he will find all things succeed exactly as I described them there. But if it be bigger or less, as 30, 40, 50, or 70 degrees, the Refraction will be accordingly bigger or less, and consequently the Image longer or shorter. If his Prism be pretty nearly equilateral (such as I suppose are usually sold in other places as well as in England) he may make use of the biggest angle. But he must be sure to place the Prism so, that the Refraction be made by the two planes which comprehend this angle. I could almost suspect, by considering some circumstances in Mr. Linus's Letter, that his error was in this point, he expecting the Image should become as long by a little refraction as by a great one; which yet being too gross an error to be expected of any Optician, I say nothing of it, but only hint this to Mr. Gascoin, that he may examine all things.}

{2. Having such a Prism, he must place it so, that its Axis be perpendicular to the rays N. 84, p. 4091, lin. 18, 19. A little error in this point makes no sensible variation of the effect.}

{3. The Prism must be so placed, that the Refractions on both sides be equal N. 80, p. 3077: which how it was to be readily done by turning it about its Axis, and staying it when you see the Image rest between too contrary motions, as I explained in my late Descriptions, so I hinted before N. 80. p. 3077, lin. 34, 35, 36. If there should be a little error in this point also, it can do no hurt.}

{4. The Diameter of the hole I put $\frac{1}{4}$ of an inch N. 80, p. 3077, and placed the Prism close to it, even so close as to be contiguous, N. 80, p. 3077, lin. 4, 5. But yet there needs no curiosity in these circumstances. The hole may be of any other bigness, and the Prism at a distance from the hole, , {sic} provided things be so ordered, that the light appear of a round form, if intercepted perpendicularly at its coming out of the Prism. Nor needs there any curiosity in the day. The clearer it is the better; but if it be a little bit cloudy, that cannot much prejudice the Experiment, so the Sun do but shine distinctly through the cloud.}

{These things being thus ordered, if the refracted light fall perpendicularly on a wall or paper at 20 foot or more from the Prism, it will appear in an oblong form, cross to the axis of the Prism, red at one end, and violet at the other; the length five times the breadth (more or less according to the quantity of the refraction,) the sides, streight lines, parallel to one another, and the ends confused, but yet seeming semi-circular.}

{I hope therefore, Mr. Linu's {sic} Friends will not entertain themselves any further about incongruous surmises, but try the Experiment as Mr. Gascoin has promised. And then, since Mr. Gascoin tells you, That the Experiment being of it self extraordinary and surprizing, and besides ushering in new Principles into Opticks, quite contrary to the common and received, it will be hard to perswade it as a truth, till it be made so visible to all as it were a shame to deny it: if he esteem it so extraordinary, he may have the priviledg of making it so visible to all, that it will be a shame to deny it. For, I dare say, after his testimony no body else will scruple it. And I make no question but he will hit of it, it being so plain and easy, that I am very much at a loss to imagine what way Mr. Linus took to miss.}

{Dat. Cambridge Feb. 29 167$\frac{5}{6}$.}

[1]See Fig. 1.