<53r>

For Henry Oldenburg Esq.

< insertion from the top of f 53r >

An Mr Newtons Answer to ye precedent Letter,
sent to the Publisher.

< text from f 53r resumes > < insertion from the top left of f 53r >

The Copy of this is sent to Liege to Mr Lucas Aug. {23}. 1676.

< text from f 53r resumes >

The angle indeed wch I used was but about 63degr., 12min, & his is set down 60degr: the difference of wch from mine being but 3degr., 12min, is too little to reconcile us, but yet it will bring us considerably nearer together. And if his angle was not exactly measured, but ye round number of 60degr. set down by guess or by a less accurate measure (as I suspect by the conjectural {illeg}|me|asure of ye refraction of his prism by ye ratio of ye sines 2 to 3 set down instead of {illeg} at ye same time instead of an experimental one,) then might it be two or three degrees less then 60, if not still less: & all this, if it should be so, would take <53v> {away} the greatest part of ye difference between us.

But however it be, I am well assured my own observation was exact enough. For I have repeated it divers times since ye receipt of Mr Lucas's letter, & that wthout any considerable difference of my observations either from one another or from what I wrote before. And that it might appear experimentally how ye increase of ye angle increases ye length of ye Image, & also that no body who has a mind to try ye experiment exactly might be troubled to procure a Prism wch has an angle just of {illeg}|y|e bigness assigned by me; I have tryed ye experiment wth divers angles; {illeg} & have have set down my trialls in ye following table; where ye first column expresses the six angles of two Prisms wch I used, wch were measured as exactly as I could by applying \them/ to ye angle of a Sector; & ye second column expresses in inches the length of ye image made by each of those angles; its breadth being two inches: its distance from ye hole in ye window shut \Prism/ 18 feet & 4 inches, & ye breadth of ye hole in ye window shut $\frac{1}{4}$ of an inch.

$\begin{array}{cc}\begin{array}{r}\text{The angles of}\\ \text{degr}\phantom{\rule{0.7em}{0ex}}\text{min}\end{array}& \begin{array}{c}\text{The lengths}\\ \text{of}\phantom{\rule{0.5em}{0ex}}{\text{y}}^{\text{e}}\phantom{\rule{0.5em}{0ex}}\text{Image}\end{array}\\ {\text{y}}^{\text{e}}\phantom{\rule{0.5em}{0ex}}{\text{1}}^{\text{st}}\phantom{\rule{0.5em}{0ex}}\text{Prism}\phantom{\rule{0.5em}{0ex}}\left\{\begin{array}{rr}56\phantom{\rule{0.2em}{0ex}}.& 10\phantom{\frac{0}{0}}\\ 60\phantom{\rule{0.2em}{0ex}}.& 24\phantom{\frac{0}{0}}\\ 63\phantom{\rule{0.2em}{0ex}}.& 26\phantom{\frac{0}{0}}\end{array}& \begin{array}{c}\phantom{0}7\frac{3}{4}\\ \phantom{0}9\frac{1}{2}\\ 10\frac{1}{3}\end{array}\\ {\text{y}}^{\text{e}}\phantom{\rule{0.5em}{0ex}}{\text{2}}^{\text{d}}\phantom{\rule{0.5em}{0ex}}\text{Prism}\phantom{\rule{0.5em}{0ex}}\left\{\begin{array}{rr}54\phantom{\rule{0.2em}{0ex}}.& \phantom{0}0\phantom{\frac{0}{0}}\\ 62\phantom{\rule{0.2em}{0ex}}.& 12\phantom{\frac{0}{0}}\\ 63\phantom{\rule{0.2em}{0ex}}.& 48\phantom{\frac{0}{0}}\end{array}& \begin{array}{c}\phantom{0}7\frac{1}{3}\\ 10\frac{1}{8}\\ 10\frac{3}{4}\end{array}\end{array}$[1]

You may perceive that the lengths of ye images in respect of ye angles that made them, are something greater in the 2d Prism then in ye first: but that was because ye glass of wch ye second Prism was made, had ye greater refractive power.

The days in wch I ma{illeg}|d|e these trialls were pretty clear but not so clear as I desired, & therefore afterward meeting wth a day as clear as I desired, I rep{illeg}|e|ated ye experiment wth ye second Prism, & found ye lengths of ye image made by its severall angles to be those set down in this table about $\frac{1}{4}$ of an inch greater then before, the measures being those set down in this table.

$\begin{array}{cc}\begin{array}{r}\text{The angles of}\\ \text{degr}\phantom{\rule{0.7em}{0ex}}\text{min}\end{array}& \begin{array}{c}\text{The lengths}\\ \text{of}\phantom{\rule{0.5em}{0ex}}{\text{y}}^{\text{e}}\phantom{\rule{0.5em}{0ex}}\text{Image}\end{array}\\ {\text{y}}^{\text{e}}\phantom{\rule{0.5em}{0ex}}{\text{2}}^{\text{d}}\phantom{\rule{0.5em}{0ex}}\text{Prism}\phantom{\rule{0.5em}{0ex}}\left\{\begin{array}{rr}54\phantom{\rule{0.2em}{0ex}}.& \phantom{0}0\phantom{\frac{0}{0}}\\ 62\phantom{\rule{0.2em}{0ex}}.& 12\phantom{\frac{0}{0}}\\ 63\phantom{\rule{0.2em}{0ex}}.& 48\phantom{\frac{0}{0}}\end{array}& \begin{array}{c}\phantom{0}7\frac{2}{3}\phantom{\rule{0.2em}{0ex}}\text{.}\\ 10\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\text{.}\\ 11\phantom{\rule{0.2em}{0ex}}\text{.}\phantom{\frac{0}{0}}\end{array}\end{array}$

The reason of this difference I apprehend was \{partly}/ that in ye clearest days, the light of ye \white/ skies wch dilutes & renders invisible the faintest colours at ye ends of ye Image is a little diminished in a clear day & so gives leave to ye l|c|olours to appear to a greater length; the Sun's light at ye same time becoming brisker & so strengthening ye colours & making ye faint ones at ye two ends <53ar> more conspicuous. For I have observed that in days something cloudy, whilst ye Prism has stood unmoved at ye window, the image would grow a {illeg}little longer or a litt{illeg}|l|e shorter accordingly as ye Sun was more or less obscured by thin clouds wch passed over it; ye image being shortest when ye cloud was brightest & ye suns light faintest. Whence it is easy to apprehend that if ye light of ye clouds could be quite taken away, so yt ye Sun might appear surrounded wth darkness, \or if the suns light was much more stronger then it is/ the colours would still appear to a greater length.

In all these observations ye breadth of ye Image was just two inches. But observing that ye sides of ye two Prisms I used were {illeg}|n|o{illeg}|t| exactly pl{illeg}|a|in but a little convex, (the convexity being about so much as that of a double convex glass of an \sixteen or/ eighteen foot Telescope), I took a third Prism whose sides were as much concave as those of ye other were convex; & this {illeg} made ye breadth of ye Image to be two inches & a third part of an inch: the angles of yt \this/ Prism & ye lengths of this|e| Image made by each of those angles being those exprest in this Table

$\begin{array}{cc}\begin{array}{c}\text{The angles}\\ \text{of the Prism}\\ \text{degr.}\end{array}& \begin{array}{c}\text{The lengths of}\\ \text{of}\phantom{\rule{0.5em}{0ex}}{\text{y}}^{\text{e}}\phantom{\rule{0.5em}{0ex}}\text{Image in inches.}\\ \phantom{\text{degr.}}\end{array}\\ \begin{array}{c}58\phantom{\frac{0}{0}}\\ 59\frac{1}{2}\\ 62\frac{1}{2}\end{array}& \begin{array}{c}\phantom{0}8\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\text{.}\\ \phantom{0}9\phantom{\rule{0.2em}{0ex}}\text{.}\phantom{\frac{1}{2}}\\ 10\frac{1}{3}\phantom{\rule{0.2em}{0ex}}\text{.}\end{array}\end{array}$

In this case you see ye concave figure of ye sides of ye Prism by making ye rays diverge a little, causes ye breadth of ye Image to be greater in proportion to its length then it would be otherwise. And this I thought fit to give you notice of, that Mr Lucas may examin whether his Prism have not this fault. If a Prism may be had wth sides exactly plain, it may do well to try ye experiment wth that: but it's better if ye sides be about so much convex as those of mine are, because ye Image will thereby become much better defined. For this convexity of ye sides does ye same effect as if you should use a Prism wth sides exactly plain, & between it & ye hole in ye window shut, place an object-glass of an 18 foot Telescope to make ye round image of ye sun appear distinctly defined on ye wall when the Prism is taken away, & consequently the long image made by ye Prism to be much more distinctly defined (especially at it's streight sides) then it would be otherwise.

One thing more I shall ad{illeg}|d|: Th{illeg}|at| yee utmost length of yee Image from ye faintest red at one end to ye faintest blew at ye other, must be measured. For in my first letter about colours where I set down the length to be five times the breadth, I called that {illeg}length ye utmost length of ye image; & I measured ye utmost length, because I account all that length to be caused by ye im{illeg}med{illeg}iat{illeg}e light of ye sun, seing <53av> the colours (as I noted above) become visible to ye greatest length in ye clearest days, that is, when ye light of ye Sun transcends most ye light of ye clouds. Sometimes th{illeg}|e|re will happen to shoot out from both ends of ye Image a glaring light {illeg} a good way beyond these colours, but this is not to be regarded, as not apperteining to ye Image. If ye measures be taken right ye whole length will exceed ye length of ye streight sides by about ye breadth of ye Image.

By these things set down thus circumstantially, I presume Mr Lucas will be enabled to accord his trials of ye Expt wth mine; so nearly at least that there shall not remain any very considerable difference between us. For if some little difference should still remain, that need not trouble us any further {illeg}|seei|ng there may be many various circumstances wch may conduce to it; such as are not only ye different figures of {illeg} prisms, but also ye different refractive power of glasses, ye different diameters of ye Sun at divers times of ye year, & ye little errors that may happen in measuring lines & angles, or in placing ye Prism at ye {illeg}d window: though for my part I took care to do these things as exactly as I could. However Mr Lucas may make sure to find ye Image as long as|or| longer then I have set down, if he take a Prism whose sides are not hollow grownd, but plain, or (wch is better) a very little convex, & whose refracting angle is as much greater then that I used as that he has hitherto tryed it with is less; that is, whose angle is about 66 or 67 degrees, or (if he will) a little greater.

Concerning Mr Lucas's other experiments, I am much obliged to him that he would take these things \so far/ into consideration, & be at so much pains for examining them; & I thank him so much the more because he is ye first yt has sent me an experimental examination of them. By this I \may/ presume he really desires to know what truth{illeg} there is in these matters. {illeg}|B|ut yet it will conduce to his more speedy & full [2][3]satisfaction if he a little change ye method wch he has propounded, & instead of a multitude of things try only the Experimentum Crucis. For it is not number of Expts, but weight to be regarded; & where one will do, what need {illeg} many?

Had I thought more requisite, I could have added more. For before I wrote my first letter to you about colours I had taken much pains in trying experiments about them & written a Tractate on that subject wherein I had set down at large & considered ye principall of ye experiments I had tryed; {illeg} amongst {the rest} \which/ there has happened to be the principal of those wch Experiments wch Mr Lucas has now sent me. And as for ye Experiments set down in my first letter to you, they were only such as I thought convenient to sele{illeg}|c|t out of that Tractate.

<53br>

But yet suppose those had been my whole store, yet Mr Lucas should not have grownded his discourse upon a supposition of my want of experiments till he had examined those few. For if any of those be demonstrative, they will need no assistants nor leave room for further disputing about what they demonstrate.

The main thing he goes about to examin is ye different refrangibility of light. And this I demonstrated by ye e|E|xperimentu Crucis. Now if this demonstration be good, there needs no further examination of ye thing; if not good ye fault of it is to be shewn: for ye only way to examin a demonstrated proposition is to examin ye demonstration. Let that expt therefore be examined in ye first place, & that wch it proves be acknowledged, & then if Mr Lucas want my assistance to unfold ye difficulties wch he fancies to be in ye experiments he has propounded, he shall freely have it; for then I presume a few words may make them pl{illeg}|a|in to him: whereas should I be drawn from a demonstrative experiment to begin with those, it might create us both ye trouble of a long dispute, & by ye multitude of words cloude rather then clear up ye truth. For if it has already cost us so much trouble to agree upon ye matter of fact in ye first & plainest experiment, & yet we are not fully agreed: what an endless trouble might it create us, if we should give or selves up to dispute upon every argument that occurs, & what would become of truth in such a tedious dispute. [4]The way therefore that I propound being ye shortest & clearest (not to say ye only proper way,) I question not but Mr Lucas will be glad that I have recommended it, seeing he professes that it is {illeg}|ye| knowledge of truth that he seeks after. And therefore at prsent I shall say nothing in answer to Mr his experimental discourse but this in general: that it has proceeded partly from some misunderstanding \of/ what he writes against, & partly from want of due caution in trying experiments; & that amongst his experi{illeg}|m|ents there is one, wch when duely tryed, is, next to ye Experimentum Crucis, the most conspicuous Experiment I know for proving the different refrangibility of light, wch he brings it to d{is}prove against.

By ye Post-script of Mr Lucas's letter, one not acquainted wth what has passed, might think, that he quotes ye Observation of ye R. Society against me; whereas the relation of their Observation, wch you sent to Leige, conteined nothing at all about the just proportion of ye Length of ye Image to it's {illeg}|B|readth according to ye angle of ye Prism, nor any thing more (so far as I can perceive by yor last) than what was pertinent to the things then in dispute, viz, that they found them succeed as I had affirmed. And therefore since Mr Lucas has found the same success, I suppose <53bv> suppose {sic} yt when he expresses|d| that he much rejoyced to see ye trialls of ye R. Society agree so exactly wth his, he meant only so far as his agreed wth mine.

And because I am again upon this first experiment, I {illeg} \shall/ desire that Mr Lucas will repeat it with all \ye/ exactness & caution that may be, regard being had to ye information about it, {illeg}|set| down in this letter; & then I desire to have the length & breadth of ye Image wth its distance from ye hole in ye window shut, \Prism/ set down exactly in feet & inches & parts of an inch, that I may have an opportunity to consider what relation it's length & breadth have to ye sun's diameter. For I know, that Mr Lucas's Observation cannot hold where ye refracting angle of ye Prism is full 60degr:, & the breadth of ye Im \day is clear & the/ full length of ye colours is measured, & ye breadth of ye Imag{illeg}|e| answers to ye sun's diameter: & seeing I am well assured of ye truth & exactness of my own observation, I shall be unwilling to be diverted by any other experiments from having a fair end made of this in ye first place.

Sr

I am

Yor humble Servant

Is. Newton.

Cambridge
Aug {illeg}|18|. 1676

Postscript.

Experimentum Crucis, & such others as shall
be made for knowing ye nature of colours;
be made wth Prisms which refract so much
as to make ye length of ye Image five times
it's breadth, & rather more then less; for,
otherwise Expts will not succeed so plainly wth
others as they have done wth me.

[1] Yyyy 6.

[2] Zzzz {7} 703

[3] pray {ed}{2d} turn {t} a {Leaf}

[4] {4 Zz 704}