R A I
( 955 )
R A I
Again, upon computing the Deflexions of the Rays, which, like the 23 (F«. 4;-J coming from the Centre of the Sun, and be- ing received into the lower Part of the Drop, we have fuppofed t0 be twice reflected, and twice refracted, and to enter the Eye D y Lines like that 67 (Fig. 47 ) • we find that which may be ac- counted effectual, as 6 7, with the Line 86 drawn from the Cen- tre of the Sun, contains an Angle 867, of about 52 Degrees : Whence it follows that the effectual Ray from the higheft Part of the Sun, with the fame Line 86 includes an Angle lefs by 16 Minutes ; and that from the lowed Part of the Sun, an Angle greater by 16 Minutes.
Thus, iince ABCDEF is the Path of the efficacious Ray from the higheft Part of the Sun to the Eye in F; the Angle 86 E becomes of about fifty one Degrees, and forty four Minutes. In like manner, fince GHIKLM is the Way of an effectual Ray from the lowed Part of the Sun, to the Eye, the Angle 86 M becomes nearly of fifty two Degrees, and fix-teen Minutes.
Since then we admit feveral Rays to be effectual, befide thofe from the Centre of the Sun ; what we have faid of the Shack will need fome Alteration : For, of the thtee Rays defcribed (Ffc.45 & 46.) only the two extreme ones will have a Shadow join- ing to them, and that only on the outer Side. Hence it is evi- dent that thefe Rays are perfectly difpofed to exhibit all the Co- lours of the Prifii.
For the great Quantity of denfe or intenfe Light, i. c. the Bundle of Rays collected together in a certain Point, v. gr. in tie Point of Reflection of the effectual Rays, may be accounted as a lucid or radiant Body, terminated all around by Shack. But the feveral Rays thus emitted to the Eye are both of different Colours ; that is, fitted to excite in us the Ideas of different Co- lours; and ate differently refracted out of the Water into Air, notwitbftanding their falling alike upon the refracting Surface. See Colour, &c.
Hence it follows that the different or heterogeneous Rays will be feparated from one another, and will tend feparate ways ; and thehomogeneous Rays be collected, and tend the fame way: And therefore this lucid Point of the Drop, wherein the Re- fraction is effected, will appear fringed, or border'd with feveral Colours; that is, red, green, and blue Colours will arife from the extremes of the red, green, and blue Rays of the Sun tranf- mitted to the Eye from feveral Drops one higher than another; after the iame manner as is done in viewing lucid, or other Bo- dies through a Prijht. See Prism.
Thus, adds Sir Ifaac Newton, the Rays that differ in refrangi- bility, will emerge at different Angles ; and confequenrly, accord- ing to their different Degrees of Refrangibility, emerging moft copioufly at different Angles, will exhibit different Colours in different Places. See Refrangibility.
A great number then of thefe little Globules being diffufed in the Air, will fill the whole Space with thefe different Colours; provided they be fo difpofed as that eftedual Rays may come from them to the Eye ; and thus will the Rainbow, at length, arife.
Now to determine what the Difpofition mud be ; fuppofe a right Line drawn, from the Centre of the Sun through the Eye of the Spectator, as the Line VX, (Fig. 46.) call'd theLineof s/f- peti: Being drawn from fo remote a Point, it may beedeernd parallel to all other Lines drawn from the fame Point : But a right Line falling on two Parallels makes the alternate Angles e- qual. See Alternate.
If, then, an indefinite Number of Lines be imagin'd drawn from the Spectator's Eye to a part oppolite to the Sun where it rains; which Lilies make different Angles with the Line of Afpect, e- qual to the Angles of Refraction of the differently refractible Rays, e. gr. Ang'es-of 42 , 1', and of 40 , 16'. Thefe Lines falling on Drops of Rain illumined by the Sun, will makes An- gles of the fame Magnitude with Rays drawn from the Centre of the Sun to the fame Drops. And therefore the Lines thus drawn from the Eye will reptefent the effectual Rays that occa- fion the Senfation of any Colour.
That, e. gr. making an Angle of 42 ° 1 reprefenting the leaft refrangible or red Rays of the feveral Drops, and of 40 16', the moft refrangible or violet Rays : The intermediate Colours, and refrangibilities will be found in the intetmediate Space Ee. See Red, Violet, &c.
Now, 'tis known that the Eye being placed in the Vertex of a Cone, fees Objects upon its Surface as if they were in a Cir- cle; and the Eye of our Spectator is here in the common Ver- tex of feveral Cones, form'd by the feveral Kinds of efficacious Rays, with the Line of Afpect. And in the Surface of that whofe Angle at the Veitex or Eye is the greateit, and wherein the o- thers are included, are thofe Drops or Parts of Drops which ap- pear red; and in the Surface of that Cone whofe Angle is leaft, are the purple Drops : And in the intermediate Cones are the green, blue, &c. Drops. Hence then feveral Kinds of the jJrops mult appear as if difpofed into fo many circular colour'd
- afci<e or Arches, as we fee in the Rainbow.
This part of the Solution Sir lfaac Newton expreffes more art- fully thus : Suppofe O {Fig. 48.) the Eye, and OP a Line Parallel to 'he Sun's Rays, and let POE, POFbe Angles of 40° 17', and 42°
- • And fuppofe the Angles to turn about their common Side
OP, with their other Sides OF. and OF, they will defcribe the Hounds or Verges of the Rainbow.
For, if EF be Drops placed any where in the conical Surface defcribed by OE OF; and be illuminated by the Sun's Rays SE, SF, the Angle SEO being equal to the Angle POE or 40° 17' fliall be the greateft Angle in which the moft refrangible Rays can, after Refleflion, be refrafled to the Eye ; and therefore all the Drops in the Line OE fliall fend the moft refrangible Rays moft copioufly to the Eye, and thereby ftrike the Senfes with the deeped Violet Colour in that Region.
And in like Manner the Angle SFO beingrr: to the Angle POf~+ 2 ° 2', fhall be thegreated, in which the lead refrangi- ble Rays after one ReBeflion can emerge out of the Drops; and thefe Rays fhall come moft copioufly to the Eye, from the Drops in the Line OF, and ftrike the Senfes with the deeped red Colour in that Region.
And by the fame Argument the Rays, which have intermediate Degrees of Refrangibility, fhall come moft copioufly from Drops between E and F, and fo ftrike the Senfes with the intermediate Colours, in the Order which their Degrees of Refrangibility require; that is, in the Progrefs from E to F, or from the in- fide of the Bow to the outflde, in this Order, Violet, Indigo, Blue, Green, Yellow, Orange, Red: Though the Violet, by the mixture of the white Light of the Clouds, will appear faint, and incline to a purple.
And fince the Lines OE OF may be fituated any where in the abovemention'd conical Surface; what is raid of the Drops and Colours in thefe Lines is to be undetftood of the Drops and Colours throughout the whole Superficies. Thus is the primary, or inner Bow form'd.
Sccundary, or outer Rain-Bow.
As to the fecundaty or fainter Bow, ufuallv furrounding the former ; in alligning what Drops would appear coloured, we ex- cluded fuch as Lines drawn from the Eye, making Angles a little greater than 42° 2' fliould fall upon; but not fuch as fliou'd contain Angles much greater.
For, if an indefinite Number of fuch Lines be drawn from the Spectator's Eye, fome whereof make Angles of 50° 57', with the Line of Afreet; e. gr. OG; o:her Angles of 54° f, e. gr. OH ; thole Drops whereon thefe Lines fall, muft of ne- ceflity exhibit Colours. Particularly thofe of 50 57'.
E. gr. the Drop G will appear red ; the Line GO being the fame with an effectual Ray, which after two Reflections and°two Refraftions, exhibits a red Colour. Again, thofe Dtops which receive Lines of 54° 9', e. gr. the Drop H will appear Purple, the Line OH being the fame with an effectual Ray which after two Reflections, and two Refractions,' exhibits Purple.
Now, there being a fufficient Number of thefe Drops, 'tis e- vident there mud be a fecond Rainbow, form'd after the like man- ner as the fird.
Thus, Sir Ifaac Newton: In the leaft refrangible Rays, the leaft Angle at which a Dtop can fend effectual Rays after two Reflexions, is found by computation to be 50 57', and in the moft refrangible the leaft Angle is found 54° 7'.
Suppole, then, O the Place of the Eye, as before, and POG, POH to be Angles of 50 57', and 54 7'. And thefe Angles to be turn'd about their common Side OP; with their other Sides OG, OH, they will delcribe the Verges or Borders of ths Rainbow CBDG.
For, if GH be Drops placed any where in the conical Super- ficies defcribed by OG OH, and be illumined by the Sun's Rays • the Angle SCO being equal to the Angle POG or ;o° 57 fhall be the lead Angle, in which the then leaft refrangible Rays, can, after two Reflections, emerge out of the Drops ; and there- fore the leaft refrangible Rays lhall come moft copioufly to the Eye from the Drops in the Line OG, and ftrike the Senfe with the deepeft Red in that Region.
And the Angle SHO being equal to POH, 54° 7', fhall be the lead Angle in which the moil refrangible Rays, after two Reflections, can emerge out of the Drops; and therefore chofe Rays fhall come mod copioufly to the Lye from the Drops in the Line OH, and fo ftrike the Senfes with the deepeft Violet in that Region.
And by the fame Argument, the Drops in the Region between G and H, fhall ftrike the Semes with the intermedate Co- louts, in the Order which their Degrees of Refrangibility re- quire ; that is, in the Progrels from G to H, or from the inlide of the Bow to the outer, in this Order : Red, Orange, Yellow, Green, Blue, Inaico, Violet.
And fince the Lines OG, OH, may be fituated any where in the conical Sutface ; what is faid of the Drops and Colours in thefe Lines, is to be underftoou of the Drops and Colours every where in thefe Superficies.
Thus are form'd two Bows, an interior, and ftronger, by one Reflection; and an exterior and fainter by two; the Light becom- ing weaker and weaker by every Reflexion.
Their Colours will lie in a contrary Order to one another; the fird having rhe Red without, and the Purple within ; and the fecond the Purple without and Red within ; and fo of the reft.
Artificial Rain-Bow. This Doctrine of the Rainbow is confirm'd by an eafy Experi- ment : For upon hanging up a Glafs Globe full of Water in the 11 K Sun-
