RAIxMBOW. 



of drops, which appear red ; and in the furfacc of that cone 

 whofe angle- is Icait, arc tlie purple drops ; and in the in- 

 termediate cones, arc the green, blue, &c. drops. Hence, 

 then, feveral kinds of the drops mud appear as if difpofed 

 into fo many circular coloured fafcix, or arches, as we fee 

 in the rainbow. (Rohault's Syftcm of Nat. Phil. vol. ii. 

 part iii. cap. 17.) Tliis part of the folution fir Ifa.ic New- 

 ton exprcfles more precifely, thus : fuppofe O {ftg. 4.) the 

 eye, and O P a line parallel to the fun's rays ; and let 

 PO E, POF, be angles of 40^ 17', and 42° 2'. And 

 fuppofe the angles to turn about their common fide O P, 

 with their other fides O E and O F, they will defcribe the 

 bounds, or verges, of the rainbow. 



For if E, F be drops placed any where in the conical 

 furface defcribed by O E, O F, and be illuminated by the 

 fun's rays S E, S F ; the angle S E O being equal to the an- 

 gle P O E, or 40° 17', (hall be the greateft angle in which 

 the moll refrangible rays can, after refleftion, be refrafted 

 to the eye ; and, therefore, all the drops in the line O E 

 (hall fend the mod refrangible rays moft copioufly to the eye, 

 and therefore ftrike the fenfes with the deepeil violet colour 

 in that region. 



And in like manner the angle S F O being = to the an- 

 gle P O F = 42° 2', (hall be the greateft in which the Icall 

 refrangible rays after one refleftion can emerge out of the 

 drops ; and thefe rays (hall come moft copioufly to the eye 

 from the drops in the line O F, and (Irike the fenfes with the 

 deepeft red colour in that region. 



And, by the fame argument, the rays which have inter- 

 mediate degrees of refrangibihty, fliall come moft copioufly 

 from drops between E and F, and fo ftrike the fenfes with 

 the intermediate colours, in the order which their degrees of 

 refrangibihty require ; that is, in the progrefs from E to F, 

 or from the infide of the bow to the outiide, 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. 



Here it may be obferved, that all the rays but the violet 

 in the line S E will emerge from E in a greater angle than 

 S E O made by the violet, and confequently will pais below 

 the eye ; and all the lays but the red in the line S F will 

 emerge from F in a Icfs angle than S F O made by the red, 

 and confequently will pafs above the eye ; by which means 

 only red will appear in the line S F, and only violet in the 

 Hne S E. . 



And, fince the lines O E, OF, may be iituated any 

 where in the above-mentioned conical furface ; what is laid 

 of the drops and colours of thefe lines, is to be under- 

 ftood of the drops and colours throughout the whole fuper- 

 •icies. Thus is iht: primai-y or inner how formed. 



Rainbow, Sfcmdar^, or Outo: As to the fecondary, or 

 fainter bow, ufually lurrounding the former, in affigning 

 what drops would appear coloured, we excluded fuch as 

 lines drawn from the eye, making angles a little greater than 

 42° 2', fliall fall upon, but not fuch as ftiould contain angles 

 much greater. 



For, if an indefinite number of fuch lines be drawn from 

 the fpeftator's eye, fome of which make angles of 50^ 57', 

 with the line of afped, f. gr. O G ; other angles, of 54" 7', 

 -. gr. O H ; tliofe drops on which thefe lines fall niuil of 

 aecelfity exhibit colours ; particuharly thofe of 50° 57'. 



£. gr. The drop G will appear red ; the line G O being 

 the fame with an effeftual ray ; which, after two reflections, 

 and two rcfraftions, exhibits a red colour. Again, thofe 

 drops which receive lines of 54° 7', e. gr. the drop H, will 

 appear purpk ; the line O H being the fame with an effec- 



tual i"ay ; which, after two refleflions and two rcfraftions-, 

 exhibits purple. 



Now there being a fufficient number of thefe drops, it is 

 evident there muft be a fecond rainbow, formed after the like 

 manner as the firft. 



Thus, according to fir Ifaac N.'wton, in the leaft refran- 

 gible rays, the leaft angle at which a drop can fcndefteftual 

 rays after two rcfleftions, is found by computation to be 

 50^ 57' ; and in the moft refrangible, tiie leaft angle is found 



54" 7'. 



Suppofe, then, O the place of the eye, as before, and 



P O G, P O H, to be angles of 50^ 57', and 54^ 7' ; and 

 thefe angles to be turned aV^out their conunon fide OP; with 

 their other fides O G, OH, tin y will defcribe the verges, 

 or borders, of the rainbow C H D G. 



For, if G, H be drops placed any where in the conical 

 fuperficies defcribed by O G, O H, and be illuminated by 

 the fun's rays, the angle S G O, being equal to the angle 

 P O G, or ^d' 57', ftiall be the leaft angle m which the 

 ihen leaft refrangible rays can, after two refleftions, emerge 

 out of the drops ; and, therefore, the leaft refrangible rays 

 (hall come moll copioufly to the eye from the drops in the 

 line O G, and ftrike the fenfes with the deepeft red in that 

 region. 



And the angle S H O being equal to P O H, 54" 7', 

 fliall be the leall angle in which the moft icfrangible rays, 

 after two refleftions, can emerge out of the drops ; and, 

 therefore, thofe rays fhall come moft copioufly to the eye 

 from the drops in the line O H, and fo ftrike the fenfes with 

 the deepeft violet in that region. 



And, by the lame argument, the drops in the region, be- 

 tween G and H, (hall ftrike the fenfes with the intermediate 

 colours, in the order which their degrees of refrangibihty 

 require ; that is, in the progrefs from G to H, or from the 

 infide of the bow to the outer, in this order : red, orange, 

 yellow, green, blue, indigo, violet. 



And fince the lines O G, O H, may be fituated any where 

 in the conical furface ; what is faid of the drops and colours 

 in thefe lines is to be underftood of the drops and colours 

 every where in this fuperficies. 



Thus are formed two bows, an interior and ftronger, by 

 one reflection ; and an exterior m\A fainter, by two ; the light 

 becoming weaker and weaker by every reflection. 



Their colours will lie in a contrary order to one another ; 

 the firft having the red without, and the pnrple within ; and 

 the fecond, the purple without, and red within ; and fo of 

 the reft. 



Rainbow, Artificial. This doftrine of the rainbow is con- 

 firmed by an cafy experiment ; for upon hanging up a glafa 

 globe, full of water, in the fun-fhine, and viewing it in 

 fuch a pofture as that the rays, which com.e from the globe 

 to the eye, may, with the fun's rays, include an angle either 

 of 42% or 50° ; if, e. gr. the angle be about 42°, the fpec- 

 tator, fuppofcd at O, will fee a full red colour in that fide 

 of the globe oppofite to the fun, as at F. And if that 

 angle be made a little lefs, fuppofe by deprefling the glo- 

 bule to E, the other colours, yellow, green, and blue, will 

 appear fuccelTively, in the fame fide of the globe, alfo ex- 

 ceedingly bright. 



But if the angle be made about 50°, fuppofe by raifing the 

 globule to G, there will appear a red colour in that fide 

 of the globe towards the fun, though fomewhat faint ; and 

 if the angle be made greater, fuppofe by raifing the globe 

 to H, this red w'ill change fucceffively to the other colours, 

 yellow, green, and blue. 



The fame thing is obferved in letting the globe reft, and 



raifing or deprefling the eye fo as to make the angle of a juft 



1 1 magnitude. 



