RAINBOW. 



rays, as 2 3, and the like ; which, bciiijT refrnftcd from 

 3 to 4, and refleftcd to j, and from 5 to 6, may at length, 

 by refraftion at 6, arrive at the eye 7, placed beneath the 

 drop. 



Thus much is obvious ; but to determine precifely the 

 quantities of rcfraftion of each ray, there mull be a calcu- 

 lation ; by fucli calculation it appears, that the rays wliich 

 fall on the quadrant A D, arc continued in hncs, like ihofe 

 here drawn in the drop A D K N ; wherein there are tlircc 

 things very confidcrable : firft, that the two refrattions of 

 the rays, in their ingrefs and egrefs, are both tlie fame way ; 

 fo that the latter does not deftroy the effe£l of the former. 

 Secondly, that of all the rays palfing out of A N, N P, 

 and thole adjoining to it, are the only ones capable of affeft- 

 ing tlie fenfe, as being fnfficiently clofe and contiguous, and 

 becaufe they come out parallel ; wliereas the reft are diverg- 

 ing, and difperfed too far to have any fenfible effedi, at leaft 

 to produce any thing fo vivid as the colours of the bow. 

 Thirdly, that the ray N P has (hade or darknefs under it ; 

 for, fincc there is no ray comes out of the furface N 4, it 

 is the fame thing as if the part were covered with an 

 opaque body. We might add that the fame ray N P has 

 darknefs above it ; fince the rays that are above it are 

 ineffeftual, and fignify no more than if there were none 

 at all. 



Add to this, that all the elTeftual rays have the fame point 

 of refleftion, /. c the parallel and contiguous rays, which 

 alone are effeftual after refraftion, will .ill meet in the fame 

 point of the circumference, and be reflected thence to the 

 eyes. 



Farther, it appears, that the angle O N P, mcludcd be- 

 tween the ray N P, and the line O N drawn from the centre 

 of the fun, is the angle by wliich the rainbow is diftant from 

 the oppofite point of the fun, and which makes the femi- 

 diameter of the bow. The method of determining it ivill be 

 feen in the fcquel of the article. But fince, bcfides thofe rays 

 coming from the centre of the fun to the drop of water, 

 there are many more from the fevcral points of its furface ; 

 there are a great many other efteftual rays to be confidered, 

 efpecially that from the uppermoft, and that from the 

 loweft part of the fun's body. 



Since, then, the apparent femidiameter of the fun is 

 about 16 minutes, it follows, that an effeftual ray from the 

 upper part of the fun will fall higher than the ray E F by 

 16 minutes: thus does the ray G H (f^. 2.) which, be- 

 ing refraftod as much as E F, deflefts to I, thence to L, 

 and at length emerging equally refrafted with the ray N P, 

 proceeds to M ; and makes an angle O N M with the line 

 O N. In the like manner, the effeftual ray Q R coming 

 from the loweft part of the fun, falls on the point R, 16 

 minutes lower than the point F on which the ray E F falls ; 

 and this, being refrafted, dechnes to S, whence it is re- 

 fleAed to T ; where, emerging into the air, it proceeds to 

 V ; fo that the line T V, and the ray O T, contain an angle 

 whofe magnitude will be afcertained. Again, upon com- 

 puting the deflexions of the rays, which like that 23 {Jig. i.) 

 coming from the centre of the fun, and being received into 

 the lower part of the drop, we have fuppofed fo be twice 

 refleAed, and twice refrafted, and to enter the eye by lines 

 like that 67 {fig. 3.) we find that which may be accounlrjd 

 effeftual, as t"] with the line 86 drawn from the centre of 

 the fun, contains an angle 867 ; whence it follows, that the 

 efFeftual ray from the highell part of the fun, with the 

 fame line 86, includes an angle lefs by 16 minutes ; and 

 that from the loweft part of the fun, an angle greater by 1 6 

 minutes. 



Thus, fince A B C D E F is the path of the cfScacious 



ray from the higheft part of the fun to the eye in F, the 

 angle 36 F becomes of a certain magnitude afcertained 

 below. In like manner, fince GHIKLM is the way 

 of an efledual ray from the loweft part of the fun to the 

 eye, the angle 86 M becomes greater than the former by 1 6 

 minutes. 



Since, then, we admit f-veral rays to be cffeftual, befidej 

 thole from the centre of tl.e fun, what we have faid of thr 

 (liade will need fome tlteration ; for of the three rays 

 delcribed (^^-f. 2 and 3.), only the two extreme ones will 

 have a iliadow joined to them, and that only on the outer fide. 

 Hence it i.s evident, that thcfe rays are perfedtly difpofed to 

 exiiibit all the colours of the prifm. 



Fur the great quantity of denfe or intenfe light, i. e. 

 the bundle of rays coUedled together in a certain point, v.^r. 

 in the point of refletiion of the effeftual rays, may be ac- 

 counted as a lucid or radiant body, terminated all around by 

 (hade. But the feveral rays, thus emitted to the eye, .ire 

 both of different colours ; that is, they are fitted to excit? 

 in lis the ideas of different colours ; and are differently re- 

 frafted out of the water into the air, notwithftanding their 

 falling alike upon the refrafting furface. 



Hence it follows, that the different or heterogeneous rays 

 will be feparated from one another, and will tend fcparatc 

 ways ; and the homogeneous rays will be collefled, and tend 

 the fame way ; and, therefore, this lucid point of the drop 

 in which the refraftion is effefted, will appear fringed or 

 bordered with feveral colours ; that is, red, green, and 

 blue colours vvill arife from the extremes of the red, green, 

 and blue rays of the fun, tranlmitted to the eye from fe- 

 veral drops, one higher than another, after the fame 

 manner as is done in viewing luCid or other bodies through a 

 prifm. 



Thus, adds fir Ifaac Newton, the rays that differ in re- 

 frangibility, will emerge at different angles ; and, confe- 

 quently, according to their different degrees of refrangibility, 

 emerging moft copioufly at different angles, they will exhibit 

 different colours in different places. 



A great number, then, of thefe little globules being dif- 

 fufed in the air, will fill the whole fpace with thefe dif- 

 ferent colours ; provided they be fo difpofed as that effeftual 

 rays may come from them to the eye ; and thus will the rain- 

 bow, at length, arife. 



Now, to determine what that difpofit'ton muft be, fuppofc 

 a right line drawn from the centre ot the fun through the 

 eye of the fpeftator, as the line VX [Jig. 2.) called the 

 line of aj'pell, or axis of vi/ion ; being drawn from fo remote 

 a point, it maybe elteemed parallel to all other lines drawn 

 from the fame point ; but a right line, tailing on two parallels, 

 makes tlie alternate angles equal. 



If, then, an indefinite number of lines be imagined drawn 

 from the fpeflator's eye t© a part oppofite to the fun where 

 it rains ; which lines make dificrent angles with the line of 

 afped, equal to the angles of rcfraftion of the differently 

 refrangible rays, thcfe lines, talluig on drops of rain illu. 

 mined by the fun, will make angles of the fame magni. 

 tude with rays drawn from the centre of the fun to the fame 

 drops. And, therefore, the lines thus drawn from the eye 

 will reprefent the effeftual rays that occafion the fenfation of 

 any colour. 



Now it is known, that the eye, being placed in the ver- 

 tex of a cone, fees objefts upon its furface, as if they were 

 in a circle ; and the eye ot our fpectator is here in the com- 

 mon vertex of feveral cones, formed by the feveral kinds of 

 efficacious r-ays, with the line of afpeft. Now in the furface 

 of that whofe angle at the vertex, or eye, is the grcateft, and 

 in which the others are included, are tliofe drops, or parts 



Z z 2 oi 



