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.ay' ed. ,b, tha, díverge from e, fall in the fame manner
upon ,he drop ac d and b, as the rays Av, } w, would fall upon
it at v and 'tU; and Id, eb, ar~ juft "5 mufl inclined tO the
refraéting (urface .db, as /"" }"" would be. 'o ,be (urface
tI"LIJ. Froln heoce it follows. th"t the rays ed, eb, emerging at
ti and D, will be refraéted in ,he (ame manner, and wil! have
the fame direétioo in refpeél: of one aoother, as ~vJ kw, would
h~ve. Bu,}v and }.¡1I would be parallel aft<f refraétion.
Therefore ed and eD \viII emerge in line. dp, bo, fa as ' o be
p.nllel ,p one ano,her. and cODfequently (o a. to be effec·
tual.
J/o'hm ray" Ihal l/re effeflaaf em"ge fr011l a drop 0f rain
"jier IflJJQ refleflionJ and two refraflionJ. Ihop which
are mojJ refrangibü rwil/ al Iheir etnafion male a grul/'
er angle rwith Ihe indd,nt raJ.I Ihan l /ufo do w hich
are leajl refrangible; and by IhiJ ,man¡ Ihe rayr o.f dif–
j<rml 'colollrJ .'WiJl D" ftparaledfrom one anolh".
If rays of differen, coloun. which -are differently refran·
gible, emerge at .ny poin' D, (No. 4).) ,hefe rays will nOI
be .11 of ,hem equally refraéted frQm ,he perpendicular.
Thus. if Do i. a red ray, which is of all o,hers ,he lea{l re·
frangible, and ¡'m is a viole< ray, which is of alr o,hers ,he
mon refrangible;. when theCe two ray' emerge at !J, the vio–
Jel "y will be refraéted more from Ihe perper,dicular DX ,han
the red rayo and ,he refraBed angle xDm will be grea'er Ihan
the refraéted angle xbo. From hence i, follow•• Ihal thefe
two rays, arter eme-rfion, will diverge from one aoother. [o
like inanner, the rays thal emerge al d \ViII divorge from
one anothe.r i a red uy will emerge in the 'line dp, a violet
ray in ,he line dI . So ,hat ,hough all the effeétual red rays
of tbe beam bdml are paralld to one ano,he .... and all ,be
e:ffeétual red rays of the beam hdop a(e likewife paralld 'o
one anolher, ye, tbe violel rays will nOI be parallel 'o ,he
red ones, bu, the violet beam will diverge from the red
beam·. Thus the rays of differenl colou," \Viii be feparated
from one anolher.
This \ViII appear fanher. if we conGder \Vhal Ihe pio·
poGtionaAlrms, That any violel or mof\ refrangible ray will
a gtea,er angle wi,h the incideDt ray•• ,han any red
or le. {l refrangible ray m.kes wilh Ihe Came incident ray• .
Thus if)'1JJ is aD ¡ncident ray, bm a vi~Jet ray emerging
from the point D • •mI DO a red ray emerging from .the Came
poinl ¡ the angle \Vhich Ibe viole< "y make. with tbe in.
<ident one is yrm, and that which the red ray makes
with it is )lD. Now yrm is a grealer angJe than }lO.
For in th. triang\e Drs the i'lteroal angle b" i. lefs t~an
Iny tbe external angle at the bafeo Euc . b. 1. prop. 16.
BUI yrm is the co",plemeDt of D" or of bry lO IWO right
enes, and l / O is the complement'of /Jl} lO two right ones.
Thert fore, fince bry i. lefs than DJy. ,he complemen, of
irJ la two , igh' angles will be greater than the comple.
meo'y of DJy to IWO ,ight .ngles; or yrm \viII be greater
than yJO.
Or o,herwife: BOlh ,he rayo biJ a.d ¿111, wheo they are
• efraBed in pafling ou, of ,he drop a' D. are turned round
upon the poio, j from the perpendicular Dx. Now ei,her
of thefe lines bm migh' be luroed round in ,hi. m. n·
ner. liII i, made a right angle \Vi,h J'W. Confequeotly. ,hat
uy which i. mol! tUTned rouod upoñ b. or whicb is mo{l
refraBed. will make an aogle withJ'W tha, will be Dearer to a
right one ,h.n that ray makes wi,h it which i. le.{l turno
cd round upon 6, or which is Ic:úl refraaed. Therefore
1 e s.
Ih.1 ray which is mo{l rofraBed will make a gre>!er aa.
gle wi,h ,he inciden, ray ,han Iha, which is leaR rcf..éleJ.
. But fince the emerging rays, as they are d,ff~rendy re.
(rangible, make diff.:renc aogles with the fame incident ray
y'W, the refraét¡on which ,hey fuqú at emerGon will fe.
parate them froOl ODe another.
The. angle yrm, which the mofl refrangible or violet rayo
make Wilh che iccident ones, is found by ca(culalioo [O be 54
degrees 7miou«.; and the anglepo, which the leafl refrangible
or red rays make with theincitlent ones, is (ound to be 50 de.
gree. 57 minu,e.: the angle•• "(hich ,he rayo of the iD.
termechatecolours, indigo, blue, greco, yellow, aod orange,
make with the iocident !aYS, are intermediate aagles be–
IweeD 54 degrees 7 minu,es .nd 50 degree. 57 minu,e•.
lf a liIU is luppofid lo 6e dra'Wn fro", Ihe centre ol lhelun
Ihrough lhe eye o.f Ihe/peflalor ; Ihe angle. owhich, al"r
' 'JJ,..orefran;onltllJd Iwo riflr:t1ion/, anJ ~ff(aual raJ llIaí,rl
'Wilh Ihe iflcidenl raJ, will De 'qu.I lo Ihe angl, 'llIDicb
;1 malus wiln Ihat lin(.
Ify'W, (No 45.) i. an incidenl ,ay, 60 ao effeBual rayo
and 'In a line drawn from Ibe centre of Ihe fun through ..
Ihe eye of the fpeéta,or.: the angle JlO. which the effe/loal
ray makes with rhe i.ncidenc'ray, is equal tO Ion the angll!
which the fa me eff.étual ray m.kes wi,h ,he line 'In. For
J'W and 'qlJ, confidererl as drawn from the centre oE 'lhe rUD,
are parallel; DO croffes ,hem, aod coofequeotly make. the
alte'rnílleanglesJ'o, Ion, equal to one ¡cother. Euc. b.l:
prop. 29.
Whm Ibe lun /hina upon Ihe droplof rain 111 Ihey arefaU–
ing'; Ihe rayl Ihal come frdJ!: Ih0ft drop, l. ¡f" eye./
11[pe{}alor, a/ler 1'UJ~ r!fi~flion/ aná Iwo rifrtJnjonJ, }r~
duu Ihe Ite~ndarJ rain6o'W.
- The fecondary rainbow is tbe outermo{l CHD, No. 46.
When the Cun !hines upon a qrop of uin H; and the rayo
HO, which emerge at Ji Ca a. 'o be effeétual. make aa
.ngle H O P of 54 degrees 7 minute. with LO.P a lin.
from ,he fuo through the eye of ,he fpeétator; the fame ef·
feétual rayo will make likewife.n aogle of 54 degrees 7 mi·
nutes with the uys S, and the uy! which emerge
al ,bis angle are viole< one., by what was obferved above.
Therefore. if the fpeBatOr'. eye i. al O. none bu, .iolet
rays \ViU en'er it: for •• aU the other rayo • leC.
angle wi,h Op, they will fall aboye ,he fpelhtOr'. eyi:.
lo like manner. if the effeétual rays th~, emerge from ,be
drop G make ao angle of 50 degree. 57 mioute. wi,h Ibe
lioe OP, they wiU likewife make the fame .ngle wilb ,be
incident rayo S; and coofequently, from the drop G to ,be
fpeéhtor's eye at O, DO uys will come bUI red one.; for ~I
Ihe o,her rays, ma~ing a greater .ogle wi,h the lineOP. wllI
fall below the eye at O. For ,he fame reafon, tbe rayo c'
merging from ,he intermedia.. drops between H ¡nd G. and
comiog to the fpeétator's eye at O, will emerge at ¡oterme·
dlate angles, and lhererore wiJl have the intermediatt colours.
Thus. ir there are feveo drop. from H 10 G ioclufively•
their colours will be violet, indigo, blue. greeo, yellow,
orange and red. Thi. coloured line is ,be bread,b of Ibe
fecoodary rain1]ow,
Now, if HOP was to 'urn rouDd upoo the lioe OP, like
a pair of comp.ffes upon ooe of the le~. OP wilb !be op<o–
ing HOP, it is froOl the fuppofition. that, ID Cuch a
revolution of the drop H, the angle HOP. ,"ould be the
{ame,