1000000031

fall. above Ihe

",'S'14,

Ihis are

pOllg

\ViII deereafe.

We have hitherto fpoken of the poin.. on the hindor

part of the drop. where the ray' paC, out of it; bu.t this

was

íor

the Cake of determining (he points

(rom

whence

thoC. rayo are reOeéted, wh ich do no' paC, out behind

the drop. FOT,

explaining the rain.bow, we have no

f.rther reaCon 'o conGder thoCe rayo which go through

1he drop ; (ince they can never come to tbe eye of a

fpeélato, pl aced any where iD ,he lines

with his

face to wards the drop.

Now.

as there are many rays

whieh paC, ou, of ,be drop be,ween

and

fo fome few

r ay' will be refleéted from thence; and eonfequently the

feveral poiou between

and

which are the poio..

where fome of Ihe ray' paf, ou, of the drop, are like·

\ViCe the poi".. of rea . étion for ,he rell. whieh do no,

p.Cs

out. Therefore, iD reCpeét of thoCe , ays 'which are

reOeaed, \Ve may e.1I

,he are of reOeétion; .nd may

fay, Iha, this are of reOeaion increaCes, as Ihe dillance

of (he incident ray fram the axis

l a

¡ncreares,

till \Ve

come 'o Ihe ray

I d;

Ihe are of rtOe,'1ion is

for Ihe ray

l b,

it i.

(or the ray

l e,

and

t I'

for Ihe ray

I d.

BUI

after this, as the

dlna nc~

of lhe incident ray (rom lhe

axis

111

¡ncreares, the are of reReétion decreafes

for

leC. Ihao

is the are of relleétioo for Ihe ray

le,

aod

i. Ihe are of r. Oeétioo for Ihe ray

if.

From

neDee

is obvious, that fome one ray, which

fall. above

'Id,

may, be rell. éted from , he fam e poin,

wi.h fome otber ray which fall, belo\V

Id.

Thus, for

inllaoce, Ihe ray

will be reOeéted from the poinl

• nd Ihe

raylrwill

be reOeéted from the f.m e poinl ; ana

conCequently, when Ihe reOe{led

r~ys

nr, ' nq,

are refrac·

ted as ,hey paf. ou, of lhe drop a,

and

Ihey wiJl

be parallel , by whal has been fuewn in Ihe fo rmer part

of ,h i. propofilioo. Bu! finte Ihe

incermedi.le

ray',

whieh enler Ihe d rop be!weeo

and

Ih,

are nO.I reOee.

ted from Ihe

f.me

poin,

IheCe two rayo . Ione \ViII bt

parallel lO one anolher \Vhen Ihey come out of the drop,

.nd Ihe inlermediale rayo will nOI be parallel tO Ihem.

A nd conCequendy Ihefe rayo

ru, ql ,

,hough Ihey are p' .

rallel afler Ihey emerge a!

and

will nOI be eonti·

guau., and for Ihal

re~ron

wiJl nOl be e!fe{lual ; Ihe ray

i. ,.lIea ed from

whieh has beeo.Olewn 10 be Ihe

Jimi, of the are of reOeétion ; fueh ray" a. faJl j ull a.

bove

and j ull below

Id,

wiJl be reOeéted from nearly

the fame point

a, appea" from whal ha, been alread y

fu ewn. Thefe rayo !herefore wiJl be parallel, bee.uCe

Ifley are reflcéted from Ihe Came point

1';

aod Ihey \ViJl

JikewiCe be eonlÍguous, becauCe Ihey aJl of Ihem enter rhe

drop al one and Ihe Came place very nea r

ConCe·

quentl y, fuch rayo as enler Ihe d rop a'

and are relleéled

fr om

Ihe limil of Ihe are of refl eétion, wi Jl be e!fe{lual ;

lince, when Ihey emerge a' Ihe fore p. r' of Ihe d rop

becween

and

lhey. wiJl be bOlh par.lld aod conli.

&uou•.

. I f we can make oul hereafler lhal Ihe rain

bo'N

is pro.

duced by Ihe rayo of Ihe Cun wllich are Ihus reReéted

from drops of roi n as they f. JI "hilO Ihe Cun fui nes upon

theOl, this propofi tion m:ty ferve

fh ew

U3,

that this

'ppearance i. nOl produeed by any rayo Ihat fali upon a ,

ny pan and are r<Oefteu from any pan " f lhore d rops :

fince this ;¡¡ ppearanct: cann'H be produced

any ray' but

' Ihote whieh are

eJfe~"aJ· i

aod . u .étllal r. y' mlll!

al.

4 37

wa~s

enter cach

d ~op

a,t one certain pbce in the

rure-part.

of 11., . nd mull IIkewlre be reBeéteu fl Oll1 Olle ce".io

place in Ihe hinder ru,faee.

When Ntl f Ihal nr. ,jJdl ual 'emuge frol/1 a drop . •

rain

aJi~r

OT1e

rl'jlr:tli()n and

Iw() rifruflionr.

Ih;Je

'Which are moji

r~f,.allgible

will,

Ihdr

t l1urjit-",

moJu

lifJ

ang le

'Wilh

incidenl

ra)'r Ihan

Iho/~

do 'tl'hlch are

hafl refrangible;

Q/1d

IhiJ

lII(QU./

Ihe rays

di./Ju""1

coloun will he flporoled f rolll

IJn~

anolh(r,

L et

f h

and

gi,

(No . 44 ' ) be <!feétual viole! rayo

emerging from Ihe drop

¡g;

andfn,

gp,

e/F<étual red

rays emerging from ,he fa me d rop al Ihe Came ph ce. NolV,

Ihough al r Ihe viole! rays are parallel 10 one anolher

beeauCe Ihey are fuppoCed effeélual; and Ihou oh . 11

Ih~

red rays are likewile paralld la one anolher fO;' he f. llle

reaCon; ye! Ihe vial.. ray' will nOl be parallel lO Ihe

red rays. TheCe rays, as Ihey have differeot colours,

and di!ferenl degrees of refr.ngibiJilY, will diverge from

o~e ~n.other;

any violem ray

gi,

which emerges at

g .

w,1I dlverge fro m any red ray

gp,

whicb emerge.

Ihe

fame place. N ow, bOlh !he violel ray

gi,

and ,he red ray

tI',

as Ihey p. C, OUI of Ihe dlop of \Vacer iOlo ,he air

\ViII be refra{led from ,he p.erpendieular

lo.

B u! lhe vio:

1 ..

ray i. more refrao¡¡ible , h. n Ihe red one, and fo r Ihat

reafoo

gi,

or Ihe refraéted violet ray, will make a grea,er

angle wilb lhe perpendicular Ihan

Ihe refraéted red

ray; or ,he angle

igo

will be greacer Ihan Ihe angle

Pgo .

SuppoCe the incidenI ray

10 be continued in rhe di.

re{lion

I~,

aDd Ihe violel ray

10 be conlinued backward

in lhe

dir~élio?

il ,

tiJi it

meets

lhe incideot

ray

.f.

S uppofe hkew,Ce Ibe red ray

to be eonlinued back.

wards in the (ame manner

tiJl

meets

the incident say

W .

T he angle

i. Iha, whieh ,he violet ray, or

mofl refrangible ray

al its

ernerCion, makes

with the

'in.

cident ray ; and Ihe angle

!,WI

i, lhal whicb Ihe red ray,

or leall refrangIble ray a!

lIS

emerr:on, m. kes wilh Ilre '

incident rayo The angle

I~I

is Jer. Il¡an Ihe angle

pWf.

For, in

~he

trii\oglegwl, gw./

PWJ

is the externa)

angle at Ihe baCe, and

g~,!"

iAI

i. One of Ihe interna!

oppofile angle.; and . ilher inlernal oppofi .. angle is ler.

Ihan ' Ihe eXlernal angle

Ihe baCe. Euc. b.

prop.

16. W h.. has been fu ewn lo be Irue of Ihe rays

g i

and

might be fu ewn i.. Ihe

f.me

mander of Ihe rays

and

fl/ ,

o r of any olher rayo Ih.. e merge "rp, étively pa.

rallel

and

gp.

BUI.II

Ihe e/Feaual violel rayo are

parall la

gi.

and

. U

lhe e/Feétua l red ray' are par . lld lO

!tI>.

T herefore Ihe dre,'1 ual vial.. rays al Iheir <me,fion

make a leCs aogle wilh lbe ineidenlone. Ihan Ihé erFd lQ"J

red ones. And for lhe {ame reafon, in alJ lhe otber

fon

of r.;ys, (hore which are

!non

re(rangible, al

Iheir

cmer~

fion (rom a drop of rain afcer one rd leaion. will make

a I, r. angle wi lh Ihe incidenl rays, Ihan IhuCe do IVhicu

are

leC.

r.rrangibl~.

O r olhe rw.ife : When Ihe

ray'gi

and

emer!.!e al

11'e

fame

pOlOt ,fJ

as lhey both

come

OU t

o( water

iOlO

;:Ur

and confequt:ntl y are refraéted from a perpendi cular, in :

nead ofgoing nraighl forw. rdsin Ihe line

conl inued, IIt<y

will bOlh be lurned

ro~n?

upon ,he

poin~

from Ihe pe,.;

pendicular

go .

N ow

11 15

eafy to concelve, tl,at eÍlhcrof

thef~

Jines might be ! urned in this manoer upon rhe pvi'.1

S .""