1000000031

496 / 868

o p T
:ln,g,le ",ith lhe incident n ys, in whateycr. p:lrl of lhe: :¡rc
ATfYIl ,he drop ",as 'o ue. There(ore, ",hc,her ,he drop
is al A. 01'" al T. or al Y, or al llt 01" \I,'ht:rc·ever elfe it is
in IIIi5 wholc are, it wOllJd ólppear reJ, as il docs al F . T hc
drops o( r;.tin, as they falJ , ¡ re nel indcctl tu rnco round in
this Jnanner : but then, as innumcnlble of them are f:.lling
¡t once in right lines (rom {he cloud, whiHi one d rop is a l ...,
there will be other! al Y, al T, a l B, al A, and io evrry
OIh« part of ,he are ATfYB: . r.d all ,he(e drops will be
red for l'le rame reafon that the drop F would llave bctn
red, ir it had been in ,he fAme place. Thercrore, when lhe
fun Chines upon the rain as it (alls, there wiJl ue <1 red
.rc ATFYB oppoli,e 'o Ihe fi,n . In Ihe fame manner, be–
(3ufe the drop E is violet, \I.'C: might prove th;u any othc:r
drop. which, whilft it is (alling, IS in an,. pan of the.arc
AVEXIl, \Viii be ,·iole, •• nd confequcntly. al ,he (..,e
,ime ,h., ,he red are 1\TFYB appears, ,here will hkewife
be a víole, are AVEXB below or "'i,hin it. FE is Lhe
d.flance betweco thefe t\Vo coJourcd arcs; and from what
has been raid it foll ows, lhat the intermediare fpace bet~eeo
'hefe ' wo are. will be 611ed up wi,h are. of ,he in:ermediale
colours, orange, ydlow, blue. greco, aod indigo. AH lhefe
coloured arcs together make up the primary rainhow.
1''1 primar,) rainó01JJ j¡ ntVtr a grta(tr are Ihan a fimi.
eire/e.
Sinee Ihe line LOP j. drawn (rom ,he fim ,hrough ,he
'ye of tlie fpeCla,or, and fince P (No. 46.) i. ,be centre
or the rainbow; il follows, lh,u lhe ceorre of lhe rainbow
i. alway. oppoG,e 'o ,he fun. The angle FOP is an angle
of ,p: degrees :2 minutes, as was abrerved, ar F tbe highcdl:
pan of the bow is 42 degtees 2 minutes from P the cent re
of it. Ir Ihe fun i5 more than 42 d('grees 2 minutes high ,
P the centre of the rainhow, which ís oprorite tO lhe (un,
wilJ be more Ihan 42 degrees :2 minutes bcla\V Ihe horizon;
ánd confequently F ,he ,op of ,he bow, whirh i. only 42 de–
grees 2 minutes from P, \IIill be be'low tbe horizon; lh at ¡sJ
when the fun is more Ihan '12 degrees 2 minutes lIigh, no
primary r.inbow will be feen. lf -,he (un i. f~me,hing lef.
,han 42 degrees 2 minu,es high . ,hen P will be fome' hing lefs
than 42 dtgrees 2 . minutes below the horizon; and conCe·
quendy F, which ¡s ooly 42 de~recs 2 minutes from P, will
be jufi above tbe boriz )o ; rhat ¡s, a {lJlalJ part of lhe bow
a, ,hi. heigh, of,he (un will 'ppear c10fe ' o ,he grollnd op'
'o ,he fun . If ,he fun is 20 degrees high, ,hen P will
be 20 degrees below ,he horizon ; and F ,he ,op of ,he bow,
being 4'1 dcglees 2 minutes from P, wilJ be 22 degrees 2 mi–
nutes above the horizon; therefore, at lhis height of the 'un,
tlle bow wiJl be an are of a circle whofe centre is befow lhe
horizon; 2nd confeq uently thal are of rhe cirele, which is
aboye the horizoo, or rhe bo\V, , wi]) be ltf5 thilO a (em¡cir.
ele. If the fun is in the horizon. lhen P, the cenlre of
the bow, will be in ,he op?oG,e part of ,hc horizon; F, ,he
'op of ,he bow, will be 4' degrees ~ minu,es ,bove ,he ho·
flzon; :tod Ihe bow ¡trelf. becau fe lhe horizoll pít(fcs thro'
the centre of ¡t, will be a fcmici rc1e. ~lore lhotO a rcmici rcle
Cln never appear ; becaufe ir lhe bow was more than fem i·
arele, P the centre of il mull be above the horizon ; but P
is always oppofit e 10 the fun. thererore P cannot be ahove
,he horizon, unlcfs (be (un is beJow it ; and when the fu :'! is
fel, or is belo\V lhe horizon, it cannot Otine u,pon lhe ctrC'ps
c¡( ••in, as ,hey f. lI ; . nd confequendy. when Ihe l'un is belo\V
toe horizon. no bow~at al1 cao b,: fccn.
VOL . III N° S? 2
e s. 4 39
IV! rn Ih, ra)', oí Ih, {u n íall "1'01/ Q :lro/, DÍ r. in, Jo"" oí
IhrnJ, nfler l'UJONjlcfliQIII QlJd IruJO rejrllflionl, may CQIIJr:
(o Ihe eye of a Jpef!alor, 'tuno I'"J hi¡ hud lr,wardJ Il:e
¡un and hi¡ fau lowllrd, ¡he drop .
If hg<v, (No. 45 .) is a drop of rain, and p.,.lId ray'
co~i nc from ~he lun, as zv, )W, fal! upon t he JoWcr pdrt
of It, lhey wdJ be refr~éled tnw:uds [he perpendicubus vI,
wl, as they enter imo ¡t, ano wi lJ deferibe fome fu eh Jincs
as vII, w i . At h aod i cre~l pd rt of there rays wi ll pafs
ou' of Ihe drop ; bUI fome of Ihem \ViII be rcfltClcd fo 001
thence in the lioes J.f, ig. ,Alíandg ag.u n, grc,f.[ piln of
che rays, lhat \Vere refletled lhither. \ViII pars OUt of the
d rop. BUI ,hefe rays woll no, come 'o ,he eye of. (peé!. –
tor al (). H owevcr, here again all the nys \\ ill nOl pars OUt J
bu t fome few \ViII be reflcéted from¡ and g, in fome fach
line. as íd, gh; and ,hefe, when ,hey emerge 0111 of ,""
drop of water into lhe air &t b and d, wlH be refraéterl from
the -pcrpendiculars, and, defcribing the 1ines dI, ho. OX\y
<"ome [Q lhe eye of a rpeéhtor who has his back towards
,he (un and his (ace ,owards Ihe drop.
rO)'/, 'lllhich tire porallr!/ (o one anolher' df/er Ih~'y
bave han once re/rafled and olJee rljleflul il1 ti drop of
rain, 'tui/! he eifeflun/ whrn Ihe,) u llerge afltr Iwo r: e
frJlIir,1/1 and Iwo rtfitflionl.
No rays can be dreétual, unlcfs the~' are conticuOUE, and
panlleL From what was fRid, it appears, that when rays
come OUI of a drop of rain contiguous to one another, eie
Iher after one or after IWO refl eél:ioos, thcy mufi entcr the
drop nearly a' one and ,he place. And If fue!, r.y.
as are con ticuous are parallel after {he lidl refleél:ioa, they
,,·ill emerge par. Uel, and ,herefore will be cffd lll'/' L ec
zv andyw be contiguous rays which come frol11 che fun. and
are parallel to one another when they fall upoo Ihe Jower
par, of ,he drop hg'v, (No. 45.) (uppofe , hefe rayo 'o be
refracl ed at v and "W, and to be reAeéted at h anti i; if they
are parallel tO one anocher, as ~r. gi. after thi5firfi renca ion,
rhen, after Ihey are rd a fecond lime from/andg, and
re a fecond time as they emerge~ at d and b, tbey \\jiU
go ou, o( ,he drop par. lle1 'o 001••no,her in ,he j,nes dr and
DO, and will Iherefore be effeClu./.
The nys zv, .)1», are refraétc:d lowards the perpendicu –
lars vi, w/, when [hey eoter the drop., and will be maoe to
converge. As thefe rays are very obliq ue, thcir focus wiU
nOl be fa r from ,he (ur(.ce V'W. I( , hlS fotus is a, A. ,he
, a(,er ,hey have paffed ,he focus, wiJl diverge (rom
thence in the direélions lh, !ti-: and if /ti IS the prinl ipal rocal
oinanee of lhe concave reflelllOg fu tfacc hi, Ihe rc{)célcd
, ays hj'. ig. will be par.Jle/. Thefe '"ys hj'. ig, are rcflec·
red agai n from rhe ConCí'tve furface /g, anti wllI meet in a
(ocus a' <, fo ,h., g' wilJ be the p" ncipal (ocal dill.nce of
,his refl cCling furfaech. And e hi and íg >re parls
or lthe fame fphere, lhe princi pal focal dinances gt .wd /ti
\ViII be equal lO one . no, her. ' Vhen ,he rays paffed
lhe focus e. they will diverge froll1 lhence in lhe lines I'tI.
eb: and \Ve are 10 (h ew, that, when lhry emc:-ge at a' and b,
2nd are rcfraéll!rl thr'rc:, lhcy ",i il become para llcl.
Now if the rdys v.t, 'tUl, wh(:n they ha\·!.! mct at A, w('re
to be turncd back acain in the direllions ..fu, /t'tU, ;¡nd \\IC'le
t O emcrr,e at v and 'IV, they wOllld be rerT3éltd inlo the lines
o r their incidence v z , -¡.l/y, and thcrc(ole wou ld be pandld.
BJt (jn ce ge is equíll 10 ¡.t, as has airead y b~cn Che\\ o, the
5 'S t '"ys