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n computing the Deflexions of the Rays, which,
F. 4y.) coming from the Centre of the Sun, and be-
nto the lower Part of the Drop, we have fuppofed
efleed, and twice refracted. and to enter the Eye
that 67 (FPg. 47.); we find that which may be ace
tual, as 67, with the Line 86 drawn from the Cen-
m, contains an Angle 867, of about S2 Degrees:
4lows that the effectual Ray from the higheff Part
with the fame Line 86 includes an Angle lefs by I6
d that from the lowelt Part of the Sun, an Angle
Minutes.
ABCDEF is the Path of the efficacious Ray from
irt of the Sun to the Eye in F; the Angle 86 FI
ibout fifty one Degrees, and forty fbur Minutes.
er, fince GHIKLM is the Way of an effedual
loweft Part of the Sun, to the Eye, the Angle 86
early of fifty two Degrees, and fixteen Minutes.
we admit feveral Rays to be effheual, befide thofe
itre of the Sun; what we have faid of the Shade
e Alteration: For, of the three Rays defcribed
only the two extreme ones will have a Shadow join-
and that only on the outer Side. Hence it is evi-
thefe Kays are pertefly dilpoled to exhibit all the Cow.
he PriJY.
e great Quantity of denfe or intenfe Light, i. e. the
Rays colleaed together in a certain Point, v. gr. in
of Refledftion of the effe6tual Rays, may be accounted
or radiant Body, terminated all around by Shade. But
al Rays thus emitted to the Eye are both of different
;bat is, fitted to excite in us the Ideas of different Co-
d are differently refrated out of the Water into Air,
anding their falling alike upon the refraating Surface. See
it follows that the different or heterogeneous Rays will
rtea trom one another, and will tend separate ways; and
geneous Rays be colle6ted, and tend the fame way:
refore this lucid Point of the Drop, wherein the Re-
is effected, will appear fringed, or border'd with feveral
, that is, red, green, and blue Colours will arife from the
te red, green, and blue Rays of the Sun trani-
Eye from feveral Drops one higher than another;
nmanner as is done in viewing lucid, or other Bo-
a rimn. Sbee PRISM.
s Sir Ifaac Newton, the Rays that differ in refrangi-
A will emerge at different Angles; and consequently, accord-
itheir diffirent Degrees of Refrangibility, emerging moft
Bly at different Angles, will exhibit different Colours in
ent Places. See REFRANGIBILITY.
reat number then of thefe little Globules being diffused in
Vr, will fill the whole Space with thefe different Colours;
ied they be fo di/pofed as that effedtual Rays may come from
to the Eye; and thus will the Rainbow, at length, arife.
Dw to determine what the Dirpoftiox muff be; fuppofe a
Line drawn, from the Centre of the Sun through the Eye
e Spe&ator, as the Line VX, (Fig. 46.) call'd the Lineof Af
Being drawn from fo remote a Point, it may be efteem'd
lto all other Lines drawn from the fame Point: But a
Line falling on two Parallels makes the alternate Angles e-
See ALTERNATE.
then, an indefinite Number of Lines be imagin'd drawn from
;peaaror's Eye to a part oppofite to the Sun where it rains;
i Lines make different Angles with the Line of Afpe&, e-
to the Angles of Refra6ion of the differently refra6tible
e. gr. Angles-of 42f. I, and of 4o0, x6r Thefe Lines
g on Drops of Rain illumined by the Sun, will makes An-
of the fame Magnitude with Rays drawn from the Centre
i Sun to the fame Drops.  And therefore the Lines thus
n frorm hi- T7-   - will -fnrl-rt the WE-4-a1  1 úvc * cJhe4at
n of any Colour.
making an Angle of 420 1 ac reprefenting the 1e4&
ed Rays of the feveral D~rops, and of 4O0 ii6',
gible or violet Rays: The intermediate Colours,
es will be found in the intermediate Space Ee.
LET) &C.
:own that the Eye being placed in the Vertex of
)jests upon its Surface as if they were in a Cir-
Ie of our Speaator is here in the common Ver-
ones, form'd by the feveral Kinds of efficacious
Line of Afped. And in the Surface of that whofe
ertex or Eye is the greateft, and wherein the o-
ed, are thofe Drops or Parts of Drops which ap-
i the Surface of that Cone whofe Angle is leaft,
Drops: And in the intermediate Cones are the
Sc. Drops.  Hence then feveral Kinds of the
ear as if difpolid into fo many circular colour'd
:s, as we fee in the Rainbow.
the Solution Sir Ifaac Newton expreffes more art-
,ofe 0 (Fig. 48.) the Eye, and OP a Line Parallel to
and let POE, POFbe Angles of 4oG 17', and 4.Q
fe the Angles to turn about their common Side
other Sides OR and OF, they will defcribe the
ps of the Rainbow.
RA
For, if EF be Drops placed any where in the conical Surface
defcribed by QE OF; and be illuminated by the Sun's Rays SE´
SF, the Angle SEQ beingequal to the Angle POE or 409 172
ball be the greatefi Angle in which the Imoff refrangible Rays
can, after Reflection, be refraced to the Eye; and therefore all
the Drops in the Line OE thall fend the moft refrangible Rays
mofl copioufly to the Eye, and thereby ftrike the Senfes with
the deepeff Violet Colorw in that Region.
And in like Manner the Angle SVO being_ to the Angle
POF-+7f 2; (hall be the greatefi, in which the leafl refrangi-
ble Rays after one Rellefion can emerge out of the Drops; and
thefe Rays fhall come mofi copioufly to the Eye, from the
Drops in the Line OF, and firike the Senfes with the deepef
red Colour in that Region.
And by the fame Argument the Rays, which have intermediate
Degrees of Refrangibility, h all come moftcopiou ny from Drops
between E and F, and o nrike the SenfSes with the intermtediate
Colours, in the Order which their Degrees of Refrangibility
require; that is, in the Progrefs from E to F, or from the inm
fide of the Bow to the outride, in this Order, Violet, Indigo, Blue,
Green, toelow, Orarge, Red: Though the Violet, by the mixture
of the white Light of the Clouds, will appear faint, and incline
to a putpke.
And fince the Lines OE OF may be fituated any where in
the abovemention'd conical Surface; what is faid of the Drops
and Colours in thefe Lines is to be undertood of the Drops and
Colours throughout the whole Superficies. Thus is the primary,
or ianer Bow  f form'd.
Secundaary, or owter RAIN-Bow.
As to the fecundary or fainter Bow, ufually furrounding the
former; in afligning what Drops would appear coloured, we ex-
cluded fuch as Lines drawn from the Eye, making Angles a little
greater than 42  2' hould fall upon ; but not such asf hou'd
contain Angles much greater.
For, if an indefinhte Number of fuch Lines be drawn from
the Spe~tator's Eye, fome whereof make Angles of 5o0 57'
with the Line of Afpe~t;i e. gr. OG;i other Angles of 54Y 9',
e.gr. OH;g thofe Drops whereon thefe Lines fall, mui'c of ne-
qeflity exhibit Colours. Particularly thofe of 5o0'  7 '
E. gr. the Drop G will appear red; the Line GO being the
fame with an effetual Ray, which after two Reflections and two
Refra6tions, exhibits a red Colour. Again, thofe Drops which
receive Lines of 54' 9,' e. gr. the Drop H will appear Purple,
the Line OH being the fame with an effecaual Ray which after
two Reflections, and two Refradions; exhibits Purple.
Now, there being a fufficient Number of thefe Drops, 'is e-
vident there muft be ajecond Rainbow, form'd after the like man-
ner as the firfb
Thus, Sir Ifaac Newton: In the leaft refrangible Rays, the
leaft Angle at which a Drop can fend effe6Eual Rays after two
Reflexions, is found by computation to be 50" 57', and in the
moft refrangible the leaft Angle is found 5y4   7'.
Suppofe, then. 0 the Place of the Eye, as before, and POG,
POL tobc Angles of 5o0 57', and 549 7'.  And thefe Angles
to be turn'd about their common Side OP; with their other
Sides OG, OH, they will defcribe the Verges or Borders of the
Rainbow CHFDG.
For, if GH be Drops placed any where in the conical Super-
ficies described by OG OH, and be illumined by the Sun's Rays;
the Angle SGO being equal to the Angle POG or 50" 57,
fhall be the leaft Angle, in which the then leaft refrangible Rays,
can, after two Reflections, emerge out of the Drops; and there-
fore the leaft refrangible Rays (hall come moff copioufly to the
Eye from the Drops in the Line OG, and ftrike the Senfo with
the deepeni Red in that Region.
And the Angle SHO being equal to POH, 540 7, fhall be
the leaff Angle in which the moft refrangible Rays, after two
Refletions, can emerge out of the Drops; and therefore thofe
Rays fhall come moll copioufly to the Eye from the Drops in
the Line OH, and lb ftrike the Senfes with the deepeft Violet in
that Region.
And by the fame Argument, the Drops in the Region between
G and Hl, fhali ftrike the Senfes with the intertnedate Co-
lours, in the Order which their Degrees of Refrangibility re-
quire; that is, in the Progrefs from G to H, or from the infide
of the Bow to the outer, in this Order: Red, Orange, DelAw,
Green, Blue. Irnico, Violet.
And fince the Lines OG, OH, may be fituated any where in
the conical Surface; what is Laid of the Drops and Colours in
thefe Lines, is to be underftood of the Drops and Colours every
where in thefe Superficies.
Thus are form'd two Bows, an interior, and ftronger, by one
Reflection; and an exterior and fainter by two; the Light becom-
ing weaker and weaker by every Reflexion.
Their Colours will lie in a contary Order to one another;
the firif having the Red without, and the Purple within; and the
fEcond the Purple without and Red within; and fo of the reft.
-,tifidal RAIN-BOW.
This Do&rine of the Rainbow is confirm'd by an eafy Experi-
ment: For upon hanging up a Glafs Globe full of Water in the
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