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Chambers, Ephraim, 1680 (ca.)-1740 / Cyclopædia, or, An universal dictionary of arts and sciences : containing the definitions of the terms, and accounts of the things signify'd thereby, in the several arts, both liberal and mechanical, and the several sciences, human and divine : the figures, kinds, properties, productions, preparations, and uses, of things natural and artificial : the rise, progress, and state of things ecclesiastical, civil, military, and commercial : with the several systems, sects, opinions, &c : among philosophers, divines, mathematicians, physicians, antiquaries, criticks, &c : the whole intended as a course of antient and modern learning

R - Rectification,   pp. 951-966 PDF (18.2 MB)

Page 956

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Sun-ihine, and viewing it in fuch a Pofture as that the Rays which
come from the Globe to the Eye, may, with the Sun's Rays in-
clude an Angle either of 429, or 5o9; if, e. gr. theAngle be a-
bout 42Q; the Spedator, fuppofed at 0, will fee a full red Co-
lour in that Side of the Globe oppofite to the Sun, as at F. And
if that Angle be made a little lets, fuppofe by depreffing the Glo-
bule to E, the other Colours, Yellow, Blue, and Green, will ap-
pear fuccellively, in the fame Side of the Globe, alfo exceed-
ingly bright.
But if the Angle be made about 5of, Cuppofe by railing the
Globule G, there will appear a red Colour in that Side of the
Globe towards the Sun; though that foomewhat faint; and if the
Angle be made greater, fuppofe by railing the Globe to H; the
Red will change fucceffively to the other Colours, Yellow,
Green, and Blue.
The fame thing is obferv'd in letting the Globe reft, and rai-
fing, or deprelling the Eye to make the Angle of a jull Magnitude.
Dimenfions of the RAIN-BOW.
Des Cartes firif derermin'd its Diameter by a tentative, and in-
dired Method; laying it down that the Magnitude of the Bow
depends on the Degree of Refraftion of the Fluid; and ailuming
the Ratio of the Sine of Incidence to that of Refra.tion, to be
in Water as 250 to I57. See REFRACTION.
But, Dr. Halley has fince, in the Philofoph. Tranfae7. given us
a femple, aired Method of determining the Diameter of the
Rainbow from the Ratio of Refradfion of the Fluid being given;
or vice verfa, the Rainbow being given, to determine the refra-
dtive Power of the Fluid. The Praxis is as follows.
Firft, The Ratio of Refrat7ion being given; tofind the Angles of
Incidence, and Refrae~ion of a Ray which becomes efletual ajter a-
zay given N'umber of Refletlions. Suppofe any given Line as AC
(ab . Opticks, Fig. 49.) which divide in D; lo, as that AC be
to AD in the Ratio of Refradaion; and again divide it in E, fo
as AC be to AE as the given Number of Reflexions increased
by Unity, is to Unity; with the Diameter CE defcribe a Semicir-
cle CBE, and from the Centre A with the Radius AD defcribe an
Arch DB interfeding the Semicircle in B.  Then drawing AB,
CB; ABC or its Complement to two right Angles, will be the
Angle of Incidence; and AC3 the Angle of Refradtion required.
Secondly, The Ratio of Refraffion, and any Angle of Inczaence
being given to find the Angle which a Ray of Light emerging out of
a refraaing Sphere, after a givenNumber of Refiec7ions, makes with
the Line of Afiet4 or an incident Ray; and confequently to find the
Diameter of the Rainbow. The Angle of Incidence, and the Ra-
tio of Retradion being given, the Angle of Refradion is given;
which Angle being multiplied by double the Number of Re-
flexions increased by 2) and double the Angle of Incidence fub-
flra6ted from the Produ&, the Angle remaining is the Angle fought.
Thus fuppofing, the Ratio of Refraation to be, as Sir Ifliac
Newton has determined it, viz. as 0o8 to 8x, in the red Rays,
as I19 to 8I for the blue Rays, &c. the preceding Problem will
give the Diftances of the Colours in the
I. RAIN-Bow, S e 4IQ
I  le40
1.RAIN-Bow, S Red 5o
II.     ~~~ Blue 54
12   The Spetator's Back
58    being turned to
58 the Sun.
If the Angle made by a Ray after three or four Refledions,
were required. and therefore the Diameters of the third and
fourth Rainbew, (which are fcarce ever feen, by reafon of
the great Diminution of the Rays, by fo many repeated Re-
flexions) they will be found.
Ill. Rainbow, Red 41 f
B Riue 3n7
IV. Rainbow,  Red 43
(Blue 49
3 7 The Spetator being
9  turned towards the
5  Sun
Hence, the Breadth of the Rainbows is eafily found: For the
greatell Semidiameter of the firif Bow, i. e. from Red to Red
being 42f I', and the leaft, viz. from Purple to Purple 4o0
I6; the Breadth of the Fafcia or Bow, meafured a-crofs from Red
to Purple will be I0 45 S and the greateft Diameter of the fe-
cond Bow being S4' 9', and the leaft 500 58'1 the Breadth of
the Paficia will be 30 io' And hence the Diflaxce between the
two willbefound 89 qJ.
In thefe Meafures the Sun is only efteem'd a Point; where-
fore as his Diameter is really about 30' fo much muft be added
to the Breadth of each Fafcia or Bow, from Red to Purple, and
fo much be fubftrated, from the Diftance between them.
This will leave the Breadth of the primary Bow, 2 9 15I that
df the fcondary Bow 39 40', and the interval between the Bows
90 2S'; which Dimenfions deduced by Calculation, Sir Iaac
Newton afrures us from  his own Obfervations, agree very exadtly
with thofe found by  acdual Menfuration in the Heavei1
par itaular Phenomena of the RAIN-BOW, qwith the Canfes thereof
FroW sic Theory of the Raiow, all the  prticular Phno-
mena are eafily deduced: Hence we fee why the Iris is alw
of the fame Breadth; by reafon the intermediate Degrees of re-
frangibility of the Rays between Red and Violet, which are its
extreme Colours, are always the fame.
-Secondly, Why it is more diffmndly terminated on the Side of
the Red, than orn that of the Violet? There being no efficacious
Rays in the $pace adjoining to the red Drops, i. e. to the Space
between the Bows; whence it terminates abruptly; whereas in the
Space on the Side of the Violet ones there are fome Rays emit-
ted to the Eye, which though too feeble to affedt it ftrongly,
yet have this effed, that they foften the Violet Edge infenfibly.
fo that 'tis difficult to determine precisely where it terminates.
Tbirdly, Why the Bow fhifts its Situation as the Eye does;
and, as the popular APrafe has it, flies tbofe whofollow it, and fel-
lows thfe thatfly it ? The colour'd Drops being difpofed under a
certain Angle abott the Line of Afpe&, which is different in
different Places: Whence, alfo, it follows that every different
Spedator fees a different Bow.
Fourthly, Why the Bow is fometimes a larger Portion of a
Circle, fometimes a lefs ? Its Magnitude depending on the grea-
ter, or lefs Part of the Surface of the Cone, above the Surface
of the Earth at the Time of its appearance; and that Part being
greater or lefs as the Line of Afpe: is more inclined or oblique
to the Surface of the Earth; which inclination, or obliquity, is
greater as the Sun is higher: Whence, alfo, the higher the Sun,
the lefs the Rainbow.
Ffthly, Why the Bow never appears when the Sun is above a
certain Altitude? The Surface of the Cone wherein it fhould be
feen, being loft in the Ground, at a little Diflance from the Eye,
when the Sun is above 4z' high.
sixthly, Why the Bow never appears greater than a Semicircle.
on a Plane? Since be the Sun never fo low, and even in the Ho-
rizon; the Centre of the Bow is ftill in the Line of Afpedt;
which, in this Cafe, runs along the Earth, and is not all rais'd at,
bove the Surface.
Indeed, if the Spedator be placed on a very confiderableEmi-
nence, and the Sun in the Horizon; the Line of Alpedt wherein
the Centre of the Bow is, will be notably rais'd above the
Horizon, (confidering the Magnitude of the Circle whereof the
Bow ufes to be a Part.)  Nay, if the Eminence be very high,
and the Rain near, 'tis poffible the Bow may be an entire
Seventhly, How the Bow may chance to appear inverted, i. A.
the Concave Side be turn'd upwards ? To wit, a Cloud happeming
to intercept the Rays, and prevent their thining on the upper
Part of the Arch: In which Cafe only the lower Part appear.
ing, the Bow will feem as if turn'd upfide down: Which proba-
bly has been the Cafe in feveral Prodigies of this Kind, related
by Authors.
Indeed the Bow may appear inverted from another Caufe:
For, if, when the Sun is 419 46' high, his Rays fall upon the
imooth Surface of fome fpacious Lake, in the middle whereof a
Spetator is plac'd; and if, at the fame time there be Rain fall-
ing to which the Rays may be refleded from the Lake: 'Twill
be the fame as if the Sun Ihou'd thine below the Horizon, and
the Line of View be extended upwards: Thus the Surface of
the Cone wherein the coloured Drops are to be placed, will be
wholly above the Surface of the Earth.
But fince the upper Part will fall among the unbroken Clouds;
and only the lower Part be found among the Drops of Rain,
the Arch will appear inverted.
Eighthly, Why the Bow fometimes appears inclined? The ac-
curate roundness of the Bow depending on its great Diftance,
which prevents us from judging of it exadly; if the Rain which
exhibits it, chance to be much nearer, we Ihall fee its irregula-
rities; and if the Wind in that Cafe drive the Rain fo as the
higher Part be further from the Eye than the lower, the Bow
will appear inclined.
Ninibly, Why the Legs of the Rainbow fometimesappear un-
equally diftant? If the Rain terminate on the Side of the Speda-
tor, in a Plane fo inclined to the Line of Afie& as to make an
acute Angle on the left Hand, and an obtufe Angle on the right;
the Surface of the Cone which determines what Drops will ap-
pear, will fall upon them  in fuch manner as that thofe on the
left Hand, will-appear further from the Eye than thofe on the
Right. For the Line of Afpe& being Perpendicular to the Plane
of the Bow, if you fuppoie two re6tangular Triangles a Right
and Left, the Cathetus of each to be Line of View, and the Bafe
the Semidiameter of the Bow, inclined as above: 'Tis evident,
fince thofe Angles of the Triangles, next the Eye. muff always
be the fame, (viz. 43 9 in the inner Bow) the Batis of the Right.
hand Triangle will appear much longer than that of the Left.
The Moon, fometimes, alfo, exhibits the Phbenomenon of an
Iris or Bow; by the Refradtion of her Rays ia the Drops of
Rain in the Night-time. See MOON.
4ripetk fays, he was the firfr that ever oblerved it; and ad&s,
that it never happens. i. e. is never vifible, but at the Time of the
Full-Moon; her Light at other tithes being too faint to affit
the Sight, after two Ref ra~ions, and one Refletion.
*     \                           as~~~~~Th

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