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order is reversed, the red being inside and the violet outside. Its angular radius is about 57°. It is also to be noticed that the space between the two bows is considerably darker than the See also:

REST (O. Eng. rest, reste, bed, cognate with other Teutonic forms, e.g. Ger. Rast, Riiste, rest, and probably Gothic Rasta, league, i.e. resting or stopping place)

rest of the See also:

SKY (M. Eng. skie, cloud; O. Eng. skua, shade; connected with an Indo-European root sku, cover, whence " scum," Lat. obscurus, dark, &c.)

sky. In addition to these prominent features, there are sometimes to be seen a number of coloured bands, situated at or near the summits of the bows, See also:

close to the inner edge of the primary and the outer edge of the secondary bow; these are known as the See also:

SPURIOUS

spurious, supernumerary or complementary rainbows. The formation of the rainbow in the heavens after or during a shower must have attracted the See also:

ATTENTION (from Lat. ad-tendo, await, expect; the condition of being " stretched " or " tense ")

attention of See also:

man in remote antiquity. The earliest references are to be found in the various accounts of the See also:

DELUGE, THE (through the Fr. from Lat. diluvium, flood, diluere, to wash away)

Deluge. In the Biblical narrative (Gen. ix. 12–17) the bow is introduced as a sign of the See also:

covenant between See also:

God and man, a figure without a parallel in the other accounts. Among the Greeks and See also:

Romans various speculations as to the cause of the bow were indulged in; See also:

Aristotle, in his Meteors, erroneously ascribes it to the reflection of the sun's rays by the rain; See also:

SENECA

Seneca adopted the same view.

The introduction of the See also:

IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

idea that the phenomenon was caused by See also:

refraction is to be assigned to Vitellio. The same conception was utilized by See also:

THEODORIC

Theodoric of Vriberg, a Dominican, who wrote at some See also:

time between 1304 and 1311 a See also:

TRACT (from Lat. tractare, to treat of a matter, through Provencal tractat and Ital. trattato)

tract entitled De radialibus impressionibus, in which he showed how the primary bow is formed by two refractions and one See also:

INTERNAL

internal reflection; i.e. the light enters the drop and is refracted; the refracted See also:

ray is then reflected at the opposite See also:

SURFACE

surface of the drop, and leaves the drop at the same See also:

side at which it enters, being again refracted. It is difficult to determine the See also:

INFLUENCE (Late Lat. influentia, from influere, to flow in)

influence which the writings of Theodoric had on his successors; his See also:

WORKS

works were apparently unknown until they were discovered by G. B. Venturi at See also:

Basel, partly in the See also:

CITY (through Fr. cite, from Lat. civitas)

city library and partly in the library of the Dominican monastery. A full See also:

account, together with other See also:

early contributions to the See also:

SCIENCE (Lat. scientia, from scire; to learn, know)

science of light, is given in Venturi's Commentari sopra la storia de la Teoria del Ottica (See also:

Bologna, 1814). See also:

John See also:

FLEISCHER, HEINRICH LEBERECHT (1801-1888)

Fleischer (sometimes incorrectly named See also:

Fletcher), of See also:

BRESLAU (Polish Wraclaw)

Breslau, propounded the same view in a pamphlet, De iridibus doctrina Aristotelis et Vitellonis (1574); the same explanation was given by Franciscus Maurolycus in his Photismi de lumine et See also:

UMBRA (Lat. for shade or shadow)

umbra (1575)• The most valuable of all the earlier contributions to the scientific explanation of rainbows is undoubtedly a See also:

TREATISE

treatise by Marco See also:

Antonio de See also:

DOMINIS, MARCO ANTONIO DE (1560-1624)

Dominis (1566-1624), See also:

ARCHBISHOP (Lat. archiepiscopus, from Gr. apxceatorcoros)

archbishop of Spalatro. This See also:

WORK

work, De radiis visas et lucis in vitris perspectivis et iride, published at See also:

Venice in 1611 by J. See also:

BARTOLUS (1314–1357)

Bartolus, although written some twenty years previously, contains a See also:

CHAPTER (a shortened form of chapiter, a word still used in architecture for a capital; derived from O. Fr. chapitre, Lat. capitellum, diminutive of caput, head)

chapter entitled " See also:

VERA, AUGUSTO (1813-1885)

Vera iridis tota generatio explicatur," in which it is shown how the primary bow is formed by two refractions and one reflection, and the secondary bow by two refractions and two reflections. See also:

DESCARTES, RENE (1596-1650)

Descartes strengthened these views, both by experiments and geometrical investigations, in his Meteors (See also:

LEIDEN

Leiden, 1637). He employed the See also:

law of refraction (discovered by W. Snellius) to calculate the radii of the bows, and his theoretical angles were in agreement with those observed.

His methods, however, were not See also:

FREE

free from tentative assumptions, and were considerably improved by See also:

Edmund See also:

HALLEY, EDMUND (1656–1742)

Halley (Phil. Trans., 1700, 714). Descartes, however, could advance no satisfactory explanation of the See also:

CHROMATIC (Gr. xpcoµaruc6s, coloured, from xpwµa, colour)

chromatic displays; this was effected by See also:

Sir See also:

ISAAC (Hebrew for " he laughs," on explanatory references to the name, see ABRAHAM)

Isaac See also:

Newton, who, having explained how See also:

white light is composed of rays possessing all degrees of refrangibility, was enabled to demonstrate that the order of the colours was in perfect See also:

ACCORD (from Fr. accorder, to agree)

accord with the requirements of theory (see Newton's Opticks, See also:

BOOK

book i. See also:

PART

part 2, prop. 9). The geometrical theory, which formed the basis of the investigations of Descartes and Newton, afforded no explanation of the supernumerary bows, and about a See also:

CENTURY (from Lat. centuria, a division of a hundred men)

century elapsed before an explanation was forthcoming. This was given by See also:

Thomas See also:

Young, who, in the Bakerian lecture delivered before the Royal Society on the 24th of See also:

NOVEMBER (Lat. novem, nine)

November 1803, applied his principle of the interference of light to this phenomenon. His not wholly satisfactory explanation was mathematically examined in 1835 by See also:

Richard See also:

Potter (Camb. Phil. Trans., 1838, 6, 141), who, while improving the theory, See also:

LEFT

left a more See also:

COMPLETE

complete See also:

SOLUTION (from Lat. solvere, to loosen, dissolve)

solution to be made in 1838 by Sir See also:

George Biddell See also:

AIRY, SIR GEORGE BIDDELL (1801-1892)

Airy (Camb. Phil. Trans., 1838, 6, 379)• The geometrical theory first requires a See also:

CONSIDERATION (from Lat. considerare, to look at closely, examine, generally taken to be from con-, and the base seen in sidus, sideris, a star, the word being supposed to be originally an astrological or astronomical term)

consideration of the path of a ray of light falling upon a transparent See also:

SPHERE (Gr. vclsa?pa, a ball or globe)

sphere. Of the See also:

TOTAL

total (See also:

LEA, HENRY CHARLES (1825–1909)

lea- amount of light falling on such a sphere, part is reflected or metrical scattered at the incident surface, so rendering the drop m visible, while a part will enter the drop.

Confining our t: ory. attention to a ray entering in a See also:

PRINCIPAL

principal See also:

PLANE

plane, we will determine its deviation, i.e. the See also:

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle between its directions of incidence and emergence, after one, two, three or more internal reflections. Let See also:

EA be a ray incident at an angle i (fig. 1) ; let AD be the refracted ray, and r the angle of refraction. Then the deviation experienced by the ray at A is i—r. If the ray suffers one internal reflection at D, then it is readily seen that, if DB be the path of the reflected ray, the angle See also:

ADB equals 27, i.e. the deviation of the ray at D is 7r-2r. At B, where the same as at A, viz. i—r. The total deviation of the ray is consequently given by D=2(i—r)+7r—2r. Similarly it may be shown that each internal reflection introduces a supplementary deviation of ,r—2r; hence, if the ray be reflected n times, the total deviation will be D=2(i—r)+n(~r—2r). The deviation is thus seen to vary with the angle of incidence; and by considering a set of parallel rays passing through the same principal plane of the sphere and incident at all angles, it can be readily shown that more rays will pass in the neighbourhood of the position of minimum deviation than in any other position (see REFRACTION). The drop will consequently be more intensely illuminated when viewed along these directions of minimum deviation, and since it is these rays with which we are primarily concerned, we shall proceed to the determination of these directions. Since the angles of incidence and refraction are connected by the,relation See also:

sin i =µ sin r (See also:

Snell's Law),µ being the See also:

INDEX

index of refraction of the See also:

MEDIUM

medium, then the problem may be stated as follows: to determine the value of the angle i which makes D =2(i—r)+n(7r—2r) a maximum or minimum, in which i and are connected by the relation sin i=µ sin r, µ being a See also:

CONSTANT, BENJAMIN (1845-1902)

constant. By applying the method of the See also:

DIFFERENTIAL

differential calculus, we obtain See also:

cos i=~{(µ2—I)/(n2+2n)) as the required value; it may be readily shown either geometrically or analytically that this is' a minimum.

For the angle i to be real, cos i must be a fraction, that is n2+2n>See also:

A2(z)

A2—1, or (n+I)2>i2. Since the value ofµ for See also:

WATER

water is about t, it follows that n must be at least unity for a rainbow to be formed; there is obviously no theoretical limit to the value of n, and hence rainbows of higher orders are possible. So far we have only considered rays of homogeneous light, and it remains to investigate how See also:

LIGHTS, CEREMONIAL USE OF

lights of varying refrangibilities will be transmitted. It can be shown, by the methods of the differential calculus or geometrically, that the deviation increases with the refractive index, the angle of incidence remaining constant. Taking the refractive index of water for the red rays as W, and for the violet rays as g?, we can calculate the following values for the minimum deviations corresponding to certain assigned values of n. Red. Violet. I 7r— 42°.1 7r— 40°.22 2 27r—129°•2 27r—125°•4~8p 3 37r—231°•4 31r -227°.08 4 47r—317°•07 47r—310°.07 To this point we have only considered rays passing through a principal See also:

section of the drop; in nature, however, the rays impinge at every point of the surface facing the sun. It may be readily deduced that the directions of minimum deviation for a See also:

PENCIL (Lat. penicillus, brush, literally little tail)

pencil of parallel rays See also:

lie on the surface of cones, the semi-See also:

VERTICAL (from Lat. vertex, highest point)

vertical angles of which are equal to the values given in the above table. Thus, rays suffering one internal reflection will all lie within a See also:

CONE (Gr. Kwvos)

cone of about 42°; in this direction the See also:

ILLUMINATION

illumination will be most intense; within the cone the illumination will be fainter, while, without it, no light will be transmitted to the eye. Fig. 2 represents sections of the drop and the cones containing the minimum deviation rays after I, 2, 3 and 4 reflections; the order of the colours is shown by the letters R (red) and V (violet).

It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their See also:

AXIS (Lat. for " axle ")

axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays. The observer will,therefore, see a coloured See also:

BAND

band, about 2° in width, and coloured violet inside and red outside. Within the band, the illumination Fro. 2 will be faint; outside the band there will be perceptible darkening until the second bow comes into view. Similarly, drops transmitting rays after two internal reflections will be situated on covertical and coaxial cones, of which the semi-vertical angles are 51° for the red rays and 54° for the violet. Outside the cone of 5¢r there will be faint illumination; within it, no secondary rays will be transmitted to the eye. We thus see that the order of colours in the secondary bow is the See also:

REVERSE

reverse of that in the primary; the secondary is See also:

HALF

half as broad again (3°), and is much fainter, owing to the longer path of the ray in the drop, and the increased See also:

dispersion. Similarly, the third, See also:

FOURTH

fourth and higher orders of bows may be investigated. The third and fourth bows are situated between the observer and the sun, and hence, to be viewed, the observer must See also:

FACE (from Lat. fades, derived either from facere, to make, or from a root fa-, meaning " appear "; cf. Gr. cbatvstv)

face the sun. But the illumination of the bow is so weakened by the repeated reflections, and the light of the sun is generally so See also:

bright, that these bows are rarely, if ever, observed except in artificial rainbows. The same remarks apply to the fifth bow, which differs from the third and fourth in being situated in the same part of the sky as the primary and secondary bows, being just above the secondary. The most conspicuous See also:

COLOUR (Lat. color, connected with celare, to hide, the root meaning, therefore, being that of a covering)

colour band of the principal bows is the red ; the other colours shading off into one another, generally with considerable blurring.

This is due to the superposition of a See also:

GREAT

great number of spectra, for the sun has an appreciable apparent See also:

DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter, and each point on its surface gives rise to an individual spectrum. This overlapping may become so pronounced as to produce a rain-bow in which colour is practically absent; this is particularly so when a thin See also:

CLOUD (from the same root, if not the same word, as " clod," a word common in various forms to Teutonic languages for a mass or lump; it is first applied in the usual sense in the late 13th century; the Anglo-Saxon chid is only used in the sense of " a ma

cloud intervenes between the sun and the rain, which has the effect of increasing the apparent diameter of the sun to as much as 2° or 3°. This phenomenon is known as the " white rainbow " or " Ulloa's See also:

RING (O.E. hring; a word common to Teutonic languages; and probably cognate with the Lat. circus, Gr. KtpKOS or KpLKOS, Skt'. chakra, wheel, circle, cf. also " harangue "); in art, a band of circular shape of varying sizes, made of any material and used f

Ring or Circle," after Antonio de Ulloa. We have now to consider the so-called spurious bows which are sometimes seen at the inner edge of the primary and at the outer edge of the secondary bow. The geometrical theory can physkal afford no explanation of these coloured bands, and it has theory. been shown that the complete phenomenon of the rainbow is to be sought for in the conceptions of the See also:

WAVE

wave theory of light. This was first suggested by Thomas Young, who showed that the rays producing the bows consisted of two systems, which, although emerging in parallel directions, traversed different paths in the drop. Destructive interference between these superposed rays will there-fore occur, and, instead of a continuous maximum illumination in the direction of minimum deviation, we should expect to find alternations of brightness and darkness. The later investigations of Richard Potter and especially of Sir George Biddell Airy have proved the correctness of Young's idea. The mathematical discussion of Airy showed that the primary rainbow is not situated directly on the line of minimum deviation, but at a slightly greater value; this means that the true angular radius of the bow is a little less than that derived from the geometrical theory. In the same way, he showed that the secondary bow has a greater radius than that previously assigned to it. The spurious bows he showed to consist of a See also:

SERIES (a Latin word from serere, to join)

series of dark and bright bands, whose distances from the principal bows vary with the diameters of the raindrops. The smaller the drops, the greater the distance; hence it is that the spurious bows are generally only observed near the summits of the bows, where the drops are smaller than at any See also:

LOWER

lower See also:

ALTITUDE (Lat. altitudo, from altus, high)

altitude.

In Airy's investigation, and in the extensions by Boitel, J. Larmor, E. Mascart and L. Lorentz, the source of light was regarded as a point. In nature, however, this is not realized, for the sun has an appreciable diameter. Calculations taking this into account have been made by J. Pernter (Neues fiber den Regenbogen, See also:

Vienna, 1888) and by K. Aichi and T. Tanakadate (Jour. See also:

COLLEGE (Collegium)

College of Science, See also:

TOKYO (or TOKIO, formerly called Yedo)

Tokyo, 1906, vol. xxi. See also:

art. 3). Experimental See also:

CONFIRMATION (Lat. confirmatio, from confirmare, to establish, make firm)

confirmation of Airy's theoretical results was afforded in 1842 by See also:

William Hallows See also:

Miller (Camb.

Phil. Trans. vii. 277). A See also:

HORIZONTAL

horizontal pencil of sunlight was admitted by a vertical slit, and then allowed tc fall on a See also:

COLUMN (Lat. columna)

column of water supplied by a See also:

JET (Fr. jais, Ger. Gagat)

jet of about -nth of an See also:

INCH (O. Eng. ynce from Lat. uncia, a twelfthpart; cf. " ounce," and see As)

inch in diameter. Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's See also:

ANALYTICAL

analytical values. Pulfrich (Wied. See also:

Ann., 1888, 33, 194) obtained similar results by using cylindrical See also:

glass rods in See also:

PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place of the column of water. In accordance with a See also:

general consequence of reflection and refraction, it is readily seen that the light of the rainbow is partially polarized, a fact first observed in 1811 by See also:

JEAN

Jean See also:

BAPTISTE

Baptiste See also:

BIOT, JEAN BAPTISTE (1774-1862)

Biot (see POLARIZATION). Lunar rainbows. The moon can produce rainbows in the same manner as the sun. The colours are much fainter, and according to Aristotle, who claims to be the first observer of this phenomenon, the lunar bows are only seen when the moon is full. Marine rainbow is the name given to the chromatic displays formed by the sun's rays falling on the spray See also:

DRAWN

drawn up by the See also:

wind playing on the surface of an agitated See also:

sea.

Intersecting rainbows are sometimes observed. They are formed by parallel rays of light emanating from two See also:

SOURCES

sources, as, for example, the sun and its See also:

IMAGE (Lat. imago, perhaps from the same root as imitari, copy, imitate)

image in a See also:

SHEET

sheet of water, which is situated between the observer and the sun. In this See also:

case the second bow is much fainter, and has its centre as much above the See also:

HORIZON (Gr. 6pfTwv, dividing)

horizon as that of the See also:

DIRECT

direct See also:

SYSTEM

system is below it.

End of Article: RAINBOW

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