951 



RAINBOW. 



RAINBOW. 



033 



nnall receiving Teasel U preferred by some observers to a larp. r .-n. . 

 The arc* of the aperture muit be accurately ascertained. The circular 

 form u the beet, nine* it admit* of being turned in a Uthe. The rim may 

 be made to project, n u to retain the water which splashes up, 

 especially in oblique showers. The divisions of the measuring jar 

 should be tested by weighing the water. Some observe prefer to 

 estimate the amount by weight, and an easy method of doing so in 

 given in Drew's useful little volume entitled ' Practical Meteorology,' 

 !- >. 



RAINBOW, tk circular arch of Yarionaly coloured light which is 

 visible in the heaven* when the sun or moon U shining, and when, at 

 the same time, a shower of rain Is falling on the opposite aide of the 

 spectator. When the rain is abundant, n second bow is commonly 

 B6eu on the exterior, and concentric with the first ; their common 

 centre being in a line drawn from the luminary through the eye of 

 the spectator and produced towards the opposite part of the heavens. 

 Both bows consist of concentric bands of the different prismatic colours 

 arranged as they appear in the solar spectrum, but the order in which 

 they are disposed in the first bow is inverted in the second. The 

 lower edge of the interior bow is violet and the upper edge is red ; on 

 the contrary, the lower edge of the exterior bow is red and the upper 

 edge is violet. 



The rainbow is a phenomenon which appears at all times to have 

 been understood to depend upon the light of the sun or moon and the 

 drops of falling rain ; but the first complete explanation of the circum- 

 stances connected with it is due to Newton (' Optics,' book i., p. 2, 

 prop. 9). In the beginning 'of the 16th century no better notion was 

 entertained of the cause of the phenomenon than that the interior bow 

 was a distorted reflection of the sun's image from the surface of a 

 cloud, and that the exterior bow was a reflected image of the first. 

 But the reflection of light is not capable of producing different colours, 

 and it is said that Fleischer of Breslau (1871) was the first who enter- 

 tained the idea that the particles of light from the sun entered into 

 the drops of rain. His opinion was that a ray of light suffered one 

 refraction on entering and another on leaving a drop; and that it 

 entered the eye of the spectator after reflection from the surface of a 

 second drop. It appears that Kepler, in a letter to Harriot (1606), 

 suggested that the particles of light, in a ray which is a tangent to 

 some part of the surface of a drop of rain, might enter the drop by 

 refraction, and that this ray, being subsequently reflected at the 

 interior surface of the latter, might enter the eye of the spectator after 

 being again refracted on leaving the drop. The hypothesis is worthy 

 of Kepler's sagacity ; and, as far as it goes, it differs from the fact only 

 in the manner in which the incident ray is supposed to fall on the 

 drop. Newton ascribes the first idea of the true explanation to Antonio 

 de Oominis, bishop of Spalatro, whose work, ' De Radiis visus,' was 

 published in 1611, but is said to have been composed in 1590: the 

 work however appears to have been so obscurely written, and to betray 

 so much ignorance of the laws of optics, that it is doubtful whether or 

 not the author had any more than a vague conception of the cause of 

 the colours. (See Montucla, ' Histoire des Math.,' torn, ii.) 



Descartes is certainly the first who has distinctly explained the 

 causes by which the two bows are produced, and he states (' Moteora,' 

 cap. viii.) that he detected those causes on observing the phenomena 

 presented by a glass globe filled with water, which he placed in various 

 positions with respect to the sun. He shows that the interior or 

 primary bow is produced by rays from the sun falling upon the drops 

 of rain near their upper surfaces, where, being refracted, they pass to 

 the side of Hhe drop which is farthest from the sun and spectator ; from 

 thence they are reflected towards the lower surface, and, on quitting 

 the drop, they suffer a second refraction. He shows also that the 

 exterior or secondary bow is produced by rays from the sun falling 

 upon the drops of rain near their lower surfaces, where, being refracted, 

 they pass, u before, to the farther side of the drop ; from thence they 



'I' 



are reflected toward* the upper surface, and there they suffer a second 

 reflection. After this they pass to the side of the drop which is nearest 

 ' i In; mm, and from thence they emerge after a second refraction. 



Now it is not sufficient that the pencils of light which are incident on 

 the drops of rain should be so refracted and reflected ; it is moreover 

 necessary that each pencil on emerging from the drop should con 

 parallel rays of light, that, when it enters the eye of the spectator, it 

 may produce in the mind the perception of brightness ; and Descartes 

 determined by computation the positions of the incident and emergent 

 rays so that this effect may be produced. 



Thus, let HI (f<j. 1) be a rery slender pencil of rays of some one 

 colour incident on a spherical drop of water at the angle A I s, ami 1< t 

 this angle be such that the rays in the pencil may, by the laws of 

 refraction in water, converge at B ; then, though many rays will pass 

 through the drop at that point and be dispersed, yet many will ! 

 reflected from thence as from a radiant point, and wiu emerge at K in 

 jwrallel directions, as they entered at I, so that if K E be the direction 

 of the emergent pencil, the angle c K E will be equal to A I s : the angle 

 made by the lines 8 1 and E K produced was found by Descartes to be 

 about 42 degrees. If the angle A I s were varied, the rays of the pencil 

 would leave the drop in a divergent state, and then the impression 

 which they would make on the eye might be too feeble to prodn. 

 sensation of brightness. Again, let s I (fy. 2) be a very slender pencil 



Tig. 2 





of rays of some one colour incident on a spherical drop of water at the 

 angle A I s, and let this angle be such that, by the laws of refraction in 

 water, the rays, after crossing at x and being reflected from n, may 

 pass from B to c in parallel directions ; then, after a second reflection 

 crossing at Y and being refracted at K, they will emerge in paralle 

 directions as they entered at i, so that if K E be the direction of the 

 emergent pencil, the angle D K E will be equal to A I s : the angle made 

 by the lines s I and x K was found by Descartes to be about 52 degrees. 

 If the angle A I s were varied, the rays of the pencil would leave the 

 drop in a divergent state. 



Now let A, D, o, D (fy. 8), be four globules of rain in a cloud covering 



Fig. ?. 



a considerable part of the heavens ou one side of the horizon. Let K 

 be the eye of the spectator, and, on account of the remoteness of the 

 sun, let the rays of light which proceed from his disc be considered as 

 parallel to one another. Let B E be n line drawn from the sun through 

 the eye of the spectator, and let it be produced towards o ; also let s A 

 s n, &o., be very slender pencils of parallel rays (supposed at present to' 

 be of ono colour) falling upon the globules of water. Let the refraction 

 anl n-tloction of theao pencils in A and n be similar to thoso which are 

 shown in ,//. I ; anrl tint refraction ami rellection in o and D be 



iujtg.2; also from the points of emergence suppose lines to 

 be drawn to r. It is evident, on account of the parallelism of the lines 

 8 0, 8 A, &c., that if the angle A K o or B K o were nearly equal to 42, 



