52 



OPTICS. 



farthest from E, yet it is otherwise with 

 those that enter on the side nearest 

 E, as shown in Jig. 49. The ray S'R 

 refracted at R, and suffering reflexion 

 at r, v and /, v', will emerge at r', v", 

 and reach the eye of the observer 

 at E. The inclination of the violet 

 ray v E, to S 11 will now be 54 10', 

 and that of the red ray 50 58'; and 

 hence the breadth of the bow will 

 be 540 10' 50 58' = 30 12'. This 

 bow, which is called the secondary rain- 

 bow, will be without the primary one, 

 and will have the colours reversed, the 

 violet being uppermost and the red un- 

 dermost. The breadth will be nearly 

 twice as great as that of the primary 

 bow ; but its light will be much less in- 

 tense, in consequence of the rays by 

 which it is formed having suffered two 

 reflexions within the drop, the effect of 

 which is often to render the outer bow 

 invisible. This secondary rainbow, con- 

 sequently, is formed by two reflexions and 

 two refractions of the drops of rain. 



The two rainbows are shown in fig. 50., 

 where / r' r' is the red, and v' v' v' the 

 violet circle of the first bow ; and r r r 

 the red, and v v v the violet of the se- 

 condary bow. 



If we suppose the rays v' v", r 1 r",fig. 

 49, to suffer a third reflexion, it may be 

 shown that a third bow will be formed, 

 but it will be between the observer and 

 the sun, with a diameter of 80 40', and it 

 will be formed by drops of rain between 

 the observer and the sun. In like manner, 

 if we suppose the rays to be four times 

 reflected within the drop, they will form 

 a fourth bow, whose diameter will -be 

 91 6'. None of these bows, however, 

 have been seen ; both on account of the 

 faintness of the light which forms them, 

 and from the circumstance of their 

 light being more overpowered by the 

 sun's rays'than if they were opposite to 

 that luminary. The following Table 

 shows at one view the proportions of 

 these rainbows. 



No. of Reflexions. Mean Diameter of the BOUT. Position. 



Primary Rainbow 1 82 18' Opposite the Sun. 



Secondary Rainbow 2 10.5 8' Opposite the Sun. 



Tertiary Rainbow 3 80 40' Round the Sun. 



Quaternary Rainbow 4 91 6' Round the Sun. 



When no rain is falling between the 

 observer at O, and the part of the sky 

 through which the bow passes, apart of 

 the bow will be wanting at that place ; so 

 that portions of rainbows are frequently 

 seen, particularly near tlje horizon. 



When the prismatic spectrum is 

 formed from a very narrow pencil of 

 light, the yellow and blue colours dis- 

 appear almost wholly ; and when it is 

 formed from a broad disk or band of 

 light, whose breadth exceeds the angular 

 separation of the red and violet rays, the 

 green will disappear, and there will be two 



primary coloured arches, separated by an 

 arch of white light. Hence in summer, 

 when the sun's diameter is least, the 

 colours of the rainbow are more con- 

 densed and homogeneous than in win- 

 ter; when, from the size of his disk being 

 a maximum, the yellow and blue will 

 be more copious. If a rainbow should 

 appear when the sun is eclipsed, the 

 colours of the bow would be more homo- 

 geneous in one part than in another. 



The following will be the character of 

 the primary rainbows seen in the differ- 

 rent planets. 



Colours. 



MERCURY. Red, orange, yellow, white, greenish blue, indigo, violet. 

 EARTH. Red, orange, yellow, blue, indigo, violet. 

 SATURN. Red, orange, green, indigo, and violet. 



Within the primary rainbow, and 

 immediately in contact with it, there 

 have been seen what are called super- 

 numerary rainbows, each of these bows 

 consisting of red and green. On the 

 29th July, 1813, we were fortunate 

 enough to see four of these. The red 

 of the first supernumerary bow was in 

 contact with the violet of the primary 

 bow, and this was followed by green, red, 

 green, red, green, red, green, red. M. 

 Dicquemarre observed similar supernu- 

 merary rainbows on the outside of the 

 secondary bow. These bows have not 

 been satisfactorily explained. 



Lunar rainbows have been occasion- 

 ally seen ; but they differ in no respect 

 from those formed by the solar rays, 

 excepting in the faintness of their light. 

 In the autumn of 1814 we saw in a 

 dense fog, near Berne, a fog-bow, which 

 resembled a nebulous arch, in which 

 the separation of the colours could not 

 be distinguished. 



2. Halos and Parhelia. A halo is a 

 circle, (either composed of white light, 

 or consisting of the prismatic colours,) 

 which is occasionally seen round the 

 sun or moon. When one or more halos 

 are seen round the sun, they are gene- 



