454 Transactions. — Miscellaneous. 



may only be observed in a slight increase in the width of the 

 band of coloured light, and some blending of the colours at 

 the top of the arc; but if the sun be at some considerable 

 elevation the rainbow formed by the light from the reflected 

 sun will have its centre high up in the heavens, while that of 

 the primary and secondary bows will be below the horizon. 



(See PL LI., fig. 6.) 



In Sir David Brewster's treatise on optics published in 

 1853 he mentions such a third arc as having been observed by 

 Dr. Halley, in 1698, from the walls of Chester, the Eiver Dee, 

 which was unruffled by wind, forming the necessary reflector. 

 Dr. Halley supposed that the third bow " was only that part 

 of the circle of the primary bow that would have been under 

 the castle, bent upwards by reflection from the river." _ He was 

 evidently wrong!^ By no operation of the laws of optics could 

 such a bending-up of an image which had no existence occur. 

 It was, indeed, the result of reflection on the mirror of the 

 unruffled Dee ; but the reflection was that of the sun, and this 

 reflected sun acted as a second sun, and produced a second 

 rainbow. In this case the sun must have been about 5^° 

 above the horizon when the rainbow was formed (PI. L., fig. 7), 

 as the top of the arch of the rainbow coincided with the top 

 of the arch of the original secondary bow, and, the colours 

 being in reverse order, this portion of the two bows was white, 

 the two spectra counteracting on each other. Other examples 

 of rainbows formed by the reflection of the sun in calm 

 water are recorded, and the mode in which such appearances 

 are produced is sufficiently simple; but the question as to 

 whether the sun's rays refracted and reflected in the rain- 

 drops may be so reflected again from the surface of a calm 

 sheet of water as to produce in the observer's eye an image of 

 a rainbow in the water, and, if so, what would be the form 

 and colouring of that image, is much more difficult of solution. 

 Professor Tyndall puts the question thus : " Whether a rain- 

 bow which spans a tranquil sheet of water is ever seen re- 

 flected in the water," and his reply is, " The rays effective in 

 the rainbow are emitted only in the direction fixed by the 

 angle of 41°. Those rays, therefore, which are scattered from 

 the drops upon the water do not carry along with them the 

 necessary condition of parallelism, and hence, though the 

 cloud on which the bow is painted may be reflected from the 

 water, we can have no reflection of the bow itself." Of the 

 bow itself, you observe ; but he does not say of any other bow 

 that a reflection is impossible. Of the bow itself it is evi- 

 dently impossible ; for, think only of the concentrated parallel 

 rays which produce in our eyes the impression of the highest 

 point of the arch : they come directly from the raindrop 

 there to our eyes, and therefore cannot touch the water and 



