240 Rev. W. Scoresby on some remarkable Rainbows. 



Thus Dr Hutton, in his Philosophical and Mathematical Dic- 

 tionary, ascribes the appearance to a cloiid happening to inter- 

 cept the rays, and preventing them from shining on the upper 

 part of the arch ; in which case only the lower part appearing, 

 the bow, he supposed, might seem as if turned upside down ; 

 *' which," says he, " has probably been the case in several pro- 

 digies of this kind, related by authors." — Article Rainbow. 



But the preceding facts and principles afford us, I conceive, a 

 satisfactory solution of the phenomenon, in all cases where there 

 is a smooth reflecting surface of water, suitably situated at the 

 place of the inverted bow being seen ; and I am not aware that 

 it has been seen under other circumstances. 



Suppose the sun's altitude to be 42° (the outer semi-diameter 

 of the primary bow nearly), and the circumstances to be favour- 

 able for the production of the bow by the sun's rays reflected 

 from a perfectly calm surface of water, then arches, if not circles, 

 resembling figure S, might occur, provided the quantity of re- 

 flected rays, at such an angle of incidence, were capable of pro- 

 ducing the iris. Here c c, as in the other figures, represents the 

 primary bow of reflection, having its centre 42 degrees above 

 the horizon ; d d the secondary bow of reflection^ which, how- 

 ever, in this case, from the quantity of rays absorbed by the 

 water, might not be visible ; and b, a segment of the common 

 secondary rainbow, the primary one not appearing above the 

 horizon, on account of the greatness of the sun's altitude *. 



The only doubt that I conceive likely to arise against this ex- 

 planation of inverted rainbows appearing entirely above the ho- 

 rizon, is the small number of rays which are reflected from a 

 surface of water, at the required angle of incidence, compared to 



• The relative position of the bows of reflected and direct rays, is simply 

 illustrated by inscribing on paper the circles c and d complete, the same on 

 both sides of the paper from the same centre. Then cut away all the blank 

 paper witfumt the outer circle d, and also the blank paper within the inner cir- 

 cle c, except a narrow slip, as a diameter // (defined by dotted lines), and 

 graduate this diameter as in the figure. If, then, the lower edge of the dia- 

 gram be doubled up at the mark of 42% a representation will be given of the 

 reflected and direct bows, similar to fig. 3, when the sun's altitude is 42*. Or, 

 if it be doubled up at 74°, it will represent fig. 2, or any other appearance of 

 the combined phenomena, according to the altitude of the sun at the time. 

 Hence when the sun is in the horizon, the bows of direct and reflected rays; 

 will cover one another and coincide. 



