Phenomena bf the Rainbow. 285 



point infinitely distant. This being granted, there will be, from the ante- 

 rior surface of the drops, a partial reflexion of all the colours which com- 

 pose the incident light, and which will form a whitish tint, spread over the 

 whole surface of the cloud ; but, besides this, there will be seen two con- 

 centric arcs, coloured with all the colours of the spectrum. For if through 

 the eye O be drawn a right line O V, forming with O C an angle of 

 40 17', and that it be supposed to revolve round O C, describing a 

 conical surface, all the drops which are found in this surface will have 

 the position in which the most refrangible violet rays, after having 

 suffered two refractions and one reflexion, will emerge parallel, and will 

 reach the eye at 0, and this will not take place in any other part of the 

 cloud ; in virtue, therefore, of these rays alone, the spectator will see 

 upon the cloud a violet bow, of which O C will be the axis, and O the 

 centre. There will, in like manner, be an infinite number of concentric 

 arcs exterior to the last, each formed by one description of simple rays; 

 and as the rays become less refrangible, their arcs will be of larger 

 diameter, so that the largest, composed of the extreme red, will subtend 

 an angle R O C of 42 y 2'. Thus the total extent of the coloured band 

 will be 42 2' - 40 17', or 1 Q 45', the red being without, and the violet 

 within. 



' It will be the contrary after two reflexions. If the lines O R', O V, 

 be drawn, making with O C angles of 50 59' and 54 9', and then made 

 to revolve round O C as an axis, the first will intersect all the drops, 

 which, after two refractions and two reflexions of the red rays, will trans- 

 mit them in parallel lines to the eye ; and the second will determine the 

 analogous limit for the extreme violet rays. Between these two arcs 

 there will be others of all the intermediate colours of the prism, and they 

 will form a second coloured band, having a width of 54 9' - 50 59', or 

 3 10'. This band will have its colours in an order the inverse of the 

 first, that is to say, the red will be inside, and the violet outside ; and the 

 distance between the two red arcs will be 8 57'.' 



In this account it is assumed that no sensible effect is pro- 

 duced on the eye of the spectator, after one or two internal 

 reflexions, except by those drops which are included within 

 the angles subtended by the coloured bands ; although it is 

 said that the whole expanse of the shower will exhibit a degree 

 of whiteness, in consequence of the reflexion of the sun's 

 rays from the anterior surfaces of the drops. These two 

 statements are, to a certain extent, I think, irreconcilable ; 

 for if the rays reflected from the internal surfaces would be 

 rendered insensible by their divergence, so also, I conceive, 

 would those reflected from the external surfaces. The disper- 

 sion of the former will not account for the supposed difier- 

 YOL, I. FEB. 1831, U 



