1884.] on Rainbows. 457 



doubt whetlier among the pleasures of the intellect there is any more 

 pure and concentrated than that experienced by the scientific man 

 when a difficulty which has challenged the human mind for ages 

 melts before his eyes, and recrystallises as an illustration of natural 

 law. This pleasure was doubtless experienced by Descartes when he 

 succeeded in placing upon its true physical basis the most splendid 

 meteor of our atmosphere. Descartes showed, moreover, that the 

 " secondary bow " was produced when the rays of light underwent two 

 reflections within the drop, and two refractions at the points of inci- 

 dence and emergence. 



It is said that Descartes behaved ungenerously to Snell — that, 

 though acquainted with the unpublished papers of the learned Dutch- 

 man, he failed to acknowledge his indebtedness. On this I will not 

 dwell, for I notice on the part of the public a tendency, at all events 

 in some cases, to emphasise such shortcomings. The temporary weak- 

 ness of a great man is often taken as a sample of his whole character. 

 The spot upon the sun usurps the place of his " surpassing glory." 

 This is not unfrequent, but it is nevertheless unfair. 



Descartes proved that according to the principles of refraction, 

 a circular band of light must appear in the heavens exactly where 

 the rainbow is seen. But how are the colours of the bow to be 

 accounted for ? Here his penetrative mind came to the very verge 

 of the solution, but the limits of knowledge at the time barred his 

 further progress. He connected the colours of the rainbow with 

 those produced by a prism ; but then these latter needed explanation 

 just as much as the colours of the bow itself. The solution, indeed, 

 was not possible until the composite nature of white light had been 

 demonstrated by Newton. Applying the law of Snell to the different 

 colours of the spectrum, Newton proved that the primary bow must 

 consist of a series of concentric circular bands, the largest of which 

 is red, and the smallest violet ; while in the secondary bow these 

 colours must be reversed. The main secret of the rainbow, if I may 

 use such language, was thus revealed. 



I have said that each colour of the rainbow is carried to the 

 eye by a sheaf of approximately parallel rays. But what determines 

 this parallelism? Here our real difficulties begin, but they are 

 to be surmounted by attention. Let us endeavour to follow the 

 course of the solar rays before and after they impinge upon a spherical 

 drop of water. Take first of all the ray that passes through the 

 centre of the drop. This particular ray strikes the back of the drop 

 as a perpendicular, its reflected portion returning along its own 

 course. Take another ray close to this central one and parallel 

 to it — for the sun's rays when they reach the earth are parallel. 

 When this second ray enters the drop it is refracted ; on reaching the 

 back of the drop it is there reflected, being a second time refracted 

 on its emergence from the drop. Here the incident and the emergent 

 rays enclose a small angle with each other. Take again a third 

 ray a little further from the central one than the last. The drop 

 ■^ 2 H 2 



