142 Mr potter, on THE PROBLEM OF THE RAINBOW, 



is only in referring tlie problem to Physical Optics, and considering 

 the interference of tlie light which arises, that we understand how the 

 size of the drops varying and determining the angular positions of the 

 bright and dark fringes for any colour, causes the appearances to vary, 

 by. modifying the extent of the overlapping of the various colours. 



The existence of the supernumerary bows furnishes a still more 

 weighty objection to the common explanation ; which supposes only 

 one maximum of intensity for each colour, at the angle at which two 

 consecutive rays emeige from the drop parallel to each other. But 

 these supernumerary bows shew that the true explanation must furnish 

 reasons for a succession of maxima and minima for each colour, and 

 this the princijjle of interference does in a manner perfectly in accord- 

 ance with recorded observations of the phenomena. 



It was not until after I had finished the mathematical investigations, 

 that I learned from ]\Ir Whewell, that Dr Young had previously applied 

 the principle of interferences to explain the supernumerary rainbows. 

 If I had known this earlier, I probably should never have entered fur- 

 ther into the subject ; as it is, it will be found that I have shewn a 

 method of obtaining the result, which I am not aware that he has 

 any where given ; and at any rate I shall have awakened the attention 

 of mathematicians to this interesting phenomenon. 



Dr Young's account is very concise, and insufficient as a mathema- 

 tical explanation ; he, however, notices the brilliancy of some of the 

 colours being assisted by the interference of the others. At page 470 

 of his Lectures on Natural Philosophy, he says, " We have already seen 

 that the light producing the ordinary rainbow is double, its intensity 

 being only greatest at its termination where the common bow appears, 

 while the wliole light is extended much more widely. The two por- 

 tions concerned in its production must divide this light into- fringes ; 

 but unless almost all the drops of a shower happen to be of the same 

 magnitude, the effects of these fringes must be confounded and de- 

 stroyed; in general however they must at least co-operate more or less 

 in producing one dark fringe, which must cut off the common rainbow 

 much more abruptly than it would otherwise have been terminated, and 



