80 Mr. J. H. Pratt on the Supernumerary Bows in the Rainbow. 



Put the first approximate value of a^ in the second term, 



(1 \2 4 

 a- j/9j = 5 A ••• /9*is neglected, 



2 , 1 ^ 



Call these two values a and — a'. 



7. This shows that for every value of ^ there ate two values 

 of a, one positive and the other negative, and nearly equal to 

 each other; that is, there are always two values of <^, one less 

 than </>! and the other greater, which give the same deviation 

 Oi—^; and therefore the corresponding rays emerge parallel to 

 each other. It is the interference of these rays, which take dif- 

 ferent courses in the drop of rain and emerge parallel, which 

 causes the supernumerary bows. This I proceed to show. 



The manner in which these rays pass through the drop is 

 shown in the accompanying figure (fig. 2). The dark line in 

 the middle is the ray of least deviation, cE and dW emerge 

 parallel, and the pencils mix on reaching the eye. 



Fig. 2. 



