THE KAINBOW DUE TO A CIRCULAR SOURCE OF LIGHT. 20 



intensity of the rainbow is proportional to the ~'Ah power of 

 the number of the drops. Then, the numbers in the curves in 

 PI. Ill and PL V are increased by 2-(0.02ö)'5 and (0.05)^, 

 or 1 and 1.2G respectively, and we see that the intensity curves 

 of the former are sharper than those of the latter. Thus, the 

 above result of observation is explained only by saying that there 

 was a comparatively large quantity of drops. But, we have 

 another cause on which the above observation must depend ; 

 namely, the imperfectness of Airy's theory for large values of d. 

 In the strict sense, we can not compare the corresponding 

 suj)ernumerary bows due to two drops of different sizes, because 

 the value of being different, the approximation of Airy's and 

 consequently of our theory is not the same in both cases. So 

 far as Airy's theory holds good, we can say that the super- 

 numerary bow due to large drops is less distinct ; leaving out 

 of consideration both the factor rs and the number of the drops. 



The above discussion only holds for supernumerary bows ; 

 on the contrary, the principal bow is more distinct for large 

 drops, as PI. Ill and PI. V show. Thus a white rainbow is 

 probably caused by small drops, or rather mixed drops of dif- 

 ferent sizes. In fact, in many cases in nature, it is absolutely 

 important to consider the inequality of the size of the drops, 

 though actual discussion of this point is almost impossible. 



In conclusion, we have to thank Prof. Nagaoka for suggest- 

 ing the problem and for giving kind advice during the course 

 of our investigations. 



