THE RAINBOW DUE TO A CIRCULAR SOURCE OF LIUHT. 25 



corresponding to tlie case of the point source, and PI. Ill and 

 ri. V to the circular source (2<I>=32' mean anguh^r diameter of 

 the sun), r in PL II and PI. Ill being 0.025 cm., and in PI. 

 IV, PI. V 0.05 cm. The intensity of the scarlet ray is given 

 by dotted ; green by broken ; blue by solid lines, and the sum 

 of the three intensities, i.e. the total intensity, by curve (1), 

 which is compounded of a portion of white and a portion of the 

 two primary colours. 



For example, in PI. II : — 

 I at41°5 consists of 27 percent, scarlet, 48 percent, green, 25 i)ercent. white, 

 40°5 „ 14 „ blue, 14 „ scarlet, 72 ,, wliite, 



38'^ ,, 23 „ green, 77 ,, blue, ,, white. 



In PI. Ill:— 



I at 4i'^5 consists of 24 percent, scarlet, 43 i)ercent. green, 33 percent, white, 



40°j „ 21 „ blue, 9 „ scarlet, 70 „ while, 



38° „ 9 „ green, 19 „ blue, 72 ,, white. 



where the angles correspond to S(j(?o = D — ^ in § 4. 



The above calculation shows that in the colours of the 

 supernumerary bows due to the sun, white predominates, and we 

 can not distinguish many numbers of the supernumerary bows. 

 This explains the fact tliat the rainbow in nature is accompanied 

 by only a small number of supernumerary bows, while according 

 to Airy's theory the rainbow ought to be accompanied by îiumer- 

 ous bows. 



According to § 6, we notice that the difference between the 

 maximum and minimum values of intensity increases witli the 

 size of the drop for a point source ; l)ut for a circular source 

 the intensity depends on two factors, one of w^hich enjoys the 

 same property as for a point source, l)ut the otluT produces a 



