14 ART. 3. — AICHI AND TANAKADATE : THEORY OF 



AiO, but there exists a direction whicli makes the angle d with 

 Ai Bi, and the intensity in this direction is given by 



/,^(^) = c,A/-L(^+^'cos^)| . 

 Thus, in the plane Syco we have as the total intensity 



and in the plane S;po 



In this case, therefore though i(d) and i(d) do not exist in one 

 direction nor in one plane, they exist in the same arc of the 

 rainbow which is specified by 6. Hence, the distribution of the 

 intensity of the rainbow can not be considered as uniform along 

 the arc of the rainbow. 



The above method is directly applicable to the case of a 

 circular source of light. To determine the position of a point 

 in the source of liglit, take the centre Sq of the source as the 

 origin from which (p is measured, the diameter D,, of the source 

 which lies in the plane s^co as the axis from which (p is mea- 

 sured, and the direction of the minimum deviation due to Su as 

 the 2/-axis from which 6 is measured. Then, in the plane s^co, 

 the intensity of the rainbow is given by 



I(ö)=const.Aj A>^{d + ip)\dip , («) 



-•x> 



<1> being the angular radius of the circle. Pernter took this in- 

 tegral as the general expression of the intensity of the rainbow 

 due to a circular source, of light and condemned our result, but 

 this holds only in the plane SqCo. Let us consider anothei' plane 

 which cuts the source in another line L and contains c and o. 



