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



contrary effect. Montigny'^^ says that sapernumerary bows are 

 numerous when the drops are small. This holds for the case 

 of a circular source and supports our view, l)ut he considers this 

 as the result of Airy's theory, i.e. of a point source, which we 

 cannot understand. 



10. Summary. 



From the above discussion, we obtain the following result, 

 where (1) represents the case of a point source, (2) a circular 

 source : — 



{a) The positions of the maxima and minima of (2) ap- 

 proximately coincide with those of (I). Strictly speaking, the 

 first maximum of (2) is displaced by a small amount towards 

 ^ = as compared with (1), and for other maxima and minima 

 this displacement becomes smaller and smaller. But the maxima 

 of (2) may correspond to the minima of (1), and the minima 

 to the maxima. 



(b) The value of (2), which corresponds to the maximum 

 of (1), is smaller than that of (1), and the value of (2), which 

 corresponds to the minimum of (1) is greater than that of (1). 

 This difference between (1) and (2) increases with the value of 

 <1> (i.e. with the increased diameter of the source). 



(c) As the value of 6 increases, the maximum value of (1) 

 and (2) gradually decreases. AVhile the minimum value of (1) 

 always remains 0, the mininunn value of (2) gradually increases 

 until it becomes equal to tlie maximum value and assumes a 

 stationary value, then the maxima and minima interchange, the 

 difference of the maximum and minimum values at first increases 

 and then decreases, then again assumes a stationary value, and 



fl) riiil. Mag. IX. p. 389 (1880). 



