28 ART. 3. AICHI AND TANAKADATE : THEORY OF 



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that when the breadth of the slit is increased, the positions of 

 the bows (or fringes in this case) change very little. As an- 

 other effect of the increase of the breadth of the slit, the bows 

 become indistinct, especially the supernumerai-y bows. This 

 effect is remarkable when the diameter of the rod is large. We 

 could not observe the turning point, at which the maxima and 

 minima interchange, as the difference of the intensities is very 

 small. But we can roughly say that the point at which the 

 bows become almost indistinguishable corresponds to the position 

 at which the angular breadtli of the bow coincides with that 

 of the slit. 



Again, using white light, it is easy to see that the colours 

 of the supernumerary bows change when the magnitude of the 

 rod is changed, and that the supernumerary bows almost lose 

 colour and become indistinct when the breadth of the slit is 

 increased. 



In the table experiment, we always observed that, when the 

 breadth 'of the slit is not too large, the supernumerary bows are 

 numerous for a cylinder with a large radius, but fewer for a 

 small cylinder. This fact may be explained by the presence of 

 the factor r^?. In the case of natural rainbows where, as Pernter 

 indicated, the supernumerary bows were observed when the drops 

 were large, we can nut take into account the factor r's directly, 

 because the intensity depends, at the same time, on the number 

 of drops which are contained in a unit volume of space, and it 

 is probable that when the radius of the drop is large the num- 

 ber of the drops is smalh For instance, let us take the cases 

 r = 0.025 cm. and r = 0.05 cm., and suppose that the quantilies 

 of tlie dro})S \M'r unit volume is e(|ual in the two cases, so that 

 the ratio of the numbers of the drops is '2' : 1, and that the 



