460 Mr. James C. M c Connel on the 



example, when its maximum is at 32°, must have a breadth of 

 over 5° in homogeneous light (see fig. 2). 



We are now in a position to understand the observations 

 better. The most complete measurements are those of (7). 

 Here the mean radius of the dark space between the two 

 bows is 35° 40 7 . This is 6° less than the mean radius of the 

 geometrical bow. Assuming this is given by ?n = 2*50, the 

 values of m corresponding to the radii observed are as 

 follows : — 



Outside or red of outer bow . . 



. . 0-12 



Middle „ . . 



. . 0-98 



Inside „ . . 



. . 2-12 



Outside of inner bow . . 



. . 2-89 



Inside or red ,, . . 



. . 3-88 



The agreement with fig. 1 is as good as could be expected. 

 Also by fig. 3 the inner bow is small enough to be distinctly 

 coloured. The drops are larger than in the second case of 

 fig. 2. We find indeed for equation (2), taking % as 67r/180, 

 q as 0*465, m as 2*48, and \ as 0'00056 millim., that their 

 average diameter is 0'041 millim. 



In (1) the outer radius is greater than that of the geo- 

 metrical bow. This finds its explanation in fig. 2. 



(2) seems to be a transition stage between a rainbow and 

 an ordinary fog-bow. 



(5) By fig. 1 the first supernumerary is much narrower 

 than the main bow. 



Taking the radius of (9) as 37° 8 / we find the average 

 diameter of the drops 0'018 millim. 



In (17) the measurements of the inner bow show con- 

 clusively that it was the main primary bow, the drops being 

 much the same size as in the second case of fig. 2. So the 

 faint outer bow must have been a modified form of the 

 secondary rainbow. It may be remarked that the effect of 

 the drops being small on the secondary rainbow is similar to 

 the effect on the primary, except that the supernumeraries 

 are outside and the radii are made larger instead of smaller. 



It will be observed that the air- temperature in (3), (4), 

 (5), (6), (7), (10), and (18) is below freezing-point ; in (5) 

 as low as 15°*7 F. I have nevertheless assumed throughout 

 that the phenomena are due to drops of water and not to any 

 form of ice. The correctness of this assumption is established 

 by the agreement of observation with Airy's theory, as well 

 as by the identity of the phenomena above freezing-point; 



