204 THE EAINBOW 



resembles the ridge of a hill, or a watershed, from 

 which the land falls in a slope at each side. In the 

 case before us the divergence of the rays when they 

 quit the raindrop would be represented by the steep- 

 ness of the slope. On the top of the watershed that 

 is to say, in the neighbourhood of our maximum is a 

 kind of summit-level, where the slope for some distance 

 almost disappears. But the disappearance of the slope 

 indicates, in the case of our raindrop, the absence of 

 divergence. Hence we find that at our maximum, and 

 close to it, there issues from the drop a sheaf of rays 

 which are nearly, if not quite, parallel to each other 

 These are the so-called ' effective rays ' of the rainbow. 

 Let me here point to a series of measurements which 

 will illustrate the gradual augmentation of the deflec- 

 tion just referred to until it reaches its maximum, and 

 its gradual diminution at the other side of the maxi- 

 mum. The measures correspond to a series of angles 

 of incidence which augment by steps of ten degrees. 



1 There is, in fact, a bundle of rays near the maximum, which, 

 when they enter the drop, are converged by refraction almost exactly 

 to the same point at its back. If the convergence were quite exact, 

 then the symmetry of the liquid sphere would cause the rays to qiiit 

 the drop as they entered it that is to say, perfectly parallel. But 

 inasmuch as the convergence is not quite exact, the parallelism after 

 emergence is only approximate. The emergent rays cut each other 

 at extremely sharp angles, thus forming a ' caustic ' which has for 

 its asymptote the ray of maximum deviation. In the secondary 

 bow we have to deal with a minimum, instead of a maximum, the 

 crossing of the incident and emergent rays producing the observed 

 reversal of the colours. (See Engel and Shellbach's published dia- 

 grams of the rainbow.) 



