662 



THE POPULAR SCIENCE MONTHLY. 



a sheaf of approximately parallel rays. But what determines this par- 

 allelism ? Here our real difficulties begin, but they are to be sur- 

 mounted by attention. Let us endeavor to follow the course of the 

 solar rays before and after they impinge upon a spherical drop of 

 water. Take first of all the ray that passes through the center of the 

 drop. This particular ray strikes the back of the drop as a perpen- 

 dicular, its reflected portion returning along its own course. Take 

 another ray close to this central one and parallel to it for the sun's 

 rays when they reach the earth are parallel. When this second ray 

 enters the drop it is refracted ; on reaching the back of the drop it is 

 there reflected, being a second time refracted on its emergence from 

 the drop. Here the incident and the emergent rays inclose a small 

 angle with each other. Take again a third ray a little farther from 

 the central one than the last. The drop will act upon it as it acted 

 upon its neighbor, the incident and emergent rays inclosing in this in- 

 stance a larger angle than before. As we retreat farther from the 

 central ray the enlargement of this angle continues up to a certain 

 point, where it reaches a maximum, after which further retreat from 

 the central ray diminishes the angle. Now, a maximum resembles the 

 ridge of a hill, or a water-shed, 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 rain-drop would be represented by the steepness of the slope. 

 On the top of the water-shed that is to say, in the neighborhood of 

 our maximum is a kind of summit level, where the slope for some 

 distance almost disappears. But the disappearance of the slope indi- 

 cates, in the case of our rain-drop, 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 deflection just referred to until it 

 reaches its maximum, and its gradual diminution at the other side of 

 the maximum. The measures correspond to a series of angles of inci- 

 dence which augment by steps of ten degrees : 



i d 



10 10 



20 1936' 



30 28 20' 



40 35 36' 



50 40 40' 



i d 



60 42 28' 



T0 39 48' 



80 31 4' 



90 15 



The figures in the column i express these angles, while under d we 

 have in each case the accompanying deviation, or the angle inclosed 



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



