Descartes proved that, according to the principles of refraction, a circular band of light must appear in the heavens exactly where the rainbow is seen. But how are the colors of the bow to be accounted for? Here his penetrative mind came to the very verge of the solution, but the limits of knowledge at the time barred his further progress. He connected the colors of the rainbow with those produced by a prism; but then these latter needed explanation just as much as the colors of the bow itself. The solution, indeed, was not possible until the composite nature of white light had been demonstrated by Newton. Applying the law of Snell to the different colors of the spectrum, Newton proved that the primary bow must consist of a series of concentric circular bands, the largest of which is red and the smallest violet; while in the secondary bow these colors must be reversed. The main secret of the rainbow, if I may use such language, was thus revealed. I have said that each color of the rainbow is carried to the eye by a sheaf of approximately parallel rays. But what determines this parallelism? Here our real difficulties begin. 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 centre of the drop. This particular ray strikes the back of the drop as a perpendicular, 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 further from the central one than the last. The drop will act upon it as it acted upon its neighbor, the incident and the emergent rays inclosing in this instance a larger angle than before. As we retreat further 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 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 steepness of the slope. On the top of the watershed--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 indicates, as 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. They are the so-called “effective rays” of the rainbow.