But though the step here taken by Descartes and Newton was a great one, it left the theory of the bow incomplete. Within the rainbow proper, in certain conditions of the atmosphere, are seen a series of richly colored zones, which were not explained by either Descartes or Newton. They are said to have been first described by Mariotte, and they long challenged explanation. At this point our difficulties thicken, but, as before, they are to be overcome by attention. It belongs to the very essence of a maximum, approached continuously on both sides, that on the two sides of it pairs of equal value may be found. The maximum density of water, for example, is 39° Fahr. Its density, when 5° colder and when 5° warmer than this maximum, is the same. So also with regard to the slopes of a watershed. A series of pairs of points of the same elevation can be found upon the two sides of the ridge; and, in the case of the rainbow, on the two sides of the maximum deviation we have a succession of pairs of rays having the same deflection. Such rays travel along the same line, and add their forces together after they quit the drop. But light, thus reinforced by the coalescence of non-divergent rays, ought to reach the eye. It does so; and were light what it was once supposed to be--a flight of minute particles sent by luminous bodies through space--then these pairs of equally deflected rays would diffuse brightness over a large portion of the area within the primary bow. But inasmuch as light consists of _waves_, and not of particles, the principle of interference comes into play, in virtue of which waves alternately reinforce and destroy each other. Were the distance passed over by the two corresponding rays within the drop the same, they would emerge as they entered. But in no case are the distances the same. The consequence is that when the rays emerge from the drop they are in a condition either to support or to destroy each other. By such alternate reinforcement and destruction, which occur at different places for different colors, the colored zones are produced within the primary bow. They are called “supernumerary bows,” and are seen, not only within the primary, but sometimes also outside the secondary bow. The condition requisite for their production is that the drops which constitute the shower shall all be of nearly the same size. When the drops are of different sizes, we have a confused superposition of the different colors, an approximation to white light being the consequence. This second step in the explanation of the rainbow was taken by a man the quality of whose genius resembled that of Descartes or Newton, and who in 1801 was appointed Professor of Natural Philosophy in the Royal Institution. I refer, of course, to the illustrious Thomas Young.