Science is an organic growth, and accurate measurements give coherence to the scientific organism. Were it not for the antecedent discovery of the law of sines, founded as it was on exact measurements, the rainbow could not have been explained. Again and again, moreover, the angular distance of the rainbow from the sun had been determined and found constant. In this divine remembrancer there was no variableness. A line drawn from the sun to the rainbow, and another drawn from the rainbow to the observer’s eye, always inclosed an angle of 41°. Whence this steadfastness of position--this inflexible adherence to a particular angle? Newton gave to De Dominis[4] the credit of the answer; but we really owe it to the genius of Descartes. He followed with his mind’s eye the rays of light impinging on a raindrop. He saw them in part reflected from the outside surface of the drop. He saw them refracted on entering the drop, reflected from its back, and again refracted on their emergence. Descartes was acquainted with the law of Snell, and taking up his pen, he calculated, by means of that law, the whole course of the rays. He proved that the vast majority of them escaped from the drop as _divergent_ rays, and, on this account, soon became so enfeebled as to produce no sensible effect upon the eye of an observer. At one particular angle, however--namely, the angle 41° aforesaid--they emerged in a practically _parallel sheaf_. In their union was strength, for it was this particular sheaf which carried the light of the “primary” rainbow to the eye. There is a certain form of emotion called intellectual pleasure which may be excited by poetry, literature, nature, or art. But I doubt whether among the pleasures of the intellect there is any more pure and concentrated than that experienced by the scientific man when a difficulty which has challenged the human mind for ages melts before his eyes, and re-crystallizes as an illustration of natural law. This pleasure was doubtless experienced by Descartes when he succeeded in placing upon its true physical basis the most splendid meteor of our atmosphere. Descartes showed, moreover, that the “secondary bow” was produced when the rays of light underwent two reflections within the drop, and two refractions at the points of incidence and emergence.