1884.] on Rainbows. 459 



for the violet band being 40° 30'. The entire width of the primary 

 rainbow is therefore 2°, part of this width being due to the angular 

 magnitude of the sun. 



We have thus revealed to us the geometric construction of the 

 rainbow. 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-coloured 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 atten- 

 tion. It belongs to the very essence of a maximum, approached con- 

 tinuously 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° 

 Fahrenheit. Its density when 5° colder, and when 5° warmer, than 

 this maximum is the same. So also with regard to the slopes of our 

 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 rain- 

 bow, 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 

 can 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 colours, the coloured 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 pro- 

 duction 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 diflerent colours, an approxima- 

 tion 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 eighty-two 

 years ago was appointed Professor of Natural Philosophy in the Royal 



* Prior of St. Martin-sous-Beaune, near Dijon. Member of the French 

 Academy of Sciences. Died in Paris, May 1684. 



