AND ITS CONGENERS. 205 



The figures in the column t express the angles of inci- 

 dence, while under d we have in each case the accom- 

 panying deviation, or the angle enclosed by the incident 

 and emergent rays. It will be seen that as the angle t in- 

 creases, the deviation also increases up to 42 28', after 

 which, although the angle of incidence goes on aug- 

 menting, the deviation becomes less. The maximum 

 42 28' corresponds to an incidence of 60, but in reality 

 at this point we have already passed, by a small quantity, 

 the exact maximum, which occurs between 58 and 59. 

 Its amount is 42 30'. This deviation corresponds to 

 the red band of the rainbow. In a precisely similar 

 manner the other colours rise to their maximum, and 

 fall on passing beyond it ; the maximum 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 con- 

 struction 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 rain- 

 bow 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 difficul- 

 ties thicken, but, as before, they are to be overcome by 

 attention. It belongs to the very essence of a maxi- 

 mum, approached continuously on both sides, that oft. 

 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 re- 



* Prior of St. Martin-sous- Beaune, near Dijon ; member of the 

 French Academy of Sciences. Died in Paris, May, 1684. 



