AND ITS CONGENERS. 205 



The figures in the column i 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 i 

 increases, 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, 1 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 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 



1 Prior of St. Martin-sous-Beaune, near Dijon ; member of tho 

 French Academy of Sciences. Died in Paris, Mayl684, 



