R A I 



to somewhat more than 91,751 cubic miles of water, which must lie sup- 

 plied by evaporation from the surface of the earth and sea. See Eva- 

 poration. The dry land amounting to 52,745,253 square miles, the quan- 

 tity of rain falling on it will amount to 30,960 cubic miles. The quantity 

 of water running annually into the sea is estimated at 13,140 cubic miles, 

 a quantity of water equal to which must be supplied by evaporation from 

 the sea, otherwise the land would be soon completely drained of its 

 moisture. 



The area of England and Wales = 46,450 square miles, taking there- 

 fore Dalton's mean at 36 inches, we shall have the annual quantity of 

 rain and dew falling in England and Wales = 28 cubic miles of water. 



RAINBOW. (Wood.) 



1. If a ray of light refracted into a sphere, emerge from it after any 

 given number of reflections, to find the angle contained between the di- 

 rections in which it is incident and emergent. 



Let $ and $ =. angles of incidence and refraction, p = number of re- 

 flections, then the deviation, or inclination of the emergent to the inci- 



dent ray is 



20 2(p + l)?' or 2 (p + l)0' 2$. 



Cor. In the primary rainbow p = 1, /_. deviation = 4 $' 2 <p; in the 

 secondary bow p = 2; .*. deviation =. 6 $' 2 0, or its supplement. 



2. The rays of any colour will fall most copiously on the eye, when 

 the rays emerge parallel, in which case only they are efficient. 



3. When rays emerge parallel, the increment of the angle included be- 

 tween the incident and emergent rays = 0, and tangent of incidence : 

 tangent of refraction :: p -f. 1 : 1. 



Cor. Hence it is easy to shew that if the ratio of refraction m, 



Ex. 1. If the pencil be parallel red rays incident upon a sphere of wa- 

 ter, and suffer two refractions and one reflection, as in the primary bow, 



vn -5-, and p = 1 .*. cos. <p A/ when the rays emerge parallel, 



or <p 59. 23' ; also <p' = 40. 12' ; ,*. deviation, or angle between the 

 incident and emergent rays, -- 4 <p' 2 <p 42. 2'. 



When the violet rays are thus incident and emergent, p = 58. 40% $ 

 = 39. 24', and deviation = 40. 16'. . 



Ex. 2. If the pencil be parallel red rays incident upon a sphere of wa- 

 ter, and suffer two refractions and two reflections, as in the secondary 

 .tow, p = 2, and .'. when the rays emerge parallel, <p = 71. 50' j ^ ~ 

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