R A I 



450. 27', .'. 6<p' 2 $ 1290. 2', the supplement of which, or the devia- 

 tion, = 500. 58'. 



When violet rays are thus incident, <p = 71. 26', @' 44. 47', and the 

 deviation 54<>. 10'. 



4. Construction of the primary and secondary Rainbow. 



The red rays we have seen 

 are efficacious when the / 

 between the incident and 

 emergent rays = 42. 2', and 

 the violet rays when the 

 same /_ 40. 16' ; hence if 

 H Q be the horizon, S, S', 

 S" rays proceeding from the 

 sun, O the eye of the spec- 

 tator, and the / P O R ( =i 

 / S" R O) be taken = 42. 2' 

 the drop R will transmit the 

 red rays to the eye ; and if 

 P O V (= S' V O) be taken = 40o. 16' the drop V will transmit the violet 

 rays. The drops betwixt R and V will transmit to the eye the other 

 eolours in their proper order. 



If O R and O V revolve about the axis O P, every drop of water in 

 the surface of the cones thus described \vill respectively transmit to the 

 eye a small parallel pencil of red and violet rays ; and thus a red and 

 violet arc, whose radii (measured by the angles which they subtend at 

 the eye) are 42. 2', and 40. 16' respectively, will appear in the falling- 

 rain opposite to the sun ; and the same may be said of the other colours. 



The parallel pencils of red &c. rays 

 which emerge from other drops fall 

 above or below the eye. 



The secondary rainbow is formed by 

 two refractions and two reflections. 

 In this case, as we have seen, the vio- 

 let rays are efficacious when the ^ 

 contained by the incident and emer- 

 gent rays 54. 10', and the red 

 rays when the same / = 50. 58'. 

 Hence as in the primary bow, if ^ ** "" \ x 

 P O V = 54o. 10', the drop V will trans- 

 mit the violet rays to the eye ; and if PO R = 50<>. 68' the drop R will 

 transmit the red rays. 

 227 



