﻿the Height of the Atmosphere, 



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the light, both these causes of irregularity will tend to increase 

 the angle of depression, and it is obvious that we must employ 

 the lowest value observed if we base our calculations upon the 

 properties of dry air. We shall therefore suppose that the angle 

 of depression is a little greater than 16°, with a probable error of 

 about ±30'. 



Let a ray of light from the sun, S F, be refracted so as to 

 touch the circular section of the earth at B, and, refracted again 

 to the same extent, cut the exterior circular section of the atmo- 

 sphere at L. By reflection at L and by refraction this ray again 

 touches the earth at A, causing the last gleam of twilight at A. 



Let A H and B D G be tangents both to the ray and to the 

 earth at the points A and D respectively; produce S F to K, 

 cutting B D G in G. 



Let be the angle H K S, the depression of the sun below the 

 horizon ; <f> the angle of horizontal refraction B G K, and v the 

 angle A C B. Then 2v = Z H B D = - <f>, and therefore 



Let S' L be the tangent to the ray at L, then all the circum- 

 stances attending the ray L A are the same as though the ray 

 Phil. Mag. S. 4. Vol. 41. No. 274. May 1871. 2 B 



