n E F 



REFRACTION, terrestrial ( Vince, Playfair, $cj 



1. To determine it, let E apparent elevation of a mountain from a 

 point in the plain below ; D = apparent depression of that point from 

 the top of the mountain observed at the same moment; A = ^ subtend- 

 ed at the earth's centre by the distance between them ; then 



A 4. E D 

 Refraction = ^ . 



The terrestrial refraction found by this theorem, when the elevation 

 is not very great, varies from - to pj of the ^ A, but in the mean 

 state of the atmosphere - _L of A, which, in taking the elevation of 



any object, must be subtracted from the observed E to give the cor- 

 rect elevation. Also the radius of curvature of the ray varies from 

 twice to 12 times the earth's radius, but in the mean state of the atmos- 

 phere 7 times earth's radius. When the ray is not horizontal it = 

 7 times earth's radius 

 Bin. appar. zen. disk 



2. But in determining the height of a mountain, a correction may be 

 made at once both for the curvature of the earth and for refraction thug. 

 Let L = horizontal distance of the object in English miles, then the cor- 



2 La 

 rection for curvature in feet is , (see Levelling} and for refrac- 



21 



2 1 2 9 L* 4 LS 



-- -^^ = - = feet which must be added to 

 3 21 7 



computed height, and it will give correct height both for curvature and 

 refraction. 



3. To determine the most distant point on the earth's surface that can 

 be seen from the top of a given height with and without refraction. 



Let A = given height in miles, r = earth's radius, thpn in the mean 

 state of the atmosphere, the distance of the farthest visible point = 



tj j and distance, if there was no refraction, = \'2r h ; .'. dis- 

 tance which the eye can reach with refraction : do. without : : ^ ; 

 Ve :: 14 : 13 nearly. 



Cor. A/-^- = 96.1 miles, .'. the distance of the farthest visible 

 point in miles, allowing for refraction, = 90. 1 ^ 7T. Or by the last Art, 



4. I 9 \/7 fat 



if 7i> -height in feet, -- : = h', .'. L = -^. 



