ASTRONOMY. 3? 



Near the earth's surface, the curvilineal path of the 

 ray of light may be supposed to coincide with 

 the circle of equal curvature. 



50. If the elevation of the top of a mountain 

 from a point in the plane below, and the de- 

 pression of that point from the top of the moun- 

 tain, be both observed at the same time, the 

 angle subtended at the earth's centre by the 

 distance between these points, added to the ob- 

 served elevation, and the sum diminished by the 

 depression, is double of the refraction. 



This supposes the path of a ray of light, for a small 

 part, to coincide with a circle. If, in fig 4., the 

 arch from B to A be the path of a ray, and if AH 

 and BF be perpendicular to AC, BC, in A and B ; 

 the tangents EA, EB being drawn to the path of 

 the ray, HAE is the apparent elevation of B from 

 A, and FBE the apparent depression of A from 

 B , the true elevation being HAB, and the true 

 depression FBA. It is evident that FBA = 

 BAH+ACB, or true Dep. = true Elev.-f Hor. 

 Ang. ; that is, true Elev. = true Dep. Hor. Ang. 

 But true Elev. = app. Elev. Ref. $ and true 

 Dep. = app. Dep. + Ref. ; therefore 2 Ref. = 

 Hor. Ang. + app. Elev. app. Dep. 



51. The 



