ASTRONOMY* 33 



hearty, j/=(l "\ tan x 5 where the constant co- 

 efficient 1 is to be determined by observa- 

 m 



tion. 



If. It is evident that this approximation is imperfect, 

 because it gives y infinite when ^=90, or when 

 the star is in the horizon ; and in all cases when 

 the altitude is small, it gives the refraction too 

 great. Dr BRADLEY found that the refraction was 

 more nearly as the tangent of the apparent zenith 

 distance, diminished by a certain multiple of the 

 fefraction, or that y=. A .tan (x b y}. He also 

 found A = 57" and b = 3 nearly, so that y = 57" 

 tan (x 3 y). 



To use this formula, we may suppose, for a first ap- 

 proximation, 3/ = 57" tan #, when x is not very 

 great. 



If 07=90, we must assume y^ and correct the value 

 by trials* 



The manner in which the constant quantities A and 

 b have been determined, remains to be explained. 



45. As the determination of the latitude of a 

 place, and of the declination of a star, involve 

 the effect of refraction, they are not to be em- 

 ployed for finding the refraction, except when 



VOL. II. C a 



