3% OUTLINES OF NATURAL PHILOSOPHY. 



creases the altitude, but does not affect the azi- 

 muth. 



b. Hence all the altitudes, measured as in the prece- 

 ding sections, require corrections to be applied to 

 them before the true altitudes are obtained. 



The method of making these corrections is now to 

 be explained. 



44. From the principles of optics, it is known, 

 that the rays which pass through the strata of 

 the atmosphere at right angles, or which come 

 from stars in the zenith, suffer no refraction, 

 and that, at all other elevations, the quantity of 

 the refraction is nearly as the tangent of the 

 zenith distance. 



a. If x be the true distance of a star from the zenith, 

 and y the refraction, so that the apparent distance 

 is x y, then, by the nature of refraction, sin # is 

 to sin (x y] in a constant ratio, suppose that of 

 m to n ; and since sin (x y) = sin x . cos y 



cos x . sin j/, !! sin ,r=sin x . cos^ cos x . siny, 

 m 



or = cos y ^!_f. sin y. Now if y be very 



m sin x 



small, cosy = 1 nearly; and therefore sinj/ = 



(1 _ * ) ELf = ( i _ n -} tan x. As sin y = y 

 ml cos x ml 



nearly 



