ASTRONOMY. 17 



b. Find an arc x, such that tan x = cos h X cot /. 



, cos x X sin a 



Next find an arc ?/, so that cos y = r j . 



sin i- 



the declination is the complement of = y + x. 



This solution is from its nature ambiguous ; the sum 

 of y and x must be taken, when the perpendicular 

 from the zenith, on the circle of declination, falls 

 within the triangle; their difference, when it falls 

 without. 



25. Let a, d, z be given to find /, or to find 

 the latitude from observing the altitude and 

 azimuth of a star, and knowing also its declina- 

 tion. 



Here, again, in the triangle ZPS, two sides are gi- 

 ven, and the angle opposite to one of them, to find 

 the third side, the complement of latitude. The 

 perpendicular must be let fall from the star on the 

 meridian ; and the distance of this perpendicular, 

 first from the zenith, and then from the pole, is 

 found as in the last case; the sum or difference is 

 the complement of the latitude. 



26. Let a, d and h, be given to find / ; that 

 is, the altitude and horary angle being observ- 

 ed of a star, of which the declination is known, 

 to find the latitude. 



VOL. II. B The 



