14* OUTLINES OF NATURAL PHILOSOPHY. 



cal triangle PZS, fig. 1. contained by the arches 

 joining the pole, the zenith, and the star. 



This general problem contains twenty cases, of which 

 those that follow are the most useful in astrono- 

 my. 



In all of these, we suppose d to be the declination, 

 a the altitude, h the horary angle, z the azimuth 

 of a star, and / the latitude of the place of obser- 

 vation. 



22. Suppose the altitude and azimuth of a star 

 to be observed, and the latitude to be also 

 known ; it is required to find the declination, 

 and the horary angle of the star. 



Here #, , I are given, to find d and h, or, in the 

 spherical triangle PZS, the sides ZP, ZS are gi- 

 ven, (the complements of I and d] and the angle 

 PZS, between them to find the side PS, and the 

 angle P. 



By letting fall a perpendicular from S on the meri- 

 dian, we may obtain a solution by case 1st and 2d, 

 of oblique-angled spherical triangles. 



The solution may also be expressed analytically 

 thus : 



Find 



