DECLINATION. 



589 



In the spherical triangle APE, the side PA is equal to 90 - /, 

 the side AE to 90 h, the side EP is at the polar distance A of 

 the star, or the complement of its declination. The angle h is given 

 by the vertical circle, and the corresponding reading of the verniers 

 is made on the horizontal circle. 



Putting 



the angles A and P will be given by the formulae 



cos 



A_ / 



2 / \ 



. P 



sin = 



cos S sin (S - A) 

 cos / cos h 



cos S sin (S - h) 

 cos / sin A 



A is the azimuth of the star that is to say, the angle by which 

 the arrangement must be turned, so that the telescope is in the 



Fig. 241. 



geographical meridian ; the corresponding position of the verniers 

 on the horizontal scale is then known. P is the hour -angle of the 

 star, and from it is deduced the local time of observation. 



Several corrections are necessary. As the zero of the graduation 

 of the circle does not exactly correspond with the horizontal position 

 of the telescope, two observations, with the telescope to the right 

 and to the left, give twice the zenith distance of the star. 



The height should, on the other hand, be corrected for atmo- 

 spheric refraction. Lastly, if the body is not a fixed star, the astro- 

 nomical declination changes with the time of day ; but this variation 

 does not amount to i' per hour for the sun. An approximate 



