S80 Mr. Ivory on the Theory of the Astronomical Refractions. 



nt greater zenith distances, when the manner in which the 

 atmosphere is constituted comes into play, it is not so clear 

 that they may not be subject to vary in different climates, and 

 at different localities of the same climate. If a table of refrac- 

 tions at a given observatory contain a set of fixed numbers, 

 these must be deducible from quantities not liable to change, 

 that is, from certain mean effects produced by the atmosphere 

 at the observatory. To trace the relations that necessarily 

 subsist between the mean effects that take place at a given 

 point on the surface of the earth, is the proper business of 

 geometry; if this can be successfully accomplished, the astro- 

 nomical refractions will be made to depend upon a small num- 

 ber of quantities really existing in nature, and which can be 

 determined, either directly or indirectly, by actual observa- 

 tion. 



1. The foundation of the theory of the astronomical re- 

 fractions was laid by Dominique Cassini. The earth being 

 supposed a perfect sphere, he conceived that it was environed 

 by a spherical stratum of air xmiform in its density from the 

 bottom to the top. By these assumptions the computation of 

 the refractions is reduced to a problem of the elementary 

 geometry requiring only that there be known the height of 

 the homogeneous atmosphere, and the I'efractive power of air. 

 Let the light of a star S fall upon the atmosphere at B, from 

 •which point it is refracted to the eye of an observer at O on 



the earth's surface DOE: the centre of the earth being at 

 C, draw the radii C O K, C D B H : the angle K O B = fl, 

 is the apparent zenith distance of the star ; and O B C = <{) 

 is the angle in which the light of the star is refracted on enter- 

 ing the atmosphere : now from the triangle O B C we deduce 



sin O B C = siu K O B 



CO 



CB' 



