244 



Trans. Acad. Sci. of St. Louis. 



of collimation is directed to the star s, Fig. 1. If there were 

 no astronomical flexure, the same amount of rotation of the 

 instrument about its axis would cause the line 

 of collimation to pierce the celestial sphere at 

 another point as s'. Let AB be the vertical 

 circle passing through s', s and «' being the 

 points where the line of collimation in its 

 disturbed and undisturbed positions pierces 

 the celestial sphere. Draw sr perpendicular 

 to AB and let the angle ss'r be repre- 

 sented by y. Thus the total flexure ss' may- 

 be resolved into the horizontal and verti- 

 cal components sr and s'r. It is evident that 

 both are functions of the zenith distance. 

 Later on we shall derive formulae for cor- 

 recting the observed right ascensions and declinations of stars 

 for flexure in azimuth and zenith distance when the flexures 

 in these two co-ordinates are known. The flexure in azimuth, 

 arising in part from flexure of the axes and in part from 

 non-homogeneity of the material of the telescbpe tube, seems 

 not to admit of theoretical treatment, and we proceed to 

 investigate the flexure of telescopes in zenith distance. 



Let us assume that the telescope revolves about a single 

 horizontal axis, that the tube is symmetrical in form and 

 density with reference to the point of intersection of the line 

 of collimation and the axis of revolution, 

 and also that the weight of object-glass 

 and eye-end are exactly equal — which 

 is the case with meridian circle tele- 

 scopes of the best construction. 



In Fig. 2 let^C^'O be the tube of a 

 telescope inclined at the angle d to the 

 vertical line W passing through C the 

 middle point of the line E' 0' . E'O' is 

 the position which the line of collimation 

 would have if not disturbed by flexure. 

 On account of its own weight and that 

 of the eye-end and object-glass, the tube 

 of the telescope is bent, and BO la the 



