248 Trans. Acad. Sci. of St. Louis. 



While formulae of this kind will not in practice give the 

 absolute values of the flexure, it is possible that they may 

 throw some light on the law of variation of flexure with the 

 zenith distance. 



Let us assume that the tube is of uniform transverse sec- 

 tion, that it is supported at the middle point of the line 

 joining the centers of gravity of the object-glass and eye-end, 

 that the material of the tube is homogeneous throuo[hout and 

 that the object-glass and eye-end are of the same weight, W. 

 We shall consider first the flexure due to the weight of the 

 object-glass and eye-end, and second that due to the weight 

 of the tube itself. Then for the first case the differ- 

 ential equation of the neutral axis of the upper half of the 

 tube of the telescope is, as given in Wood's Resistance of 

 Materials, p. 138 and in other text-books, 



EI ^.= — yW cosd — xTTsin^. 



For the lower half of the tube, 



EI^, = +yW co^d —xW^md. 



The zenith distance d is taken less than 90° in each of these 

 equations and the origin of co-ordinates is taken at the object 

 and eye-ends respectively in the disturbed position. The x-axis 

 is taken parallel, and the _?/-axis perpendicular to the undis- 

 turbed position of the line of collimation. E is the modulus 

 of elasticity of the material of the tube and / the moment of 

 inertia of a transverse section. 



If we put 



„ W%\\\d ^ , I^cos^ 



p=—E'r ^"^ "i^^—ET' 



the above equations become 



dy? 



px — qhj, (1) 



