Updegraff — Flexure of Telescopes. 261 



of the section. But in deducing the above formulae for the 

 absolute deflections of the two halves of the telescope tube it 

 was assumed that the moment of inertia I has the same 

 minimum value throughout the length of the tube. 



Therefore the deflections computed from these formulae 

 must be too large, and the error may be assumed to be the 

 same for each half of the tube provided that the neutral axis, 

 in the absence of longitudinal forces, passes through the center 

 of gravity of each section. If the above statements are true, 

 the astronomical flexure is not appreciably affected in theory 

 by the longitudinal forces. 



If, however, the co-efficients of elasticity for tension and 

 compression are not equal, the curve of the neutral axis does 

 not pass through the center of gravity of the sections, in the 

 absence of the longitudinal forces, and their effect will be in 

 case of one-half of the tube to move the neutral axis nearer 

 to the center of gravity and in the other case further from it. 



In one case the moment of inertia will be diminished and 

 in the other increased with corresponding increase and dim- 

 inution of the absolute flexures. This would give rise to 

 astronomical flexure. 



Until the undisturbed position of the neutral axis is more 

 accurately known, further analytical investigation of the 

 matter seems for our purpose to be impracticable. It must 

 be recognized, however, that herein lies a possible cause of 

 astronomical flexure of telescopes. 



In computing a few numerical results from the above 

 formulae I have taken first the case of the telescope of a 

 modern 5-iuch Kepsold Meridian circle. The focal length is 

 57.6 in., clear aperture of the object glass 4.80 in. and the 

 thickness of the walls of the brass tube about 0.075 inches. 

 The interior diameter of the tube is taken as 4.80 inches and 

 the weight of the object-glass with cell and the terminal flange 

 on the tube is taken as 35 lbs., the weight of the micrometer 

 and other parts at the eye-end being the same. I have taken 

 the weight of each half of the tube minus the terminal flange 

 as 10 lbs. The astronomical flexure as computed from these 

 data by the above formulae is 0".01. The weights and dimen- 



