FLEXURE OF TELESCOPES.* 

 Milton Updegraff. 



The lack of perfect rigidity of the materials of which 

 astronomical instruments are constructed has long been rec- 

 ognized as one of the chief sources of the errors to which 

 certain classes of astronomical observations are subject. 

 Instruments of the best construction are designed with a view 

 to avoid as far as possible errors of flexure, and in a good 

 instrument the linear displacement of any part due to flexure 

 is very small. But, nevertheless, in the use of telescopes in 

 connection with divided circles for the measurement of large 

 angles, the flexures of the telescope tube, of the circles and 

 of the axes about which they revolve, are often appreciable 

 even in instruments of the very best construction. 



The errors of flexure arise through distortion of the divided 

 circles and angular displacement of the line of collimation of 

 the telescope with reference to the zero-points of the circles. 

 The telescope tube being supported (as should always be the 

 case) at the middle point of its length, if the deflections of the 

 two halves of the tube are equal and in the same direction, 

 the line of collimation will suffer no angular displacement. 

 But if the absolute flexures of the two halves of the tube are- 

 unequal or not parallel, the line of collimation will be shifted 

 to a position not parallel to its normal or undisturbed position 

 and this angular displacement is called the astronomical 

 flexure. Flexure of the axes, also, may cause angular dis- 

 placement of the line of collimation. 



Let us adopt as the undisturbed position of the line of 

 collimation, with reference to the divisions of the circles, the 

 position assumed when the line of collimation is directed to 

 the nadir. Then suppose the telescope turned until the line 



* Read in less extended form before The Academy of Science of St. Louis, 

 June 1, 1896. 



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