Updegraf — Flexure of Telescopes. 263 



proven by experiment. In this case, however, we are con- 

 cerned with the difference of two flexures, and relatively small 

 errors in the absolute deflections may cause large astronomical 

 flexures. We have shown above that the astronomical hor- 

 izontal flexure may be assumed to vary as the sine of the 

 zenith distance, and also that there is a small theoretical 

 astronomical flexure which varies as the sine of twice the 

 zenith distance. Again, the effect of the displacement of the 

 neutral axis by the longitudinal forces seems to be uncertain. 



The tube of the telescope of a meridian circle as ordinarily 

 constructed consists of two tubular brass castings of the same 

 size and shape, which are bolted to a hollow cubical brass 

 portion which is cast in one piece with the horizontal axis of 

 the instrument. When the telescope is in an inclined posi- 

 tion the greatest strain comes where the parts are fastened 

 together with screws.* This tends of course to make the 

 flexures uncertain. 



According to formulae (17) and (37) the flexure due to 

 the compressive and tensile forces varies inversely as the 

 square of the coefficient of elasticity of the material of the 

 tube. Now the coefficient of elasticity of some kinds of steel 

 is more than three times as large as that of brass. t If, there- 

 fore, there is any danger of appreciable flexure errors arising 

 from the compressive and tensile forces it is advisable to 

 construct meridian circle telescopes of steel instead of brass, 

 provided that steel is as nearly homogeneous as brass. 



It is not the purpose of this paper to discuss the various 

 methods used for determining the astronomical flexure of 

 telescopes by observation or experiment, but we shall 

 touch briefly upon certain results of observation which seem 

 to be of interest in connection with the foregoing theory'. 

 The only practicable way of determining the flexure is 

 by observation or experiment, yet there has never been 

 devised any method for getting the flexure of a meridian 



* See Harkness on Flexure of Meridian Instruments, Appendix III. to 

 Washington Obs^ns for 1882, p. 14. 



t See Wood's Resistance of Materials, pp. 310-311, and Weisbach'a 

 Mechanics of Engineering, Translated by Coxe, p. 403. 



