Updegraff — Flexure of Telescopes. 269 



fully determined and corrections for them applied, but no 

 other corrections for division error were used. All other in- 

 strumental errors were, as far as known, very accurately cor- 

 rected. The Pulkowa refraction tables which were used have 

 been shown to need no correction at Madison * and the effect 

 of errors of the tabular B. J. places of the stars used is 

 small. It is evident from the above table that these errors 

 in declination do not vary as the sine of the zenith distauce. 

 They do vary much more nearly as the sine of double the 

 zenith distance. The law of change is more or less the same 

 whichever side of the telescope is in tension or compression. 



Later observations with the same instrument after being 

 corrected for sine flexure and division errors give similar re- 

 sults excepting that the absolute size of the residuals is con- 

 siderably reduced.! All of these observations indicate that 

 the eye-end of the instrument bends more than the object- 

 glass, while our theory indicates that the object-end should, 

 for direct observations, have the greatest absolute flexure. 

 Since, however, the theory cannot be expected to give even 

 roughly the absolute value of the astronomical flexure, this 

 result is not to be considered as anomalous. The question is 

 as to what extent the law of change of the flexure with the 

 zenith distance as given by theory agrees with the results of 

 observation. 



In conclusion it may be said that assuming symmetry in 

 the form and homogeneity of the material of the tube, and 

 equality in weight of the object and eye-ends of the telescope, 

 the flexure will be zero at the horizon and at the zenith and 

 nadir. It will be a maximum at zenith distances of 45° and 

 135°, in so far as the moments of the compressive and tensile 

 forces are concerned, according to the theory of elasticity and 

 resistance of materials. According to the same theory it is 

 possible that the compressive and tensile forces may produce 

 astronomical flexure by displacement of the neutral surface. 

 In a general way these forces acting in opposite directions on 

 the two halves of the telescope tube when in an inclined posi- 



* See Publications of the Washburn Observatory , Vol. IX., p. 203. 

 t The same, Vol. VIII., p. 36. 



