264 Trans. Acad. Sci. of St. Louis. 



circle telescope at all zenith distances which has proven satis- 

 factory on general application. The flexure of such a teles- 

 cope is usually small and is not easily separated from other 

 errors of the instrument in zenith distance, errors of refrac- 

 tion tables and systematic errors of division. Furthermore, 

 the flexure of a telescope may not be constant but probably 

 varies with time, temperature or the manner of using the 

 instrument.* Observers, therefore, instead of attempting to 

 determine and allow for this troublesome class of errors, have 

 usually tried to adopt some method of observing by which 

 they may be eliminated.! The founder of that celebrated 

 firm of instrument-makers, the Repsolds of Hamburg, con- 

 structed the telescopes of his meridian circles so that the 

 object-glass and eye-end could be interchanged, thinking that 

 the mean of observations in declination on any star made 

 before and after the change would be free from errors of 

 flexure. It is evident that that term of the flexure which 

 varies as sin 6 would be eliminated by this method, but that 

 the term which varies as sin 26 would not (see p. 251). A 

 better method for eliminating flexure errors is that of Bessel, 

 the star being observed four times — direct and reflected 

 circle West and the same circle East. It does not, however, 

 in theory eliminate the term of the flexure which depends on 

 sine 26. Assuming the perfect homogeneity of the telescope 

 tube the 26 term of the flexure affects zenith distances and 

 nadir distances alike and gives rise to no discrepancy Re- 

 flected minus Direct. But the sine flexure — that is the term 

 depending on sine 6 —does, when unallowed for, give rise to 

 a difference R — D amounting to twice the flexure itself since 

 this flexure term increases measured zenith distances and 

 diminishes nadir distances or vice versa. 



It is conceivable that in the same way that the sin 6 term 

 arises from non-homogeneity of the tube, the 26 term may 

 not be the same for supplementary zenith distances — that is 

 for a star direct and reflected. Also flexure arising from 

 displacement of the neutral axis of the tube or auy other 



* See V. J. S. der Ast. Oesell. 31 Jahrgang Erstes Heft, p. 41. 

 | See Valentiner's Handworterbuch der Astronomie, pp. 575-592. 



