270 Trains. Acad. Sci. of St. Louis. 



tion may be expected to have some effect on the position of 

 the line of collimation. 



Assuming that the material of the tube is non-homogeneous, 

 the effect produced by the tensile and compressive forces is 

 unknown in theory. We now have also to deal with the sine 

 flexure which is assumed to be a maximum at the horizon. It 

 is usually determined at the horizon and allowed for on the 

 supposition that it decreases toward the zenith with the sine 

 of the zenith distance. 



When the sine-flexure and all other known errors have been 

 determined and as accurately corrected as possible there usu- 

 ally appears a small systematic residual error whose cause has 

 never as yet been determined in any particular case. Three 

 instances of this have been given above. To indicate to what 

 extent this residual error may be due to the unsymmetrical 

 action of gravity on the telescope tube is the purpose of the 

 foregoing discussion. 



Derivation of Formulae for Correcting Observations 

 IN Right Ascension and Declination for Flexure of 

 THE Telescope in Zenith Distance and Azimuth. 



When the vertical and horizontal flexures of an equatorial 

 telescope are known for the zenith distance C» the observed 



right ascension and declina- 

 tion of a star at that zenith 

 distance may be corrected 

 for flexure by means of 

 formulae which we proceed 

 to derive. In the figure let 

 O be the position of the 

 observer, NES W the hori- 

 zon, Z the zenith, P the 

 north pole, and s a star. Applying to the spherical triangle 

 sPZ in the figure, the following general equations which hold 

 for the spherical triangle AB(J, 



sina sin^ = sin^ sinft (a) 



cosa = cos6 cose + siiift sine cos^ (b) 



