of Bessel's Astronomical Observations. 103 



capable of being allowed for, are the errors of division, and 

 the flexure of the telescope : on the figure of the wires in the 

 telescope there will be found in the Journal numerous obser- 

 vations of ullrsce Minoris both at the ends and the middle of 

 the field ; but I have perceived no deviation of them from a right 

 line. I have likewise in vain endeavoured to discover the in- 

 fluence of a change of temperature of the instrument on the line 

 of collimation. I am not aware of the possibility of any other 

 errors of the instrument. The possible errors of computation 

 I have sought in the refraction for the standard temperature 

 of the table and its changes. 



These errors are mixed together in the observations, and 

 must be elicited by proper methods ; the errors of division 

 have been determined by direct microscopical examination ; 

 the flexure was investigated in two different ways by the 

 images of stars reflected from a surface of water. Although 

 it is not necessary, in computing these latter observations, to 

 know the refraction itself, yet its changes must be known, in 

 order correctly to compare the observations made at different 

 times. The determination of the changes of refraction must 

 therefore precede; they may be obtained independently of 

 the errors arising from flexure and imperfect division, by not 

 mixing together the observations made in the two positions of 

 the instrument. The errors of division, the flexure and the 

 changes of refraction being known, observations of circum- 

 polar stars will give the refraction for the standard tempera- 

 ture of the tables. I now proceed to the single parts of this 

 investigation. 



1. Examination of the Errors of Division, 

 published in the Phil. Mag. for May 1824, vol. lxiii. p. 348. 



2. Examination of the Thermometer 

 published in the Phil. Mag. for April 1824, vol. lxiii. p. 307. 



3. Thermometrical Corrections of Refraction. 



Gay-Lussac's experiments on the expansion of air by heat 

 would render the astronomical investigation of this subject 

 unnecessary, if the atmospherical air were always perfectly 

 dry ; but the aqueous vapour mixed with it produces a change 

 ot refraction* so as not to agree with the true expansibility of 

 the air, but with a smaller one. Laplace shows in the 4th 

 volume of his Mccanique Celeste, p. 275, how to calculate the 

 influence of vapour on refraction : supposing the constant quan- 

 tity of refraction lor 0-76' metre height of the barometer, and 



the 



