Decli7iation of some of the principal Fixed Stars. 185 



From observations thus obtained, a near approximation to the 

 true angular distance might be inferred, by taking a mean be- 

 tween the distances of the du'ect and of the reflected images. 

 The least probable supposition concerning the flexures is, that 

 at equal inclinations above and below the horizon, they will 

 be equal, but in opposite directions ; the consequence of which 

 would be, that the direct and reflected images would approach to 

 or recede from one another by the same cjuantity : the double 

 altitudes of each star woidd be incorrectly given, but every 

 star would give the same determination of the horizontal point. 

 To suppose however the existence of such a system of flexures, 

 woiUd be to suppose that gravity produced the same change of 

 form in the instrument, as if its direction were inverted ; and 

 since the horizontal line is that at which according to the sup- 

 posed system a contrary flexure will take place, the flexure at 

 or near the horizon should be zero, where, however, according 

 to the known laws of mechanics it ought to be the greatest. 

 Such a system therefore must be considered as mechanically 

 next to impossible. 



If then an instrument give the angular distances both by 

 reflection and by direct vision the same, and the same deter- 

 mination of the horizontal line from stars of whatever altitude, 

 there are then only two hypotheses that can be formed re- 

 specting such an instrument; either that the flexures are in- 

 sensible, or that they are such as are absolutely inconsistent 

 with the laws of mechanics. Hence I conclude that the coin- 

 cidence of the results by direct vision and by reflection, and 

 the uniform determination of the horizontal point, will be the 

 strongest proof of the non-flexure of the instrument, and of 

 the accuracy of both results *. 



In illustration of the whole of the preceding observations, 

 let us examine two catalogues, those of Dr. Brinkley and 

 Mr. Bessel, which have lately much excited the attention of 

 astronomers. It is obvious, by merely inspecting these cata- 

 logues, a comparison of which with the Greenwich catalogue 

 I here subjoin, that one or both of the instruments used by 

 these astronomers must be erroneous ; and it seems to me, that 

 the source of error is the very flexure, the nature and effects 

 of which we have been considering. For, if we attend to the 

 differences between these two catalogues, we shall find that 

 the six stars near the equator differ 5" from one another, 

 whereas the stars near the zenith do not differ above 2"'5. In 

 which direction flexure will affect the zenith distances, is a 



• I must also notice that the method by reflection possesses, in common 

 with instruments turning in azimuth, the advantage of measuring the doublq 

 of the required angle. 



Vol. G2. No. 305. Sept. 1823. A a matter 



