256 Mr, Pond on the Changes in the [Oct. 



give different determinations of the horizontal point. From 

 observations thus obtained, a near approximation to the true 

 angular distance might be inferred, by taking a mean between 

 tlie distances of the direct 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 quantity : the double 

 altitudes of each star would be incorrectly given, but every star 

 would give the same determination of the horizontal point, Ta 

 suppose however the existence of such a system of flexures, 

 would 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 determi- 

 nation of the horizontal line from stars of whatever altitude, there 

 are then only two hypotheses that can be formed respecting such 

 an instrument ; either that the flexures are insensible, or that 

 they are such as are absolutely inconsistent with the laws of 

 mechanics. Hence I conclude that the coincidence of the 

 results by direct vision and by reflection, and the uniform deter-«» 

 mination 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. Bes- 

 sel, which have lately much excited the attention of astrono- 

 mers. It is obvious, by merely inspecting these catalogues, a 

 comparison of which with the Greenwich catalogue I here sub- 

 join, that one, or both, of the instruments used by these astro- 

 nomers must be erroneous ; and it seems to me, that the source 

 of error is the very flexure, the nature and eftects of which we 

 have been considering. For if we attend to the diflerences 

 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'Q'\ In which direction 

 flexure will affect the zenith distances, is a matter quite acci- 

 dental, depending on the unequal elevation or depression of the 

 object-end or eye-end of the telescope, in consequence of the 



• I must also notice that tlie method by reflection possesses, in common with instm- 

 ments turning in winiutli, Uie advantage of mcajsurini; the double vf the retiuirt'd 

 angle. 



