49 
declination of some of the fixed stars. 
tion to the true angular distance might he inferred, by taking 
a mean between the distances of the direct and of the reflected 
images. The least probable supposition concerning the flex- 
ures 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. To suppose however the existence of such 
a system of flexures, would be to suppose that gravity pro- 
duced 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 supposed 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 mecha- 
nics 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 
insensible, or that they are such as are absolutely inconsistent 
with the laws of mechanics. Hence I conclude that the co- 
incidence 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.* 
* I must also notice that the method by reflection possesses, in common with 
MDCCCXXIII. H 
