declination of some of the fixed stars. 51 
polar distances given in the Greenwich catalogue ; while 
those of all the stars in Dr. Brinkley's catalogue as regularly 
fall short of my determinations. It is not from the casual 
circumstance of my results being nearly a mean between the 
results of those two astronomers, that I intend to claim a su- 
perior weight of authority for my own ; for were this the only 
ground for preference, I should regard the question as yet 
undetermined, and should think it my duty to recommend 
the providing of new and more powerful instruments for as- 
certaining the truth. But it appears to me that from the 
observations by reflection, which I have lately made, and 
from their agreement with my observations by direct vision, 
that I am entitled to determine the share of error to which 
each of these two catalogues is liable ; not only from the 
general superiority of the Greenwich circle, which I consider 
to have been thus proved, but from this peculiar circumstance, 
that whereas in the two catalogues of Mr. Bessel and Dr. 
Brinkley, the errors cannot fail to be the greatest in stars 
near the horizon ; by my method of reflection those stars, 
which are nearest the horizon, must be determined the most 
correctly, from their double altitudes being measured on the 
smallest arc. 
In stars near the equator the catalogue of Mr. Bessel differs 
from that of Dr. Brinkley five seconds ; and from the pre- 
ceding considerations, I think we may venture to conclude 
that Mr. Bessel's polar distances are too great by about three 
seconds, and Dr. Brinkley's too small by about two : and 
since my catalogue differs from the two former from the 
zenith to equator in very nearly the same proportion, there 
can be no reason to doubt that their errors throughout are 
divided in nearly the same ratio. 
