7 2 Explanation of the preceding tables. 
Greenwich, are the quantities that must be applied to the Dublin 
and Greenwich observations to produce the interpolated catalogue. 
Table IV. contains four catalogues, in which, as no systematic 
difference can be traced, the instrument must be considered as 
perfect within the limits of the small discordances in Catalogue 
I. and II. 
Table V. contains the errors of each of the preceding cata- 
logues. From this table it appears, that the regular difference 
between the results with six and with two microscopes, is now 
nearly insensible. This must have arisen formerly from flexure ; and 
the new braces, though intended only to strengthen the attach- 
ment of the telescope to the circle, have, in fact, added strength 
and firmness to the whole frame of the instrument. (Vide Expe- 
riments on this subject in the volume of Observations for 1820.) 
Table VI. shows the difference between the results of the 
Dublin and Greenwich circle, both at the present time, and in the 
year 1812. From this it is evident that a small change has taken 
place in one of the instruments. Formerly the two instruments 
differed only one second in an arc of 90° ; at present, the diffe- 
rence amounts very exactly to double that quantity. 
Table VII. contains the two catalogues of Dr. Brinkley and 
Mr. Bessel. Here the differences are much greater and more 
irregular. 
Table VIII. contains a general catalogue of the stars, includ- 
ing several that were not very accurately observed in 1813; but 
which, nevertheless, confirm in a remarkable manner the general 
law of southern deviation. 
Tables IX, X and XI. contain observations of « Lyrae, by which 
it appears, that whatever may be the parallax of this star, it is 
not within the powers of our instrument to detect it. With Dr. 
Brinkley’s Refraction, the result would have been a very small 
fraction of a second less in favour of parallax. 
