Astronomical and Nautical Collections. 187 
The observations, from which the preceding catalogue was 
deduced, were made in the years 1818, 19, 20, and 21. Most 
of the polar distances here given are easily deduced from the 
results given in my paper in the Phil. Trans. 1821. 
These polar distances having been compared with the results 
of Dr. Bradley’s observations, as deduced by Mr. Bessel for 
the year 1755, the proper motions here given were obtained. 
The annual precession (to which the proper motion is ap- 
plied) was computed for each star from the numbers in Mr. 
Bessel’s deductions, viz. :— 
Prec. in NPD = — (20,05039—, 00009702¢) cos AR. 
t = given year — 1750. 
From these polar distances and annual variations have been 
deduced the NPD in 1813, and a comparison made with the 
polar distances deduced from observations in 1812, 13, and 14. 
(Vide 12 vol., Trans. R. I. A.) 
The differences of the catalogue of 1813 appear by this com- 
parison to be very small, and thereby is shown the consistency 
of the instrument. The number of observations, from which 
the catalogue of 1813 was deduced, were much indeed 
inferior to those by which the catalogue of 1820 has been 
determined. 
The column of proper motions is probably exact to ,35 of a 
second, and the error of the columns of annual variation can- 
not be much greater. 
