4 63 
Mr. Fallows’s catalogue of southern stars. 
effect the declinations in the Catalogue. I was compelled to 
use this method of finding the latitude, as it was impossible, 
with my present means, to discover the altitude of the Pole 
by observations of circumpolar stars at their superior and 
inferior transits. 
A considerable number of the stars in the Catalogue are 
double : the place in the brighter is always given. I cannot 
find that M. De La Caille mentions a star of nearly the 
fourth magnitude accompanying a. Crucis (see No. 139). 
To the magnitudes, I have sometimes annexed the signs 
+ or — ; the meaning of which is this ; that if a star appear 
hardly of the fourth magnitude we set it down 4 — ; if a 
little greater than a fourth, 4 -{- ; and so on of others. 
It must be remarked, that the apparent altitudes of stars 
were always reduced to the true by Dr. Young’s tables of 
refractions, inserted in the NauticaF Almanacks each year. 
Formulae, by which the apparent right ascensions and de- 
clinations were reduced to the beginning of the year,* 
S. S. 
— £R = ( -f- 3,0678 — 1,336 sin. R. tang. D ) , t - 
— 1, 239 cos. R . sec. D . cos. 0 
— 1, 350 sin. R . sec. D . sin. © 
+ 0, 643 cos. R . tang. D . cos. SI 
-f- 0,4788 sin. R . tang. D . sin. SI >. 
— 1, 103 sin. SI 
+ 0,0289 sin. R. tang. D . sin. 2 o 
+ 0,0265 cos. R. tang. D . cos. 2 0 j 
— 0,06115 sin. 20 
* The stars were all reduced to the beginning of the year in which the observa- 
tions were made, and afterwards brought up to the ist. of January, 1824, by the 
quantity of annual precession. 
