of a Phace by Observations of the Pole-Star. 449 
For nautical purposes, the correction has heen sometimes 
assumed equal to p.cos / only: and in this manner it has been 
inserted in several books of navigation. But it would be more 
proper to add M. Littrow’s second term i. sin*¢. cot z. His 
last term is wholly insensible at sea. 
The time denoted by ¢ is the horary angle of the star, or the 
sidereal time elapsed since the star passed the meridian.. If S 
denote the correct sidereal time at which the observation was 
made, and A denote the apparent right ascension of the star on 
‘the day of observation; then will ¢ = (S—AR): noting always 
to increase S by 24°, if it should be less than A. The appa- 
rent right ascension and north polar distance of the pole-star, 
for every tenth day of the year, may be obtained from the Nau- 
tical Almanac. 
I shall now subjoin an example of the use and application of 
these tables. Let p = 1°. 38’; z = 39°. 12’. 16",4; and ¢= 
4b = 60°. ; r 
Bye o » » . Logarithm. 
p= 1.388. 0,00 B=~9: 1. 2,86= 1.7983052 
= 1519 cot 39.12.16,40=10.0884646 
——— Logarithm. - — 
1.38. 1,19=3.7694653 , 1.17,05= 1.8867698 
cos 60. 0. 0,00=9.6989700 
0.49. 0,59=3.4684353 
z = 39.12.16,40 
40. 1.16,99 
| P17,05 
Y = 39.59.59,94 
Which is the same as the value deduced from the rigorous 
formula, tan uw = tan p. cos ¢ 
cos (¥—w) oh COS U. cos z 
cos 7p) 
M. Littrow has stated that the value of M, which he has 
deduced from the term + sin? /, must be multiplied by 1-02 
for every increase of one minute in the north polar distance 
of the star. This is true, within certain limits; but he has 
neglected to state that his value of N ought, for the same rea- 
son, to be multiplied by 1°03, in order to obtain the correct 
values. The trifling difference which exists between our results 
in the preceding example, is principally owing to this slight cor- 
rection, 
Vol. 59, No, 290. June 1822. 3L TABLE 
