exactly in the Meridian. 285 
If observations of this kind be made about sunrise or sunset, 
and after the passage of the stars, the telescope be pointed to 
the horizon and compared with some object there, a meridian 
mark may be set up, which may be corrected from time to time 
by subsequent observations on various stars similarly situated. 
I have already stated that in all cases of this kind, the time em- 
ployed is supposed to be sidereal time, and that if a clock or watch 
be used which marks mean solar time, the interval between the 
observations must be corrected accordingly. This correction is 
made by converting the value of dT (which is expressed in side- 
real time) into mean solar time, in the usual manner, by adding 
the acceleration of the fixed stars for that interval. Thus, in 
the case last stated, suppose that the passage of < Canis majoris 
had been observed at 12". 10’. 31”,6, and the passage of Castor 
at 12", 42’, 9”,2 mean solar time: the difference between these 
two (or dT) would be 31’. 37",6, to which the acceleration of 
the fixed stars for that interval (=5”,2) must be added; whence 
the difference will be, as before, =31’. 42’,8. So that, by means 
of this correction, it will be indifferent whether the clock shows 
sidereal or mean solar time. 
_ Before I close this paper I shall point out another important 
use to which these observations may be applied ; namely to cor- 
recting the error of the clock at the time of observation. For 
after the quantity of the deviation is found, as above explained, 
the error of the clock may be determined by means of the transit 
of either of the stars employed ; that is, of either N or S; but, 
for the sake of uniformity in the investigations, I shall confine 
my remarks to N, or the northern star. Let the observed time 
of the passage of N he denoted as before by T"; and the ap- 
parent right ascension of N by AR®, and let the error of the 
clock at the time of observation be denoted by E. ‘Then, from 
the principles laid down by M. Biot, we shall have 
dh is s sin (L—N) 
The value of ac») for the latitude of Greenwich I have 
thrown into numbers, and placed in the last line of the table at 
the end of this paper, so as to be ready for immediate use when 
required. It is denoted by c, since it serves to denote the cor - 
rection of the clock. The application of the formula is very 
simple: the rule being as follows. From the observed time of 
the transit of the northern star deduct the apparent right ascen- 
sion of the same star; to the difference add the product Ac: the 
sum is the error of the clock; which, when it is negative, shows 
that the clock is too slow. 
For example; in the first case mentioned in this paper, the 
difference 
