in the length of the pendulum vibrating seconds. 387 
Longitude. The refractions and corrections for the barometer 
and thermometer, are taken from Dr. Brinkley's Tables, 
published with the observations made at the Royal Observatory 
at Greenwich. 
In observations of the sun, the horary angle is estimated 
in solar time, but in those of the stars it must be expressed in 
sidereal time. It is most convenient, however, to employ the 
angle given by the chronometer in finding the correction of 
the apparent zenith distance, and afterwards to apply a fur- 
ther correction in the following manner. 
Let r, be the daily loss of the chronometer on solar or side- 
real time, according as the sun or star is observed ; and let 
I 1 86400— T 
Then calling the correction before found C, the 
final correction will be (C -f- 2r'C). If the clock gain upon 
the star, C must be diminished by the quantity 2 f C. 
In using the repeating circle, it is of great importance that 
its plane should be truly vertical, or that its deviation should 
be known, in order to find the correction to be added on this 
account to the observed zenith distance. On my return to 
London, I found the error of my circle in this respect to be 
4,'.48 #/ , the correction for which may be obtained by the 
following formula : 
Sin. \ (z — zf) = 
sin* I. 
tang, x! 
where z is the true zenith distance, z' the observed zenith 
distance, and I, the angle of inclination of the plane of the 
■j 
circle. In the second member of the equation, z may be taken 
= z’ without error. These formulae, as well as many others 
respecting the repeating circle, is demonstrated by M. Biot, 
in his valuable “ Traite el^mentaire d’Astronomie Physique.” 
