NO. 6.] INTRODUCTION. LATITUDE AND LOCAL TIME. XI 
pond to the mean of altitudes, the corrections to the latitude and hour angle, 
as computed by the original numbers, will be: 
_ sma@sinad cosp aim, _ ° 
Oia sin (a’ — a) He) 
dp eS 1 = Ty and dé) = dé dT" 
sin (a’ — a) 
It happened sometimes that one star was observed in both positions of 
the instrument, but the other only in one. In order to utilise the latter it 
was necessary to deduce the zenith point from the first. If a is the correction 
to the assumed zenith point, h, and h, the two altitudes of the same star, 
as following from this assumption, ¢, and ¢, the corresponding hour angles 
(suffix 1 and 2 corresponding to small and great numbers) d the declination, 
the following exact formula 
cos as . sin (Gere oS =) = cos p cos d sin ates pe 
may be safely replaced by 
a + cos p cos d sec 
ay h, +h, 
ae 2 
Se Oe er 
t, —t, being the difference of clock times reduced to sidereal time, and of 
course expressed in the same units as h, — h,. When approximate values 
of latitude and clock error have been computed from the altitudes of the two 
stars, measured in the same position of the instrument, # can be computed 
by this formula, after which the differential formule above give the required 
corrections to the preliminary results. 
The few altitudes of stars taken with the small instrument have been 
treated in the same manner, only that the mean of altitudes and mean of 
clock times have been used without further correction. The zenith point of 
this instrument was generally 180° but was found on one occasion to be 
about 179° 30°. 
During the time of the year with no Sun or only a very low Sun, but 
no stars visible to the naked eye, which interval may be rather long in high 
latitudes, Lieut. Scorr-Hansen made preliminary calculations in order to find 
the stars in the telescope of the large altazimuth, 
