NO. 6.] INTRODUCTION. LATITUDE AND LOCAL TIME. XIII 



pond to the mean of altitudes, the corrections to the latitude and hour angle, 

 as computed by the original numbers, will be: 



sin a sin a' cos q> , . _,, 

 dm = . , , -f*- d(T' T) 



sin (a' a) 



dt = s !" f cosa d(y _ T) and d 6> = 61 AT. 

 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 x is the correction 

 to the assumed zenith point, ft, and ft 2 the two altitudes of the sa/tne star, 

 as following from this assumption, , and 2 the corresponding hour angles 

 (suffix 1 and 2 corresponding to small and great numbers) d the declination, 

 the following exact formula 



cos * "T - . sin I Q - + #) = cos <P cos d sin 2 "T ' . sin -l~ - 

 may be safely replaced by 



ft 2 ft, ft 2 + ft, . tn + t. 2 , 



x - -^ g * 4- cos (p cos a sec --g - sin * ' ' . -*-g l , 



2 f, being the difference of clock times reduced to sidereal time, and of 

 course expressed in the same units as ft 2 ft,. 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, x can be computed 

 by this formula, after which the differential formulae 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. SCOTT-HANSEN made preliminary calculations in order to find 

 the stars in the telescope of the large altazimuth. 



