XII GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. [NORW. POL. EXP. 
When one star was taken near the meridian, the other near the prime 
vertical, which was frequently the case, the first could be used for the 
latitude, the other for the clock error. In some cases the reduction was 
accordingly made in this manner. But as the calculation of one of these 
quantities requires the knowledge of the other, and the drift of the ship from 
the time of the last observation was unknown, it was always necessary 
to apply corrections afterwards by a differential formula. For the great mass 
of these observations of two stars it was therefore preferred to deduce the 
definitive latitude and clock error at once by means of the two given alti- 
tudes and declinations, the difference of right ascensions and the difference 
of clock times, reduced to sidereal time. It will not be necessary to repro- 
duce here the formule used, the method being well known. As a control 
on the computation as well as on the observations, the computation was 
generally carried out in duplicate, the two altitudes taken in the same position 
of the instrument (both with “great numbers” or both with “small numbers”) 
being combined together. Both results are then affected by a possible error 
of the assumed zenith point, but in contrary directions, so that in the mean 
of the two the error will be very nearly eliminated, as may be seen from 
the following differential formule, where h and h‘ are the altitudes of the 
two stars taken in the same position of the instrument, a@ and a‘ the corres- 
ponding azimuths, g the latitude and @ the clock correction (i. e. local time 
minus clock time): 
zie sina. dh’ — sina’. dh 
a sin (a’ — a) 
cos a/ dh — cos a dh/ 
do = 3 7 
sin (a’ — a) cos p 
When the altitudes are subject to no other errors than that of the 
assumed zenith point, dz = dh‘ for the one position of the instrument and 
likewise for the other, but then with opposite sign; and as the coefficients 
depending on the azimuths are nearly the same in both combinations, the 
errors of the two results are nearly equal and opposite. The same formule 
may of course also serve to compute the correction to the zenith point when 
required. 
If one of the altitudes, or both, are the means of a series, and the mean 
of the clock times (7 or 7”) requires a sensible correction in order to corres- 
