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 formulae 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 formulae, 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, 99 the latitude and 9 the clock correction (i. e. local time 

 minus clock time): 



sin a . dh' sin a' . dh 



de = 



sin (a' a) 



cos a' dh cos a dh' 

 sin (a' a) cos <r 



When the altitudes are subject to no other errors than that of the 

 assumed zenith point, dh = 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 formulas 

 rnay 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 (T or 2") requires a sensible correction in order to corres- 



