14 ASTRONOMICAL OBSERVATIONS 



E = error of chronometer -j _ |- when j ^^°^^ j- of sidereal time at an assumed time T. 

 Eq = an assumed chronometer error and t its correction ; E = E^ + i. 



'i 'a '3 • • • = the observed times of transits of a group of stars, already corrected for rate of chronometer 

 and collimation. 



AI{^ — t, = e^ AB^—I^ = e, AR^ — t^ = e., and (-, — i'^ = n, e., — E^ = v.^ 



The values a, h and t can be deduced from the normal equations : 

 S t + 2 .la + 2 i>6 = 2 n 

 2 Jj + 2 yl^a + 2 ABh = -z An 

 xBs + s. ABa +-zB"'h=y, Bn. 



It is essential, however, that the instrument be not disturbed during the time of 

 the ti'ansits of the group of stars. 



For the reduction of the incomplete transits and for deducing the collimation 

 error, the equatorial intervals of the wires have been deduced from transits of 18 

 stars, as follows: — 



For circle eaM and upper culmination. 



The probable error of each interval is on the average + 0/07. From a prelimi- 

 nary reduction of the observations of December 15 and January 9, the daily rate 

 of the chronometer was found + 3™ 56.'0, or the rate (losing) per minute + 0.'164: 

 approximately. 



The observations of Polaris, upper culmination reflected, of Dec. 13, 1853, circle 

 east and circle west, give the collimation error c = — 1.'40 (for upper culmination 

 and) circle east, the observed chronometer times having been corrected for rate, 

 and the equatorial intervals were multiplied by i^sec. H, where H the hour angle. 

 This value of c has been used for the reduction of transits on and after Dec. 1 3 ; 

 for Nov. 18, c = 0, and between this date and Dec. 13 a gradual change was 

 assumed to have taken place. 



The immediate purpose of the following reduction is to obtain values for the 

 level and azimuthal deviation, to apply the required corrections to the observed 

 transits of the moon and moon-culminating stars ; it is, however, only the difi"erence 

 of these corrections which affects the resulting longitude. 



For the first three observations of Nov. 18, 1853, we have no means of ascer- 

 taining the above two instrumental corrections ; the level and azimuthal factors, 

 however, for the moon and the two stars are nearly equal. After these observa- 

 tions the level and azimuth were changed. 



It was found advisable to omit the observations of Polaris It. and 51 Cephei 

 s. p. R. in the conditional equations of Nov. 18 and 21, since it is probable that 

 the form of the pivots of the axis is very imperfect, or that the instrument was 

 otherwise disturbed. 



