OBSERVATIONS FOE TIME. 31 



sary for the determination of azimuth. Practically, it is determined by 

 elimination from equations involving the mean of all these stars observed 

 in each of the two positions of the instrument, after correcting' for level, and 

 as it is slightly complicated with collimation it must be reached by two or 

 more approximations. The error is essentially positive when the telescope 

 points east of south, and negative when west of south. The correction 

 applicable to any star is expressed in the following equation: 



Cor.:=« sin (tp — <S) sec £ — «A. 



It must be understood that the declination when north is positive for 

 upper and negative for lower culmination, and that with south declination 

 it is negative. 



CORRECTION FOR DIURNAL ABERRATION. 



The right ascension of stars, as taken from the Berliner Jahrbuch, must 

 be corrected for diurnal aberration, which equals S .021 cos <p sec S. This 

 correction is jjositive for upper and negative for lower culmination. 



These corrections are summarized in the following equation: 



j f-a— (/+«A + 7,B + cC). 



A, B, C, as seen above, are constants, depending upon the latitude of 

 the place of observation and the declination of the star. Tables for these 

 quantities will be found in an appendix to Annual Report U. S. Coast and 

 Geodetic Survey for 1874. 



The following is an example of the form for record of observation and 

 reduction of time observations, taken from a campaign for the determination 

 of position of Rapid, South Dakota. 



