CHAP. XIII.] OBSERVATIONS FOR ERROR 317 



should be completed shortly before that time, in order to allow 

 an interval to prepare for observing the other. 



It may be foimd that when two stars are of equal alti- 

 tudes, they are too near the meridian for obtaining the best 

 results, or that the altitudes are too great for the sextant ; in 

 which case it would be necessary to commence observations of 

 the eastern star as much as an hour earlier, and the western 

 star will then have to be observed the same time later than 

 when they would be simultaneously of equal altitude. 



As a general rule, if the difference in right ascension is less 

 than 6'\ the eastern star should be observed fu'st ; if it exceeds 

 6'\ then the Avestern star ; this is in order that the stars may 

 be observed as favourably as possible with respect to the 

 " prime vertical,"' but it will vary according to the latitude 

 and declination. It a\t[I1 be noticed that if the observations are 

 commenced with the eastern star, then they are, as a whole, 

 taken farther from the meridian than in the other case. 



If the difference in R. A. exceeds 8'\ then there will probably 

 be an interval between finishing the observations of one star 

 and beginning those of the other, and part of the advantages 

 of the method are lost ; the same remark applies if the differ- 

 ence in R. A. is less than 4^'. 



Having decided on which star to begin with, observe it 

 continuously in the ordinary Avay, until the sidereal time is 

 nearly equal to the mean R. A. of the two stars (the error of 

 chronometer on sidereal time should be rouglily known), when 

 prepare to observe the other star, commencing at the same 

 altitude as the last observation of the first star, and complete 

 the series, wliich may be divided into sets in the usual way. 



Owing to the more rapid changes in " equation of equal 

 altitudes," when there is a large difference in the declinations 

 of the stars, it ^^dll be remarked that the " middle times " vary 

 more rapidly than in the case of the sun; and the rapidity of this 

 change increases as the observations get farther away from the 

 sidereal time at which the "imaginary star" passes the meridian. 



If a mean solar clironometer be used, the chronometer 

 interval (corrected for rate) must be turned into a sidereal 

 interval, and the resulting " error of clironometer " will be the 

 error on sidereal time at that particular instant, from which 

 the error on mean time can be readily deduced. 



