226 



A MANUAL OF TOPOGRAPHIC METHODS. 



Secondly, when the star is observed off the line of eollimation, the instrument 

 remaining in the plane of the meridian, then 



2 sin 2 ir . „ .. 2 .sin 2 ir , . „ „ 



m= — -. — =-77- sin o cos n or m=—. — =-%-• i sm 2o 

 sin 1" sin 1" 



and the correction to the latitude is half of this quantity, whether the star be north or 

 south, and if the two stars forming a pair are observed off the line of eollimation, two 

 such corrections, separately computed, must be added to the latitude. If the stars 

 should be south, of the equator, the essential sign of the correction is negative. The 

 value of m for every 5° of declination is given in the following table: 



Table XXX. — For facilitating the reduction of observations, on close circumpolar stars, 

 made in determining the value <>f a revolution of the micrometer. 



[Extracted from Appendix 14. U. S. Coast and Geodetic Survey, Report for 1880.] 



Let /= difference of time of observation and elongation of the star, and «"=num- 

 ber of seconds of arc in the direction of the vertical from elongation, then 



cos 6 sin t 



sin 1" 



for which we can write 



»"==15 cos 6 | t--i(15 sin l") 2 * 3 I 



where t is expressed in seconds of time. It is convenient to apply the term £ (15 sin 

 l") 2 1 3 to the observed time of noting, additive to the observed time before, and sub- 

 tractive after, either elongation. The following table gives the value of £ (15 sin 

 l") 2 1 3 , also of the additional term • 



— T ^ ff (15 sin l") 4 t 5 when sensible, for every minute of time from elongation to65 m . 



