Astronomical Methods of Observation, 343 



Determination of the Time of the Equinox Z>y Observation. 



A 



B 



Let w A be the ecliptic, w B the equator, and the angle 

 A w B the obliquity of the ecliptic, w /3 the motion of the sun in 

 one day from the equinoctial point w, and a /3 the correspond- 

 ing change of declination , which at the present time is 23' 40" 

 at the vernal equinox, and 23' 24' at the autumnal, which 

 it has been and will continue to be for some time, on 

 account of the slow motion of the perigee and the action of 

 the planets being nearly insensible, or at least very small. 

 By similar triangles, 



«/3 : /3 w :: A B : Bo, or 

 23' 40'' ; 1'':: AB : B w in March. 

 23 24 : l^'riAB : B w in September, 

 the time from the equinox in days and fractions, depending 

 upon the observed declination A B. 



The first analogy gives 1"^-014085, and the second l°^-02564 

 for each second of arc in the declination A B. 



For days and decimal we would have, I., const, log. 

 6-847712, II., 6-852633. It would be a little more accurate 

 to take the change of declination from observations, by 

 good instruments or from accurate astronomical tables, on 

 account of the slight change in the daily variation, which 

 we have assumed to be constant for a few days before and 

 after the equinox. 



Ex. September 25th, 1835, in latitude 555656'4 and lon- 

 gitude 12' 44" W, the observed zenith distance by Kater*s 



inch was 56^ 37' 5"-4 S 



Lat. of 54 South Bridge • 55 56 56-4 N 



Sun's declination South 40 90 S 



II. Constant logarithm 6*852633 



Dec. 40' 9 " = 2409" log 3.381837 



Time after eq. 1^^-7158 log 0-234470 



