Prof. Encke on Transits. 275 



order to refer the position of p to the meridian, pole, and 

 zenith, let the following designations be assumed :— 

 Zp = 90° + i angle AZp = 90° + k 



Vp = 90° + n angle AVp = 90° + vi 



S the point'of intersection of Sp' and the equator, being a pole 

 of the great circle ¥p, m will likewise be measured by the 

 arc AS. The quantities m and n are consequently the same 

 as Bessel's. The former is the distance of intersection of the 

 plane perpendicular to the axis of rotation and the equator, 

 counted from the meridian ; the latter is the distance of this 

 perpendicular plane from the pole of the heavens, both posi- 

 tive, if eastern. 



Between the cjuantities i, k, m, n, the triangle PZp gives the 

 following relations, supposing the latitude = <p. 

 sin ti = sin i . sin (|> — cos i . sin Ic . cos (p 

 sin m . cos n = sin i . cos 4> + cos i . sin k . sin <p. 

 cos m . cos n = cos i . cos k 



sin i = sin n . sin (Ji + cos « . sin vi . cos <p 

 sin it . cos t = — sin w . cos <^ -j- cos n . sin m 



2 N 2 



sin f. 

 Assuming 



