542 Proceedings of the Royal Iri^ih Academy. 



These values of x and y having been plotted on the millimetre 

 paper, taking the position of the principal star as the origin of co- 

 ordinates, it was found possible to describe an ellipse nearly through 

 them. This is the apparent ellipse. Its centre being then joined 

 •with the origin of co-ordinates — which is the 'projection of the focus of 

 the real ellipse — and produced both ways, gave the projection of the 

 major axis of the real ellipse, and the position of the periastron and 

 apoastron on the apparent orbit. The ratio of the distance from the 

 centre to the principal star, and the distance from the centre to the 

 periastron, gave the eccentricity of the real ellipse, which was found to 

 be 0-337. The harmonic ellipse was then drawn by computing har- 

 monic means between the intercepts in the apparent ellipse on the 

 axes of X and y, and other chords drawn through the origin. The 

 ratios of the minor to the major axis of this ellipse then gave the 

 cosine of the angle of eccentricity, or the angle of inclination of the 

 Tt!al orbit, which came out 59° 20'. The position angle of the major 

 axis of the harmonic ellipse was found to be 2° 38', which is the 

 direction of the line of nodes. A chord di'awn in the apparent 

 ellipse through the origin, and bisected at the origin, gave the pro- 

 jection of the latus rectum of the real ellipse. Lines were then drawn 

 through the centre of the apparent ellipse parallel to the axis of tlie 

 harmonic ellipse, and having the same ratio, and an ellipse described 

 with these axes gave the projection of the auxiliary circle. A line 

 was then drawn through the centre C of the apparent ellipse parallel 

 to the projection of the latus rectum, and from the points T, V , where 

 this line met the auxiliary ellipse, lines were drawn parallel to the 

 projection of the major axis, and lengths laid off on each side = \it • CN, 

 N being the projection of the periastron. These lines were then 

 divided into nine equal parts, and ordinates laid off from the projec- 

 tion of the major axis on each side, equal to CTsin 10°, CTsin 20'^, 

 CT sin 30°, &c. 



The points thus found give an ephemeris curve (the projection of 

 the so-called curve of sines), and from this cuzwe the period was com- 

 puted in the usual way. This came out 30-91 years, and the epoch 

 of periastron was found from the intei'polating curve to be 1882*25. 

 ^_ The position of the periastron, A, was found by the usual formuhi, 



tan A = tan (A' - O) sec y, 



where X' is the angle between the projection of the major axis and 

 the initial line through the origin, O the position of the node, and 

 y the inclination of the orbit. 

 This gives 



tan \ = tan (- 15° 12' - 2° 38') sec 59° 20' ; 



■whence 



A = - 32° 14', or 360° - 32-14 = 327° 46'. 



