538 Proceedings of the Royal Irish Academy. 



XXIX. — On the Oebit of the Binaet Stak P Delphini. By J. E. 

 GofiE, M.E.I. A., F.E.A.S., Associate of the Liverpool Astro- 

 nomical Society. 



[Head, December 14, 1885.] 



/8 Delphini has long been known as a wide double star, the com- 

 panion being of the 11th magnitude, and distant about 34" from the 

 brighter star. In 1873, the eminent American observer, Burnham, 

 discovered that the primary star was a very close double, and a 

 few years' observations sufficed to show that it was a binary star 

 in rapid motion. As the companion star has now described over 

 180° of its apparent ellipse, a satisfactory approximation to the 

 elements of its orbit is possible. 



I have computed the orbit by a graphical method, in which the 

 dimensions and position of the real ellipse are derived from those 

 of the apparent ellipse by means of Thiele's harmonic ellipse. This 

 latter ellipse being the orthogonal projection of the harmonic circle 

 on a plane perpendicular to the line of sight, its major axis is of 

 course equal in magnitude to the latus rectum of the real ellipse, 

 and its angle of eccentricity is the angle of inclination of the plane 

 of the real ellipse to the plane of projection on the background of 

 the heavens. Thus the magnitude and position of the real orbit 

 can be fully determined. 



This method of computing the orbit devised hjThiQXe^Astronomische 

 Nachrichten, J^o. 1227) depends on the following geometrical property 

 of the ellipse : — If a number of focal chords be drawn, and the har- 

 monic means of the intercepts between the focus and curve be taken, 

 and these means laid ofi from the focus along the chord on each side, 

 the locus of the points thus found is a circle called the harmonic 

 circle, the diameter of which is the latus rectum of the ellipse, and its 

 centre the focus. 



The following are the observations from which I have computed 

 the elements : — 



