23 Transactions of the South African Philosophical Society. 



I think, however, differences even smaller than this can be dis- 

 tinguished, especially when the star is well situated as regards com- 

 parison stars. My own probable error for observations of S. Yelorum 

 is 0*05 mag., and I think this, with every precaution against error, 

 could be reduced to O03 mag. ; if so, it will be possible to determine 

 the secondary minimum of S. Velorum. 



To this paper as addenda are given : 



(1) The light curve of S. Velorum during its varying phase (p. 27). 



(2) A graphical solution of the orbit of an Algol variable. 



III. — Graphical Method of Determining the Orbit of an 



Algol Variable. 



Five elements determine the form and position of the orbit of a 

 close binary star whose period is known, viz. : 



(1) The time of Periastron passage. 



(2) The angle between the line of Apsides and the line of Nodes. 



(3) The position angle of the line of Nodes. 



(4) The inclination of the orbit. 



(5) The eccentricity of the orbit. 



When, however, the inclination of the system equals, or nearly 

 equals, 90°, the projection of the orbit becomes a straight line, and 

 only three elements remain to be determined, viz. : 



(1) The time of Periastron passage. 



(2) The angle between the line of sight and the line of Apsides in 

 the real orbit. 



(3) The eccentricity of the orbit. 



In an orbit of this nature there will be eclipse of either component 

 as the stars pass through the line of sight. In the case of a bright 

 primary star with a non-luminous satellite — as Algol — or in the case 

 of an almost non-luminous central star and bright companion — as 

 S. Velorum — there will be actual visible eclipse at only one of the 

 passages through the line of sight. In some stars, however, there 

 are two minimum phases, and it is with stars of this class that this 

 portion of the paper deals. 



Let A B C D (p. 30) be the orbit of a close binary whose inclina- 

 tion to the plane of projection is 90°. Let y be the centre of the 

 primary- star whose circumference is indicated by the unbroken 

 circular line round y. 



When the companion passes through A and C, eclipse will take 

 place, the relative duration of which will depend upon the eccentricity 

 of the orbit, and the position of its apsidal line with reference to the 

 line of sight. 



