38 Ti'cnisactioiis of tJic South African Pliilosophical Society. 



the components of which move in an orbit ahiiost coincident with 

 the Hne of sight. In the case of three Algol stars this theory is sup- 

 ported by spectroscopic evidence. It may be remarked that these 

 three cases are the only ones where such confirmation is possible, at 

 least in the present limitations of spectroscopic research. 



Now in a binary system whose orbit is situated in the plane of sight, 

 it is evident that eclipse, partial or total, will take place every 

 revolution. The amount, duration, and chief features of this eclipse 

 will depend upon the form and position of the orbit in which the 

 stars move, as well as on their relative size and brightness. Further, 

 it is possible to express in set terms and definite relations the con- 

 nection which exists between the elements of light variation and the 

 orbital elements on which the elements of light variation depend. 



It is beyond the purpose of this paper to deal with these relations. 

 Sufficient to say that the variation of C.P.D. — 41°-4511, was 

 rigorously subjected to analysis in order to ascertain the form and 

 dimensions of the orbit in which it moved. 



Subsequent observations may, to a very limited extent, modify 

 the results thus determined, but the following conclusions will not 

 be essentially altered by any new data : — 



(1) The Algol variable C.P.D. - 41°-4511 is an Algol close binary 

 star, whose period of revolution is equal to its full light cycle, viz. : — 



Id. 20h. 30m. 3s. 



(2) The epoch when the two component stars move into the line 

 of sight is — 



1901, July 2d. 16h. 17m. (C.M.T.) 



(3) The orbit is practically circular and inclined 6° to the plane of 

 sight. 



(4) The two stars are equal in size, the diameter of any one of 

 "them being equal to one-third the radius of the orbit. 



(5) The two stars are unequal in brightness, one being 6*14 times 

 brighter than the other. 



(6) The density of the system is a little less than half that of the 

 un. 



In order to test the dependence which can be placed on these 

 results we invert the problem, and from the conditions of orbital 

 movement and dimensions, compute a theoretical light curve. 



Assuming that C.P.D. - 45°-4511 moves in an orbit of which the 

 foregoing is a numerical description, then three equations are 

 sufficient to set forth the magnitude of the star at any instant. 



