Method of Determining the Orbit of an Algol Variable. 29 



If the duration of eclipse at A is longer than that at C, then the 

 periastron passage is nearer C than A. 



Again, if the periastron passage takes place on the side towards B, 



rather than towards D, the time between the two minima at A and 



C will be shorter than the time between the two minima at C and A. 



Thus we are able to determine the quadrant in which periastron 



passage lies. 



Let : tj = duration of minimum at A. 



t 2 = duration of minimum at C. 

 p x = time between min. at A and min. at C. 

 p 2 = time between min. at C and min. at A. 



Then as the fundamental law of motion round a centre of force is 

 that equal areas are described in equal times : 



Area of segment A B C ~p x 



(i) 



Area of segment C D A p. 2 

 /o\ Area of sector fi a y _ t x 



Area of sector y 8 « t 2 



We have, therefore, graphically to describe an ellipse so that the 

 line A C will divide it in the required ratio, and that also the area of 

 the two sectors p « y and y 8 £ will be to one another as the duration 

 of minima at A and C. 



When this is done roughly on a small scale, it may be made more 

 and more to correspond with the required conditions by drawing the 

 ellipse on a larger scale. 



Absolute agreement can be attained by differentiating the well- 

 known formula for angular motion round a centre of force, but as 

 the purport of this short addendum is rather to indicate in a 

 general way the relation between variation of light and orbital move- 

 ment, I shall not trouble the Society with it ; but the investigation is 

 one of more than common interest. 



The ellipse having been obtained graphically : 



(1) The relation between the major and minor axes will determine 

 the eccentricity. 



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

 be measured by a protractor. 



(3) Let this angle — e 



x — € sin x = mt 



T - mt (Pi + Pa ) 



360° 



From which the time of passing periastron, can be readily 

 determined. 



