78 
Proceedings of Royal Society of Edinburgh. [sess. 
Then if 
0^ = 3 
B 0 1 0 2 = ^> 1 
boa = </> 2 
OjB = radius of S (1) = i\ 
0 2 B = radius of S (2) \=r (2) 
= total amount of light of S (1) 
L 2 = total amount of light of S (2) 
it follows that 
( 2 ) 
Also of 
f S 2 + r - r 
cos <&, = — - 
3 2 - f + f 
C0S $2 = 0 % 2 
2r 0 8 
L 0 = light of system at any time T. 
M 0 = magnitude of star at time T. 
M = magnitude of star at constant phase, that 
is, combined mag. of S (1) and S (2) , 
then in the case where S (1) is eclipsed by S (2) , 
/(2<^> 1 - sin 2<£ 1 ) 4 - r*(2<£ 2 - sin 2 <f> 2 ) 
(3) 
Also 
(4) 
1^=1 -Li 
j7rr 
and in the case where S (2) is eclipsed by S (1) 
I K _ L | ^(20! - sin 2^) + r\{ 2<fe - sin 2c ft 2 ) 
2 ( 2irr l 
M 0 = 2-5(10- Log L 0 ) + M. 
These equations are sufficient for the determination of the orbital 
elements and relative dimensions of an Algol system when the 
light curve is known ; or the light curve when the elements are 
known. 
Some of the elements, however, as for example the eccentricity, 
can be readily determined from the general circumstance of 
eclipse. Thus if the light curve is symmetrically situated on 
either side of the minimum passage, and if equal intervals of time 
