STUDIES OX THE VARIABLES OF THE ALGOL-TYPE. 17 



(0.0092 ^'^ (0.0092f 



;/ p2 and ^3 p. . 



Under siicli process, assuming k = k'=0, Roberts obtained 

 tlie absolute maximum values of density for the star X carinfe 

 and other three stars. Finally, assuming k and k' equal, he 

 reached the average density and the mean average density of 

 the four stars was found, in the unit of the density of the sun, 

 0.13. 



The above process is very useful in finding the separate 

 density of the both components, but unless we have previously 

 determined the mass of the components, the results obtained 

 give only a general idea. At the present state of astronomical 

 knowledge, therefore, the limiting values of the mean density of 

 the system may profitably be used. 

 Now, let us denote 



n=me'dn motion of the satellite around the principal star, 

 y = mean motion of the earth around the sun 

 R- radius of the sun 



J=mean distance of the sun from the earth 

 r= radius of the principal star 

 o=density of the Algol under consideration 

 Oo= density of the sun 

 a=mean distance of the satellite. 

 Then, from the application of Kepler's third law, we have 



(v) 1^ 



J"(l+l) 



Jv(-T (1) 



+ xY\ r J, 



where x is the radius of the satellite, unit being that of the 

 principal star. But we can simplify the above formula by 

 putting Y siderial year expressed in days, and considering R 



