CHAPTERS ON THE STARS. 135 



emitted by a star not merely as indicating temperature, but as limited 

 by the quantity of matter which, impeded by friction, can come up to 

 the surface, and there cool off and afterward sink down again. This 

 again depends very largely on internal friction, and is limited by that. 

 Owing to this limitation, we cannot attribute the difference in question 

 wholly to surface brilliancy. We must conclude that at least the 

 brighter stars are, in general, composed of matter much less dense than 

 that of the Sun. Many of them are probably even less dense than air 

 and in nearly all cases the density is far less than that of any known 

 liquid. 



An ingenious application of the mechanical principle we have laid 

 down has been made independently by Mr. Koberts, of South Africa, 

 and Mr. Norris, of Princeton, in another way. If we only knew the 

 relation between the diameters of the two companions of a binary sys- 

 tem and its dimensions, we could decide how much of the difference 

 in question is due to density and how much to surface brilliancy. Now 

 this may be approximately done in the case of variable stars of the Algol 

 and ft Lyrse types. If, as is probably the most common case, the passage 

 of the stars over each other is nearly central, the ratio of their diameter 

 to the radius of the orbit may be determined by comparing the duration 

 of the eclipse with the time of revolution. This was one of the funda- 

 mental data used by Myers in his work on ft Lyras, of which we have 

 quoted the results. Without going into reasoning or technical details 

 at length, we may give the results reached by Eoberts and Norris in 

 the case of the Algol variables: 



For the variable star X Carina?, Eoberts finds, as a superior limit for 

 the density of the star and its companion, one-fourth that of the Sun. 

 It may be less than this is, to any extent. 



In the case of S Velorum the superior limits of density are: 



Bright star 0.61 



Companion 0.03 



In the case of ES Sagittarii the upper limits of density are 0.16 

 and 0.21. 



It is possible, in the mean of a number of cases like these, to esti- 

 mate the general average amount by which the densities fall below the 

 limits here given. Eoberts' final conclusion is that the average density 

 of the Algol variables and their eclipsing companions is about one 

 eighth that of the Sun. 



The work of Eussell was carried through at the same time as that 

 of Eoberts, and quite independently of his. It appeared at the same 

 time.* His formula? and methods were different, though they rested 

 on similar fundamental principles. Taking the density of the Sun as 



* 'Astrophysical Journal,' Vol. X, No. 5. 



