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. Roberts, 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 system 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 β Lyræ 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 fundamental data used by Myers in his work on β Lyræ, of which we have quoted the results. Without going into reasoning or technical details at length, we may give the results reached by Roberts and Norris in the case of the Algol variables:
For the variable star X Carinæ, Roberts 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 RS 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 estimate the general average amount by which the densities fall below the limits here given. Roberts' 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 Russell was carried through at the same time as that of Roberts, and quite independently of his. It appeared at the same time.[1] His formulæ and methods were different, though they rested on similar fundamental principles. Taking the density of the Sun as
- ↑ 'Astrophysical Journal,' Vol. X, No. 5.
