170 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



that the diameter measured by Michelson is exactly the mean of 

 the values just given. 



THE DENSITY OF THE STARS. 



If we know the angular diameter, we must then have the parallax 

 in order to calculate the linear diameter and compare it, say with 

 that of the sun. The calculation is simple enough, for the quotient 

 of the angular diameter by the parallax gives the real stellar diame- 

 ter expressed in astronomical units, that is, in terms of the distance 

 from the earth to the sun. This may then be expressed in solar 

 diameters. The following results are based on a table of Russell's 

 data : 



Star. 



Betelgcuse... 



Antares 



Aldobaran... 



Capella 



0Andromedae 



Linear 



diameter 



compared 



to the sun. 



220 



110 



44 



26 



40 



Star. 



Sirius... 



Vega 



Procyon 

 Altair... 



Linear 



diameter 



compared 



to the sun. 



1.9 

 3.6 

 1.8 

 1.4 



The contrast between the two sections of this table is striking. 

 To the right we see stars whose diameters average scarcely greater 

 than the sun's ; to the left they average 100 times greater. It is not 

 unlikely that there are stars three or four times smaller than the 

 sun. We arrive therefore at the fundamental conclusion that the 

 diameters of the stars vary through a range of 1 to 1,000. The ex- 

 treme volumes are therefore as 1 to 1,000,000,000. 



The capital interest of this result appears when we consider a 

 parallel comparison of the masses. We find that the stars with such 

 different volumes have almost the same masses. We can actually 

 calculate the masses only in the case of binary stars whose orbital 

 elements and radial velocities are known. These are unfortunately 

 small in number, perhaps 150. Their masses lie within the range 

 0.17 and 30, the mass of the sun being taken as unity. Can we draw 

 general conclusions applicable to all the stars? We do not know. 

 The discovery of an optical method for the determination of the 

 masses of single stars might help us. The principle of relativity has 

 perhaps opened the way to such a discovery, but while waiting on 

 that we are reduced to theoretical methods. The most natural is to 

 admit that there is no systematic difference between single stars and 

 the components of double ones. We will suppose then, Avhat appears 

 otherwise probable, that the masses of both are of the same order 

 of magnitude. 



