158 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



that marked " dwarfs." In this diagram 



n j 



> ' I Luminosity 



■A I San- 1) 



S *4O00 



ties, and has calculated the individual luminosities of 1,152 giant stars 

 in clusters. If we plot the logarithms of the luminosity (or the 

 absolute magnitude) against spectral type as in figure 2, the vast 

 majority of Shapley's 1,152 stars are found to lie within the belt 

 marked " giants," while of the stars previously discussed by Kussell 

 and by Adams and Joy nearly all lie either within this belt or within 



a few typical stars have 

 been marked. The stars 

 a Ononis and our near 

 neighbor Lalande 21.185 

 are examples of giant 

 and dwarf red stars. 

 The diameter of the 

 former has recently 

 been found by direct 

 measurement to be about 

 300 times that of our 

 sun, corresponding to a 

 density of the order of 

 at most one-thousandth 

 of that of atmospheric 

 air; the latter has a lu- 

 minosity only 0.009 

 times that of the sun, 

 and probably a mean 

 density comparable with 

 that of the earth. Our 

 sun and our nearest 



1-00 



OOI 



iopoo°c 



6,000 C. 3,000%. 



Fig. 2. — Luminosity-temperature diagram. 



stellar neighbor, a Centauri, are marked as typical dwarfs of type G, 

 and Sirius is a representative A-type star. 



From the known luminosity and surface temperature of any star 

 it is easy to calculate its surface and so its density. Giants of types 

 G and K are found to have densities of the order of 0.004 and 0.0005, 

 respectively, agreeing with the known densities of binary stars of 

 these types. Sirius, with a luminosity of forty-eight times, and a 

 surface temperature about one and a half times, those of our sun, 

 must have a surface nine times as great. Its mass is 3.4 times the 

 solar mass, so that its density must be about 0.2. In general it is 

 found that all giant stars must be gaseous, of density so low that the 

 ordinary gas laws will be approximately obeyed. Dwarf stars may 

 be gaseous or liquid or solid, but, if gaseous, they are so dense that the 

 gas laws will be nowhere near the truth. It is now easy to see why, 

 in the giant stars, increase of temperature and density go together; 

 this is merely a consequence of Lane's law. But the dwarfs may be 



