578 RUSSELL— RELATIONS BETWEEN SPECTRA [April 20, 



exactly alike in color and spectrum. If this is true, the giant stars, 

 which are nearly equal in mass and brightness for all spectral types, 

 must decrease very rapidly in density with increasing redness. If 

 the relative surface brightness of classes B, G, and M is as given 

 above, it is easy to show that the average density of the giant stars 

 of class G must be about 1/40 of those of class B, or about 1/250 

 of the sun's density, and that the density of the giant stars of class 

 ^I must average only about 1/15,000 of that of the sun. There is 

 no escape from this conclusion unless we assume that the relation 

 between spectral type and surface brightness is radically different 

 for the giant and dwarf stars, in spite of the practical identity of 

 the lines in their spectra and the distribution of energy in the con- 

 tinuous background. 



The nature of the connection which class B forms between the 

 two series is now evident. If all the stars are arranged in order of 

 increasing density, the series begins with the giant stars of class 

 M, runs through the giant stars to class B, and then, with still in- 

 creasing density, through the dwarf stars, past those which so 

 closely resemble the sun, to the faint red stars. 



This arrangement is in striking accordance with the theoretical 

 behavior which a mass of gas, of stellar order of magnitude, might 

 be expected to exhibit if left to its own gravitation and radiation, 

 at a very low initial density. While the density remains low, the 

 ordinary " gas laws " will be very approximately obeyed, and, in 

 accordance with Lane's law, the temperature must rise in order that 

 the body may remain in equilibrium as its radius diminishes. At 

 first the central temperature increases in inverse ratio to the radius, 

 and that of the radiating layers near the surface also rises, though 

 more slowly (because we see less deeply into the star as it becomes 

 denser). As the density oi the gas increases further, it must become 

 more difficultly compressible than the simple gas laws indicate ; and 

 internal equilibrium can be maintained with a smaller rise of tem- 

 perature after contraction. The temperature will finally reach a 

 maximum, and the star, now very dense, will cool at last almost like 

 a solid body, but more slowly, for contraction will still take place to 

 some extent, and supply heat to replace much of that lost by 

 radiation. 



