174 
THE MASS-LUMINOSITY RELATION 
probable degree of ionisation. It seems likely that the ordinary failure 
of the gas laws due to finite size of molecules will occur at these high 
densities, and I do not suppose that the white dwarfs behave like perfect 
gas. The companion of Sirius would fall well below the theoretical mass- 
luminosity curve; this may be an indication that the gas laws have at 
last failed, but it might also be explained by an increase of the absorption 
coefficient arising from the close packing of the ions and electrons. 
If the gas laws were obeyed the companion of Sirius would have a 
central density of about 3,000,000 gm./cm. 3 and a central temperature 
1,000,000,000°. The temperature is of the order required to affect the rate 
of radio-active processes and bring about nuclear changes, so that a new 
series of phenomena unknown in ordinary stars may be occurring. If the 
white dwarfs could be placed at the beginning instead of at the end of 
evolution the origin of the chemical elements would be less mysterious. 
Evolution. 
120. We have been considering the luminosity-mass relation indicated 
both by theory and observation, and the consequences arising from it. 
We now turn to the luminosity-type relation which at present is a purely 
empirical one. 
Fig. 3, due to F. H. Seares, contains the known statistics of absolute 
magnitude and spectral type of the stars. Impressions formed from the 
diagram may be misleading unless attention is paid to the great influence 
of selection of data. Naturally bright stars are represented in numbers 
out of all proportion to their abundance in space. Absolute magnitudes 
found by the spectroscopic method have been more fully studied for the 
redder than for the whiter types. Nevertheless, the diagram is extremely 
instructive. 
The feature of the distribution which is generally accepted as indubitable 
is represented schematically in Fig. 4. The statistics cluster strongly to a 
pair of lines PQR. The slope of PQ is small, and it is not certain that it 
is in the direction shown; but the reduction of Seares’s visual magnitudes 
to bolometric magnitude increases the slope in this direction*. In the 
globular clusters the slope of PQ is definitely in this direction and seems 
to be larger than in our local system. 
We may either suppose that PQR is the track of evolution of an average 
star, or we may suppose that stars born with different masses develop 
rapidly until they reach a point on PQR and then stick there almost 
indefinitely. The line is either a track of evolution or a locus of equilibrium 
points or a mixture of both. 
* Ordinary giants of types A and F which would lie on the direct line of PQ 
are scarce, and the stars shown on Seares’s diagram are chiefly Cepheids or pseudo- 
Cepheids.