166, 167] White Dwarfs 183 
start at S, since it has no means of increasing its luminosity to the value 
appropriate to S. It accordingly starts at R', a configuration of the same 
mass and luminosity as R. Thus ranges such as SR' } UT' are never traversed 
by stars in their normal course of evolution ; they can only be occupied by 
binaries which have evolved by fission. 
Thus the configurations open to a system of stars contracting without 
fission consist of a series of branches such as P'R, R'T , T'V, etc., each being 
lower than the preceding. The distinctness of these branches results from the 
distinctness between K- ring, Z-ring and M -ring stars. If we disregard this 
distinctness, and look at the problem in a more “coarse-grained” manner, 
the configurations open to a star of given mass M form roughly a slant line 
stretching across the diagram, the direction of slant being such that high 
luminosity goes with low surface-temperature and conversely. 
On the hypothesis of gaseous stars the configurations open to a star of 
given mass M also formed a slant line stretched across the diagram—but the 
slant is in the opposite direction (§ 158), high luminosity accompanying high 
surface temperature. Thus a diagram shewing the observed configurations of 
stars of given masses in the sky ought to provide a test between the two 
theories. 
Such a diagram has been obtained by Seares* and is shewn in fig. 166. 
As this diagram was obtained by purely statistical methods, it is not “ fine 
grained ” enough to shew any clear distinction between ii-ring, Z-ring and 
iff-ring stars. Moreover it omits white dwarfs entirely. 
The general direction of slant is unmistakably in the sense of high 
luminosity accompanying low surface-temperature. That is to say, the slant 
is in the direction needed to confirm the hypothesis of liquid stars, and is 
antagonistic to the hypothesis of gaseous stars. The direction of slant is 
reversed in the region (approximately) of Q type stars. The diagram, however, 
represents visual absolute magnitudes whereas theory is concerned only with 
bolometric absolute magnitudes. The effect of applying the bolometric cor 
rection, so as to reduce visual magnitudes to bolometric, is to raise all the 
curves in the diagram throughout the regions of G, K and M spectral type ; 
the topmost chain line in the diagram shews the corrected curve for stars of 
mass ten times that of the sun. When all the curves are similarly treated the 
reversal of slant and corresponding minimum luminosity at about type K 0 
disappears from all curves except those representing stars of the highest mass, 
and Seares considers that the results for these stars are relatively uncertain, 
being obtained only by extrapolation of observational data. As a general 
statement we may say that the curves as a whole slant from high luminosity 
and low surface-temperature to low luminosity and high surface-temperature, 
as is required by the hypothesis of liquid stars. 
Astrophys. Journ. lv. (1922), p. 412, 
i 2-2