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THE MASS-LUMINOSITY RELATION 
171 
matter is still a long way from the maximum density and therefore behaves 
as a perfect gas. 
We realise at once where the search should begin, for it happens that 
the white dwarf stars have raised this very question. “Strange objects, 
which persist in showing a type of spectrum entirely out of keeping with 
their luminosity, may ultimately teach us more than a host which radiate 
according to rule.”* The most famous of these stars is the Companion of 
Sirius. 
The mass of Sirius comes is found from the double star orbit and is 
quite trustworthy. The determinations range from 075© to 0-95©; we 
adopt 0-85. The absolute magnitude is ll m -3 corresponding to a luminosity 
■jTq of that of the sun. The faintness would occasion no surprise if this 
were a red star; but in 1914 W. S. Adamsf made the surprising discovery 
that the spectrum is that of a white star not very different from Sirius 
itself. The spectrum is F 0, or, if anything, a little earlier (towards A). 
Assuming that type F corresponds to an effective temperature 8000°— 
it can scarcely be less in so dense a star—and using the absolute magnitude 
ll m -3 we find by (87*2) the radius 18,800 km. Apparently then we have 
a star of mass about equal to the sun and of radius much less than Uranus. 
The calculated density is 61,000 gm. per cu. cm.—just about a ton to the 
cubic inch. 
This argument has been known for some years. I think it has generally 
been considered proper to add the conclusion “which is absurd.” 
Apart from the incredibility of the result, there was no particular 
reason to view the calculation with suspicion. The mass is well established 
and the radius is found by the method used in predicting the radii of 
a Orionis, Antares, etc.—predictions afterwards confirmed by direct 
measures with the interferometer. It has been suggested that the light 
is reflected from Sirius, the companion being of low density and having 
little light of its own. Apart from any intrinsic difficulties in this suggestion, 
nothing is gained by explaining the companion of Sirius in a way which 
will not apply to the other white dwarfs that have been discovered. The 
bright component of o 2 Eridani is a white dwarf and it has no bright and 
hot star in its neighbourhood. 
It seems that Sirius comes either has the enormous density above 
stated, or else at some low effective temperature probably below 3000° 
it is able by unexplained means to produce an imitation of the leading 
features of the F spectrum sufficiently close to deceive the expert observer. 
I suppose that until recently the first alternative was considered incredible. 
It seemed that the radiation of the white dwarfs must be set down as one 
of those paradoxes which arise from time to time when imperfect theoretical 
* Centenary Address, Monthly Notices, 82, p. 436 (1922). 
f Pub. Astr. Soc. Pac. 27, p. 236 (1915).