SURVEY OF THE PROBLEM 
from studies of absolute magnitude and spectral type and more directly 
from the calculated densities of eclipsing variables. The confirmation that 
is most easily grasped is afforded by the recent interferometer measure 
ments of the angular diameters of stars at Mount Wilson. These show that 
certain stars such as Betelgeuse, Antares and o Ceti, are of enormous bulk, 
capable of containing the whole orbit of the earth inside them. We are 
therefore compelled to extend our ideas of the nature of stars beyond 
anything that would be suspected from knowledge of the sun. 
The great bulk of these giant stars is due to low density rather than 
great mass. Betelgeuse for example has a radius of the order 250 million 
km. and a volume 50 million times greater than the sun. But the mass, or 
amount of matter contained in it, is probably between 10 and 100 times 
greater, so that the density is about a million times less. It is rather 
interesting to notice that Einstein’s theory of gravitation has something 
to say on this point. According to it a star of 250 million km. radius 
could not possibly have so high a density as the sun. Firstly, the force of 
gravitation would be so great that light would be unable to escape from 
it, the rays falling back to the star like a stone to the earth. Secondly, 
the red-shift of the spectral lines would be so great that the spectrum 
would be shifted out of existence. Thirdly, the mass would produce so 
much curvature of the space-time metric that space would close up round 
the star, leaving us outside (i.e. nowhere). The second point gives a more 
delicate indication and shows that the density is less than 0-001; for even 
at that density there would be a red-shift of the spectrum too great to be 
concealed by any probable Doppler effect. 
Lest this argument should be regarded by our more conservative 
readers as ultra-modern, we hasten to add that it is to be found in the 
writings of Laplace— 
A luminous star, of the same density as the earth, and whose diameter 
should be two hundred and fifty times larger than that of the sun, would not, 
in consequence of its attraction, allow any of its rays to arrive at us; it is 
therefore possible that the largest luminous bodies in the universe may, through 
this cause, be invisible*. 
7 . For many years Lane’s discovery had little effect on the accepted 
theories of stellar evolution. Sir Norman Lockyer accepted it and accord 
ingly classified the stars in an ascending and descending temperature 
sequence; but he was almost alone in his views. Astrophysicists in general 
regarded the hottest stars as the earliest and the coolest stars as the latest 
in order of development!. Probably they did not realise that any of the 
I am indebted to Dr H. Jeffreys 
* Laplace, Système du Monde, Book 5, Cp. vi. 
for this reference. 
t The expressions “early” and “late” type of spectrum are still commonly 
employed for high-temperature types (B and A) and low-temperature types (K and 
M) respectively. 
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