60 
The Light from the Stars 
[CH. II 
The Temperature-Luminosity Diagram. 
56. The foregoing table has given the absolute bolometric magnitudes 
and the effective temperatures of certain stars. The former of these two 
quantities serves to specify the quantity of radiation emitted by a star, while 
the latter specifies its quality, at any rate in respect of its more essential 
features. 
We can conveniently exhibit the quantity and quality of light emitted by 
a number of stars by representing each star as a point in a plane diagram. 
We shall find it convenient to take the stars’s absolute bolometric magnitude 
M as ordinate, and the logarithm of its effective temperature, log T e , as 
abscissa. Further, we shall place the stars which radiate most energetically at 
the top of the diagram, and those of lowest effective temperature to the right. 
This is a modification of a procedure introduced by Russell in 1913. Russell 
took absolute visual magnitude as ordinate and spectral type as abscissa, 
but the quantities we have selected are far more fundamental, and consequently 
far more intimately connected with the physical condition of the star. 
We have seen (§ 49) that a star’s emission of radiation E in ergs per second 
is given by 
log E = 35 52 -04M. 
It is also given by 
E = 4 - 7 rr 2 <rT e 4 , 
where r is the radius of the star, a is Stefan’s constant, and T e is the star’s 
effective temperature. From these two equations we obtain 
log r = 19'33 - 2 log T e — 0 2M (56T), 
which gives a star’s radius in terms of T e and M. If R is the radius measured 
in terms of the radius of the sun (6'95 x 10 10 cms.), the equation takes the form 
log R = 8-49 - 2 log T e - 0-2M (56'2). 
We see that stars of a specified radius lie on a straight slant line in a 
diagram in which M and log T e are taken as ordinate and abscissa. 
Such a diagram is shewn in fig. 5. The slant lines represent the lines of 
constant radii equal to 001, 0T, 1,10,100 and 1000 times the radius of the sun. 
The points surrounded by small circles represent the stars within 4 parsecs 
of the sun, as given in Table IV. Three of these are omitted owing to their 
spectral type and effective temperature being insufficiently known. The 
remaining points, marked by small crosses, represent stars which appear in 
Table IX, but not in Table IV. These stars are of exceptional interest but 
are in no sense typical of the whole mass of stars. The best sample of the 
stars as a whole is formed by the stars within 4 parsecs of the sun, and so 
by the stars enclosed in circles in fig. 5.