36 The Light from the Stars [ch. n 
to the emission per unit area of the radiator, which we have taken to be aT*. 
Thus the two constants a and o- of Stefan are connected by the relation 
<j = \aC (40-5). 
The values of a and G already given lead to the value 
a = 7*63 x 10 -15 in C.G.s. centigrade units (40'6). 
Effective Temperature. 
41 . When a star’s distance is known, we can calculate its total emission 
of radiation from measurements of the amount of radiation received on earth. 
When the diameter of the star is also known, we can deduce its emission of 
radiation per square centimetre of surface. If this is put equal to aT e 4 , T e is 
defined to be the “effective temperature” of the star. With this definition, a 
star emits as much radiation as a perfect radiator of equal surface raised to 
the temperature T e . 
According to Abbott and Fowle, the “solar constant” has the mean value 
T938, which means that outside the earth’s atmosphere, every square centi 
metre directly facing the sun receives T938 calories of radiation a minute. 
The mean angular diameter of the sun is 32'0", so that the earth’s mean 
distance from the sun is equal to 
1 radian 
32' 0” 
107*4 
diameters, or 214*8 radii of the sun. Every square centimetre of the sun 
accordingly discharges (214*8) 2 times as much radiation as falls on a square 
centimetre of the earth’s atmosphere. Thus the rate of emission per square 
centimetre of the sun’s surface is 1*938 x (214*8) 2 or 89,400 calories a minute. 
Since a calorie is equal to 4*184 x 10 7 ergs, the radiation per square centimetre 
is 6*24 x 10 10 ergs a second; each square centimetre of the sun’s surface dis 
charges enough energy to work an 8 horse-power engine. 
If we put 6*24 x 10 10 — arTe, we find for the effective temperature of the 
sun’s surface 
T e = 5750° absolute = 5470° Centigrade. 
The foregoing calculation has shewn that to calculate a star’s effective 
temperature, it is not necessary to know a star’s radius and distance from the 
earth separately; it is enough to know the ratio of these quantities as ex 
pressed by half of the angular diameter of the star. The ratio of the radiation 
received by each square centimetre of the earth’s surface to the radiation 
emitted by each square centimetre of the star’s surface is the square of the 
ratio just mentioned, so that a knowledge of this ratio makes it possible to 
calculate o*T e 4 and hence T e . 
The calculation for an actual star is best performed by using the sun’s 
radiation as a stepping-stone. Let the angular diameter of the star be 1/n 
times the angular diameter of the sun, and let the total radiation received