14 
SURVEY OF THE PROBLEM 
the sun (absolute bolometric magnitude +4-9; effective temperature 
5740°; radius 6-95 . 10 10 cm.) as intermediary. The difference of absolute 
magnitude m is converted into ratio of total radiation L by the formula* 
Also we have 
m — m Q = — f log 10 (L/Lq). 
L _ R*T* 
L q ~ R 0 *T 0 *’ 
the rate of radiation being proportional to the fourth power of the effective 
temperature. Hence 
m - m 0 = - 5 log 10 {R/R q ) - 10 log 10 (T e /T Q ) (12-1). 
13 . Applying the theory developed in the succeeding chapters to the 
observational data we obtain the following collected resultsf. 
Capella (bright component). 
Parallax = 0"-0632. 
Apparent visual magnitude = + 0 m -74. 
Spectral type = G 0. 
Effective temperature = 5200°. 
Mass = 4T8 x O = 8-30.10 33 gm. 
Absolute bolometric magnitude = — 0 m -36 = 5 m -26 brighter than the 
sun. 
Total radiation = 127 x O = 4-80 .10 35 ergs per sec. 
Radius = 13-74 xQ = 9-55 . 10 11 cm. 
Mean density = -00227 gm. per cu. cm. 
At the centre— 
Temperature = 7-20 . 10 6 degrees. 
Density = -0547 gm. per cu. cm. 
Pressure = 2-23 . 10 13 dynes per sq. cm. = 22 million atmospheres. 
Of this pressure the fraction -694 is ordinary gas pressure and -306 is 
radiation pressure. 
The mean temperature of the whole mass is 4| million degrees. 
A sphere of radius 0-646 of the radius of the star contains 93-4 per cent, 
of the mass. At the surface of this sphere— 
Temperature = 1-89 . 10 6 degrees. 
Density = -00121 gm. per cu. cm. 
Pressure = 1-07 . 10 11 dynes per sq. cm. 
* By definition a change of five magnitudes signifies a hundredfold increase or 
decrease of light; one magnitude corresponds to a light ratio of (100) 5 or 2-512. 
f These results are calculated for a central molecular weight 2-1, and to allow 
for the ionisation decreasing outwards the molecular weight has been taken to vary 
as T~^ (§ 94).