temperature 
;e of absolute 
he formula* 
SURVEY OF THE PROBLEM 15 
A sphere of radius 0-831 of the radius of the star contains 99-5 per cent, 
of the mass. At a point on this sphere— 
Temperature = 0-81 . 10 6 degrees. 
Density = -000107 gm. per cu. cm. 
Pressure — 3-62 . 10 9 dynes per sq. cm. 
E the effective 
(12-1). 
All but 1 per cent, of the mass is at a temperature above a million 
degrees but the remainder is of very low density and occupies nearly half 
the volume of the star. 
The maximum temperature gradient in the interior is 1°-1 per kilo- 
apters to the 
ter than the 
metre—very much less than the temperature gradient in our own atmo 
sphere. This maximum occurs about ^ of the way from the centre to the 
surface; it is a very flat maximum and the gradient throughout the greater 
part of the star is not much below the maximum value. 
Gravity at the surface is 1/45-2 times that at the surface of the sun 
or about f of gravity on the earth. The absolute value is 606 cm. sec. -2 . In 
the interior it rises to a maximum of 4 times this value and then falls to 
zero at the centre. 
The average rate of liberation of heat in the interior required to supply 
that lost by radiation from the surface is 58 ergs per sec. per gm. By its 
radiation Capella is losing mass at the rate of about 500 million tons per 
second. 
Radiation Pressure. 
itmospheres. 
3 and -306 is 
□rees 
14 . It is necessary to take account of a phenomenon ignored in the 
early investigations, which may have a considerable effect on the equili 
brium of a star, viz. the pressure of radiation. It is well known that electro 
magnetic waves, including light waves, possess mass and momentum and 
exert a force on anything which obstructs their progress. Ordinarily the 
pressure of radiation is extremely minute and can only be demonstrated 
by very delicate terrestrial experiments; but the radiation inside a star 
is so intense that the pressure is by no means negligible as regards the 
conditions of equilibrium of the material. At a point in the interior the 
»3-4 per cent. 
radiation pressure shares with the gas pressure the task of supporting 
the weight of the superincumbent layers of material. The radiation pressure 
is proportional to the fourth power of the temperature; it amounts to 
2,550 atmospheres at 1,000,000°, 
25,500,000 atmospheres at 10,000,000°. 
Id increase or 
or 2-512. 
The outward flowing radiation may thus be compared to a wind 
blowing through the star and helping to distend it against gravity. The 
formulae to be developed later enable us to calculate what proportion of 
taken to vary 
the weight of the material is borne by this wind, the remainder being 
supported by the gas pressure. To a first approximation the proportion is