CHAPTER III 
GASEOUS STARS 
General Configurations of Equilibrium. 
58. The preceding chapter has exhibited the stars as a series of bodies shew 
ing very wide ranges of size and density and considerable ranges of mass and 
surface-temperature. Much labour has been expended in building up a physical 
theory of the structure of the stars. The first attempts treated the stars as 
spheres of gas, in which the pressure of the gas resisted the tendency of the 
star to collapse under its own gravitational attraction. And as the study of 
the internal constitution of the stars is still best approached through this 
conception, we shall examine it in some detail before turning to more realistic, 
but also more complex, theories of stellar structure. 
We start, then, with the consideration of a sphere of gas which is at rest 
throughout, the pressure of the gas exactly balancing gravitational forces at 
every point. If p is the pressure, p the density and g the force of gravity at 
a point distant r from the centre of the star, the condition that gas-pressure 
and gravitational force shall exactly balance is expressed by the usual equation 
of hydrostatic equilibrium 
This differential equation enables us to find p if p is given, or p if p is 
given, but does not determine the arrangement of both p and p of itself; for 
this some further relation or datum is necessary. 
59. If we replace r by ar, the new co-ordinate ar is suited for the study 
of the original mass of gas after its linear dimensions have been uniformly 
stretched a-fold. This stretching changes the original density p into a~ 3 p. 
Now ii we replace r and p by ar and a~ 3 p, and at the same time replace p by 
a~ 4 p, equation (58‘3) becomes 
(58*1). 
The value of g, the force of gravity, is 
(58-2), 
where 7 is the gravitation constant (7 = 666 x 10 “ 8 ). 
Substituting this value for g into (58T), we readily obtain 
(58-3). 
Lanes Law. 
1 d {ar)- d{a~*p) 
(aryd(ar) _a~ 3 p d{ar) 
+ 4 ^ 7(0 3 p) = 0 (59T),