61-63] Adiabatic Equilibrium 69 
More accurate figures will be given later as the result of a detailed study 
of stellar models. But at the outset of this study we may notice that, apart 
from all particular models, the gravitational attraction of the molecules of 
a star endows the stellar matter with a temperature of the order of 10 7 degrees 
centigrade. 
Adiabatic Equilibrium. 
63. Let us now return to the general equation of equilibrium (58'3), 
namely 
¿¿© +4,rw=0 (63 ' 1) - 
As we have already noticed, this does not of itself enable us to determine 
the distribution of density inside a sphere of gravitating gas; we can only do 
this by introducing some further assumption as to the conditions in the star’s 
interior. 
In the early discussions of the problem the supposition usually made was 
that the star’s interior was in a state of “adiabatic” or “convective” equi 
librium such as prevails in the lower regions of the earth’s atmosphere. As 
ordinary gaseous conduction is easily shewn to be too slow a process to account 
for the violent flow of heat to the star’s surface (cf. § 71 below), it was sup 
posed that the greater part of the heat was transferred from the star’s centre 
to its surface by convection currents. If the whole of a star’s interior is kept 
mixed and stirred up by such convection currents, the state of equilibrium in 
its interior is readily determined. We can imagine any two elements of the 
star of equal mass to become interchanged in the process of mixing; after 
they have expanded or contracted until their pressures are suitable to their 
new positions the stars must again be in equilibrium as before. The process 
of expansion is so rapid in comparison with the process of transfer of heat 
by conduction, that any transfer of heat by conduction may be neglected, and 
the condition for equilibrium is simply that the energy-contents of the two 
elements of gas must originally have been identical. 
When this is the case throughout the star, the pressure p and density p 
are connected by a relation of the form 
p = Kp K (632), * 
where A” is a constant and k is the ratio of the specific heats of the gas. 
Here, then, is a possible further relation between p and p, and from equations 
(63T) and (63'2) both p and p can be determined. 
Replacing p by its value Kp K , equation (63T) assumes the form 
Kk d 
r 2 dr 
[rY 
= 0 
(63'3), 
a differential equation which determines the way in which p depends on r.