SURVEY OF THE PROBLEM 
9 
/ 
nfurcation of 
l Shapley on 
warf stars of 
ree eclipsing 
of air. There 
sity but is a 
higher types 
As already 
3 giant stars 
il differences 
fication into 
3 method of 
t and dwarf 
lty; but the 
latLockyer, 
ddence that 
though con- 
are greater 
ich that the 
than under 
v in a very 
)urse. 
nternal dis- 
arches. We 
r one of the 
n be calcu- 
(8-1), 
! molecular 
re only two 
differential 
conditions : 
he pressure 
; the layers 
es that the 
somatically 
of the star 
• equations 
he two in- 
any point. 
Hence the distribution of pressure, density and temperature is found. 
The general scheme of distribution is (in the first approximation) homo 
logous from star to star; that is to say, all gaseous stars copy the same 
model each on its own appropriate scale of mass, length, temperature, etc. 
The heavy work of the solution can be done once for all, and it is then 
only a question of adapting it to the scale of the particular star considered. 
We do not here enter into details; the problem is fully treated in Chapter iv. 
In order to obtain definite numerical values of the temperature inside 
a star according to Lane’s theory it was necessary to have the following 
data— 
M the mass, 
R the radius, 
/x the mean molecular weight of the material, 
y the ratio of specific heats of the material. 
The first two define the star under consideration; but we might suppose 
that the values of the last two in any star could only be guessed by con 
sidering the probable chemical composition of the interior—as to which 
we know practically nothing. We shall explain how this difficulty has been 
surmounted. 
Actually the value of y gave no serious trouble. It cannot exceed f, 
the value for a monatomic gas; and it cannot be less than f without 
rendering the star unstable—which we know it is not. The difference in 
temperature distribution corresponding to the limits f and f is of some 
account; but there is no important change in its general character, and 
either limit gives an approximation good enough for many purposes. The 
constant y, however, no longer concerns us. We shall abandon that part 
of Lane’s theory responsible for its introduction, replacing Lane’s hypothesis 
of convective equilibrium by radiative equilibrium. In all the earlier 
researches it was supposed that heat was carried from the interior to the 
surface of the star by convection currents, so that the interior was kept 
thoroughly stirred and followed the same law of thermal equilibrium as 
the lower part of the earth’s atmosphere. But it appears now that the 
heat is transferred by radiation and the temperature distribution is con 
trolled by the flow of radiation; convection currents, if they exist, will 
strive to establish a different distribution, but the temperature continually 
slips back to radiative equilibrium since the transfer by radiation is much 
more rapid. Radiative equilibrium was first adopted by R. A. Sampson* 
in 1894; but it could not be developed fully without the more recent 
progress of thermodynamics. K. Schwarzschildf brought it into promi 
nence in a famous paper on the condition of the sun’s atmosphere. Our 
task is to apply the same principle to the interior of the sun and stars. 
* Memoirs R.A.S., 51, p. 123. f Gottingen Nachrichten, 1906, p. 41.