SURVEY OF THE PROBLEM 
5 
ng periods of 
unt of energy 
3rsion process 
hat, since the 
nic processes, 
liberation of 
icult problem 
ation of sub- 
11 ar radiation, 
tie more than 
to argue that 
supplied to a 
)es not follow 
: of the mains 
station, 
different ways 
nade to agree, 
¿ng the water 
will be a flood 
would involve 
fact that the 
¿iat for actual 
gned constitu- 
le same result; 
dw the adjust- 
•gy just meets 
3 flow of water 
e pipe; and so 
le temperature 
he expenditure 
? of subatomic 
r to balance its 
ndent problem. 
Derature within 
omer Lane en- 
the Hypothesis 
•nal Heat, and 
Experiment*.” 
17. 
This was followed and amplified by investigations on similar lines by 
A. Ritter*, Lord Kelvinf, and others, culminating in the systematic and 
exhaustive research of R. Emden. Although we find it necessary to break 
away from these ear her investigations on a fundamental point, viz. the 
mode of transfer of heat within the star, they contain much that is 
sufficiently general to be adapted to present theories. The calculations and 
tables in Emden’s remarkable book Gaskugeln (Teubner, 1907) have been 
extensively used by the author. 
Lane reached the striking result that if a star contracts the internal 
temperature rises so long as the material is sufficiently diffuse to behave 
as a perfect gas. Until recently it was believed that the gravitational 
energy converted into heat by contraction was the only important source 
of maintenance of a star’s heat. In that case the star through radiating 
heat must contract, and the heat generated by the falling in of material 
must be sufficient not only to replace the radiation lost but to raise the 
internal temperature to a higher level. Lane’s result thus took the para 
doxical form that a star by losing heat automatically grows hotter. 
Lane’s investigation is not, however, bound up with any particular 
views as to the source of a star’s heat. It sets forth the change of tempera 
ture necessary to preserve equilibrium. The star has the option to obey 
Lane’s law or to collapse; it is obvious that actual stars have not chosen 
the latter alternative, but the reason lies outside Lane’s theory. Accepting 
the modern belief that the heat is supplied by liberation of subatomic 
energy, we still suppose that stars are formed by gradual condensation of 
primordial matter; so that the course of evolution is from low to high 
density and therefore by Lane’s law from low to high temperature. At 
least in the earlier stages the internal temperature of a star is gradually 
rising. If in the later stages of high density the material no longer behaves 
as a perfect gas the temperature may ultimately fall again. 
6. In Lane’s time there was no evidence that any star existed for which 
the theory of a perfect gas would be applicable. The mean density of the 
sun is 1-41 gm. per cu. cm., and long before reaching such a density 
terrestrial gases cease to conform to the perfect gas law. There was at 
that time no reason to doubt that the sun’s density was tjqncal of stars 
in general. But we now know that there exist stars (“giant stars”) with 
mean densities comparable to that of air or even to the density in an 
ordinary vacuum tube. These at least can be treated as composed of 
perfect gas; so that there will be no lack of opportunity for application 
to actual stars of results obtained for perfect gas. 
The existence of stars of low density is now a commonplace of astronomy, 
and it is unnecessary to survey the abundant proofs derived indirectly 
* Wiedemann's Annalen, 1878-1889. 
f Phil. Mag., Series 5, 23, p. 287 (1887). 
}