APPENDIX II 
REFERENCES 
The two lines of investigation which are brought together in the present theory 
of the equilibrium of a star originate in two classical papers— 
1. J. Homer Lane. On the Theoretical Temperature of the Sun. Amer. Journ. of 
Sci. and Arts, Series 2, Vol. 4, p. 57 (1870). 
2. K. Schwarzschild. Ueber das Gleichgewicht der Sonnenatmosphàre. Gottingen 
Nachrichten, 1906, p. 41. 
The latter paper develops the theory of radiative equilibrium in a form appro 
priate to the outer layers of a star. 
Investigations up to the year 1907 are brought together in 
3. R. Emden. Gaskugeln: Anwendungen der Mechanischen Wârmetheorie. 
(B. G. Teubner, Leipzig and Berlin, 1907.) 
which contains important developments by Emden himself. The most relevant 
portions are here summarised in §§ 54-63. Schwarzschild’s work, which had 
newly appeared, is described by Emden, p. 330, but the book is in the main a 
study of convective equilibrium. 
Two further references of historic interest may be added— 
4. R. A. Sampson. On the Rotation and Mechanical State of the Sun. Memoirs 
R.A.S. 51, p. 123 (1894). 
5. I. Bialobjesky. Sur l’Équilibre Thermodynamique d’une Sphère Gazeuse 
Libre. Bull. Acad. Sci. Cracovie, May, 1913. 
The first definitely postulates radiative equilibrium rather than convective 
equilibrium in the sun’s interior. The second takes account of radiation pressure 
and demonstrates its importance in investigations of the internal equilibrium 
of a star. 
For other early papers the references in Emden’s Gaskugeln should be con 
sulted. 
My own investigations originated in an attempt to discuss a problem of 
Cepheid variation. The line of thought is indicated in an article (published a 
year later) 
6. A. S. Eddington. The Pulsation Theory of Cepheid Variables. Observatory, 40, 
p. 290 (1917). 
The problem was to find if possible some cause maintaining the mechanical 
energy of pulsation against loss by dissipative forces—some method by which 
mechanical energy could be automatically extracted from the abundant supplies 
of heat at different temperatures in the star without violating the second law 
of thermodynamics. This might happen if the material of the star acted as the 
working substance of a simple thermodynamic engine (§ 137), or if the radiation 
pressure varied in the manner necessary to perform mechanical work. 
The equations developed for this study naturally laid stress on the opacity 
(which must serve as the valves of the engine), the transport of heat by radiation, 
and on radiation pressure. None of these were treated in the investigations of 
the stellar interior then customary ; so that before discussing the small oscillations 
the conditions of the steady state had to be investigated anew. The Cepheid