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Proceedings of the Eoyal Society of Edinburgh. [Sess. 
numbered 1, 2, 3, 4, 5 respectively, in the history of a constant mass of 
any monatomic gas (k = 1*5; k — If) in approximate convective equilibrium 
while heat is being radiated from it into space. The abscissas represent 
distance from the centre. The ordinates in figure 1 represent temperature, 
reckoned from absolute zero; OT x , . . . OT 5 , being proportional to 1, 1052, 
1T08, 1T69, 1*235 : figure 2 gives the corresponding density curves. 
§ 54. The remarkable result we have arrived at for P gases (for which 
alone, as we have seen, convective equilibrium can be realised), that the 
internal energy of a given mass in approximate convective equilibrium 
increases through gradual loss of heat by radiation into space, was first 
suggested as a possibility by Homer Lane; the suggestion being given 
in his paper referred to in § 2. To understand it more fully, go 
back to equation (62), and observe that in the case of P gases <j is 
continually diminishing, while the globe is shrinking through loss of 
heat. The adiabatic constant A, which determines the relation between 
temperature and density throughout the fluid at any instant, must there- 
fore also continually diminish as time goes on [see (22) above]. Thus, we 
find from equation (19) that, although the density and temperature of the 
gas near the centre of the sphere are increasing, as we see from figures 1 
and 2, and the total energy is increasing, in reality the temperatures at 
places of the same density are continually diminishing. And this diminu- 
tion of temperature at places of the same density causes a diminution of the 
elastic resistance of the gas to compression which allows the gravitational 
forces to effect a contraction of the gaseous mass. 
§ 55. It seems certain that, as the condensation illustrated in figures 1 
and 2 continues with increasing total energy, a time must come when the 
resistance to compression of the matter in the central regions must become 
much more than in accordance with the laws of perfect gases ; and after 
that occurs, the cooling at the surface, with continual mixing of cooled fluid 
throughout the interior mass, must ultimately check the process of becoming 
hotter in the central regions, and bring about a gradual cooling of the 
whole mass. 
§ 56. The application of the above theory of approximate convective 
equilibrium to the sun, regarded as a mass of matter in the monatomic 
state, requires that the law of increase of density from the surface inwards 
should be such that the density at the centre is about six times the mean 
density (see Appendix, § 16). The mean density of the sun is about 1*4, 
the density of water being taken as unity. From this fact itself it seems 
certain that the sun is not gaseous as a whole. Disregarding, therefore, 
the high velocities which we know to exist in portions of the sun’s atmo- 
