CONSTITUTION OF THE STARS RUSSELL 147 



temperatures throughout this layer that gives the effective surface 

 temperature. As the density of the star varies, the depth of this 

 layer will alter, and in such a way that it always contains the same 

 number of tons of material per square foot, since it is upon this 

 quantity that the amount of scattering of light passing through the 

 layer depends. As the star contracts, the total quantity of matter 

 in this superficial radiating layer will therefore diminish propor- 

 tionally to the surface area; that is, the radiating layer will form 

 an ever decreasing part of the whole mass of the star, and its depth 

 will be a smaller fraction of the star's radius. If the depth were a 

 fixed fraction of the radius, we could apply the law of correspond- 

 ing points and say that the temperature would vary inversely as 

 the radius; but, in fact, after contraction the new radiating layer 

 will form only the upper portion of the layer which " corresponds " 

 to the old radiating layer, and its average temperature will be lower 

 than that of the " corresponding " layer. On any reasonable assump- 

 tions regarding the way in which the temperature varies in the 

 outer part of the star, it is found that the effective temperature of 

 the surface will increase as it contracts, but much more slowly than 

 the central temperature. 



All these conclusions are based upon the fundamental assumption 

 that the simple gas laws hold good throughout the star. This may 

 safely be assumed if the density is low — say, not more than 20 times 

 that of air — but when the density begins to approach that of water, 

 it will certainly be very far from the truth. As the density in- 

 creases, the compressibility diminishes, so that, at the same tem- 

 perature, it takes a greater increase of pressure to produce a further 

 increase of density than would be necessary in a perfect gas. In 

 other words, the material is better able than a perfect gas to stand 

 up under pressure. Hence, referring to the argument by which 

 Lane's law was proved, we see that a smaller increase of temperature 

 than is demanded by this law will enable it to meet the changing 

 conditions resulting from contraction. Indeed, a point will in time 

 be reached when no further rise of temperature at all is needed, the 

 decreased compressibility of the dense gas taking the whole load. 

 Beyond this the increased pressure due to contraction acting alone 

 will be insufficient to produce the necessary increase in density, and a 

 fall in temperature must complete the adjustment. 



We see, therefore, that a sphere of real gas, contracting under 

 its own gravitation, will follow Lane's law only while its density 

 is small. As it contracts further its temperature will rise more 

 slowly than this law indicates, reach a maximum, and then gradu- 

 ally diminish. During this long process, the model upon which 

 the mass is built will itself gradually change — the increase of density 

 toward the center diminishing — but this will not alter the general 



