CONSTITUTION OF THE STARS RUSSELL 151 



in all directions by the electrons, or absorbed in detaching some 

 fast-knit electron from the remnant of an atom, only to be re- 

 emitted when recombination took place. In either case the energy 

 would be relayed back and forth from atom to atom, now in this 

 direction, again in that, until in the lapse of ages it leaked gradually 

 outward to the cooler parts of the star, on its way to the surface. 



Jeans was, I believe, the first to call attention to this extraordinary 

 state of things, and Schwarzschild to point out the fundamental im- 

 portance of the exchange of radiation in determining the conditions 

 of equilibrium within a star ; but the general solution of the problem 

 came later, from Eddington, who was the first to appreciate one of 

 its most fundamental features. 



The flood of entrapped radiation, in its attempts to escape, exerts 

 a pressure outward in all directions, just as a compressed gas would 

 do. The existence of this radiation pressure was pointed out long 

 ago by Maxwell's theory of light. With any light obtainable on 

 earth, even full sunlight, it is so minute that apparatus of the most 

 delicate sort is required to indicate its existence; but at the tempera- 

 tures which prevail inside the stars it may amount (as Eddington 

 pointed out) to hundreds of tons per square inch and be an important 

 factor in preventing the collapse of the star's interior under the 

 weight of the outer parts. Indeed, under some conditions, it may do 

 more than the gas pressure due to the motions of the atoms and 

 electrons, huge as the latter is. Following this lead, and working out 

 the laws of flow of energy outward down the temperature gradient, 

 he showed that certain simple and probable assumptions about the 

 opacity of the medium led to the conclusion that, all through the 

 star, the gravitational pressure would be proportional to the fourth 

 power of the temperature, and that the shares of this pressure which 

 were sustained by the gas pressure and the radiation pressure would 

 be everywhere in the same ratio. These conditions, combined with the 

 law of gravitation and the gas laws, suffice to determine completely 

 the model upon which the star is built, and to tell us practically all 

 that we need to know about it. 



For the case where the simple gas laws hold, the mathematical 

 work had already been done by Emden, who found that the outer 

 regions of the star were of very low density, while there was a rapid 

 concentration toward the center, where the density reaches fifty-four 

 times the mean density. The central temperature of such a star 

 obeys Lane's law, while the surface brightness varies inversely in the 

 square root of the radius. This means that the whole amount of 

 energy radiated from the star's surface will be independent of its 

 size — the increase in surface brightness and decrease in area, as it 

 contracts, balancing one another exactly. The amount of the star's 

 radiation depends upon the opacity of its material — -diminishing as 



