CHAPTERS ON THE STARS. 143 



attraction will also be doubled, because the diameter of the spherical 

 shell is the same, while the amount of matter within it is twice as great. 

 Hence the hydrostatic pressure per unit of surface will be four times as 

 great, or will vary as the square of the density. The elasticity at equal 

 temperatures being proportional to the density, it follows that were the 

 temperature the same in the two 'masses, the elasticity would be double 

 in the case of mass B; whereas, to balance the hydrostatic pressure it 

 should be quadrupled. The temperature of B must, therefore, be twice 

 as great as that of A. It follows that in the case of stars of equal 

 volume, but of different masses, the temperature must be proportional 

 to the mass of density. 



But how will it be if we suppose the density to be always the same, 

 and, therefore, the mass to be proportional to the volume? In this 

 case the attraction at a given point will be proportional to the diameter 

 of the body. If, then, we suppose one body to have twice the diameter 

 of the other, but to be of the same density, it follows that at correspond- 

 ing points of the interior, the hydrostatic pressure will be twice as 

 great in the larger body. The density being the same, it follows that the 

 temperature must be twice as high in order that equilibrium may be 

 maintained. It follows that the stars of the greatest mass will be at 

 the highest temperature, unless their volume is so great that their den- 

 sity is less than that of the smaller stars. 



Stellar Evolution. 



It follows from the theory set forth in the last chapter that the 

 stars are not of fixed constitution, but are all going through a progress- 

 ive change — cooling off and contracting into a smaller volume. If we 

 accept this result, we find ourselves face to face with an unsolvable 

 enigma — how did the evolution of the stars begin? To show the prin- 

 ciple involved in the question, I shall make use of an illustration drawn 

 from a former work.* An inquiring person wandering around in what 

 he supposes to be a deserted building, finds a clock running. If he 

 knows nothing about the construction of the clock, or the force neces- 

 sary to keep it in motion, he may fancy that it has been running for 

 an indefinite time just as he sees it, and that it will continue to run 

 until the material of which it is made shall wear out. But if he is ac- 

 quainted with the laws of mechanics, he will know that this is im- 

 possible, because the continued movement of the pendulum involves 

 a constant expenditure of energy. If he studies the construction of the 

 clock, he will find the source of this energy in the slow falling of a 

 weight suspended by a cord which acts upon a train of wheels. Watch- 

 ing the motions, he will see that the scape wheel acting on the pendulum 



* 'Popular Astronomy,' by Simon Newcomb; Harper & Bros., New York. 



