See — Temperature of the Sun and Ages of Stars and Nebulae. 13 



Lord Kelvin has computed these curves by a process differ- 

 ent from that employed by Lane, and finds the density of the 

 center of the sun about 32 times that of water. This result 

 is based on the supposition that k= 1.4, as in common air, 

 and most terrestrial gases. The rise in temperature near the 

 center of the sun is quite as remarkable as the increase in 

 density. If all the radiation comes from the photosphere, 

 which Lane assumes to have a depth equal to one twenty- 

 third part of the radius, the central temperature would be 

 about 32 times that of the radiating layer ; and if the effective 

 temperature of the photosphere be taken at 8000° C. (as found 

 experimentally by Wilson and Gray, Phil. Trans. ^ 1894), we 

 shall be led to conclude that the central temperature is ap- 

 proximately 256000°C. Though a temperature of a quarter 

 of a million degrees at the center of the sun is not improbable, 

 we find it very difficult to appreciate its physical significance. 



We shall now investigate the effects of an increase of 

 density towards the center on the potential of the sphere 

 upon itself. The surrounding shell is supposed to have the 

 density A., and hence the element of the potential is 



4 i?3 

 dY = ^ira ^ . ^irXBhlB ( 20 ) 



The density of a gaseous heavenly body which has attained a 

 state of bodily equilibrium undoubtedly increases rapidly 

 towards the center, and in general is a function of tlie radius. 

 It thus happens that the bodies of gaseous stars and planets 

 are made up of successive layers of uniform density. And 

 since a spherical shell of uniform density exercises no attrac- 

 tion upon the particles within, the determination of the 

 potential upon itself of such a heterogeneous sphere requires 

 us to consider merelv the action of each successive sphere 

 upon its surface layer. If therefore we integrate equation 

 (20) we shall find the amount of energy given up by the 

 particles of a heterogeneous sphere in falling together from 

 infinite expansion. 



aXR^dR (21) 









