358 POPULAR LECTURES AND ADDRESSES. 



tion of one-tenth per cent, of the diameter, 

 if the density remained uniform throughout the 

 interior, would, as Helmholtz showed, be equal to 

 20,000 times the mechanical equivalent of the 

 amount of heat which Pouillet estimated to b( 

 radiated from the sun in a year. But in reality 

 the sun's density must increase very much towards 

 his centre, and probably in varying proportions, 

 as the temperature becomes lower and the whole 

 mass contracts. We cannot, therefore, say whethei 

 the work actually done by mutual gravitation 

 during a contraction of one-tenth per cent, of the 

 diameter, would be more or less than the equivalent 

 of 20,000 years' heat ; but we may regard it as 

 most probably not many times more or less than 

 this amount. Now, it is in the highest degree 

 improbable that mechanical energy can in any 

 case increase in a body contracting in virtue of 

 cooling. It is certain that it really does diminish 

 very notably in every case hitherto experimented 

 on. It must be supposed, therefore, that the sun 

 always radiates away in heat something more than 

 the Joule-equivalent of the work done on his 



