See — Temperature of the Sun and Ages of Stars and Nebulae. 33 



pressure are obviously the resistance due to the increase in the 

 mean density, and a possible change in temperature which 

 might affect the elasticity of the gas. But the surface density 



(R \3 



of the original mass was <7 \ and hence we have a' = a\ I -^ J . 



By hypothesis the equilibrium of the globe is maintained 

 by the elastic force of the gas under the heat developed by 

 the gravitational shrinkage of the mass. If therefore the 

 globe was in equilibrium when the mass had a temperature T , 

 to remain in equilibrium in the condensed condition, T must 



R 



be multiplied by ^. As T R is a constant, we may write 



the law of temperature 



T=- R (58) 



So great is the author's confidence in the significance of 

 physical causes, that he does not hesitate in the belief that this 

 simple formula expresses one of the most fundamental of all 

 the laws of Nature.* 



Its application of course is confined to gaseous bodies, but 

 it is safe to assume that millions of stars and nebulae approx- 

 imate this condition closely, and give this law profound 

 import. It is obvious that the equations of pressure and 

 temperature above applied to the external layer of the globe 

 will apply equally well to any concentric layer of which the 

 globe is made up, and thus it is unnecessary to consider 

 anything more than the surface layer. 



Contemplating now the fundamental law of temperature, 



T =~d' we see that it will obviously hold true for the mean 



temperature of the condensing mass, whatever be the law of 

 internal density and temperature, so long as the globe is 

 wholly gaseous, and maintained in convective equilibrium by 



* A distinguished foreign astronomer, writing under date of April 29, 

 1899, says : "1 am profoundly glad that you have had the courage to gener- 

 alize. The fear is that our outstanding men of science will go on accumu- 

 lating data till they became crushed under the load of their observations. 

 You call your law a fundamental law. I am sure it is so." 



