34 Trans. Acad. Set. of Si. Louis. 



free radiation into surrounding space. For if the globe be 

 made up of i isothermal layers of uniform density \, tempera- 

 ture T { , and mass m t ; then a theorem of the form 



T 4 = ^ (59) 



will hold for each layer of the giobe. And for the mean 

 temperature of the whole we shall have 



1=0 



When the mass condenses the temperature of each layer rises 

 proportionally, and we have the same law as before. 



The above reasoning assumes that the globe is composed 

 of one kind of gas throughout, and that its properties are 

 the same under all conditions of temperature and pressure. 

 The Sun and stars appear to be compounded globes of different 

 gases which freely interpenetrate one another. If such in- 

 terpenetrating globes be of unequal dimensions under given 

 conditions of temperature and pressure, as seems probable, 

 on account of the elements rising to heights inversely as the 

 atomic weights, then the relative percentage of the several 

 elements which would appear in a layer of the mixed gas 

 would be a function of the distance of that layer from the 

 center. As the specific heats of the different elements are 

 unequal, we may take each layer of mass m i to have an 

 average specific heat C«, the effects of which may be included 

 in the constants 2T„ and the resulting value written K[. 

 The temperature formula for any layer would thus become 



T t = -jj, and the mean temperature of the globe would 

 be 



_ 1 ^! Kjm, 



(61) 



t=0 



4 

 The mass of any layer is m 4 = q "" \ {R/' — R 3 i-i), and 



the amount of heat in any such layer is m, C,- T f . 



