64 Trans. Acad. Sci. of St. Louis. 



A new state of equilibrium will result in which 



C 2 T 2 

 P ~ 2-irkK* {5) 



__ 2CTR „ 



M=-^- =M . 



The relation of final to initial temperature was shown to be 



T= P T r 

 It follows that at the surface of the mass M, 



« = P % 

 and 



P = P ^ Q . 



The work done upon the spherical mass by the superposed 

 gravitating mass while the radius shortens by dR is 



dW=-4irR 2 PdR 

 2G2T2 dE. 



k 



In this equation 



R 2 T 2 



T 2 = P 2 T 2 



"0^0 



o ~~ R 2 



Inserting this value of T 2 in the last equation, the work done 

 upon the spherical mass while the radius shortens from R to 

 Rh 



^__!£!^f|_!$!*i» ( ,_ 1): (6) 



Let H represent the heat produced in the mass M during 

 this operation, J, the mechanical equivalent of heat, and s the 

 specific heat of the gas. Then 



