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



A new state of equilibrium will result in which 



fyrp 



C 2 T 2 



1 2irkR 2 {b) 



The relation of final to initial temperature was shown to be 



T= P T . 

 It follows that at the surface of the mass M, 



« = A. 



and 



P = P *P Q . 



The work done upon the spherical mass by the superposed 

 gravitating mass while the radius shortens by dR is 



d W=-47rR 2 PdR 



= - 2 ^dR. 

 k 



In this equation 



R 2 T 2 



rp2 — n 2>T'2 — . 



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

 upon the spherical mass Avhile the radius shortens from R to 

 i?is 



*R 

 I dR 

 R 2 



C R 



W=- ~ 7 ° ™ = j^--« (,_!);■ (6) 



Let Z/ represent the heat produced in the mass M during 

 this operation, J 9 the mechanical equivalent of heat, and s the 

 specific heat of the gas. Then 



