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



A new state of equilibrium will result in which 



OT 



The relation of final to initial temperature was shown to be 



It follows that at the surface of the mass Jtf , 

 and 



The work done upon the spherical mass by the superposed 

 gravitating mass while the radius shortens by dH is 



k 

 In this equation 



dR. 



7?27'2 



772 _ ^2772 — . 



J- - P J-Q - ^2 



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

 upon the spherical mass while the radius shortens from R^ to 

 ^is 



'R 





2C^TlRl I dR _^ 2C^TIR, 

 W- ^ 1^2- ^ (P-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 



