280 Trans. Acad. Sci. of St. Louis. 



The pressure which the superposed layers are capable of 

 producing is 



00 



P= I a'd'dP, 



P= g'd'c 



R 



Substituting these values from (21) and (22) 



r 



P,= (l + n)(l-nO—J^ I 



00 



dR 



R^ 

 R 



= (l + n)(l-n2)i^_^. (23) 



By reference to (20) it will be observed that this pressure 

 is (1 + w) /> times as great as that necessary to hold the 

 gaseous sphere in equilibrium, if no rise of temperature be 

 assumed. 



Applied to the initial condition, the equation for a perfect 

 gas is 



^^ CT,. 



^ 



Applied to the final condition after contraction has taken 

 place, the same equation becomes 



f,(l+»),o'"- '^ eT„(l+n),»'- = CT 



where 



T=T,{l+n)(jjJ'\ (24) 



When 71 = , in which case the temperature was initially 

 constant throughout the mass, this equation becomes 



Tr=T,r,. (25) 



