280 Trans. Acad. Set. of St. Louis. 



The pressure which the superposed layers are capable of 

 producing is 



F= g'd'dR 



Substituting these values from (21) and (22) 



00 





(7277202 



(72772^2 



= (l + '^)(^-''^)^;^- (^^> 



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

 is (1 -{- n) p 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 



Applied to the final condition after contraction has taken 

 place, the same equation becomes 



Po(l-\-n)p'^'--^^ (77;(l+7i)/>i-« = CT 



%p 



where 



y= 2; (i+») (!!«)''". (24) 



When 7z = , in which case the temperature was initially 

 constant throughout the mass, this equation becomes 



Tr=T,r,. (25) 



