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



The pressure which the superposed layers are capable of 

 producing is 



J CO 

 g'd'dB 

 E 



Substituting these values from (21) and (22) 



^ 00 



P^=:(l + n)(l-nO-^ I -^ 



"^ R 



= (l + «)(l-'.^)^- (23) 



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 



^= CT,. 



Applied to the final condition after contraction has taken 

 place, the same equation becomes 



P,(l+n)p'"-" '_ cTAl+n)p^-' = GT 

 where 



T= 2;(l + ;0(^«)' ". (24) 



When n = , in which case the temperature was initially 

 constant throughout the mass, this equation becomes 



Tr=T,r,. (25) 



