560 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



T' 2 ;be the analogous quantities for any given layer in the mass 2 

 and 2'. We thus have 



P\ = Pi + Po - Pi P\ = Pi ~ (Pi - Ph) 



^ / 1 , ft ~ Pi \ ■ . . 



= 1 j I 1 + a ) approximately. 



\ Pi I 



With this last approximate value, which holds good in proportion 

 as p Q — p h is small relative to p h , we obtain for mass 1 



T T' — P° — ft 



C v J" (2\ - T[) dm, - - ( Po - Pi ) h v 

 Similarly for the other mass 2 we obtain 

 T T> - ft ~ ft 



-* 2 J 2" —p. 



C p .«2 



Cp J (^ - ^2) ^2 = (ft - Ph) K 



Hence when h t and h 2 are small enough to allow of this approxi- 

 mate method we have 



C p j (T - V) dm = fa - p h ) h 2 - ( Po - Pt ) h t 



From stable equilibrium we now pass on to the limiting case of 

 neutral equilibrium within the masses 1 and 2 ; we have 



to-Jl-grY' and p. _ J 1 + 



^p ■* ti / . V C p T t 2 



whence approximately 



Pi ~ Pp = Pi S^r and p - ft = ft gh * 



K1 il R 1 12 



C p ( (T- V) dm = \h 2Pi | . r « 7* = iMF 



^ = ft ~/>A = Pi K T i2 + ^2 T il 

 g " * ^ft ^2 



F 2 = 2 g fe l fe 2 (^2 - ?ft) 



A i r »2 + a 2 r t . t 



