552 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



P\ — P2 + i m i an( i fro* 11 the assumption that gm x is small relative 

 to p 2 there follow 



P 2 I \ P2 I \ P2 



C P (T 2 -T>)= -gm t ^= - gmi 



P 2 th. 



The contribution of the whole mass M 2 to the right-hand side of 

 equation (3) is 



/<2 



C p UT 2 - T' 3 ) dM 2 = - gmA—1 = - gm^dz = - gmjt 



where h is the altitude of the mass M 2 at the initial stage. 



The overturning of the masses is brought about by the slightest 

 initial impulse, and kinetic energy develops when the equation 



- d (P + I) = m t J C p T x [ 1 - (t*y - gh J . .(4) 

 has a positive value. 



§(15) Continuous distribution of temperature. We will first assume 

 that the separation between w, and M 2 was only made for the 

 convenience of computation and that in the initial stage the tem- 

 perature is a continuous function of the altitude throughout 

 these masses. The value of h must differ from that appropriate 

 to the final stable position, but it may be chosen small enough 

 to allow us to assume T 2 expressible as a linear function, viz., 



dT 



T = T, = T. — az a = — — . 



dz 



With this function of the temperature the equation a gives us 

 p h _/T t -ah\<" Ra 



Pi V T t 



whence assuming ah to be small relative to 7\ we get 



Ph\ K /1 ah\ 0/c P a _ gh g(g-C p a) h 



m \~T t ) =1 C p T^ 



