57§ SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5] 



the center of gravity remains unchanged. The resulting (V) has 

 the same form (eq. Ill) as for the thin horizontal layer considered 

 above, provided we now let T indicate the average temperature of 

 the whole mass and let p x and p 2 indicate the initial values of the 

 pressures at the base. 



Again let there be resting in these chambers masses whose dis- 

 tribution of entropies is such as was assumed in the second 

 analysis, see section 25; this equation (I) or (I*) applies to their 

 overturning even in this present case of constant volume. For 

 the same differences of pressure at the base, and for smaller 

 differences above, and when p 01 — p 02 is a small fraction, as is the 

 case in our atmosphere, equation (I) gives a much larger value 

 of the living force than equation (III). 



It seems now to have been abundantly demonstrated that the 

 available kinetic energy of such a system is not dependent materially 

 on the horizontal differences of pressure but on the distribution of 

 entropy and the buoyancy dependent thereon. 



H33) Appendix to the fourth analysis. Study of Joule' s experi- 

 ment relative to the mutual independence of the internal energy and 

 the volume of a gas. 



In the first chamber of fig. 1 let the horizontal layer of gas be 

 under the pressure p t but let the other chamber be empty or p 2 — o ; 

 we now have the same arrangement as in Joule's experiment, if 

 we 1 nit k x — \h. 



For this case the first equations of our fourth analysis, §31, 

 become 



P' = 2 - r Pi 



_ Cy k Pi n-9 1_r ) 

 R 2 



If T is the initial temperature in chamber one, then the mass of 

 the gas is 



2 RT 



whence 



M 2 



