580 SMITHSONIAN MISCELLANEOUS COLLECTIONS \(>L. 51 



Hence if C v = fi? or y = f we have (V) = (u). This is the value 

 of r that is found for non-atomic gases but for other gases y is less 

 than | and (V) is greater than (u). 



§(34) Comparison of the problem above treatedwith analogous analy- 

 ses for incompressible liquids. 



We will now consider a system of liquids each of which retains 

 its constant density during its change of position. The available 

 kinetic energy is to be computed by the equation 



dK + (R) = - OP 



The potential energy of position for a unit column of a homo- 

 geneous body between the altitudes ^ and ^ n is given by 



[P] = J z g*l>-dz = gfl — 2— 



(A) Let thechamberi (fig. i) contain liquid of the constant density 

 fi v the chamber 2 a liquid of smaller density y..,. So long as the screen 

 separates the two chambers there is neutral equilibrium on both 

 sides of it. The volumes 1 and 2 are in this ease assumed constant 

 and therefore equal to 1' and 2' respectively, B being the area of 

 either base. We now have for the initial and final stages 



- B h 2 - B If 



p i« = -^gUi ~2 P -'« = "2 2-" 2 "2 



_ h 2 - 'Mr 



After the removal of the vertical screen the available kinetic energy 

 becomes 



Let 



(7 



£o = g^// 



