MECHANICAL EQUIVALENT OF PRESSURE — -MARGULES 509 



(b.) Adiabatic solution 



If we define the average temperature (T) of the disturbed strata 

 by the equation 



7?TT1 (*<*> ~ \~0dzlRT 



e Jo dz 



r \t] r°° _ ) ° 



g 



= 



then under adiabatic conditions in the atmosphere we have 



JO 



a- 1 . r ^pA(U...Us. 



r g. J \2 



i(i 



■ y^r. ( \ h 



(116) 



If we confine our attention to the first term of this series then it 

 is true that, as before in (la*) and (16*) so now for the atmosphere 

 for equal value of T and for adiabatic changes of conditions, with 

 equal value of a A is y times greater than for isothermal changes, 

 but with equal values of e, A is i/y times as large as (i. e., smaller 

 than) for isothermal changes. 



(3.) STATIONARY WHIRLS IN THE ATMOSPHERE 



Let a distribution of pressure of the kind assumed in the preced- 

 ing article be produced in the atmosphere by a stationary whirl; 

 we wish to know the ratio between the kinetic energy of the moving 

 mass and the potential energy of the difference of pressure. 



Let the atmospheric particles describe circles around the vertical 

 axis of the cylinder whose radius is p; the hypsometric formula 

 applies as before. Such a motion is possible in frictionless air, 

 that is to say, the assumptions are compatible with the aerody- 

 namic equations, provided the velocity is constant along the vertical. 



(a.) Whirl in a quiet atmosphere 



For the change of pressure in the horizontal direction we have the 

 relation 



G 2 1 dp . 



- = («) 



r n dr 



