5IO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



where G is the velocity of a particle and r the radius of its circular 

 path. For the kinetic energy of the whirl we have 



J, J„ 9r 



\ f ' - >* 



Jo <^ 



= 7T — . 



where the notation is similar to that of the preceding pages. 

 The assumptions of a very large volume k' of quiet air in comparison 

 with the volume of the whirl k and no change in pressure for the outei 

 region where r "> p , are also retained. 

 Thus by partial integration we obtain 



,, RT Cp 



K = — 2 71 P I e rar 



g Jo 



Only negative values of e are possible. 



Using the value of e = — c (i — r/p) adopted in the preceding 



example we find: 



K = ?:p 2 . P . . - 



g s 



If M is the mass of the air in a cylinder of radius p under pressure 

 y5 mm an( j the temperature T, then for K, the kinetic energy of the 

 whirl, and for A, the potential energy of the distribution of pressure 

 produced by the whirl, we have 



K = MRT - 



A = MRT — 

 12 



K 4 



A ~ ~c 



For c = 15/760 we find K two hundred times larger than A. For 

 c = 30/760 we have K still ioo times A. 



