512 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



If in equation (/?) we substitute 



l d P = RT d£ 

 p. dr dr 



then for positive values of G we have 



\ dr 2 RT \ M f r 2 dr / J 



Example. For this example, and for the sake of abbreviating 

 the computation, we here assume another law for the distribution 

 of pressure, i. e. : 



r 2 



-c[ 1 -_ 



P 2 



(for the region over which r < p) 

 We thus obtain 



K-U.R.TiL-fLL.lfJl+tKEc-l)). 



2 \ 4 i?r c \ \ f ^ / J 



If we assume the following special numerical values 



log j = 6.01337 - 10; RT = 287.273 m 2 sec" 2 ; 



30 4 RT 



c = ; c = 1 



760 f p 2 



corresponding to a whirl of 1080 km. radius, with the barometric 

 pressure 73o ram at the center, in latitude 45 , then we find 



K = M.RT - 0.268. 



If the earth be not rotating (that is to say if j = o) and the other 

 conditions be retained, we should only be able to maintain this 

 same distribution of pressure by assuming a whirl whose kinetic 

 energy is 



K = MRT - 

 2 



