MECHANICAL EQUIVALENT OF PRESSURE MARGULES 513 



For both these cases, under the newly assumed law for e we find 

 the potential energy of the pressure distribution to be 



A = M.RT. - 

 6 



hence the ratio A/K is 1/20 for the rotating earth, but 1/76 for the 

 non-rotating earth. 



Although this ratio is thus seen to be appreciably increased 



from 1/76 = 0.013 to 1/20 = 0.050 



by the action of the so-called deflecting force of the earth's rota- 

 tion, still even in whirls of the middle latitudes the potential 

 energy of the distribution of pressure is far less than the kinetic 

 energy of the relative motion. 



(4.) PROGRESSIVE WHIRLS IN THE ATMOSPHERE 



One may ask whether the progressive cyclones are more properly 

 compared with single waves or with revolving whirls. Cyclones 

 have one feature in common with waves, i. e., the partial interchange 

 of the moving masses. On the other hand the dust fall progressing 

 over broad areas with some individual cyclones (notably from 

 Sicily to the North Sea on March 10 and 11, 1901) is a proof that 

 a large portion of the atmosphere remains constrained to move 

 in true whirls. 



As regards the ratio K/A of the kinetic to the potential energies, 

 cyclones are to be considered as whirls rather than as waves. 

 According to Lord Rayleigh, "Theory of Sound," this ratio is unity 

 for progressive plane waves of air. In our present case we find it 

 from the following rough estimate: 



Let M be the moving mass of air, [G 1 ] the average of the squares 

 of the velocity, [e 2 ] the average of the squares of the relative 

 diminutions of pressure, then we have 



K-M^-.A- mrtW : * - [(?] 



2 A RT [e 2 ] 



where \/RT is the speed of propagation of isothermal waves or 

 the so-called Newtonian velocity of sound and is 280 meters per 

 second for temperature o° C. 



