82 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



and the angular velocity of the ring by oo, and its radius by p; then, as 

 is well known, 



n=oop^ (3) 



and therefor co must vary inversely proportionally with p^. If we 

 indicate the mean radius of the earth by R = 6379600 metres, the 

 geographical latitude by /i, and the velocity of diurnal rotation of the 

 earth by coo, then the corresponding relative velocity at the earth's 

 surface for a ring of air that preserves a calm at the equator is 



R 



p {CO — GJo) = cjQ \ — — Ecos/i 



For air that is resting quietly at the equator in the zone of calms and 

 is thence pushed up to tbe latitude of 10^, this expression gives the ac- 

 quired wind velocity 14.18 metres per second, and similarly for air 

 jiushed up to latitude 20^,57.63 metres, and for 30^, 133.65 metres per 

 second. 



Since 20 metres per second is the velocity of a railroad express train, 

 therefore these numbers show without further consideration that such 

 gales do not exist over any broad zone of the earth. We therefore 

 ougbt not to make the assnmption that the air which has risen at the 

 equator reaches the earth's surface again unchecked in its motion even 

 20° farther northwards. 



The matter is not much better if we assume the atmospheric ring 

 resting at some intermediate latitude. In that case it would give an 

 east wind at the equator, but a west wind at 30° latitude ; but both ve- 

 locities would far exceed the ordinary velocities of the observed winds. 



Since now in fact observations do demonstrate a circulation of the 

 air in the trade- wind zone, therefore the question recurs : By what 

 means is the west-east velocity of this mass of air checked and altered? 

 The resolution of this question is the object of the following remarks: 



II. ON THE EQUILIBRIUM OF ROTATING RINGS OF AIR AT DIFFER- 

 ENT TEMPERATURES. 



If we introduce into equations (1) only rotatory motions about the 

 axis, whereby &?, n, and p retain the significance just given them we 

 then have 



v= —z 00= —z.—f 

 w=yoo=y: 



I 



