<518 Sir Napier Shaw [March 10, 



r the angular radius of a small circle on the earth's surface which 

 indicates the path of air in a cyclone. 



A the latitude of the place of observation. 



o> the angular velocity of the earth's rotation. 



We require also some convention as to the positive and negative 

 of v. — 



V positive represents the wind when the pressure difference A ^ 

 represents higher pressure on the right of the path. 



The fundamental relation between the velocity of the wind at 

 any level and the pressure-gradient there is 



s = ^ = 2 0. ^' p sin X ± ^ /J cot r . . (F) 



The two terms which make up the right hand side of this equa- 

 tion are of different importance in different places and circumstances ; 

 for example, if the air is moving in a great circle r is 90° and cot r 

 is zero ; the first term alone remains. On the other hand, at the 

 equator the latitude A = ; sin A is zero and the second term alone 

 remains. Away from the equatorial region the second term is also 

 relatively unimportant unless the velocity v is great. In temperate 

 and polar latitudes the path of the air differs little from a great 

 circle, except in rare cases, near the centres of deep depressions ; 

 consequently the first term may be regarded as the dominant term in 

 these regions. 



We call the wind, computed according to the first term, the 

 geostrophic wind, and regard it as generally representing the actual 

 wind of temperate and polar regions. 



We call the wind, computed according to the second term, the 

 cyclostrophic wind, and regard it as representing the actual wind (in 

 so far as there is any regular or persistent wind at all) in the 

 equatorial regions. It represents the wind of tropical hurricanes, 

 and winds of the same character may also occur locally in temperate 

 regions as tornados and other revolving storms. 



Thus we have the following auxiliary equations : — 



Horizontal gradient of pressure 



d V 

 s = — ^ . 

 dl 



Horizontal gradient of temperature 



dO 



Winds of temperate and polar regions, geostrophic winds 



•s- = 2 w V p sin A . . • (1) 



