IQ-2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



and the centrifugal force are directed outward and the deflecting 

 force of the rotation of the earth is directed toward the center. We 

 shall have then 



fi U 2 



-G=2cosm6.U- (7) 



P r 



and 



Po - P 

 P 



% {2 to sin 8 . Ur - U 2 ) (8) 



Equation (7) demands that the angular velocity — be less than 



r 



2 co sin 8 because the gradient must be positive. 



Chapter VI 



PERMANENT SYSTEMS OF WIND 



§24. Permanent wind-systems of the first order 



In nature tornadoes and waterspouts represent examples of 

 cyclones of the first order, but meteorological observations of these 

 phenomena being very scarce do not suffice to show us the changes 

 of pressure and velocity which take place in them. We cannot as 

 yet by mathematical analysis construct a complete system of wind. 

 However, we shall consider some simple cases which show analogies 

 with the systems of nature and from them we shall seek to deduce 

 applications. 



In the general equations of § 19 we may neglect the components 

 X , Y , Z , X x and Y l and we shall consider the density as constant 



The equations assume the form 



g + 



(1) 



du d v dw 



= -T- + -r- + -r- (2) 



d x dy d z 



