358 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



Under these assumptions the equation (9a) assumes the very 

 simple form 



0.001 G = - + 0.0001 v 

 r 



or, if we indicate by /? x and /3 2 the pressures at the two ends of a line 

 whose length is one degree of a great circle, lying in the direction of 

 the gradient, this becomes 



G = ft - & = 1000^ +0.01i/ (10) 



r 



From this we at once conclude that in centered whirls there must be 

 gradients of 2 mm or n mm or ioi mm per degree of a great circle, 

 at distances of 100 kilometers, 10 kilometers, and 1 kilometer 

 respectively from the center, where there is a wind velocity of 10 

 meters per second at these points. 



Gradients like 101 mm per degree never occur or at least only over 

 very limited regions, and 10 meters per second is not a strong wind, 

 but from this paragraph we see very clearly how powerfully cen- 

 trifugal force comes in play even in moderate winds in the neighbor- 

 hood of the center, and how remarkably large the gradients must be 

 (nearly four-fold when v = 20 meters per second) if centrifugal move- 

 ments are not to replace centripetal. 



But in ordinary cyclones, beginning at a definite and often consider- 

 able distance, the wind velocity diminishes with approach to the 

 center and so also does the magnitude of the gradient, so that even in 

 this portion the whirl may remain centered, as was already shown in 

 the above case of an accurately defined example of the typical cy- 

 clone. 



However, the idea seems not to be excluded that even in these 

 latter, descending currents may replace the ascending, whenever at 

 moderate altitudes centritugal movements replace the centripetal, 

 and in so far as the masses of air required to supply these cannot be 

 obtained from below. At least the diminution of the cloudiness in 

 the neighborhood of the center, which is often recognized as the 

 "eye of the storm," speaks very decidedly in favor of this conclu- 

 sion. 



On a subsequent page we will explain how these conditions adjust 

 themselves in the tornadoes proper and in the waterspouts. 



In the second place, we will inquire whether it is probable that a 

 cyclone that is centered at its base will also possess this peculiarity 

 at greater altitudes. 



