THEORY OF CYCLONES VON BEZOLD 357 



gradient, must increase, except in so far as a compensation does not 

 occur by reason of a simultaneous diminution of velocity. This 

 increase of inclination or gradient must obtain to a still larger extent 

 when the velocity v also increases with approach toward the center. 

 In immediate proximity to the center, even with a uniform velocity 

 for the inner and the outer rings the gradient becomes infinite, which 

 of course is impossible. On the other hand, the increase of the 

 centrifugal force due to the diminution of r can be counteracted or 

 even overcompensatedbya corresponding diminution of the velocity 

 so that in the immediate neighborhood of the center the gradient 

 again diminishes precisely as has been frequently observed. We 

 see from what has just been said that at least so far as we limit our- 

 selves to a purely qualitative consideration of the subject the rela- 

 tions here expressed as the condition for the existence of the cen- 

 tered cyclone are in reality frequently met with, and that therefore 

 the existence of centered cyclones is by no means improbable. 



Even when we study the matter more closely and numerically we 

 come to the same conclusion and find that cyclones which are at 

 least approximately centered at their base, can scarcely be said to 

 be rare. 



In order to acquire a starting point, I have computed the wind 

 velocities that would be necessary in order that a cyclone should be 

 centered when the pressure distribution is such as Sprung 13 found for 

 the average of four well-developed cyclones. 



The velocities that I found for the respective distances from the 

 center are 



and these numbers are not contradictory to the wind velocities read 

 off from the synoptic charts for the respective days. 



This is still more easily seen if we assume that the cyclone is 

 located at latitude 45 and that in the portions under considera- 

 tion the prevailing temperature is io° C. and pressure 73o mm ; or 



g 



15 C. and 745 mm , etc.; in such cases 0.00012237 - = o. 001 and 



0.0001458 sin <p = 0.0001031 or nearly o. 0001. 

 13 Sprung: Lehrbuch, p. 150. 



