THEORY OF CYCLONES VON BEZOLD 359 



Of course this question would be at once answered affirmatively if 

 it were allowable to assume that the wind movement and the baro- 

 metric gradient were uniform above every point of a large portion 

 of the base of such a cyclone. 



But since ihis is only true in exceptional cases and in layers of 

 moderate thickness, therefore the question is to be modified to the 

 inquiry whether changes of the two elements in question, such that 

 the condition of centering still remains fulfilled, are conceivable. 



We most easily attain a summary view of these relations by the 

 following consideration : 



Let z be the altitude of a point above the horizontal base, then 

 in the case of a symmetrical circular form for the whole whirl, we 

 have the equations 



p - / (r, z) 

 and 



v = (r, z) 



Making use of equation (96) and recalling that 



P 273 



9 = 9o ft ~T 



where p = 1.293, P = 7^°' an< ^ ^ ^ s ^ e absolute temperature, we 

 can put this equation in the form 



g/U3-6 T dl = v^ 

 Po 27S ' p ■ dr " r +V 



or, if T is constant for each horizontal plane or for every value of 

 z considered as constant, this assumes a still simpler form 



K' dp 1? 



P dr r 



If now we consider the relation above assumed according to which 



v = (r, z) 



dp 

 then, instead of the total differential quotient — we have the partial 



differential quotient and get 



K' dp [<P(r,z)] 2 



