THEORY OF CYCLONES— VON BEZOLD 349 



"Are the movements observed within a cyclone exclusively the 

 consequence of the presence 'of the lighter air at its center or, con- 

 versely, is the latter wholly or partly the consequence of these 

 movements, in which case these latter must, of course, result from 

 exterior causes?" 



If we consider only a portion of the whirl, then an affirmative 

 reply to this last question only shows that the cause of the motion 

 must lie outside the portion under consideration without forcing 

 us to seek it outside the whole whirl. 



Unfortunately, even the simple question whether in any portion of 

 the whirl the observed movements are wholly explained by the dis- 

 tribution of pressure cannot be answered in its generality because 

 one must still make some more or less arbitrary assumptions as to 

 the coefficients of friction and as to the influence of neighboring 

 strata. 

 ' On the other hand, this question can be at once answered in the 

 negative if the so-called angle of deflection (of the wind from the 

 gradient) is equal to or greater than 90 , that is to say, if the direc- 

 tion of the wind agrees with the isobar or has a component against 

 the gradient. 



For under such conditions work is being done that can not be due 

 to the gradient force present in the cyclone or in the portion of the 

 cyclone under consideration, since in the first case the gradient force 

 is perpendicular to the direction in which the work (which consists 

 of overcoming the friction) is being done ; whilst in the second case 

 there must exist a component of force that is directed oppositely to 

 the only one that can arise from the distribution of pressure. 



Of these two cases, the first is easily accessible to mathematical 

 treatment, and therefore the following remarks apply to it, that is 

 to say, this investigation is confined to cyclones with circular iso- 

 bars and winds whose direction coincide with such isobars, or accord- 

 ing to Sprung's notation 7 to cyclones of circular symmetrical form 

 and having angles of deflection of 90 . 



Perhaps such cyclones might be designated as "centered cyclones" 

 or in general such whirls as "centered whirls" by analogy with 

 "centered optical systems." 



Now it might appear as if by the limitation of our consideration 

 to such centered whirls we have pushed the specialization of the 

 problem to the furthest limit and thus rendered the results quite 

 valueless. But this thought is not quite justified, for, on the one 



7 Sprung: Lehrbuch, p. 208. 



