356 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



ence of a centered cyclonic whirl that very precise relations must 

 exist between the wind velocity and the distribution of atmospheric 

 pressure. 



Hence in all cases where the wind circles about a center in the 

 strict sense of the word there must be a very exact distribution of 

 pressure that renders possible the continuation of such a whirl, 

 and inversely for every symmetrical circular distribution of pressure 

 there must be corresponding definite velocities belonging to it. 



The entire omission of the friction in this theorem implies the 

 assumption that this is overcome by forces that do not appear in 

 this calculation, as, for instance, the difference of velocity in neigh- 

 boring strata which on its part must of course be maintained by 

 causes that are outside the region under consideration. In no case 

 can these resistances within a centered whirl be overcome by the 

 forces arising from the distribution of pressure, and this is a funda- 

 mental point for the following discussion. 



The questions that interest the meteorologist with reference to 

 the centered whirl are the following: 



(1) Are there really any cyclones that show, at least at the earth's 

 surface itself, such a distribution of pressure and wind as must 

 exist in the centered cyclone? 



(2) Can these conditions be satisfied simultaneously in layers 

 of great vertical extent, under the conditions prevailing in our 

 atmosphere, or is it improbable that a cyclone that appears as a 

 centered whirl at the earth's surface may also possess the same 

 peculiarity at greater or even only moderate altitudes? 



(3) When the equation of condition (9a) is not satisfied but 

 when departures therefrom are present in any given direction, what 

 conclusions can be drawn from that fact? 



Let us consider the formula 



g tg a = + v k sin <p 



r c 



from the point of view proposed in the first of these three questions, 

 after writing it in the simpler form 



v 2 

 g tg a = — + vK 



since r i no longer occurs in the following discussion and since we 

 may always limit the investigation to some one definite value of <p. 

 We note, first, that for diminishing values of r, i. e., with approach 

 toward the center, the inclination of the isobaric surface, or the 



