350 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



hand, the synoptic charts show that in strongly developed cyclones 

 the winds very frequently favor the isobars, i. e., the direction 

 agrees with that of the tangent to the isobar; and, on the other hand, 

 we are not yet able in theoretical investigations to free ourselves 

 from the simplifying assumption of circular isobars. 



On the other hand, I can but think that the investigation of this 

 simplest case should suffice to considerably further our understanding 

 of the cyclonal and anticyclonal motions and illuminate many points 

 in reference to which an incorrect view has often been maintained. 



Moreover, the centered whirl or the centered portion of such has a 

 special interest in that it represents the limiting case between 

 whirls with centripetal and with centrifugal motion or between the 

 corresponding portions of such a whirl. 



It is now necessary first to express exactly the fundamental con- 

 dition for the existence of the centered whirl, which is very easily 

 done. 



Three forces are acting on every particle of the whirl; the centri- 

 fugal force p c arising from the rotation about the axis of the whirl ; 

 the deflecting force p i of the earth's rotation, which we can also 

 represent as a centrifugal force directed toward the center of curva- 

 ture of the inertia curve; finally, the gradient force r which is the 

 force arising from the difference of the atmospheric pressure. 



In a centered whirl, in which each particle describes a circle, 

 these three forces all act in the direction of the radius of this circle 

 and it is only the directions of each that differ according as they 

 have to do with a gradient directed inward or outward, i. e., with 

 cyclonal or ant^clonal rotations and distributions of pressure. 



The fundamental condition for the maintenance of a centered 

 whirl is therefore 



Pc + Pi + r = (1) 



where the summation is algebraic and we must first give each quan- 

 tity its correct sign. 



If we consider the absolute values of the quantities p c ; p { and r 

 as known and give each its proper sign, then we have to distinguish 

 four cases : 



(A) Cyclonal rotation with gradients directed inward, or, as 

 we may appropriately say with cyclonal distribution of pressure. 

 In this case, which we see presented in the lower strata of the ordi- 

 nary cyclones, p c and p { have the same signs, but T the opposite 

 sign and thus the equation reads 



p e + Pi - r - (2) 



