362 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



ment as that above considered, which has a feeble centripetal com- 

 ponent at the earth's surface, must change into a centered whirl as 

 it extends into higher strata and eventually in fact into a centrifugal 

 whirl. 



Therefore the second of the questions above formulated is to be 

 answered negatively and to the effect that it is most improbable that 

 cyclones should remain centered through any considerable vertical 

 extent. We are rather to expect centrifugal movements in the 

 upper portions of such cyclones even if they must proceed against 

 the gradients. 



The preceding section, which was devoted strictly to answering 

 the second of the three questions above formulated, contains also 

 the reply to the third. This latter refers to the conclusions that can 

 be drawn from the non-fulfillment of the conditions that apply to the 

 centered whirl. 



By the introduction of the idea of the critical surfaces these con- 

 ditions can be expressed in the following simple form: "In centered 

 whirls the critical surfaces and the surfaces of equal pressure must 

 coincide." 



According to what precedes, the inclination of the isobaric surface 

 measures the magnitude of the effective gradient toward the axis, 

 but the inclination of the critical surface measures the component 

 of the force directed from the axis arising from the centrifugal 

 force and the rotation of the earth. 



If therefore at any given location the critical surface has an 

 inclination less than that of the isobaric surface, then we have to do 

 with a resultant directed inward or centripetal, but if the critical 

 surface is more strongly inclined than the isobaric surface then the 

 resultant is outward or centrifugal. 



But in this matter we must recall that even for symmetrical circu- 

 lar isobars the critical surfaces are surfaces of rotation only when the 

 atmospheric motions proceed in circular whirls whose planes are 

 perpendicular to the axis and whose centers also lie in this axis. 



But under these conditions the centered condition is unstable 

 unless the isobaric surfaces and the critical surfaces have the same 

 inclination at every point and coincide throughout the whole region 

 under consideration. 



Notwithstanding this instability the study of this case, which is 

 of course only to be thought of as a transition stage, has some 

 interest in that, as already mentioned, the observed movements actu- 

 ally do come extraordinarily near to being circular, whereas, on the 



