PAPER BY PROF. OBERBECK. 153 



the following simple assumption is made :* If we adopt a system of rec- 

 tangular coordinates such that the plane of ,*■ // is the horizontal plane 

 while the axis of z is directed vertically upward, then for the vertical 

 component of an ascending current of air we have the expression 



iv^c.z. 



If the boundary of the region above which this current ascends is 

 known, while outside this boundary' the movement is exclusively hori- 

 zontal, then the whole system of winds (the cyclone) is thereby com- 

 pletely determined. The quantity c can be designated as the constant 

 of the ascending air. For regions with descending air currents ihe 

 tiegative sign must be given to the constant. 



The region for which 



w=c.z 



will, for brevity, be designated as the inner region of the cyclone ; that 

 for which 



ic=0 



will be designated as the outer region. 



The vertical component is to be considered only in connection with 

 the equation of continuity. Therefore for the outer region this equa- 

 tion becomes 



^Aj,='^ • • • (^«) 



and for the inner region 





For bo:h regions, moreover, the ordinary equations of hydro-dynamics 

 for movements in one plane hold good, namely : 





- , + M — + r ~-= 1 — 



in which the letters have the ordinary signification. 



The accelerating forces whose components are A' and Fmust express 

 the influence of the rotation of the earth and of friction. 



The consideration of the earth's rotation necessitates the introduction 

 of a forcet whose components are 



A'l = — Xv, Yi = -f \v. 



*This agrees eutirely wirli the assumption of Guldbero; and Mohn as to the vertical 

 currents. (See Etudes, 187G, part 1, p. '28.) 



tSee G. Kirchhoti', Vorlesitngen iiber llechanik, Leipzig, 1876, pp. 87-95. 



