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 x y 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 



w=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 the 

 negative sign must be given to the constant. 



The region for which 



1C = C.S 



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



for which 



m?=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 



^ + ^ =0 (1<l) 



and for the inner region 



- 4- ; =— c (lb). 



For boch regions, moreover, the ordinary equations of hydro-dynamics 

 for movements in one plane hold good, namely : 



(2) 



in which the letters have the ordinary signification. 



The accelerating forces whose components are A' and I r must express 

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



The consideration of the earth's rotation necessitates the introduction 

 of a force! whose components are 



A'j = — A 1?, Yi = + Aw. 



"This agrees eutirely with the assumption of Guldberg and Mohn as to the vertical 

 currents. (See Etudes, 1870, part 1, p. 28.) 



tSee G. Kirchholt', Vorlesungen iiher Mechanik, Leipzig, 1876, pp. 87-95. 



