PAPER BY PROF. OBERBECK. 159 



In regions of pure horizontal motion, and for moderate loind velocity, 

 the angle between the direction of the wind and the gradient is constant 

 and depends only on the constant of rotation and the constant of friction 

 and is independent of the direction of the isobars. 



The ^bove given relation had beea found by Guldberg and Mohn* 

 for the special cases of rectilinear and circular isobars. 



The general solutions contained in equatious (18, 19, and 20) can now 

 be so applied that we may adapt the function cp to any other given 

 system of isobars. When this is achieved, then the motions of the 

 air are determined by the first two of these equations. 



If, for instance, we have to do with a region that is under the in- 

 -fluence of numerous but distant maxima and minima of pressure, then 

 we can approximately put 



cp=2 c. log p. 



In this expression p indicates the distance of the point (xy) from the 

 vertical currents of the individual regions, assuming that the dimensions 

 of these regions are small in comparison with the distances. This 

 value of q) would be exactly correct if all inner regions [namely, 

 as defined on page 153] were bounded by circles. Then p would 

 indicate the distance from the center of the circle. The constauts c 

 depend upon the intensity of the respective vertical currents. They 

 are positive for the minima and negative for the maxima [i. e.,for areas 

 of low and high pressure respectively]. The assumption 



F{x-{-iy) = {x-\-iy)^=(p+i/p 



whence 



(p=x'-y' ; 



?f^=2xy 



leads to a special example already treated of by Guldberg and Mohn.t 

 The potential curves 



jc'^ — j/-=constant 



and the stream lines 



2xy—Y{x^—y'^)= constant 



are systems of equilateral hyperbolas. 



* See their Etudes, etc., ParL i, pp. Q3-2(). \Etudes, Part ii, pp. 51, 52. 



