158 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



The compoueut velocities are: 



^^^^_A ^ ^=^^j^l ^ (18) 



riually, from equation (17) we obtain 



= cou.taut_(l + ^:)|.^+j[(;;|/+(|')']}.. ,20) 



All these expressions still contain the as yet undetermined function qj^ 

 which is only limited by the condition J<^=0. Such functions can be 

 easily found in various ways. Thus if we bring the function of a com- 

 plex variable x-\-\\j into the form 



F [x^hj) = (p^if, 



then both q) and also ?/' satisfy the above given difl'erential equations. 

 Moreover, both functions stand in the following relations to each other. 



With the assistance of these equations one can easily find the general 



equation for the path of the wind. We obtain this from the diflerential 



equations 



u cly=v (Ix, 



^ J ^^dx+^^-dy I =^^dy-^'^dx. 

 k \ M ^ :^y ^ j M ?y 



If we introduce //• into the right-hand side of this equation we obtain 

 as the equation for the path described by the wind 



//•—'-^^= constant (21) 



The path of the wind intersects the system of lines defined by the 

 condition q)= constant at an angle that is everywhere the same. 

 If we designate by s the angle that the direction of the wind makes 

 with the normal to the curves g)= constant then we have 



tan £=^. 

 k 



For currents of air of moderate velocity the term 



in equation (20) can be neglected in comparison with qj. In this case 

 the isobars, for which p equals a constant, are identical with the curves 

 fp= constant and we obtain the following general theorem : 



