MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 



243 



§36. Influence of the rotation of the earth on the vertical currents 



As we have shown in §19, the force produced by the rotation of 

 the earth depends also on the vertical velocity. Let us consider 

 in the first place a steady vertical current and assume the horizon- 

 tal velocities u ana* v to be zero. The equations of motion assume 

 the following form, denoting by a the angle between the axis X 

 and the meridian (see fig. 53): 



1 dp 



p dx 



1 dp 



P dy 

 1 dp 

 o dz 



— 2 co cos 6 sin a w 



— 2 co cos 6 cos a iv 



dw 



= - g-w 



dz 



It follows that the vertical motion goes on in the same way as 

 we have developed in §15, but that there exists a horizontal grad- 

 ient. Denoting this gradient by G we have 



- . G = 2 co cos 6 w 

 P 



(1) 



and this gradient is directed toward the east, when wis positive which 

 is true for ascending currents. For descending currents w is neg- 

 ative and the gradient is directed toward the west. The gradient 

 produced by the vertical current has its maximum value at the 



