23 8 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



In order to determine the angle e between the radius r and the 

 gradient, we notice that the gradient is normal to the isobar and 

 consequently 



(dp) 



Une—4 ~-±±l (14) 



rd<£> 



•m 



dp 

 dr 



Assuming that N and M are independent of the time, we shall 

 find by differentiating equation (12) 



W 



U r cos (<p — a) 



tange = 



kUr W 



+ U 2 + ■ - - U r sin (<p - a) 

 cos a r 



(15) 



Along the axis of the isobar where we have <p — a + 90 or (p = 

 a — 90 , e becomes zero. The maximum value of £ occurs for cp = a 

 and we find 



W 



tang£ m = 



kr 



(16) 



cos a 



+ U 



We conclude therefore that the angle (p between the wind and the 

 gradient has its minimum value (a — £ m ) along o b (fig. 50) at the 

 anterior limit and its maximum value (a + £ m ) in the opposite direc- 

 tion. 



