>2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 I 



For, by differentiating (12) we have 



d (tang 4>) 2 co d S 2 co X 



dx k + 2 c dx k + 2 c 



Substituting this value and the value of U cos <p from equation (2) 

 we have 



2coX 2co 



Xc + Xcx = Xc + c8 = (k + 2 c) 6 - (k + c) • (6 - e) 



h c = (k + c) e 

 Whence 



e = 



k + c 



By eliminating from equations (3) and (4) we find the gradient 

 dx 



G = ~ • U cos 4> (k + c + 2 co 6 tang 0) . . . . (14) 



The radius of curvature of the trajectory is found by the equation 



ds dx 



R = = 



cfy cos ^ (/ ^ 



From equation (12) we deduce 



dil> 2 co dd 2coX 



cos 2 (p d x k + 2 c dx k + 2 c 

 and we thus have 



R= k + 2c . _L_ (15) 



2w ^ cos 3 <f> 



It is evident that at the point of maximum velocity c changes its 

 sign, and that in nature at this point the equation c = o must be 

 true. 



In a system of parallels we have two horizontal currents, one along 

 the surface of the earth and the other in the upper strata, For the 

 last we can employ the same equations as for the first, but for want 



