146 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



§10. Horizontal currents of air with rectilinear isobars — the 

 latitude is supposed to be constant 



When a permanent current of air flows over rectilinear isobars 

 the mass of air that flows perpendicularly to the isobars in the unit 

 of time must be constant. Expressing by <p the angle between the 

 gradient and the tangent to the trajectory then the equation of 

 continuity becomes 



v cos (/> = constant 



(1) 



Decomposing the five forces (see §8) in the directions of the 

 tangent and the normal we shall have 



- G cos <p = k v + v — 

 o ds 



u v 2, 



-G sin 6 = 2 a) v sin 6 -\- 



R 



(2) 

 (3) 



2 ojy vJW, Q+ -£ 



FIG 4 



Differentiating equation (1) we have, 



d v = tan (J/ d </> 

 and introducing the value of the radius of curvature 



1 <f<p 



R = ~ ~ds 



we shall have 



fl d (/> 



- G cos 6 = v (k + v tan d> , 

 p T as 



P- 



G sin </» = v (2 co sin 8 



d</> 



d s 



(4) 

 (5) 



