244 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



equator where 8 = o and it disappears at the poles where 8 = 90 . 

 For a mean value of p we have 



G — 0.16 cos 8 w 



Let us consider an inclined current and seek the conditions under 

 which the horizontal gradient produced by the vertical velocity 

 is zero. Suppose that the inclined current lies in the plane Z X. 

 We assume the component v = o. 



By substituting 



dp = dp = Q 



dx dy 



the equations of motion take the following form: 



no a ■ du dw 



= — 2 co cos 8 sin a w — u — — w — . . . . (2) 



dx dz 

 = 2 co sin 8 u — 2 to cos 8 cos aw (3) 



1 dp . . dw dw ... 



. — = — g + 2 co cos 8 sin a u — u — — w — . . (4) 

 p dz dx dz 



From equation (3) we obtain 



= cotg 8 cos a (5) 



w 



The horizontal gradient being zero, it is necessary that p be a func- 

 tion of z only and consequently from equation (4) we shall obtain 



du = dw = 



Eliminating u between the equations (2) and (5) we shall find 



dw 



— = — 2 co sin 6 tang a (6) 



dz 



Supposing that the density p is a function of z only, the equation of 

 continuity is put under the form 



p w = constant 



