On substituting (34) into (33) we have 



r \0x oy " oy ox] " r cur 



and with M = - — , 



- curl, B . V |f - o„l,T - S n(^|B-|f|g) 



Only, if D = constant 



+ curl, R = - V 4J + curl T , (36) 



z oy z 



and the equation expresses a balance between the curl of internal 

 stresses (friction), and the planetary vorticity and the curl of 

 the wind stress. The differential equation was used in this form 

 in the preceding papers on the wind driven circulation. 



b) The last term on the right hand side of (35) can be inter- 

 preted as the z-component of a vector product of two vectors, 

 grad D = a and grad S = b . If 6 is the angle between the 

 vectors a and b , then 



d£_ dD d£ dD . _, 



oT^ 57 " ay e£ - ab 



-> -» 



would mean that a H b , and the lines of equal dynamic height of 



the sea surface (relative to a level surface) are parallel to the 



lines of equal depth D. 



Similarly, the term 



i£o)D $V dD _ Q 

 dx dy ' dy dx ' 



would express the requirement that the lines of equal D and the 



isopycnals p are parallel. Approximately 35 years ago, Bj. Helland- 



43 



>y oy sln6 = ° 



