OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 1 1 3 



to the isobaric surface p = p2, and finally along this surface back to the 

 starting point (fig. 27). Along the isobaric surfaces, dp = 0, and 

 therefore 



N==-ladp=[{-f;;adp\ + {-£adp);\ 



= 10 (D^ - Ds). (VI, 30) 



If circulation relative to the earth is considered, the deflecting force 

 has to be taken into account. Accord- q p = p ^ 



ing to Bjerknes, this is represented by 



= - i^^v- 



2 122, (VI, 31) 



where S represents the projection on 

 the equatorial plane of the area that 

 is enclosed by the curve c, and 12, as 

 before, means the angular velocity of 

 rotation of the earth. 



Consider the same curve as before, 

 and assume that the upper line, p = p\, 

 moves at a velocity Vi at right angles 

 to the line A-B, whereas the lower 

 line, p = p2, moves at a velocity V2, 

 and let the distance A-B be called 

 L. Then the time change of the projection on the equator plane is 



p = p. 



Fig. 27. Location in the pressure 

 field of a curve along which the time 

 change of circulation is examined. 



Vi 



V2 



L sin (p 



Assume now that the circulation is constant (C = 0). It then 

 follows that the velocity difference z;i — ?;2 must be expressed by the 

 equation 



Da - Db 



Vi 



V2 = 10 



XL 



(VI, 32) 



This is the equation for computing ''relative" currents which Helland- 

 Hansen derived from the theorem of circulation, assuming stationary 

 conditions and neglecting friction, and which can be arrived at on the 

 basis of more elementary consideration (VI, 17).* 



The complete theorem of circulation contains a great deal more than 

 the simple statement expressed by equation (VI, 32), but so far it has 

 not been possible to make greater use in oceanography of Bjerknes' 



* In the literature, some confusion exists as to the signs in these equations. The 

 above signs are consistent with the coordinates used. The "relative" velocity is 

 positive — that is, the "relative" current is directed away from the reader if A lies to 

 the right of B and if Da is greater than Db. 



