114 OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 



elegant formulation of one of the fundamental laws governing the motion 

 of nonhomogeneous fluids. 



Transport by Currents. The volume transport by horizontal 

 currents has the components 



T^ = j^ v^ dz and Ty = f^ Vy dz, (VI, 33) 



and the mass transport has the components 



M^ = f pv^dz and ^y "= L P ^y ^^y (^I' ^^) 



where d is the depth to the bottom. 



The actual volume transport can be computed only if the actual 

 velocities are known, but the volume transport by ''relative" currents 

 can be derived from the distribution of mass. By means of equations 

 (VI, 17) and (VI, 23) one obtains 



^^ ^ X Jo ^^^ "^^ ^^ = - T Jo ^ ^'' (^^' ^^^ 



Introducing the equation for AD (VI, 23) and writing, in accordance with 

 Jakhelln, 



one obtains 



10 aQ , ^ 10 aQ 



— ^— and Ty = r- ^- 



\ dy \ dx 



r, = i^Z^ and r„=--^^- (VI, 36) 



The quantit}^ Q is easil}^ computed, because AD is always determined 

 if velocities are to be represented. 



In practice the numbers that represent the geometric depths are also 

 considered as representing the pressures in decibars (p. 102). When 

 computing Q the integration is therefore carried to the pressure p decibars 

 and the depth d meters, which are both expressed by the same number, 

 but a small systematic error is thereby introduced. Jakhelln has 

 examined this error and has shown that the customary procedure leads to 

 Q values that are systematically 1 per cent too small, but this error is 

 negligible. 



Curves of equal values of Q can be drawn on a chart, and these curves 

 will bear the same relation to the ''relative" volume transport that the 

 curves of AD bear to the "relative" velocity, provided that the deri- 

 vations of Q are taken as positive in the direction of decrease. Therefore 

 the direction of the volume transport above the depth to which the 

 Q values are referred will be parallel to the Q lines, and numerical values 

 will be proportional to the gradient of the Q lines. The factor of pro- 

 portionality will depend upon the latitude, however, and, between two 

 parallel Q lines that indicate transport to the north, the transport will 



