22 MARION AXD GENERAL GREENE EXPEDITIONS 



The question also arises as to how closely computed velocities agree 

 with actual velocities where dynamic heights have been calculated 

 to the nearest millimeter. From our experience it is doubtful 

 whether the velocity lines on the profiles can claim a greater accuracy 

 than 1 centimeter per second or, expressed in dynamic height for the 

 mean latitude of the area investigated, this is equal to a slope of 

 about 9 dynamic millimeters in a distance of 20 miles. 



The volume of current, or the transport, through a given vertical 

 section may be found either graphically from the sum of the products 

 of cross-sectional areas and their mean velocities or by numerical 

 integration in accordance with a method described by Jakhelln 

 (1936). 



Jakhelln's method, briefly, takes advantage of the fact that in the 

 development of the equation of the volume of the current (i. e., the 

 transport), the value of the distance between two stations appearing 

 in both numerator and denominator, is eliminated. 



U=vzL (1) 



where U is the net transport ; v is the mean velocity, surface to a 

 depth, s, where the current is assumed zero. 



Further — 

 But— 



v-2= \v-dz (2) 



2-o:-L-sm<t> ^'^^ 



where E represents the anomaly of dynamic height. Substituting 

 (3) in (1), results in the above-mentioned cancelation of L and 



or exju-essed in different form — 



U=a[ fAE^dz- r^Esdz] (5) 



where A = ^ . — -• (For values of A, see Smith 1926, table VI.) 



2a> sin ^ ' ' ^ 



Since it is more convenient to deal with the values of the anomaly 

 of specific volume A^^ than the anomaly of dynamic height, aA", 

 we can from (5) express the equation in final form — 



^=^[rr^^-"^^^-xi^''»'''-'] 



(6) 



The ])ractical application of Jakhelln's method to any two sta- 

 tion's, ^1 and B, is, first, to find the station anomalies of specific 

 volume in the usual manner and then integrate the same, for each 

 station, from the assumed common motionless depth to the surface. 

 The difference between the two station integrals when divided by 

 2w sin (see table VI, Smith 1926), gives the value of the net volume 



