such that no important features of the current pattern are missed, 

 the equation then becomes : 



•^■, y 



'Ax, j/ = 2j {u/^y-v^x) 



•fo, ya 

 where u and v are the average x and y components of the velocity 

 over the distance A?/ and ls.x. 



The basic procedure is first to resolve the current vectors into 

 X and y components and then numerically integrate along the track 

 line from station to station beginning from an arbitrarily chosen 

 starting station where \\) is let equal to zero. This series of com- 

 putations will result in values of i|) for each station. 



Where the track line crosses or approaches upon itself or returns 

 to the starting point will serve as a test of the three assumptions 

 since the value of i|» must be the same. If the values do not agree, 

 then steps must be taken to bring them into accord. This may be 

 done by discarding certain questionable vectors, by assigning rela- 

 tive weights to more desirable vectors, or by apportioning the dif- 

 ference over a segment of the track line which would give the 

 best fit. 



A similar method is to divide the survey into a grid of x and y 

 lines. Each row of squares is denoted by a value of b and each 

 column of squares by a. The size of the square is dependent on 

 the interval of the stations and the scale of the chart. All the 

 components falling within each square are averaged and assumed 

 to apply at the midpoint of the square. ts.x and t^y may then be 

 equated to unity and the computations performed as before. This 

 method expedites the process and averages out random errors, but 

 may tend to smooth out true currents over a greater width than 

 they actually occupy. 



An intensive survey over a small area where the track line 

 crosses many times provides numerous instances where \\i must be 

 brought back into agreement with previously determined values. 

 To do this by trial and error may become very laborious and often 

 impossible. A method employing a statistical approach devised by 

 Pritchard ^ is herein summarized for practical application to this 

 case. This method determines the most probable value of the 

 stream function for each midpoint of a grid such as described in 

 the preceding paragraph. Values of ij>^ and \\)y for each square are 

 found by interpolation from the equations: 



(i/'Ja, M= / u^y and {yp^)a+\, 6= > i'A.r 



'y = 



x = o 



•' Pritcliard. D. W., "Streamlines from a discrete vector field," Jour. Mar. Res. Vol. VII, 

 pp. -296-303, New Haven, 1948. 



The notation used herein has been changed to avoid confusion. 



37 



