A separate value of t|'„ and \[\r is thus computed for each square, 

 there being n squares in the x direction and m squares in the y 

 direction. \\i,. and i|),^ must now be composed to produce the com- 

 plete stream function for each square. Theory for this process 

 utilizes the statistical method of least squares to obtain a distribu- 

 tion of i|t which will best fit the observed data. This derivation is 

 not shown but the result is to compute constants of Aa and Bb 

 which when added respectively to i[',r and \]»y determine \p. The con- 

 stants of A (Aj, Ao, • . • . ) are computed for each horizontal row 

 (b = 1, b =z 2, . . . . ) by the formula: 



an = n a = n a = n a = n x 



and constants of B (B^, Bo, • • • • ) are computed for each vertical 

 column (a = 1, a = 2, . . • . ) by the formula : 



,b — m h = m h — m 



5=1 ^6 = 1 ^b = l / 



m 



Then the stream function may be computed from the following 

 equation : 



If the three primary assumptions are strictly true, then a value of 

 y\) obtained from either equation will be the same. In practice, 

 however, this will rarely be true and the mean is considered to be 

 the most probable value. 



Once the stream function has been determined for each square 

 or station, the current map is produced by contouring the chart 

 along lines of equal \\) in multiples of 5, 10, or 20 to suit the scale 

 of the chart. The contours or streamlines will, of course, show 

 the current direction at a particular position. The speed of the 

 current is represented by the crowding of the streamlines, and is 

 computed by dividing the interval of the streamline units by the 

 distance between the streamlines in units which were used for 

 IS.X and A?/. These units may be any convenient arbitrarily selected 

 units of length. 



Current charts utilizing the above methods have agreed rather 

 well with maps of dynamic topography made simultaneously. The 

 former reflect to a much greater degree transitory and tidal cur- 

 rents. 



It should be noted that in producing a map by directly integrat- 

 ing current components from station to station, the cumulative 

 error may reach such proportions as to produce a fictitious overall 

 picture, while smaller areas will be reasonably valid when studied 

 separately. 



38 



