136 



274. The computation of the corrections is completed in the follow- 

 ing tabulation. 



Corrections 



The residuals from column (12), divided by 6=0.0746 are entered 

 in column (13). The divisor, l-^2Fvlb, of equation (174) is derived 

 from the numerical value of v, column (2) and of F, column (8), and 

 entered in column (14). Since an initial value of 5o is not loiown, 

 the computation of 8 in columns (15) and (16) is started with an 

 initial correction of zero at hour. At 0.5 horn-, 6o + -R/6 = + .13 = 

 .13. Applying the di\'isor, column (14) the first determination of 5 

 at 0.5 hour is 0.04. At 1.0 hour 5o+i?./6 = 0.04-0.13 = — 0.09; and 8 

 B.t 1.0 hour is —0.03. A continuation of the process gives 5=0.04 

 ■at 12 hours. With this initial value the computation is repeated in 

 -columns (17) and (18) until, at 1 hour, the value of 8 becomes that 

 previously found. The adjusted velocities are then found, in column 

 (19) by applying the final values of 8 to the velocities in column (2). 

 'The velocities, before and after this final adjustment, are shown in 

 figure 43. 



275. Discussion. — ^The final corrections, 8, developed in the pre- 

 ceding example, are so small that the corrected velocities do not differ 

 substantially from those used in their determination, and a recompu- 

 tation is unnecessary. Since the surface head assumed in their 

 derivation has a simple harmonic fluctuation, these corrections are 

 due only to the variation of r and C with the rise and fall of the tide. 

 Such corrections depend upon the relative timing of the tide and cur- 

 rent and on the relation between the tidal range and channel depth, 

 For a given tidal range and channel depth they are the greatest when, 



