58 MANUAL OF CURRENT OBSERVATIONS 
modified phases: flood strength, slack before flood increased by 3.10 hours, slack after 
flood decreased by 3.10 hours, and ebb strength increased or decreased by 6.21 hours. 
Before taking the average the several items must be made comparable by the addition 
or rejection of the tidal period 12.42 hours when necessary. 
153. Reference to currents.—When the current phases at the subordinate station 
are referred to the corresponding phases at a current reference station, the latter may be 
tabulated in Form 451 below the tabulations for the subordinate station as illustrated 
in Figure 30. Differences are obtained between the times of the observed currents at 
the subordinate station and the times of the corresponding currents at the reference 
station, the difference being considered as positive or negative according to whether 
the current at the subordinate station is later or earlier than at the reference station. 
The differences are then averaged for each phase of the current.. Next, the Greenwich 
intervals for the several current phases at the subordinate station are obtained by apply- 
ing the average differences to the corresponding Greenwich intervals for the reference 
station. The mean current hour may then be obtained in the manner described in the 
preceding paragraph. 
154. A double flood or double ebb may be referred to either tides or currents. In 
the example in Figure 29, the phases of the flood period are referred to low water and the 
phases of the ebb period to high water at the reference station. The average difference 
for each group is obtained and applied to the Greenwich interval of the tide phase 
to which it is referred. 
155. Velocity reduction factor.—The velocity of the observed tidal current may be 
reduced to a mean value by the application of a factor derived from the tidal range or 
the current velocity at the reference station. When the reference is to a tide station, 
the reduction factor is obtained by dividing the best determined mean range of tide 
at the reference station by the range for the period covered by the observations at the 
current station. If the current at the subordinate station is chiefly hydraulic, the 
square root of the factor as computed above is taken as the reduction factor. When a 
current reference station is used, the reduction factor is obtained by dividing the best 
determined average velocity at the reference station by the average velocity for the 
period covered by the observations. 
156. The reduction factor obtained by either of the above methods is to be applied 
only to the tidal portion of the observed current. In simple cases the tidal current is 
obtained by taking the half sum of the average observed flood and ebb velocities at 
their strengths, and the nontidal part of the current is obtained by taking the half 
difference of these velocities. After the reduction factor has been applied to the tidal 
current it is recombined with the nontidal part to obtain the corrected flood and ebb 
velocities, which are usually indicated in the reduction forms by the letter “ec.” It 
will be noted that the nontidal current will be in the flood or ebb direction according to 
whether the observed flood or ebb velocity is the stronger. In recombining the non- 
tidal current with the tidal current it will be added for the direction in which it is acting 
and substracted for the opposite direction. 
157. A more general method of applying the reduction factor, which is applicable 
when the observations include double flood or double ebb strengths, is described as 
follows: Considering all velocities in the flood direction as positive and all velocities ' 
in the ebb direction as negative, find the nontidal current by taking the algebraic 
mean of these velocities. The sign of the result will indicate whether this current is in 
the flood or ebb direction. Subtract algebraically the nontidal current from each of 
the observed velocities and multiply the remainders by the reduction factor. Restore 
