HARMONIC ANALYSIS! AND PREDICTION OF TIDES 147 
angular changes for computing the settings for any day of the year 
may be obtained from tables 16 and 17. 
PREDICTION OF TIDAL CURRENTS 
433. Since the tidal current velocities in any locality may be 
expressed by the sum of a series of harmonic terms involving the 
same periodic constituents that are found in the tides, the tide- 
predicting machine may be used for their prediction. For the cur- 
rents, however, consideration must be given to the direction of flow, 
and in the use of the machine some particular direction must be 
assumed. At present the machine is used for the prediction of 
reversing currents in which the direction of the flood current is 
taken as positive and the maximum velocity in this direction corre- 
sponds to the high water of the predicted tide. The ebb current is 
then considered as having a negative velocity with its maximum 
corresponding to the low water of the predicted tide. Rotary cur- 
rents may be predicted by taking the north and east components 
separately but the labor of obtaining the resultant velocities and 
directions from these components would be very great without a 
machine especially designed for the purpose. Predictions can, how- 
ever, be made along the main axis of a rotary movement without 
serious difficulties. Formulas for referring the harmonic constants of 
the north and east components to any desired axis are given in Coast 
and Geodetic Survey Special Publication No. 215, Manual of Current 
Observations. 
434. The harmonic constants for the prediction of current velocities 
are derived from current observations by an analysis similar to that 
used in obtaining the harmonic constants from tide observations. In 
the current harmonic constants, however, the amplitudes are expressed 
in a unit of velocity, usually the knot, instead of the linear unit that 
is used for the tidal harmonic constants. Forms 444 and 445 for the 
computation of the settings for the tide-predicting machine are 
applicable for the current predictions and the procedure in filling out 
these forms is essentially the same as described in paragraphs 421-432 
for the tide predictions. The node factors (f) and arguments (V,+ 1) 
are the same as for the tides. The height dial, marigram gear and 
scale suitable to the current velocity can be obtained from the table 
on page 138. Instead of a sea level elevation there should be entered 
in the column of ‘“‘Remarks’’ the velocity of any permanent current 
along the axis in which the predictions are tobemade. This velocity 
should be marked plus (+) or minus (—) according to whether the 
permanent current is in the flood or ebb direction. 
435. The predicting machine is set with the current harmonic con- 
stants in the same manner as for the tidal harmonic constants. To 
take account of the permanent current the height summation wheel 
should be brought to its zero position and the height hand then set 
at a dial reading corresponding to the velocity of the permanent 
current, the hand being set to the right of the scale zero if the per- 
manent current is in the flood direction and to the left if in the ebb 
direction. The hand crank should be then turned to bring the 
height hand to its zero position and the curve-pen set at the medial 
line of the paper, this line now representing zero velocity or slack 
water. 
