70 MANUAL OF CURRENT OBSERVATIONS 
that there shall be provided for each graph a basic Greenwich transit time scale reck- 
oned from the time of the moon’s transit over the meridian of Greenwich. Along this 
basic scale may be indicated according to the Greenwich intervals the times of the tidal 
phases. All velocities are plotted as positive regardless of direction. Information 
pertaining’ to the times, directions and velocities of the various current phases is readily 
obtainable from these graphs. For the representation of the hourly velocities and 
directions by polar coordinates see paragraph 22. 
Harmonic Reduction 
169. As tidal currents result from the same periodic forces that cause the rise and 
fall of the tide, they may be represented by similar harmonic terms, current velocities 
taking the place of tidal heights. In the harmonic analysis* of currents, however, the 
question of direction must be considered. For a reversing current, the analysis is 
applied to the movement along the axis of the stream, flood velocities being. considered 
as positive and ebb velocities as negative. For rotary currents the north and east 
components are analyzed separately. For a short series of observations the reduction 
is based upon a comparison with tidal constants from a simultaneous series of tide 
observations or predictions at a suitaple reference station, but if the current observa- 
tions cover a period of 29 days or more the analysis is carried on in the same manner 
and with the use of the same forms as employed for a tidal series. 
170. For a 29-day series of observations, it is recommended that the analysis be 
made for the M series, the S series, and for Nz, K,, and O;. For longer series additional 
constituents may be included. In the analysis of current velocities, the harmonics of 
the higher degrees such as M, and M, may be expected to be of relatively greater magni- 
tude than they are in the tides. From theoretical considerations it may also be shown 
that the magnitude of the diurnal constituents as compared with the semidiurnal 
constituents in a simple tidal oscillation is only about one-half as great in the current 
as in the tide. However, because of the complexity of the tidal and current movement, 
the actual relation between the various constituents as determined by the analysis is 
subject to wide variations. The constituent S;, which is usually negligible in the tides, 
may be found to be of appreciable magnitude in offshore currents because of the effect 
of daily periodic land and sea breezes. However, as this constituent has a speed very 
nearly the same as that of K, it can be separated from the latter only by a long series of 
observations, preferably a year or more. 
171. Harmonic comparison.—Form 723 (fig. 31) provides for the determination of 
harmonic constants from a series of current observations by comparison with corre- 
sponding constants from a tidal series covering the same period of time. This compari- 
son is to be used if the series of observations is less than 29 days and may be used for 
longer series if desired. For the purpose of this comparison the hourly predicted heights 
at the tide station are usually to be preferred to actual observations since meteorological 
irregularities appearing in observed tides do not necessarily appear in a similar manner 
in the observed currents. In this work both currents and tides for the simultaneous 
period are to be summed for constituents M, S, N, K, and O; and the analysis is then 
carried through Form 194 (Tides: Harmonic Analysis) to obtain the values of R’ and ¢’ 
*A detailed discussion of the harmonic analysis of tides and tidal currents is contained in United States Coast and Geodetic Survey 
Special Publication No. 98, Manual of the Harmonic Analysis and Prediction of Tides. 
