HARMONIC ANALYSIS AND PREDICTION OF TIDES 119 
representation of such currents it is, therefore, necessary to have two 
series—one for the north and the other for the east component. 
332. For the analysis of either type of current the original hourly 
velocities or the resolved hourly velocities are tabulated in the same 
form used for the hourly heights of the tide. To avoid the incon- 
venience of negative readings in this tabulation, a constant, such as 
3 knots, is added to all velocities. These hourly velocities are then 
summed with the same stencils that are used for the tides, and the 
hourly mean velocities are analyzed in the same manner as the hourly 
heights of the tide. The same forms are used for the currents, with 
the necessary modifications in the headings. The rotary currents 
will be represented by a double set of constants, one for the north 
components and the other for the east components. 
333. For a 29-day series of observations, it is recommended that 
the analysis be made for the M series, the S series, and for No, 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 
magnitude than they are in the tides. From theoretical considera- 
tions it may also be shown that the magnitude of the diurnal constit- 
uents 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 move- 
ment, the actual relation between the various constituents as deter- 
mined by the analysis is subject to wide variations. The constituent 
S,, which is usually negligible in the tides, may be found to be of ap- 
preciable 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. 
334. Form 723 (fig. 20) provides for the determination of harmonic 
constants from a series of current observations by comparison with 
corresponding constants from a tidal series covering the same period 
of time. This comparison 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 meteor- 
ological 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 ¢’ for each constituent. The harmonics M,, Mz, and Mg 
are to be obtained for the current series, but may be omitted in the 
tidal series. 
335. Enter in Form 723 the accepted H and « of the principal tidal 
constituents for the reference station and also the values of R’ and ¢’ 
obtained from the analyses of the simultaneous series of tides and 
currents. The necessary calculations in the form are self-explana- 
tory. The corrected velocity amplitude of each current constituent 
is obtaied by a ratio on the assumption that for each constituent the 
relation of the corrected amplitude to the uncorrected amplitude is 
the same for both tide and current. The ratio derived for the con- 
