72 MANUAL OF CURRENT OBSERVATIONS 
for each constituent. The harmonics My, Mg, and M, are obtained for the current series, 
but may be omitted in the tidal series. 
172. Enter in Form 723 the accepted H and «x 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-explanatory. The corrected velocity amplitude of each current constituent 
is obtained 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 constituent M, is used also for the higher harmonics of M, this 
being considered more reliable than ratios determined directly from the much smaller 
amplitudes of these harmonics. The corrected epoch (x) for each current constituent 
is calculated on the assumption that the difference between the corrected and uncor- 
rected epoch is the same for tide and current. For convenience the zetas (¢) rather than 
the kappas (x) from the simultaneous observations are used in the form and a longitude 
correction, column (10), is introduced to allow for this fact. Differences in column (9) 
for the higher harmonics of M, are derived from the difference for that constituent 
because of the uncertainty in the determination of epochs of constituents of verysmall 
amplitudes. 
173. Half-hourly velocities.—Short series of current observations are frequently 
taken at half-hourly intervals. As individual observations are somewhat rough, the 
utilization of the half-hourly observations will add materially to the accuracy of the 
results obtained from an analysis. Moreover, the closer spacing of the half-hourly 
values will give a better development of the higher harmonics of M which are of greater 
relative importance in the currents than in the tides. Special stencils have been pre- 
pared for the summation of these observations. Observations taken on the exact 
hour are tabulated in Form 362c as usual, while observations on the half-hour are 
offset to the right on the intermediate lmes. As the series of observations under con- 
sideration are short, provisions have been made for obtaining only the diurnal constitu- 
ents K, and O,; the semidiurnal constituents Mo, S2, and N2; and the higher harmonics 
of M. 
174. For the diurnal constituents, the special stencils provide for the same distri- 
bution, with the inclusion of the half-hourly values, as is obtained with the standard 
stencils used for the hourly values only. Hourly means for the constituents are ob- 
tained and entered in Form 194 and all subsequent computations are the same as those 
based upon the use of the standard stencils. 
175. For the semidiurnal constituents Mo, S:, and No, the semidiurnal period is 
divided into 24 parts. Special stencils for the constituents M, and N, provide for the 
distribution of the observed half-hourly velocities into the 24 groups indicated by this 
division. No stencil is required for the constituent S., the necessary grouping being 
accomplished by combining sums for afternoon observations with those for the fore- 
noon observations of corresponding hours. Thus, the noon observations will be in- 
cluded with those taken at midnight, and the observations at 12:30 p.m. with those 
taken at 0:30 a. m. 
176. The resulting means obtained for the semidiurnal constituents by the method 
described above are in reality half-hourly means, but in adapting Form 194 for the 
analysis, these means may be entered in order in the spaces provided for the hourly 
means. Then, after doubling all subscripts in the form, the necessary computations 
may be carried out as indicated. Thus, all computations for the semidiurnal constit- 
uents will be made in the spaces originally designed for the diurnal constituents 
