HARMONIC ANALYSIS AND PREDICTION OF TIDES ia) | 
stituent 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 uncorrected epoch is the same 
for tide and current. For convenience the zetas (¢) rather than the 
kappas 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 uncer- 
tainty in the determination of epochs of constituents of very small 
amplitudes. 
336. 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 ma- 
terially 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 prepared for the summation of these observations. Obser- 
vations taken on the exact hour are tabulated in form 362 as usual, 
while observations on the half-hour are offset to the right on the 
intermediate lines. As the series of observations under consideration 
are short, provisions have been made for obtaining only the diurnal 
constituents K, and O,; the semidiurnal constituents Mo, 8;, and N2; 
and the higher harmonics of M. 
337. For the diurnal constituents, the special stencils provide for 
the same distribution, 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 obtained and entered in form 
194 and all subsequent computations are the same as those based 
upon the use of the standard stencils. 
338. For the semidiurnal constituents M2, S,, and No», the semi- 
diurnal period is divided into 24 parts. Special stencils for the con- 
stituents 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 forenoon observations of corresponding hours. ‘Thus, 
the noon observations will be included with those taken at midnight, 
and the observations at 12:30 p. m. with those taken at 0:30 a. m. 
339. 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 semi- 
diurnal constituents will be made in the spaces originally designed 
for the diurnal constituents. The computations for all higher har- 
monics of even subscripts may be carried out in the same form using 
the spaces originally designed for the harmonics with subscripts one- 
half as great. In this adaptation of the form no provision is made for 
the computation of a harmonic of odd subscript which is here of rela- 
