ANALYSIS OF OBSERVATIONS 
HARMONIC CONSTANTS 
142. In the preceding discussion it has been shown that under the 
equilibrium theory the height of a theoretical tide at any place can be 
expressed mathematically by the sum of a number of harmonic terms 
involving certain astronomical data and the location of the place. 
It has also been pointed out that for obvious reasons the actual tide 
of nature does not conform to the theoretical equilibrium tide. How- 
ever, the tide of nature can be conceived as being composed of the 
sum of a number of harmonic constituents having the same periods 
as those found in the tide-producing force. Although the complexity 
of the tidal movement is too great to permit a theoretical computation 
‘based upon astronomical conditions only, it is possible through the 
analysis of observational data at any place to obtain certain constants 
which can be introduced into the theoretical formulas and thus adapt 
them for the computation of the tide for any desired time. 
143. In the formulas obtained for the height of the equilibrium 
tide each constituent term consists of the product of a coefficient by 
the cosine of an argument. For corresponding formulas expressing 
the actual height of the tide at any place, the entire theoretical coeffi- 
cient including the latitude factor and the common general coefficient 
is replaced by a coefficient determined from an analysis of observa- 
tional data for the station. This tidal coefficient, which is known as 
the amplitude of the constituent, is assumed to be subject to the same 
variations arising from changes in the longitude of the moon’s node 
as the coefficient of the corresponding term in the equilibrium tide. 
The amplitude pertaining to any particular year is usually designated 
by the symbol R while its mean value for an entire node period is 
represented by the symbol H. Amplitudes derived directly from an 
analysis of a limited series of observations must be multiplied by the 
reduction factor F (par. 78) to obtain the mean amplitudes of the 
harmonic constants. For the prediction of tides, the mean ampli- 
tudes must be multiplied by the node factor f (par. 77) to obtain the 
amplitudes pertaining to the year for which the predictions are to 
be made. 
144. The phases of the constituents of the actual tide do not in 
general coincide with the phases of the corresponding constituents 
of the equilibrium tide but there may be lags varying from 0 to 360°. 
The interval between the high water phase of an equilibrium con- 
stituent and the following high water of the corresponding constituent 
in the actual tide is known as the phase lag or epoch of the constituent 
and is represented by the symbol « (kappa) which is expressed in 
angular measure. The amplitudes and epochs together are called 
harmonic constants and are the quantities sought in the harmonic 
analysis of tides. Each locality has a separate set of harmonic con- 
stants which can be derived only from observational data but which 
remain the same over a long period of time provided there are no 
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