ON TIDES. 301 
The upper part of the table gives the amplitudes in feet of the contributions to %, 
while the lower part gives the coefficients of the sine terms contributing to sin of for 
determining the time of High Water. Since ot is small for High Water then approxi- 
mately 1 minute in time is represented by -01 in sin ot. | We can draw the following 
conclusions from this table, supplementary to those given in 1921 ;— 
1.—The use of M, and M, as sole representatives of C, and , is entirely inadequate ; 
for 
(1) at spring tides C, and C, are thereby under-estimated in amplitude to the 
extent of 0-47 ft. and 0-28 ft. respectively, while at neap tides C, is over- 
estimated in amplitude to the extent of 0-15 ft. ; 
(2) the time of H.W cannot be given accurately at spring tides, the error being 
about 10 minutes, and if navigators use interpolation methods for heights 
at times other than H.W., the error resulting from this 10 minutes may 
mean nearly a foot at half tide. 
I1.—The use of the partial tides C, to €, alone, evenif these are correctly represented, 
cannot give accurate representation of spring tides; for 
(1) the slow convergence of the sequence of amplitudes of G,, C,, C,, at springs 
indicates a possible error of 0:3 ft., and this expectation is confirmed by 
tests on Liverpool tide records. 
(2) the slow convergence of the amplitudes of the contributions to sin ot also 
show that C,, and ©. cannot be neglected even if we desire to predict 
only H.W. times and heights. 
IiI.—The large number of constituents required by the harmonic method to express 
at all adequately even the partial tide C, and the necessity for partial tides of higher 
order, render the harmonic method unsuitable for the adequate representation of the 
shallow water effects. It is necessary, therefore, to consider alternative methods. 
One method which avoids the use of constituents, but which deals with partial tides, 
is that used in the Report for 1921, where the tide is dealt with as a whole. This method 
uses the forms given in (1) but the calculations become very intricate, and experience 
on Liverpool records leads to the conclusion that the use of partial tides is 
unsatisfactory. 
The formula (2) for the time of H.W. shows, however, that ¢ is essentially a function 
only of Rando, and ascis practically constant for the semi-diurnal tide we may consider 
fas a function of R alone. Similarly the height of H.W. is a function only of R, and 
consequently a simple table is possible giving the necessary corrections to the time 
and height of the H.W. of C, alone to give the compound H.W. data. 
It is necessary to state, however, that the form of (1) is based upon theoretical work 
on non-reflected waves in a canal of infinite length, and some care might have to be 
exercised on dealing with actual tides. At the worst, however, it might only be necessary 
to take into account the rate of increase of R. A further word of caution needs to be 
given, for friction will give sixth-diurnal tides whose amplitudes vary as R? and not 
as R* (see Appendix) ; on this point the general principle, however, remains true, that 
the shallow water effect is essentially a function of the range of tide. 
Further, the shape of the tide curve is also a function of the range of tide, and if 
hourly ordinates are required this principle can be used. 
The work required for the construction of these tables is comparatively small ; 
the tide curves should be grouped according to range and the average shape determined 
as a function of the time, measured from H.W. in each case. Analyses of the resulting 
curves by the usual methods with the appropriate period for each value of R will give 
the semi-diurnal part, and thence the tables required are easily constructed. 
Though there are difficulties yet to be overcome in the application of this method, 
e€specially when the diurnal tide is large, yet it is suggested that it offers some hope of 
solution of this difficult problem. 
Revised Harmonic Constants for Newlyn. 
6. The analysis explained in the 1921 Report has been applied to the residues from 
the whole of the year 1918 at Newlyn, and the following table of harmonic constants 
replaces that given in the 1921 Report. An error of sign with f” in the formula for B, 
_ of §17 has been found, and consequently the exposition given later in that paragraph 
_is only correct for f’=0. In dealing with the residues and with N=30 the effect of f” 
is entirely negligible, and the results of analyses are unaffected by this error. 
