222. REPORTS ON THE STATE OF SCIENCE, ETC. 
phenomena of springs and neaps are here rather complicated, but the general 
principle still holds. In the month of January there is a well-marked 
phenomenon where the springs recur at intervals of two or three days; that is, 
there is an indication of the presence of a non-Darwinian constituent. 
The residue for the month of April is very much affected by the unknown 
semi-diurnal constituents. 
A rather crude form of periodogram has been constructed from the first six 
months’ residues at Newlyn, but it suffices to show that the constituents present 
in the residue are quite distinct from those in Darwin’s schedules; it also shows 
that all the Darwinian constituents have been effectively removed. The data, 
however, are not sufficient for definitive conclusions to be drawn as to the 
nature of the residue. 
§ 9. Errors resulting from the inadequate treatment of shallow-water 
effects.—The following table gives a list of the constituents that ought to be 
taken into account in the prediction of tides for Liverpool, in order to give a 
satisfactory representation of the shallow-water effects. The amplitudes are 
approximate only. 
TABLE OF SHALLOW-WATER CONSTITUENTS AT LIVERPOOL. 
Inferred from Harmonic Constants for My, M, and Mg. 
3-Diurnal 4-Diurnal $-Diurnal 
Origin Amplitude | Origin Amplitude Origin Amplitude 
M,.M, [67] ft. || M,.M,M, [-20] M.M.M2.M, [:07] | 
8, [42] S, 19 So ‘08 
Ne "26 | No ‘ll No 05 
Ke 13 Ke 06 Ke 03 
My 07 | vy -03 ete. 
L, 07 etc. 
Ts 03 
oN 03 || My.S.S. 06 M,S..MS. 03 
2 “03 | Ne “04 MLN» “03 
a Ky 02 MK. 02 
etc. 
82.8.2 ‘07 Sy.8.8 [01] 
No “08 | Ng ‘01 i 
Ky 04 = | 
etc. ; 
Those constituents whose amplitudes are enclosed in square brackets are Pi 
the constituents usually analysed for. The residual quarter-diurnal tide, if 
all are neglected save M,.M, and M,§,, will frequently exceed six inches, 4 
and the differences between observations and predictions also serve to justify 4 
this conclusion. For Newlyn the error will not be so large, but most British 
ports are situated in estuaries where the shallow-water effect will be quite 
comparable with that at Liverpool. Hence we base upon these facts the 
statement (3) of §1. : 
It may be mentioned that the predicting machines haye not been built to 
cater for the constituents mentioned above, 
