her, so the tidal wave consists of a number of distinct
undulations superposed. Of these the ordinary lunar tide and the
ordinary solar tide are the two principal; but there are also minor
undulations, harmonics, so to speak, some originating from the moon,
some originating from the sun, and some from both bodies acting in
concert.

In the study of sound we can employ an acoustic apparatus for the
purpose of decomposing any proposed note, and finding not only the
main undulation itself, but the several superposed harmonics which
give to the note its timbre. So also we can analyze the undulation of
the tide, and show the component parts. The decomposition is effected
by the process known as harmonic analysis. The principle of the
method may be very simply described. Let us fix our attention on any
particular "tide," for so the various elements are denoted. We can
always determine beforehand, with as much accuracy as we may require,
what the period of that tide will be. For instance, the period of the
lunar semi-diurnal tide will of course be half the average time
occupied by the moon to travel round from the meridian of any place
until it regains the same meridian; the period of the lunar diurnal
tide will be double as great; and there are fortnightly tides, and
others of periods still greater. The essential point to notice is,
that the periods of these tides are given by purely astronomical
considerations from the periods of the motions theory, and do not
depend upon the actual observations.

We measure off on the curve the height of the tide at intervals of an
hour. The larger the number of such measures that are available the
better; but even if there be only three hundred and sixty or seven
hundred and twenty consecutive hours, then, as shown by Professor G.
H. Darwin in the _Admiralty Manual_ already referred to, it will
still be possible to obtain a very competent knowledge of the tides in
the particular port where the gauge has been placed.

The art (for such indeed it may be described) of harmonic analysis
consists in deducing from the hourly observations the facts with
regard to each of the constituent tides. This art has been carried to
such perfection, that it has been reduced to a very simple series of
arithmetical operations. Indeed it has now been found possible to call
in the aid of ingenious mechanism, by which the labours of computation
are entirely superseded. The pointer of the harmonic analyzer has