merely to be traced over the curve which the tide-gauge has drawn, and
it is the function of the machine to decompose the composite
undulation into its parts, and to exhibit the several constituent
tides whose confluence gives the total result.

As if nothing should be left to complete the perfection of a process
which, both from its theoretical and its practical sides, is of such
importance, a machine for predicting tides has been designed,
constructed, and is now in ordinary use. When by the aid of the
harmonic analysis the effectiveness of the several constituent tides
affecting a port have become fully determined, it is of course
possible to predict the tides for that port. Each "tide" is a simple
periodic rise and fall, and we can compute for any future time the
height of each were it acting alone. These heights can all be added
together, and thus the height of the water is obtained. In this way a
tide-table is formed, and such a table when complete will express not
alone the hours and heights of high water on every day, but the height
of the water at any intervening hour.

The computations necessary for this purpose are no doubt simple, so
far as their principle is concerned; but they are exceedingly tedious,
and any process must be welcomed which affords mitigation of a task so
laborious. The entire theory of the tides owes much to Sir William
Thomson in the methods of observation and in the methods of reduction.
He has now completed the practical parts of the subject by inventing
and constructing the famous tide-predicting engine.

The principle of this engine is comparatively simple. There is a chain
which at one end is fixed, and at the other end carries the pencil
which is pressed against the revolving drum on which the prediction is
to be inscribed. Between its two ends the chain passes up and down
over pulleys. Each pulley corresponds to one of the "tides," and there
are about a dozen altogether, some of which exercise but little
effect. Of course if the centres of the pulleys were all fixed the pen
could not move, but the centre of each pulley describes a circle with
a radius proportional to the amplitude of the corresponding tide, and
in a time proportional to the period of that tide. When these pulleys
are all set so as to start at the proper phases, the motion is
produced by turning round a handle which makes the drum rotate, and
sets all the pulleys in motion. The tide curve is thus rapidly drawn