iform. The answer is that the arc of vibration not
being a true cycloid, as it should be if true isochronism is to be
secured, but being the arc of a circle, any change of amplitude of
vibration produces a change of time in the swing given by the formula
(3/2)(a^2 - b^2) = loss in seconds per day, where a and b are the
semi-arcs of vibration estimated in degrees. Thus 10' increase of arc
in a swing of 4 deg., that is to say, .1 in. increase of arc in a total
arc of 2-1/2 in., produces an error of about a second a day. Now cold
weather, by making the oil thick and thus clogging the wheels, will
easily produce such a change of arc; dust will also make a change even
though the clock weight, acted on by gravity, still exerts a uniform
pull. Besides, if the clock has work to do of a varying amount--as
when the hands of a turret clock are acted on by a heavy wind pressure
tending sometimes to retard them, sometimes to drive them on--then it
is clear that the impulses given by the scape-wheel to the pendulum
may be very unequal, and that the arc of vibration of the pendulum may
thus be seriously affected and its isochronism disturbed.

Remontoire.

To abolish errors arising from the changes in the force driving the
escapement, what is known as the "remontoire" system was adopted. It
first came into use for watches, which was perhaps natural, seeing
that the driving force of a watch is not a uniform weight like that of
a clock, but depends on springs, which are far less trustworthy. The
idea of a remontoire is to disconnect the escapement from the clock
train, and to give the escapement a driving power of its own, acting
as directly as possible on the pallets without the intervention of a
clock-train containing many wheels. The escapement is thus as it were
made into a separate clock, which of course needs repeated winding,
and this winding is effected by the clock-train. From this it results
that variations in the force transmitted by the clock-train merely
affect the speed at which the "rewinding" of the escapement is
effected, but do not affect the force exerted by the driving power of
the escapement.

Train remontoires.

There are several modes of carrying out this plan. The first of them
is simply to provide the scape-wheel with a weight or spring of its
own, which spring is wound up by the clock-train as often as it runs
down. Contrivanc