e of the clock is increased so that the impulse on the
pallets is greater, the velocity of the pendulum is increased. But
this very increase of the driving force causes a greater pressure of
the teeth of the scape-wheel on the rest-faces of the pallets, and
hence counteracts the increased drive of the pendulum by an increased
frictional retardation. If the clock weight be enormously increased,
the frictional retardation becomes increased relatively in a greater
proportion than the drive, so that as the weight of the clock is
increased the pendulum's time of vibration is first diminished, until
at last a neutral point is reached and finally the increased loading
of the clock weight begins to make the time of vibration increase
again. It is the neutral point which it is desirable to arrange for,
and only trial and experience can so fit the shape and size of the
pallets, scape-wheel and clock weight to one another, as to secure
that a moderate variation of the driving power neither accelerates nor
retards the motion of the pendulum, while at the same time such an arc
of vibration is secured as shall be least subject to barometric error,
and not have too great a circular error. The celebrated clockmaker B.
L. Vulliamy (1780-1854) greatly improved Graham's escapement by
careful experiment, and other makers introduced further improvements
into the shape of the scape-wheel and pallets, so that the best form
of the deadbeat escapement is now fairly well determined and is given
in books upon horology. For small clocks a little slope is given to
the rest-faces so as to diminish the friction retardation. This is
known as the half-dead escapement. The pin-wheel escapement, if
properly constructed, is also "dead," that is to say, the outward
swing of the pendulum is unfettered except by the slight friction of
the teeth against the dead faces of the pallets.

[Illustration: FIG. 11.--Riefler's Escapement.]

In order to diminish the effect of the impact of the scape-wheel on
the pallets, and of the crutch on the pendulum rod, the plan has been
tried of making the crutch into an elastic spring. In theory this of
course would not destroy the isochronism of the pendulum, for it would
only be to apply upon the pendulum a force at right angles to the rod,
and varying as the displacement. Hence any acceleration given by such
a spring would, like the action of gravity, be