[Illustration: FIG. 3.--Section of House Clock.]
The general construction of the going part of all clocks, except large
or turret clocks, is substantially the same, and fig. 3 is a section of
any ordinary house clock. B is the barrel with the cord coiled round it,
generally 16 times for the 8 days; the barrel is fixed to its arbor K,
which is prolonged into the winding square coming up to the face or dial
of the clock; the dial is here shown as fixed either by small screws x,
or by a socket and pin z, to the prolonged pillars p, p, which (4 or 5
in number) connect the plates or frame of the clock together, though the
dial is commonly set on to the front plate by another set of pillars of
its own. The great wheel G rides on the arbor, and is connected with the
barrel by the ratchet R, the action of which is shown more fully in fig.
25. The intermediate wheel r in this drawing is for a purpose which will
be described hereafter, and for the present it may be considered as
omitted, and the click of the ratchet R as fixed to the great wheel. The
great wheel drives the pinion c which is called the centre pinion, on
the arbor of the _centre wheel_ C, which goes through to the dial, and
carries the long, or minute-hand; this wheel always turns in an hour,
and the great wheel generally in 12 hours, by having 12 times as many
teeth as the centre pinion. The centre wheel drives the "second wheel" D
by its pinion d, and that again drives the scape-wheel E by its pinion
e. If the pinions d and e have each 8 teeth or _leaves_ (as the teeth of
pinions are usually called), C will have 64 teeth and D 60, in a clock
of which the scape-wheel turns in a minute, so that the seconds hand may
be set on its arbor prolonged to the dial. A represents the pallets of
the escapement, which will be described presently, and their arbor a
goes through a large hole in the back plate near F, and its back pivot
turns in a cock OFQ screwed on to the back plate. From the pallet arbor
at F descends the _crutch_ Ff, ending in the _fork_ f, which embraces
the pendulum P, so that as the pendulum vibrates, the crutch and the
pallets necessarily vibrate with it. The pendulum is hung by a thin
spring S from the cock Q, so that the bending point of the spring may be
just opposite the end of the pallet arbor, and the edge of the spring as
close to the end of that arbor as possible.
We may now go to the front (or left hand) of the clock, and describe
the dial or "motion-work." The minute hand fits on to a squared end of a
brass socket, which is fixed to the wheel M, and fits close, but not
tight, on the prolonged arbor of the centre wheel. Behind this wheel is
a bent spring which is (or ought to be) set on the same arbor with a
square hole (not a round one as it sometimes is) in the middle, so that
it must turn with the arbor; the wheel is pressed up against this
spring, and kept there, by a cap and a small pin through the end of the
arbor. The consequence is, that there is friction enough between the
spring and the wheel to carry the hand round, but not enough to resist a
moderate push with the finger for the purpose of altering the time
indicated. This wheel M, which is sometimes called the minute-wheel, but
is better called the _hour-wheel_ as it turns in an hour, drives another
wheel N, of the same number of teeth, which has a pinion attached to it;
and that pinion drives the _twelve-hour wheel_ H, which is also attached
to a large socket or pipe carrying the hour hand, and riding on the
former socket, or rather (in order to relieve the centre arbor of that
extra weight) on an intermediate socket fixed to the _bridge_ L, which
is screwed to the front plate over the hour-wheel M. The weight W, which
drives the train and gives the impulse to the pendulum through the
escapement, is generally hung by a catgut line passing through a pulley
attached to the weight, the other end of the cord being tied to some
convenient place in the clock frame or _seat-board_, to which it is
fixed by screws through the lower pillars.
[Illustration: FIG. 4.]
_Pendulum._--Suppose that we have a body P (fig. 4) at rest, and that it
is material, that is to say, has "mass." And for simplicity let us
consider it a ball of some heavy matter. Let it be free to move
horizontally, but attached to a fixed point A by means of a spring. As
it can only move horizontally and not fall, the earth's gravity will be
unable to impart any motion to it. Now it is a law first discovered by
Robert Hooke (1635-1703) that if any elastic spring be pulled by a
force, then, within its elastic limits, the amount by which it will be
extended is proportional to the force. Hence then, if a body is pulled
out against a spring, the restitutional force is proportional to the
displacement. If the body be released it will tend to move back to its
initial position with an acceleration proportioned to its mass and to
its distance from rest. A body thus circumstanced moves with harmonic
motion, vibrating like a stretched piano string, and the peculiarity of
its motion is that it is isochronous. That is to say, the time of
returning to its initial position is the same, whether it makes a large
movement at a high velocity under a strong restitutional force, or a
small movement at a lower velocity under a smaller restitutional force
(see MECHANICS). In consequence of this fact the balance wheel of a
watch is isochronous or nearly so, notwithstanding variations in the
amplitude of its vibrations. It is like a piano string which sounds the
same note, although the sound dies away as the amplitude of its
vibrations diminishes.
[Illustration: FIG. 5.]
A pendulum is isochronous for similar reasons. If the bob be drawn aside
from D to C (fig. 5), then the restitutional force tending to bring it
back to rest is approximately the force which gravitation would exert
along the tangent CA, i.e.
BC displacement BC
g cos ACW = g -- = g ------------------.
OC length of pendulum
Since g is constant, and the length of the pendulum does not vary, it
follows that when a pendulum is drawn aside through a small arc the
force tending to bring it back to rest is proportional to the
displacement (approximately). Thus the pendulum bob under the influence
of gravity, if the arc of swing is small, acts as though instead of
being acted on by gravity it was acted on by a spring tending to drag it
towards D, and therefore is isochronous. The qualification "If the arc
of swing is small" is introduced because, as was discovered by
Christiaan Huygens, the arc of vibration of a truly isochronous pendulum
should not be a circle with centre O, but a cycloid DM, generated by
the rolling of a circle with diameter DQ = 1/2OD, upon a straight line QM.
However, for a short distance near the bottom, the circle so nearly
coincides with the cycloid that a pendulum swinging in the usual
circular path is, for small arcs, isochronous for practical purposes.
[Illustration: FIG. 6.]
The formula representing the time of oscillation of a pendulum, in a
circular arc, is thus found:--Let OB (fig. 6) be the pendulum, B be
the position from which the bob is let go, and P be its position at
some period during its swing. Put FC = h, and MC = x, and OB = l. Now
when a body is allowed to move under the force of gravity in any path
from a height h, the velocity it attains is the same as a body would
attain falling freely vertically through the distance h. Whence if v
be the velocity of the bob at P, v = sqrt(2gFM) = sqrt(2g(h - x)). Let
Pp = ds, and the vertical distance of p below P = dx, then Pp =
velocity at P X dt; that is, dt = ds/v.
ds l l
Also -- = -- = ---------------,
dx MP sqrt(x(2l - x))
ds ldx 1
whence dt = -- = --------------- . ---------------
v sqrt(x(2l - x)) sqrt(2g(h - x))
1 / l dx 1
= --- / --- . -------------- . ----------------
2 \/ g sqrt(x(p - x)) sqrt(1 - (x/2l))