We have examined the action of a body under the accelerating or
speed-quickening force due to gravity, the attractive force of which on
any body is always proportional to the mass of that body. Let us now
consider another form of acceleration.
[Illustration: FIG. 30.]
Take the case of a strip of indiarubber. If pulled it resists and tends
to spring back. The more I pull it out the harder is the pull I have
to exert. This is true of all springs. It is true of spiral springs,
whether they are pulled out or pushed in, and in each case the amount
by which the spring is pulled out or pushed in is proportional to the
pressure. This law is called Hooke’s law. It was expressed by him in
Latin, “Ut tensio, sic vis”: “As the extension, so the force.” It is
true of all elastic bodies, and it is true whether they are pulled out
or pushed in or bent aside. The common spring balance is devised on
this principle. The body to be weighed is hung on a hook suspended from
a spring. The amount by which the spring is pulled out is a measure
of the weight of the body. If you take a fishing rod and put the butt
end of it on a table and secure it by putting something heavy on the
end, then the tip will bend down on account of its own weight. Mark the
point to which it goes. Now, if you hang a weight on the tip, the tip
will bend down a little further. If you put double the weight the tip
will go down double the distance, and so on until the fishing rod is
considerably bent, so that its form is altered and a new law of flexure
comes into play. Suppose I use a spring as an accelerating force. For
example, suppose I suspend a heavy ball by a string and then attach a
spiral spring to it and pull the spring aside. The ball will be drawn
after the spring. If then I let the ball go, it will begin to move. The
force of the spring will act upon it as an accelerating force, and the
ball will go on moving quicker and quicker. But the acceleration will
not be like that of gravity. There will be two differences. The pull of
the spring will in no way depend on the mass of the ball, and the pull
of the spring, instead of being constant, like the pull of gravity,
will become weaker and weaker as the ball yields to it. Consequently
the equations above given which determine the relations between this
space passed through, the velocity, and the time which were determined
in the case of gravity are no longer true, and a different set of
relations has to be determined. This can be easily done by mathematics.
But I do not propose to go into it. I prefer to offer a rough and ready
explanation, which, though it does not amount to a proof, yet enables
us to accept the truth that can be established both by experiment and
by calculation.
[Illustration: FIG. 31.]
Let a heavy ball (_A_) be suspended by a long string, so that the
action of gravity sideways on the ball is very small and may be
neglected, and to each side attach an indiarubber thread fastened
at _B_ and _C_. Then when the ball is pulled aside a little, say
to a position _D_, it will tend to fly back to _A_ with a force
proportioned to the distance _A D_. What will be the time it will take
to do this? If the distance _A D_ is small, the ball has only a small
distance to go, but then, on the other hand, it has only small forces
acting on it. If the distance _A D_ is bigger, then it has a longer
distance to go, but larger forces to urge it. These counteract one
another, so that the time in each case will be the same.
[Illustration: FIG. 32.]
The question is this:—Will you go a long distance with a powerful
horse, or a small distance with a weak horse? If the distance in each
case is proportioned to the power of the horse, then the amount of the
distance does not matter. The powerful horse goes the long distance in
the same time that the weak horse goes the short distance. And so it
is here. However far you pull out the spring, the accelerative pull on
the ball is proportioned to the distance. But the time of pulling the
ball in depends on the distance. So that each neutralises the other.
Whence then we have this most important fact, that springs are all
isochronous; that is to say, any body attached to any spring whatever,
whether it is big or small, straight or curly, long or short, has a
time of vibration quite independent of the bigness of the vibration.
The experiment is easy to try with a ball mounted on a long arm that
can swing horizontally. It is attached on each side to an elastic
thread. If pulled aside, it vibrates, but observe, the vibration is
exactly the same whether the bigness of the vibration is great or
small. If the pull aside is big, the force of restitution is big; if
the pull is small, the force of restitution is small. In one case the
ball has a longer distance to go, but then at all points of its path
it has a proportionally stronger force to pull it; if the ball has a
smaller distance to go, then at all the corresponding points of its
path it has a proportionally weaker force to pull it. Thus the time
remains the same whether you have the powerful horse for the long
journey or the weaker horse for the smaller journey.
[Illustration: FIG. 33.]
Next take a short, stiff spring of steel. One of the kind known as
tuning forks may be employed.
The reader is probably aware that sounds are produced by very rapid
pulsations of the air. Any series of taps becomes a continuous sound
if it is only rapid enough. For example, if I tap a card at the rate
of 264 times in a second, I should get a continuous sound such as that
given by the middle C note of the piano. That, in fact, is the rate
at which the piano string is vibrating when C is struck, and that
vibration it is that gives the taps to the air by which the note is
produced.
This can be very easily proved. For if you lift up the end of a bicycle
and cause the driving wheel to spin pretty rapidly by turning the pedal
with the hand, then the wheel will rotate perhaps about three times in
a second. If a visiting card be held so as to be flipped by the spokes
as they fly by, since there are about thirty-six of them, we should
get a series of taps at the rate of about 108 a second. This on trial
will be found to nearly correspond to the note A, the lowest space on
the bass clef of music. As the speed of rotation is lowered, the tone
of the note becomes lower; if the speed is made greater, the pitch of
the note becomes higher, and the note more shrill. However far or near
the card is held from the centre of the wheel makes no difference, for
the number of taps per second remains the same. So, again, if a bit of
watch-spring be rapidly drawn over a file, you hear a musical note. The
finer the file, and the more rapid the action, the higher the note. The
action of a tuning fork and of a vibrating string in producing a note
depends simply on the beating of the air. The hum of insects is also
similarly produced by the rapid flapping of their wings.
It is an experimental fact that when a piano note is struck, as the
vibration gradually ceases the sound dies away, but the pitch of the
note remains unchanged. A tune played softly, so that the strings
vibrate but little, remains the same tune still, and with the same
pitch for the notes.
A “siren” is an ingenious apparatus for producing a series of very
rapid puffs of air. It consists of a small wheel with oblique holes in
it, mounted so as to revolve in close proximity to a fixed wheel with
similar holes in it. If air be forced through the wheels, by reason
of the obliquity of the orifices in the movable wheel it is caused to
rotate. As it does so, the air is alternately interrupted and allowed
to pass, so that a series of very rapid puffs is produced. As the
air is forced in, the wheel turns faster and faster. The rapidity of
succession of the puffs increases so that the note produced by them
gradually increases in pitch till it rises to a sort of scream. For
steamers these “sirens” are worked by steam, and make a very loud noise.
It is, however, impossible to make a tuning fork or a stretched piano
spring alter the pitch of its note without altering the elastic force
of the spring by altering its tension, or without putting weights on
the arms of the tuning fork to make it go more slowly. And this is
because the tuning fork and the piano spring, being elastic, obey
Hooke’s law, “As the deflection, so the force”; and therefore the time
of back spring is in each case invariable, and the pitch of the note
produced therefore remains invariable, whatever the amplitude of the
vibration may be.
Upon this law depends the correct going of both clocks and watches.
Wonderful nature, that causes the uniformity of sounds of a piano, or a
violin, to depend on the same laws that govern the uniform going of a
watch! Nay, more, all creation is vibrating. The surge of the sea upon
the coast that swishes in at regular intervals, the colours of light,
which consist of ripples made in an elastic ether, which springs back
with a restitutional force proportioned to its displacement, all depend
upon the same law. This grand law by which so many phenomena of nature
are governed has a very beautiful name, which I hope you will remember.
It is called “harmonic motion,” by which is meant that when the atoms
of nature vibrate they vibrate, like piano strings, according to the
laws of harmony. The ancient Pythagorean philosophers thought that all
nature moved to music, and that dying souls could begin to hear the
tones to which the stars moved in their orbits. They called it, as you
know, the music of the spheres. But could they have seen what science
has revealed to man’s patient efforts, they would have seen a vision
of harmony in which not a ray of light, not a string of a musical
instrument, not a pipe of an organ, not an undulation of all-pervading
electricity, not a wing of a fly, but vibrates according to the law
of harmony, the simple easy law of which a boy’s catapult is the type,
and which, as we have seen, teaches us that when an elastic body is
displaced the force of restitution, in other words, the force tending
to restore it to its old position, is proportional to the displacement,
and the time of vibration is uniform. The last is the important thing
for us; we seem to get a gleam of a notion of how the clock and watch
problem is going to be solved.
But before we get to that we have yet to go back a little.
About the year 1580 an inattentive youth (it was our friend Galileo
again) watched the swing of one of the great chandeliers in the
cathedral church at Pisa. The chandeliers have been renewed since his
day, it was one of the old lamps that he watched. It had been lit, and
allowed to swing through a considerable space. He expected that as it
gradually came to rest it would swing in a quicker and quicker time,
but it seemed to be uniform. This was curious. He wanted to measure the
time of its swing. For this purpose he counted his pulse-beats. So far
as he could judge, there were exactly the same number in each pendulum
swing.
This greatly interested him, and at home he began to try some
experiments. As he got older his attention was repeatedly turned to
that subject, and he finally established in a satisfactory way the law
that, if a weight is hung to the end of a string and caused to vibrate,
it is isochronous, or equal-timed, no matter what the extent of the arc
of vibration.
The first use of this that he made was to make a little machine with
a string of which you could vary the length, for use by doctors. For
the doctors of that day had no gold watch to pull out while with
solemn face they watched the ticks. They were delighted with the new
invention, and for years doctors used to take out the little string and
weight, and put one hand on the patient’s pulse while they adjusted the
string till the pendulum beat in unison with the pulse. By observing
the length of the string, they were then able to tell how many beats
the pulse made in a minute. But Galileo did not stop there. He
proceeded to examine the laws which govern the pendulum.
We will follow these investigations, which will largely depend on what
we have already learned.
Before, however, it is possible to understand the laws which govern
the pendulum, there are one or two simple matters connected with the
balance and operation of forces which have to be grasped.
Suppose that we have a flat piece of wood of any shape like Fig. 34,
and that we put a screw through any spot _A_ in it, no matter where,
and screw it to a wall, so that it can turn round the screw as round a
pivot.
[Illustration: FIG. 34.]
[Illustration: FIG. 35.]
Next we will knock a tintack into any point _B_, and tie a string on
to _B_. Then if I pull at the string in any direction _B C_ the board
tends to twist round the screw at _A_. What will the strength of the
twisting force be? It will depend on the strength of the pull, and
on the “leverage,” or distance of the line _C B_ from _A_. We might
imagine the string, instead of being attached at _B_, to be attached
at _D_; then, if I put _P_ as the strength of the pull, the twisting
power would be represented by _P_ × _A D_. This is called the “moment”
of the force _P_ round the centre _A_. It would be the same as if I
had simply an arm _A D_, and pulled upon it with the force _P_. It
is an experimental truth, known to the old Greek philosophers, that
moments, or twisting powers, are equal when in each case the result of
multiplying the arm by the power acting at right angles to it is equal.
Now suppose _A B_ is a pendulum, with a bob _B_ of 10 lbs. weight, and
suppose it has been drawn aside out of the vertical so that the bob is
in the position _B_. Then the weight of the bob will act vertically
downwards along the line _B C_. The moment, or twisting power, of the
weight will be equal to 10 lbs. multiplied by _A D_, _A D_ being a
line perpendicular to _B C_.
[Illustration: FIG. 36.]
Now suppose that another string were tied to the bob _B_, and pulled
in a direction at right angles to _A B_, with a force _P_ just enough
to hold the bob back in the position _B_. The pull along _D B_ × _A B_
would be the moment of that pull round the point _A_. But, because this
moment just holds the pendulum up, it follows that the moment of the
weight of the pendulum round _A_ is equal to the moment of the pull of
the string _B D_ round _A_.
Whence P × A B = 10 lbs. × A D.
Whence P = 10 lbs. × (A D)/(A B).
But _A B_ is always the same, whatever the side deflection or
displacement of the pendulum may be. Whence then we see that when
a pendulum is pulled aside a distance _E B_ (which is always equal
to _A D_), then the force tending to bring it back to _E_ is always
proportional to _E B_. But if the pendulum be fairly long, say 39-1/7
inches, and the displacement _E B_ be small,—in other words, if we do
not drag it much out of the vertical,—then we may say that the force
tending to bring it back to _F_, its position of rest, is not very
different from the force tending to bring it back to _E_. But _F B_
is the “displacement” of the pendulum, and, therefore, we find that
when a pendulum is displaced, or deflected, or pulled aside a little,
the amount of the deflection is always very nearly proportional to the
force which was used to produce the deflection. This important law
can be verified by experiment. If _C_ is a small pulley, and _B C_ a
string attached to a pendulum _A B_ whose bob is _B_. Then if a weight
_D_ be tied to the string and passed over a pulley _C_, the amount _F
B_ by which the weight _D_ will deflect the bob _B_ is almost exactly
proportional to _D_, so long as we only make the deflection _E B_
small, that is two or three inches, where say 39-1/7 inches is the
length _A B_ of the pendulum.
If _F B_ is made too big, then the line _B F_ can no longer be
considered nearly equal to the arc of deflection _E B_, and the
proposition is no longer true.
Hence then, both by experiment and on theory, we find that for small
distances the displacement of a pendulum bob is approximately equal to
the force by which that displacement is produced.
But if so, then from what has gone before, we have an example of
harmonic motion. The weight of the bob, tending to pull the bob back to
_E_, acts just as an elastic band would act, that is to say pulls more
strongly in proportion as the distance _F B_ is bigger. In fact, if we
could remove the force of gravity still leaving the mass _B_ of the
pendulum bob, the force of an elastic band acting so as to tend to pull
the bob back to rest might be used to replace it. It would be all one
whether the bob were brought back to rest by the downward force of its
own gravity, or by the horizontal force of a properly arranged elastic
band of suitable length.
[Illustration: FIG. 37.]
But the motion of the bob, under the influence of the pull of
an elastic band where the strain was always proportional to the
displacement, would, as we have seen, be harmonic motion, and performed
in equal times whatever the extent of the swing. Whence then we
conclude that if the swings of a pendulum are not too big, say not
exceeding two and a half inches each way, the motion may be considered
harmonic motion, and the swings will be made in equal times whether
they are large or small ones. In other words, a clock with a 39-1/7
inch pendulum and side swing on each side if not over two inches will
keep time, whatever the arc of swing may be.
This may be verified experimentally. Take a pendulum of wood 39-1/7
inches long, and affix to its end a bob of 10 lbs. weight. The pendulum
will swing once in each second. To pull it aside two inches we should
want a weight such that its moment about the point of support was equal
to the moment of the force of gravity acting on the bob, about the
point of support. In other words, the weight required × 39-1/7 inches =
10 lbs. × 2 inches. Whence the weight required = 1/2 lb. (nearly).
Now fix a similar pendulum _A B_ 39-1/7 inches long, horizontally,
with a weight _B_ of 10 lbs. on it. Fasten it to a vertical shaft _C
D_, with a tie rod of wire or string _A B_ so as to keep it up, and
attach to each side of the rod _A B_ elastic threads _E F_ and _E G_.
Let these threads be tied on at such a point that when _B_ is pulled
aside two inches the force tending to bring it back to rest is half a
pound. Then if set vibrating the rod will swing backwards and forwards
in equal times, no matter how big, the arc of vibration (provided the
arc is kept small), and the time of oscillation will be that of a
pendulum, namely, one swing in a second. In fact, whether you put _A B_
vertically and let it swing on the pivots _C_ and _D_ by the force of
gravity, or put it horizontally, and thus prevent gravity acting on it,
but make it swing under the accelerating influence of a pair of elastic
bands so arranged as to be equivalent to gravity, in each case it will
swing in seconds.
[Illustration: FIG. 38.]
It is this curious property of the circle that makes the vertical
force of gravity on a pendulum pull it as though it were a
horizontally acting elastic band; that is the reason why a pendulum is
equal-time-swinging, or, as it is called, isochronous, from two Greek
words that mean “the same” and “time.”
But it must be remembered that this equal swinging is only approximate,
and only true when the arc of vibration is small.
Here then we have a proof which shows us that the pendulum of a clock
and the balance wheel of a watch depend on exactly the same principles.
They are each an example of harmonic motion.
The next question that arises is whether the weight of the pendulum has
any influence upon the time of its vibration.
A little reflection will soon convince us that it has none. For we know
that the time that bodies take to fall to the ground under the action
of gravity is independent of the weight. A falling 2 lb. weight is only
equivalent to two pound-weights falling side by side.
In the same way and by the same reasoning we might take two pendulums
of equal length, and each with a bob weighing 1 lb. They would, if put
side by side close together swing in equal times. But the time would be
the same if they were fastened together, and made into one pendulum.
For inasmuch as the fall of a pendulum is due to gravity, and the
action of gravity upon a body is proportional to its mass, it follows
that in a pendulum the part of the gravitational force that acts upon
each part of the mass is occupied in moving that mass, and the whole
pendulum may be considered as a bundle of pendulums tied together and
vibrating together.
The same would be the case with a pendulum vibrating under the
influence of a spring. If you have two bobs and two springs, they will
vibrate in the same time as one bob accelerated by one spring. In
this case, however, the force of the one spring must be equal to the
combined force of the two springs. In other words, the springs must be
made proportional in strength to the masses.
Hence, then, you cannot increase the speed of the vibration of a
pendulum by adding weight to the bob.
On the other hand, if you have a bob vibrating under the influence of a
spring, like the balance wheel of a watch, then if you increase the bob
without increasing the spring, since the mass to be moved has increased
without a corresponding increase in the accelerating force acting on
it, the time of swing will alter accordingly.
But in the case of gravity, by altering the mass, you thereby
proportionally alter the attraction on it, and therefore the time of
swing is unaltered.
[Illustration: FIG. 39.]
The explanation which has been given above of the reasons why a
pendulum swings backwards and forwards in a given time independently
of the length of the arc through which it swings, that is to say of
the amount by which it sways from side to side, is only approximate,
because in the proof we assumed that the arc of swing and the line _F
B_ were equal, which is not really and exactly true. Galileo never got
at the real solution, though he tried hard. It was reserved for another
than he to find the true path of an isochronous pendulum and completely
to determine its laws. Huygens, a Dutch mathematician, found that the
true path in which a pendulum ought to swing if it is to be really
isochronous is a curve called a cycloid, that is to say the curve which
is traced out by a pencil fixed on the rim of a hoop when the hoop is
rolled along a straight ruler. It is the curve which a nail sticking
out of the rim of a waggon wheel would scratch upon a wall. I will
not go into the mathematical proof of this. Clocks are not made with
cycloidal pendulums, because when the arc of a pendulum is small the
swing is so very near a cycloid as to make no appreciable difference in
time-keeping.
I am now glad to be able to say that I have dealt with all the
mathematics that is necessary to enable the mechanism of a clock to be
understood. It all leads up to this:—
(1) A harmonic motion is one in which the accelerating force increases
with the distance of the body from some fixed point.
(2) Bodies moving harmonically make their swings about this point in
equal times.
(3) A spring of any sort or shape always has a restitutional force
proportional to the displacement.
(4) And therefore masses attached to springs vibrate in equal times
however large the vibration may be.
(5) The bob of a pendulum, oscillating backwards and forwards, acts
like a weight under the influence of a spring, and is therefore
isochronous.
(6) The time of vibration of a pendulum is uninfluenced by changes in
the weight of the bob, but is influenced by changes in the length of
the pendulum rod. The time of vibration of a mass attached to a spring
is influenced by changes in the mass.
We have now to deal with the application of these principles to clocks
and watches.
Clocks had been known before the time of Galileo, and before the
invention of the pendulum. They had what is known as balance, or verge
escapements. Strictly in order of time I ought to explain them here.
But I will not do so. I will go on to describe the pendulum clock, and
then I will go back and explain the verge escapement, which, we shall
see, is really a sort of huge watch of a very imperfect character.
As soon as Galileo had discovered that pendulums were isochronous,
that is, equi-time-swinging, he set to work to see whether he could
not contrive to make a timepiece by means of them. This would be easy
if only he could keep a pendulum swinging. When a pendulum is set
swinging, it soon comes to rest. What brings it to rest? The resistance
of the air and the friction of the pivots. Therefore what is obviously
wanted is something to give it a kick now and then, but the thing must
kick with discretion. If it kicked at the wrong time, it might actually
stop the pendulum instead of keeping it going. You want something that,
just as the pendulum is at one end and has begun to move, will give it
a further push. Suppose that I have a swing and that I put a boy in it,
and I swing him to and fro. I time my pushes. As he comes back against
my hand I let him push it back, and then just as the swing turns I give
it a further push. But I cannot stand doing that all day. I must make a
machine to do it. Now what sort of a machine?
First, the machine must have a reservoir of force. I can’t get a
machine to do work unless I wind it up, nor a man to do work unless I
feed him, which is his way of being wound up. But then what do I want
him to do? I want him, when I give him a push, to push me back harder.
I want a reservoir of force such that when a pendulum comes back and
touches it, the touch, like the pressure of the trigger of a gun, shall
allow some pent-up power to escape and to drive the pendulum forward.
This is the case in a swing. Each time that the swing returns to my
hands I give it a push, which serves to sustain the motion that would
otherwise be destroyed by friction and the resistance of the air.
Such an arrangement, if it can be contrived mechanically, is called an
“escapement.”
An arrangement of this kind was contrived by Galileo. He provided a
wheel, as is here shown, with a number of pins round it. The pendulum
_A B_ has an arm _A H_ attached to it, and there is a ratchet _C D_
which engages with the pins. The ratchet has a projecting arm _E F_.
[Illustration: FIG. 40.]
When the pendulum comes back towards the end of its beat, the arm _A H_
strikes the arm _E F_, and raises the ratchet _C D_. This releases the
wheel, which has a weight wound up upon it, and therefore at once tries
to go round. The consequence is, that the pin _G_ strikes upon the arm
_A H_, and thus on its return stroke gives an impetus to the pendulum.
As the pin _G_ moves forward it slides on the arm _A H_ till it slips
over the point _H_. The wheel now being free, would fly round were it
not that when the pendulum returned, and the arm _A H_ was lowered,
the ratchet had got into position again and its point _D_ was ready to
meet and stop the next pin that was coming on against it. At each blow
of the pins against the pendulum a “tick” is made, at each blow of a
pin against the ratchet a “tock” is sounded, so that as it moves the
pendulum makes the “tick-tock” sound with which we are all familiar.
Hence then a clock consists of a wheel, or train of wheels, urged by
a weight or spring, which strives continually to spin round, but its
rotation is controlled by an escapement and pendulum, so contrived as
only to allow it to go a step forward at regular equal intervals of
time.
But this would make only a poor sort of escapement. For the mode of
driving the pendulum adds a complication to the swing of the pendulum.
Instead of the pendulum being simply under the accelerative force of
gravity, it is also subjected to the acceleration of the pin _G_. This
acceleration is not of the “harmonic” order. Hence so far as it goes it
does not tend to assist in giving a harmonic motion to the pendulum,
but, on the contrary, disturbs that harmonic motion. Besides this, the
impulse of the pin is in practice not always uniform. For if the wheel
is at the end of a train of wheels driven by a weight, though the force
acting on it is constant, yet, as that force is transmitted through a
train of wheels, it is much affected by the friction of the oil. And
on colder days the oil becomes more coagulated, and offers greater
resistance. Moreover, as will be explained more in detail afterwards,
the fact that the impulse is administered by _G_ at the end of the
stroke of the pendulum is disadvantageous, as it interferes with the
free play of the pendulum.
From all these causes the above escapement is imperfect in character,
and would not do where precision was required.
[Illustration: FIG. 41.]
It is now time to return to the old-fashioned escapements which were
in use before the time of Galileo. These consisted of a wheel called
a crown wheel, with triangular teeth. On one side of this wheel a
vertical axis was fitted, with projecting “pallets” _e f_. Across
the axis a verge or rod _e f_ was placed, fitted with a ball at each
end. When the crown wheel attempted to move on, one of its teeth came
in contact with a pallet. This urged the pallet forward, and thereby
caused an impulse to be given to the axis, on which was mounted the
verge, carrying the balls. These of course began to move under the
acceleration of the force thus impressed upon the pallet. Meantime,
however, the other pallet was moving in the opposite direction, and by
the time the first pallet had been pushed so far that it escaped or
slid past the tooth of the crown wheel, which was pressing upon it, the
other pallet had come into contact with the tooth on the other side
of the crown wheel. This tended to arrest the motion of the verge, to
bring the balls to a standstill, and ultimately to impart a motion in
a contrary direction to them.
Thus then the arrangement was that of a pendulum not acted on by
gravity, for the balls neutralised one another. The pendulum was,
however, not subjected to a harmonic acceleration, but alternately
to a nearly uniform acceleration from _A_ to _B_ and _B_ to _A_. As
a result, therefore, the time of oscillation was not independent of
the arc of swing, but varied according to it, as also according to
the driving power of the crown wheel. At each stroke there was a
considerable “recoil.” For as each tooth of the wheel came into play it
was unable at first to overcome and drive back the pallet against which
it was pressing, but, on the contrary, was for a time itself driven
back by the pallet.
[Illustration: FIG. 42.]
Of course, so long as the motions of the wheel and verge were exactly
uniform, fair time was kept. But the least inequality of manufacture
produced differences.
Nevertheless it was on this principle that clocks were made during the
thirteenth, fourteenth and fifteenth centuries. They were mostly made
for cathedrals and monasteries. One was put up at Westminster, erected
out of money paid as a fine upon one of the few English judges who have
been convicted of taking bribes.
The time of swing of these clocks depended entirely upon the ratio of
the mass of the balls at the end of the verge as compared with the
strength of the driving force by which the acceleration on the pallets
was produced. They were very commonly driven by a spring instead of a
weight. The spring consisted of a long strip of rather poor quality
steel coiled up on a drum. As it unwound it became weaker, and thus the
acceleration on the verge became weaker, and the clock went slower.
In order, therefore, to keep the time true, it became necessary to
devise some arrangement by which the driving force on the crown wheel
should be kept more constant.
This gave rise to the invention of the fusee. The spring was put inside
a drum or cylindrical box. One end of the spring was fastened to an
axis, which was kept fixed while the clock was going; the other was
fastened to the inside of the drum. Round the drum a cord was wound,
which, as the drum was moved by the spring, tended to be wound up on
the surface of the drum. Owing to the unequal pull of the spring, this
cord was pulled by the drum strongly at first, and afterwards more
feebly. To compensate its action a conical wheel was provided, with a
spiral path cut in it in such a way and of such a size and proportion
that as the wheel was turned round by the pull of the drum the cord was
on different parts of it, so that the leverage or turning power on it
varied, becoming greater as the pull of the cord became weaker, and in
such a ratio that one just compensated the other, and the turning power
of the axle was kept uniform.
In this manner small table clocks were made which kept very tolerable
time.
[Illustration: FIG. 43.]
Huygens converted these clocks into pendulum clocks in a very simple
manner. He removed one of the balls, lengthened the verge, and slightly
increased the weight of the other ball. By this means, while the crown
wheel still continued to drive the verge and remaining ball, the
acceleration on that ball now no longer depended entirely on the force
of the crown wheel. The acceleration and retardation were now almost
entirely governed by the force of gravity on the remaining ball, and
this acceleration was harmonic.
The clock, therefore, was immensely improved as a time-keeper. Still,
however, the acceleration remained partly due to the driving power, and
this was partly non-harmonic and introduced errors.
Most of the old clocks were converted shortly after the time of
Huygens. As there was in general no room for the pendulum inside the
clock-case, they usually brought the axle on which the pallets were
mounted outside the clock and made it vibrate in front of the face.
Many old clocks exist, of which the engraving in the frontispiece is
an example, that have been thus converted. A true old verge escapement
clock is now a rarity.
The type of escapement invented by Galileo never came into vogue for
clocks, on account of its imperfections, except till after a long
interval, when, with certain modifications, it became the basis of a
new improvement at the hands of Sir George Airey.
The crown wheel fell into disuse and was replaced by the anchor
escapement, which was employed in that popular and excellent timepiece
used throughout the eighteenth and the early part of the nineteenth
century, and is now known as “The Grandfather’s Clock.” It was after
all the crown wheel in another shape. The wheel, however, was flattened
out, the teeth being put in the same plane. This made it much easier to
construct. The pallets were fixed on an axis, and were a little altered
so as to suit the changed arrangement of the teeth. The pendulum was
no longer hung on the axis which carried the pallets. A cause of a good
deal of friction and loss of power was thus removed. The pendulum was
hung from a strip of thin steel spring, which allowed it to oscillate,
and which supported it without friction. This excellent manner of
suspending pendulums is now universal. It enabled the pendulum to be
made very heavy. The bob was usually some eight or nine pounds weight.
By this means the acceleration on the pendulum was due almost entirely
to gravity acting on the bob, and thus the motion of the pendulum
became almost wholly harmonic. Whence it followed that variations in
the pendulum swing became of secondary importance, and did not greatly
alter the going of the clock.
[Illustration: FIG. 44.]
Therefore when the wheels became worn, and the pivots choked with old
oil and dust, the old clock still went on. If it showed a tendency to
stop for want of power, a little more was added to the driving weight,
and the clock kept as good time as ever.
The swing of the pendulum was by this escapement enabled to be made
small, so that the arc of swing of the bob differed but little from a
cycloid.
The secret of the time-keeping qualities of these old “Grandfather”
clocks is the length of pendulum. This renders it possible to have
but a small arc of oscillation, and therefore the motion is kept very
nearly harmonic. For practical purposes nothing will even now beat
these old clocks, of which one should be in every house. At present
the tendency is to abolish them and to substitute American clocks with
very short pendulums, which never can keep good time. They are made
of stamped metal. When they get out of order no one thinks of having
them mended. They are thrown into the ash-pit and a new one bought. In
reality this is not economy.
Good “Grandfather” clocks are not now often made. The last place I
remember to have seen them being manufactured is at Morez, in the
district of the Jura. An excellent clock, enclosed in a dust-tight iron
case, with a tall painted case of quaint old design, can be bought for
about 55_s._ The wheels are well cut, and the internal mechanism very
good.
I visited the town of Morez in the year 1893. The clock industry was
declining. The farmers of France seemed to prefer small clocks of
hideous appearance, made in Germany and in America, to the excellent
work of their own country. Probably by now the old clockmaking industry
is extinct. One I purchased at that time has gone well ever since.