I have thus described the principal features of ordinary clocks. For
the details many treatises must be studied, and knowledge acquired
which is not in any books at all.
I now, however, pass to watches. It will be remembered that a verge
escapement consists of a crown wheel with teeth, engaging two pallets
fixed upon a verge, furnished with balls at its extremities.
As the crown wheel was urged forwards each pallet in succession was
pushed till it slipped over the tooth which was engaging it. Then
a tooth on the other side came into sharp collision with the other
pallet, and drove the verge the other way, and so on.
Now here we have a driving force, and a sort of pendulum. But how did
the verge act as a pendulum to measure time? It is not a body rocking
under the action of gravity, nor under the acceleration of a spring.
How then can it act as a regulator of time, and what is the period of
its swing?
The answer to this is, that it is under the acceleration of gravity,
but that gravity does not act freely on the bobs or weights, but only
through the driving weight and teeth. The impulse that drives the
verge is really also the accelerating force upon it, and the only
accelerating force upon it.
And the worst feature about the movement is, that as the teeth and
pallets move, the leverage of the teeth on the pallets alters, and
thus the bobs on the verge are under the influence not of a uniform or
duly regulated force, but of a constantly varying one, and one that
varies in a very complicated and erratic way. It would be hopeless to
expect much time-keeping from such a contrivance. The most that could
be expected would be by putting on a very big weight to reduce to
comparative insignificance the friction, and then hope that the swings
would be uniform, so that whatever went on in one swing would go on in
the next, and thus the time-keeping be regular.
But any course tending to diminish the driving force, such as the
thickening of the oil, would greatly affect the going. It was for this
reason that Huygens turned the verge into a pendulum by removing one of
the bobs, and letting gravity thus act on the other.
For watches, however, a different plan was contrived. One end of a
slender spiral spring was affixed to the verge. The other end of the
spring was made fast to the clock frame. The verge was now, therefore,
chiefly under the action of the acceleration of the spring. To make the
acceleration of the teeth of the ’scape wheel less embarrassing, the
teeth were so shaped as only to give a short push at stated intervals,
and not interfere with the free swing of the verge under the alternate
to-and-fro accelerations and retardations of the spring. By this means
the verge became in every way an excellent pendulum, not dependent on
gravity, and permitting the watch to be held in any position.
The verge thus fitted was turned into a wheel, and became a “balance
wheel.” It was compensated for heat expansion by a cunning use of the
unequal expansion of brass and steel, in a manner analogous to the way
this unequal expansion of metals had been employed to compensate the
pendulum, and became the beautiful and accurate time-measurer that we
see to-day, with its pivots mounted in jewels to diminish friction, and
with screws round the rims of the balance wheel to enable the centre of
gravity to be exactly adjusted to its centre of rotation, and with a
delicate hair-spring of tempered steel that is a marvel of microscopic
work.
But the escapement of the early watches left much to be desired. In
order to make it clear how imperfect that early escapement was, we
have to turn back and remember what has been said about the dead beat
escapement.
It will then be remembered that it was shown that for small arcs the
pendulum would keep good time provided you let it have as much swing as
it wanted to use up the force which the escapement had applied to it,
_but not otherwise_, so the pendulums only acted really well when the
impulse was given about the middle of the swing, and they were free to
go on and stop when they pleased, and turn back at the end of it.
This essential condition was fairly approximated to in the dead beat
escapement of clocks which left them at the end of their swing with
only a very slight friction to impede their free motion.
But when you come to deal with a watch the case is quite different.
Here the escapement is of a great size compared with the balance wheel,
and the friction even of the most dead beat watch escapement that could
be contrived was so big compared with the forces acting on the balance
wheel as seriously to derange its motion, and render it far from a
perfect time-keeper.
Now about this time—I am speaking of the early part of the eighteenth
century—a demand of a very exceptional character arose for a really
perfect watch. The demand did not arise from gentlemen who wanted
to keep appointments to play at ombre at their clubs, or even
from merchants to time their counting house hours. For these the
old-fashioned watch did very well. The demand came from mariners.
But the seamen did not want to know the time merely to arrange the
hours for meals on the ship or to determine when the watch was to be
relieved, but for a far more important purpose, namely, to find out by
observation of the heavens their place upon the ocean when far out of
sight of the land. It will be very interesting to see how this problem
arose, and how the patient industry and ingenuity of man has solved it.
The ancient navigators never went very far from the shore, for, once
out of sight of land, a ship was out of all means of knowing where she
was. On clear days and nights the compass, and the sun and stars would
tell the mariner the _direction_ he was sailing in, but it was quite a
problem to determine where he was on the surface of the earth.
[Illustration: FIG. 63.]
Let us consider the problem. Suppose for convenience that the earth is
divided up into “squares,” as nearly, at least, as you can consider a
globe to be so marked out. Let us suppose that it has been agreed to
draw on it from pole to pole 360 lines of longitude, commencing with
one through say Greenwich Observatory as a starting-point, and going
right round the earth till you come back to Greenwich again. Also
suppose that there have been drawn a series of circles parallel to the
equator, but going up at equal distances apart towards the poles. Let
us have 179 of these circles, so as to leave 180 spaces, _a_ to _b_,
_b_ to _c_, etc., from pole to pole. This will divide the earth up like
a bird-cage into squares, as if we had robed it in a well-fitting
Scotch plaid. The length measured along the equator of the side _p q_
of each square at the equator is taken as exactly sixty nautical miles
(apart from a small error of measurement, which makes it in actual
practice 59·96). This is equal to sixty-nine and a quarter English
statute miles. The side of the square leading towards the poles _q s_
would also be sixty nautical miles were it not that the earth is not
truly spherical, which introduces a slight error. We may, however,
roughly say that at the equator each square measures sixty nautical
miles each way.
[Illustration: FIG. 64.]
As we get towards the poles the squares become rectangular figures,
with the heights of latitude still sixty nautical miles, but the widths
becoming smaller. Thus in England our squares measure _p q_ = 37
nautical miles and _q s_ = 60 nautical miles.
Now of course we can see at once that it is easy at any place on the
earth’s surface to find your _latitude_ by a simple observation of the
sun at noon, if you know the day of the year, and have got a nautical
almanac. For by an instrument called a sextant you can measure the
angle he appears to be above the horizon, and then, as you know from
a nautical almanac the angle he is above the equator, you can soon
determine your place _A_ on the globe. Or at night, if you measure the
angular distance that the polar star _P_ is from the zenith, or point
exactly over your head—that is, the angle _P O Z_—you can subtract it
from a right angle and get your latitude, _A O E_, at once.
[Illustration: FIG. 65.]
But how are you to determine your longitude? The pole-star, or sun,
or any other star won’t help you, for as the earth is moving they
keep shifting, and at one time or another appear exactly in the same
position to everyone on the same parallel of latitude, as it is easy to
see. The fact is that you are on a ball turning round. You know easily
what latitude you are on, but you cannot tell your longitude unless
you can tell how many hours and minutes you get to a position before
Greenwich gets to the same position. If when a particular star got to
Greenwich a gong were sounded which could be heard all over the earth,
then of course, by seeing what stars were overhead, everyone would
know their longitude at once. Perhaps by means of the new electric
waves this will before long be done, and the Greenwich hours will be
sounded all over the world for the use of mariners. But till this is
accomplished all that can be done is to keep an accurate clock on
board, so as always to give you Greenwich time.
Early attempts were made to take a pendulum clock to sea, suspending it
so as to avoid disturbance to its motion by the rocking of the ship.
These proved vain.
It therefore became desirable that a watch with a balance wheel
should be contrived to go with a degree of accuracy in some respects
comparable with the accuracy of a pendulum clock. To encourage
inventors an Act of Parliament was passed in the thirteenth year of
Queen Anne’s reign (chapter xv.) (1713) promising a reward of £20,000
to anyone who would invent a method of finding the longitude at sea
true to half a degree—that is, true to thirty geographical miles.
If the finding of the longitude were to be accomplished by the
invention of an accurate watch, then this involved the use of a watch
that should not, in several months’ going, have an error of more than
two minutes, which is the time which the earth takes to turn through
half a degree of longitude.
This was the problem which John Harrison, a carpenter, of Yorkshire,
made it his life business to solve. His efforts lasted over forty
years, but at the end he succeeded in winning the prize.
These instruments have been much improved by subsequent inventors, and
have resulted in the construction of the modern ship’s chronometer,
a large watch about six inches in diameter, mounted on axles, in a
mahogany box. Several of these are taken to sea by every ship.
The peculiarity of the chronometer is its escapement.
Let _A B_ be the scape wheel, and _C D_ a small lever attached to _C_,
the pivot on which the balance wheel and spring is fastened. Let _E G_
be a lever, with a tooth _F_ which engages the teeth of the scape wheel
and prevents it moving round. Let _H_ be a spring holding the lever _E
G_ up to its work.
[Illustration: FIG. 66.]
The lever has a spring _K E_ fastened to it at the point _K_. This
spring is very delicate. If the lever _C D_ is turned so that the
little projection _M_ on it strikes the spring _E_ from left to right,
then, as the spring rests on the lever, the whole lever is pushed over,
and the teeth of the scape wheel set free. At that instant, however,
the escapement is so arranged that the arm _C D_ is just opposite
the tooth _D_ of the scape wheel, so that the scape wheel, instead
of running away, leaps with its tooth _D_ on to the lever _C D_ and
swings the balance wheel round. The balance wheel is free to twist as
much as it pleases, but the moment it has twisted so much that the
projection _M_ passes the spring _E_, then the lever _G E_ flies back
to its place, and the scape wheel is again checked. Meanwhile the
balance wheel flies round till at last it is brought to rest by the
balance spring. It then recoils and sets out on its return path. This
time, however, the projection _M_ merely flips aside the spring _E_
and the balance wheel goes back, till again it is brought to rest and
returns. As soon as the lever comes opposite _D_ the projection _M_
then again hits the spring _E_, and releases the catch at _F_, and
another tooth of the scape wheel goes by.
There then you have a completely free escapement, and consequently an
accurate one. Many watches are made with these escapements, but they
are more expensive than those in common use.
There is but little remaining in a watch that is not in a clock, for
the wheel-trains and general arrangements are very similar.
It is possible to apply the chronometer’s detached escapement to a
clock. This was done by several clock-makers in the eighteenth and
early part of the nineteenth century. One method of doing it is as
follows:
_A_ is a block of metal fitted to the bottom of the pendulum, _B_ a
light lever pivoted on it. _C_ is the scape wheel, with four teeth;
_D_ a tooth of the scape wheel, which hops on to the projection of the
pendulum the moment that the impact of the point _E_ of the lever _B E_
has pushed aside the lever _G F_, and thus released the scape wheel.
The advantage is that it is a very easy escapement to make. But it is
in reality a detached (that is to say, a completely free) chronometer
escapement, as can easily be seen.
[Illustration: FIG. 67.]
Turret-clocks are open to considerable disadvantages, for the wind
blowing on the hands gives rise to considerable pressure, so that the
clocks are sometimes urging the hands against the wind, sometimes are
being helped by the wind. And this inequality of driving force makes
the pendulum at some times make a bigger arc of swing than at others.
But we saw above that though difference of arc of swing ought to make
no difference in the time of swing of the pendulum, yet this was only
strictly true if the arc of swing were a cycloid.
But as for practical convenience we are obliged to make it a circle,
it follows, as we saw, that for every tenth of an inch of increase of
swing of an ordinary seconds pendulum about a second a day of error is
introduced. To remove this difficulty a gravity escapement was invented
by Mudge in the eighteenth century, improved by Bloxam, a barrister,
and perfected by the late Lord Grimthorpe. The idea was to make the
scape wheel, instead of directly driving the pendulum, lift a weight,
which, being subsequently released, drove the pendulum. The consequence
was, that inequalities in wind pressure, which affected the driving
force of the scape wheel, would not act on the pendulum, which would
be always driven by the uniform fall of a fixed and definite weight. A
movement of this kind has been fixed in the great clock at Westminster,
and has gone admirably. A description of its details will be found in
the _Encyclopædia Britannica_, written by Lord Grimthorpe himself.
All sorts of eccentric clocks and watches have been proposed. For
instance, it seems wonderful to see a pair of hands fitted to the
centre of a transparent sheet of glass go round and keep time with
apparently nothing to drive them.
But the mystery is simple. The seeming sheet of glass is not one sheet,
but four. The two centre sheets move round invisibly, carrying the hour
hand and minute hand with them, being urged by little rollers below
on which they rest. When you touch the glass the outside sheets appear
at rest, and you do not suspect that it is other than a single sheet.
But beware of dust, for if dust gets on the inner plate you detect the
trick. In this way a mechanical hand was made that wrote down answers
to questions. This plan can be applied to all sorts of tricks.
Sir William Congreve, an ingenious inventor, proposed to make a clock
that measured time by letting a ball roll down an incline. When it got
to the bottom it hit a lever, which released a spring and tipped the
plane up again, so that the ball now ran down the other way. It is a
poor time-keeper, and the idea was not original, for a ball had been
previously designed for the same purpose.
Sometimes clocks are constructed by attaching pendulums to bronze
figures, which have so small a movement that the eye is unable to
detect it. The figure appears to be at rest, but is in reality slowly
rocking to and fro. It is necessary to make the movement as small as
about one four hundredth of an inch in half a second, if the movement
is to escape human observation. For a movement of one two hundredth
of an inch per second is about the largest that will certainly remain
unperceived.
In mediæval times clocks were constructed with all sorts of queer
devices. The people of the upper town at Basle having quarrelled with
those of the lower town, fought and beat them. To commemorate this
victory they put on the old bridge at the upper town a clock provided
with an iron head, that slowly put out and drew in a long tongue of
derision. This clock may still be seen in the museum. It is as though
the council of the city of London put a clock of derision at Temple Bar
to put out its tongue at the County Council.
I do not propose here to describe the striking mechanism of clocks.
There are several different ways of arranging it. They are rather
complicated to follow out, but they all resolve themselves into a
few simple principles. As the hour hand revolves it carries a cam so
arranged as to be deeper cut away for the twelfth hour, less for the
eleventh, and so on. When the minute hand comes to the hour it releases
the striking mechanism, which, urged by a weight, begins to revolve,
and, driving an arm carrying a pin, raises a hammer, which goes on
striking away as the arm revolves. This would continue for ever if
it were not that at the same moment an arm is liberated which falls
against the cam. At each stroke the arm is (by the striking apparatus)
raised a bit back into position. When it comes back into position it
stops the striking. It thus acts as a counter, or reckoner of the blows
given, stopping the movement when the clock has struck sufficiently.
If the counting mechanism fails to act, we have the phenomenon which
occasionally occurs of a “Grandfather” clock striking the whole of the
hours for the week without stopping.
A chiming clock is simpler still. For here we have a barrel covered
with pins, like the barrel in a musical box. As the pins go round they
raise hammers which fall against bells. The barrel is wound up and
driven by a spring or weight. When the clock comes to the hour, the
barrel is released, and rotating, plays the tune.
If you want to make a clock wake you up in the morning it can be
done by making the striking arrangement hammer away with no counting
mechanism to stop it until the weight has run down. If, not content
with that, you want the sheets pulled off the bed or the bed tilted
up, or a can of water emptied over the person who will not rise, a
mechanical device known as a relay must be used. It is very simple.
What is wanted is that, after the lapse of a time which a clock
must measure, a considerable force must be exerted to pull off the
bedclothes. It would be absurd to make the clock exercise this pull.
It is obviously better to attach the clothes by a hook to a rope which
passes over a pulley, and from which hangs a weight. A pin secures the
weight from falling, the pin being withdrawn by the clock. The work is
thus done by the weight when released by the clock.
In like manner, if you have a telegraph designed to print messages at
a distance, you do not send along the wires the whole force necessary
for doing the printing. You only send impulses, which, like triggers,
release the forces by which the letters are to be stamped.
Electric clocks of many kinds have been invented. The principle of an
electric escapement is similar to that of an ordinary escapement.
[Illustration: FIG. 68.]
The reader no doubt knows that, when a circuit of wire is joined or
completed leading to a source of electricity, electricity flows through
the wire.
If the wire is wound round a piece of iron, then, whenever the circuit
is joined, a current is set in motion, and the iron becomes an
electro-magnet. When the circuit is severed the iron ceases to be a
magnet.
If put at a proper position it would at each time an iron pendulum
approached give it a small impulse provided that at that instant
the current is turned on. This can easily be made to be done by the
pendulum itself. For just as the pendulum is coming back to the
central position a flipper _P_ attached to the rod can be caused
to make contact with a piece of metal fixed on its path. Then the
electro-magnet, becoming magnetised, exerts a pull on the iron
pendulum. On the return beat of the pendulum the other side of the
flipper _R_ strikes the obstruction. But if that side _R_ is covered
with ebonite or some non-conducting material no current will be set
in motion, and the electro-magnet will not (as it would otherwise do)
retard the pendulum. Such a pendulum has therefore an impulse given to
it every second beat.
Such pendulums do not act very well, because it is difficult to keep
metallic surfaces like _Q_ clean, and therefore misses often occur.
Besides, the strength of the current varies with the goodness of the
contact and with other things.
What is now preferred is to make an arrangement by which an electric
current winds the clock up every minute or so. By this means the
impulse which drives the clock is not a varying electric one, but is
a steady weight. The most successful clocks have been made on these
principles.
The advantage of electricity is, that by means of the current that
actuates the clock, or winds it up, you can at regular intervals set
the hands in motion of a great number of clocks.
So that only one going clock with a pendulum is needed. The other
clocks distributed over the building have only faces and hands, and
a very few simple wheels, to which a slight push is given by an
electro-magnet, say, every minute or so. The system is therefore well
adapted for offices and hotels.
In America, by means of electric contacts, clocks have been arranged to
put gramophones into action. You will remember that it was pointed out
that if a wire were dragged over a file a sound would be produced due
to the little taps made as the wire clicked against the rough cuts on
the file, and that the tone of the note depended on the fineness of the
cuts, and hence the rapidity of the little taps. You can imagine that,
if the roughnesses were properly arranged, we might get the tones to
vary, and thus imitate speech. This is the principle of the gramophone.
The roughnesses are produced by a tool, which, vibrating under the
influence of human speech, makes small cuts in a soft material. This
is hardened, and then, when another wire is dragged over the cuts, the
voice is reproduced.
In this way clocks are made to speak and tell the children when dinner
is ready and when to go to bed. On this simple plan, too, dolls can be
made to speak.
The modern methods of clock and watch-making are very different from
those in use in olden days. In former times the pivots were turned up
by hand on small lathes, and even the teeth of the wheels were filed
out. Each hole in the clock or watch frame was drilled out separately,
and each wheel separately fitted in, so that the watch was gradually
built up as one would build a house. Each wheel, of course, only fitted
its own watch, and the parts of watches were not interchangeable.
This has now all been altered. By means of elaborate machinery the
whole of the work of cutting out every wheel and the making of every
single part is done by tools moved independently of the will of the
workman, whose only duty is to sit still and see the things made. He
is, as it were, the slave of the machine, watching it and answering to
its calls. Or shall we rather say that he is the machine’s employer and
master? He has here a servant who never tires nor ever disobeys him.
All the machine requires is that its cutting edges should be exactly
true and sharp and microscopically perfect; then it will cut away and
make wheel after wheel. It oils itself. It only wants the man to act as
superintendent, and stop it if any cutting edge gets unduly worn. For
this purpose he measures the work it is doing from time to time with a
microscope to see that it is good and true and exact.
When all the parts have thus been made you have perhaps a hundred
boxes, each with a thousand watch parts in it, each part exactly like
its fellows. You take one wheel or bit from each box indiscriminately,
and you then have the materials for a watch, screws, fittings, pins,
and all. All you have now got to do is simply to screw them all
together, like putting together a puzzle. Everything fits; there is no
snipping or filing.
In such a watch if a bit gets broken you simply send for another bit of
the same kind and fit it into its place.
Motor cars, bicycles, and many other machines are, or ought to be, made
in this manner, so that if a driver at York breaks a part of the car he
simply sends to London for another. It comes and fits into its place at
once. But for this sort of plan you must do work true to much less than
a thousandth of an inch, and, of course, no one must want to indulge
his individual fancy as to the shape or appearance of the watch. The
whole advantage consists in dead uniformity. But the cheapness is
surprising. You can have a better watch now for 30_s._ than could have
been got for £30 twenty years ago.
Artistic people are in the habit of condemning this uniformity as
though it were inartistic and degrading. In truth, it is not degrading
to get a machine to do what you want at the expense of as little labour
as possible. You pay 30_s._ for the watch, but you have £28 10_s._
left to spend on pictures.
Only one ought not to confuse industry with art. Watches made in this
way have no pretence to be artistic products. They are simply useful.
To rule them all over with machine lines or to put hideous machine
ornament on them is purely and simply base and degrading. Let your
_ornament_ be hand work, your utility machine work.
Thus then I have endeavoured to give a very brief sketch of the modes
of measuring time, and incidentally to introduce my readers to those
laws of motion which are the foundation of so large a part of modern
science.
It only remains that I should shortly describe modern apparatus by
means of which it is possible to measure with accuracy periods of time
so short as to appear impossible. But when you see how it is done the
method seems easy enough. It is still by means of a pendulum, only a
pendulum beating time not once, but hundreds and even thousands of
times in a second.
And such pendulums, instead of being difficult to make, are remarkably
simple, and present no difficulty whatever. For we have only to use the
tuning fork which has been previously described.
The tuning fork consists of a piece of steel bent into a U shape. The
arms are set vibrating so as alternately to approach and recede from
one another.
The reason why there are two arms is that, if they come together and
recede, they balance, and hence the instrument as a whole does not
shake on its base. This balance of moving parts of a rapidly moving
machine is very important. Some motor cars are arranged so that
the engines are “balanced,” and the moving parts come in and out
simultaneously, leaving the centre of gravity unchanged whatever be the
position of the motion. This makes the vibration of the car very small.
The tuning fork is therefore balanced. Being elastic, it obeys Hook’s
law, “As the force, so the deflection.” And therefore, as we have seen,
the vibrations of the fork are isochronous.
A fork with arms about six or seven inches long will make about fifty
or sixty vibrations in a second. How are we to record those vibrations,
and how keep the tuning fork vibrating?
[Illustration: FIG. 69.]
A train of wheels is almost an impossibility, not perhaps so impossible
as might be supposed, but still very difficult. So a different method
is adopted. A little wire projects from one tuning fork arm. A piece of
glazed paper is gently smoked by means of a wax taper, and is stretched
round a well-made brass drum. The tuning fork is then put so that the
little wire just touches the paper. The tuning fork is then made to
vibrate by a blow, and while it is vibrating the drum is revolved.
Thus a wavy line is formed on the drum by the wire on the tuning fork.
If the tuning fork made fifty complete vibrations to and fro in a
second there would be one hundred such indentations, fifty to the right
and fifty to the left, and by these the time can be measured as you
would measure a length upon a rule.
[Illustration: FIG. 70.]
If an arm _a b_ be fitted to move sideways when a little string _c
d_ is pulled, and be also provided with a small wire, so as to touch
the drum, then it also will trace a straight line on the drum as the
wire lightly scratches away the thin coating of smoke. Now, if it is
suddenly jerked and flips back, then a little indentation will be
made in the line, and if when we are to measure a rapid lapse of time
a jerk is given at the beginning, and another jerk at the end of it,
we should get a diagram like that in the adjoining figure, where _a_
is the trace of the tuning fork, _b_ that of the indicating arm. The
time which has elapsed between the jerk which produced the indentation
_c_ and that which produced the indentation _d_ will be about three
and three-quarter double indentations of the tuning fork line, thus
indicating three and three-quarter fiftieths of a second. It is easy
to see how delicate this means of measurement can be made. With small
tuning forks we can easily measure times to a thousandth part of a
second, and much less if desired.
The jerk may be given by electricity if it is wished. When the current
is joined a little electro-magnet pulls a bit of iron and gives a pull
to the string. So extremely rapid is the flight of electricity that no
appreciable time is lost in its transit through the wires, so that the
impulse may be given from a distance. Thus we may arrange that when a
cannon ball leaves a gun an electric impulse shall be given. When it
reaches and hits a target another electric impulse is given. These make
nicks in the tracing line on the drum from which we can easily compute
the time that has elapsed between the leaving of the mouth of the gun
and the arrival of the shot at its destination.
[Illustration: FIG. 71.]
Such an apparatus is used in modern gunnery experiments. It is an
elaborate one, but is based on the principle above described.
Drums are sometimes driven by clockwork, and tuning forks are also
often kept vibrating by electricity, thus constituting very rapidly
moving electric clocks. The arrangement is simple. An electro-magnet
_E_ is put in the vicinity of the arm of the tuning fork. A small piece
of wire from the arm is in contact with a piece of metal _Q_, from
which a wire runs to the electro-magnet, thence to a battery, and from
the battery to the tuning fork, through which the current runs to the
wire _R_. When the fork vibrates the arm, being bent outwards, makes
the wire _R_ touch _Q_. This at once causes the electro-magnet to give
a small pull to the steel arm of the tuning fork, and thus assists the
swing of the arm. The whole arrangement is exactly analogous to an
electric clock, as may be seen by comparing Fig. 71 with Fig. 68.
There is another method of measuring rapid intervals of time which also
merits attention. It is to let a body drop at the commencement of the
period of time to be measured, and mark how far it falls in the time,
and then find the time from the equation given previously,
S = 1/2 g t².
It is practically done by letting a piece of smoked glass fall and
making a small pointer make two dots upon it, one at the beginning,
another at the end, of the time to be measured.
An interesting adaptation of this method can serve as a basis of a
curious toy.
Take a crossbow, with a bolt with a spike on it; fix it firmly in a
vice so that the barrel points at a spot _a_ on a wooden wall. On the
spot _a_ hang a cardboard figure of a cat on to a nail so contrived
that when an electro-magnet acts the nail is pulled aside, and the
cat drops. Thus let _a_ be the cat, _b_ the loop by which it is hung
over the nail _c_, that is fixed to another piece of iron furnished
with a hinge at _c_, so that when the electric current is turned on
the nail _c_ is withdrawn and the cat drops. Carry the wires from the
electro-magnet and battery to the crossbow, and so arrange them that
when the bolt leaves the muzzle one is pressed against the other, and
contact made.
Now here you have an apparatus such that exactly as the bolt leaves the
crossbow, the cat drops. Now what will happen?
[Illustration: FIG. 72.]
When the bolt leaves the bow it is subject to two motions, one a motion
of projection at a uniform pace in the direction of _b a_ from the bow
to the target.
But it is also subject to another force, namely that of gravity, which
acts on it vertically, and deflects it _in a vertical direction_
exactly as much and as fast as a body would do if dropped from rest at
the same instant as the bolt leaves the bow. But the cat is such a
body. Hence, then, since by the electric arrangement they are both let
go together, they will both drop simultaneously, and thus will always
be on the same level, and when the bolt reaches the wooden wall and
has fallen vertically from _a_ to _c_, the cat will also have fallen
vertically from _a_ to _c_, and the bolt will pin him to the wall. It
does not matter how far you take the bow from the wall, nor how strong
the bow is, nor how heavy the bolt is, nor how heavy the cat is, nor
whether _a b_ is horizontal or pointing upwards or downwards.
[Illustration: FIG. 73.]
In every case, if only the barrel is pointed directly at the cat, then
the bolt and cat fall simultaneously and at the same rate, and the bolt
will pin the cat to the wall.
In trying the experiment the bolt should be pretty heavy, say half a
pound, and have a good spike; but if carefully done the experiment will
succeed every time. It enables you also to measure the speed of flight
of the bolt. For if the distance of the bow from the wall be thirty
feet, and the cat have fallen three feet when it is struck, then the
time of fall is T² = √((2S)/g) = √(6/g) = ·43 seconds. But the bolt
in this time went thirty feet; hence its velocity was thirty feet in
·43 seconds, or seventy feet per second.
Of course if you make the bolt heavier the velocity of projection will
become slower, the time longer, and hence the cat will fall further
before it is transfixed by the bolt.
My task is now at a close. I have endeavoured not merely to give a
description of clocks and various apparatus for measuring time, but to
explain the fundamental principles of mechanics which lie at the root
of the subject.
May I end with a word of advice to parents?
There is a certain number of boys, but only a certain number, who have
a real love for mechanical science. Such boys should be encouraged
in every way by the possession of tools and apparatus, but in the
selection of this apparatus the following principles should be borne in
mind:—
_First_, that almost everything a boy wants can be made with wood, and
metal, and wire, and string, _if_ he has someone to give him a little
instruction how to do it. A bent bit of steel jammed in a vice makes an
excellent tuning fork.
_Second_, that he wants not toy tools, but good tools. If an expert
wants a good tool, how much more a beginner.
_Third_, that he ought to have a reasonably dry and comfortable place
to work in, and the help and advice of the village carpenter or
blacksmith.
_Fourth_, that he ought not to be allowed to potter with his tools, but
to make something really sensible and useful, and not begin a dozen
things and finish none.
_Fifth_, that the making of apparatus to show scientific facts is more
useful than making bootjacks for his father or workboxes for his mother.
And, _lastly_, that a little money spent in this way will keep many a
young rascal from worrying his sisters and stoning the cat; and when
the inevitable time comes at which he must face the young man’s first
trial, THE EXAMINER, he will often thank his stars that he learned in
play the fundamental formula S = 1/2 g t², and that he knows the
nature of “harmonic motion,” the two most important principles in the
measurement of time.
THE END.
APPENDIX ON THE SHAPE OF THE TEETH OF WHEELS.
[Illustration: FIG. 74.]
The teeth of wheels for watches and clocks need particular care in
shaping, and it may be of interest if I describe briefly the principles
upon which these wheels are made. What is required is that the motion
shall not be communicated by jerks as the teeth successively engage one
another, but that the motion shall be perfectly smooth. The problem
therefore becomes this: How are we to arrange the teeth of the wheels
so that as one of them turns and drives the other round the leverage
or turning power exercised by the driving wheel on the driven wheel
shall always be uniform? Now if the teeth were simple spikes one can
easily see that this would not be the case. For instance, as the arm _a
c_ turned round, driving before it the arm _b d_, the point _c_ would
scrape along, and the leverage between the two teeth would constantly
alter. Evidently some other construction must be adopted. Before we can
determine what it is to be, we must inquire what the leverage would
be between two rods, _a c_ and _d b_, mounted on pivots at _a_ and
_d_. The answer to this question is, that when a lever such as _a c_
presses with its end against another, _d b_, the power is exercised in
a direction _c e_ at right angles to _d b_. Hence the leverage between
the two arms is in the ratio of _a e_ to _d c_. The system is just as
if we had a lever _a e_ united to a lever _d c_ by a rigid rod _e c_ at
right angles to both of them.
[Illustration: FIG. 75.]
Whence then the ratio of the power is as _a e_ is to _d c_.
[Illustration: FIG. 76.]
But since the triangles _a e f_, _d c f_, are similar, _a e_ is to _d
c_ as _a f_ to _f d_. Whence then we get this general proposition: If
one body mounted on an axis is pressing upon another body mounted
on an axis, the pressure exerted between them is always exercised in
a direction, shown by the dotted line, at right angles to the two
surfaces in contact; and the ratio of the leverage is found by drawing
a line from one axis to the other, so as to cut the line of direction
of pressure in _f_. The leverage of one on the other is then as _a f_
to _f d_. Our problem has now become the following: Given a rod _b d_,
suppose that it is pressed upon by a curved surface mounted on an axis
at _a_. Then the direction of the pressure that the curved surface
(called in engineering language a cam) will exercise on the rod _b d_
is shown by the dotted line; and the ratio of the driving power to the
driven power is as _d f_ to _a f_. Now how can we shape the cam so that
as it moves round, and different parts of its surface come successively
into contact with _b c_, the ratio of the leverage is always the
same; that is to say, the ratio of _a f_ to _f d_ shall always be
constant; that is to say, the line drawn through the point of contact
perpendicular to the curve at that point, shall always pass through the
point _f_?
[Illustration: FIG. 77.]
[Illustration: FIG. 78.]
Evidently, if this is to be so, the point _d_ must be on a semicircle,
whose diameter is _f b_, for in that case the angle _f d b_ will always
be a right angle.
[Illustration: FIG. 79.]
The surface must then be so arranged that, whatever be the position of
the cam and of the rod _b d_, the point of contact between them must
always be on the semicircle _f c d_; that is to say, as the cam moves
round the axis _a_ its shape must be such that a line drawn from _f_ to
the point where it cuts the circle _f d b_ is always perpendicular to
the curve.
Now suppose that we move a circle whose centre is at _a_, and radius _a
f_, so as to roll the circle _f d b_ by simple surface friction round
its centre _o_, then any point _d_ on it would mark out a curve on a
piece of paper attached to the moving circle whose centre is at _a_,
and the direction of motion of the curve would always be such that the
point _d_ on it would at any instant be describing a circle round _f_,
and the direction of the curve would thus at any point always be at
right angles to the line _d f_ for the time being.
[Illustration: FIG. 80.]
This curve, caused by the rolling of one circle on another, is called
an epicycloid. Hence, then, for a clock, if we make the pinion wheel
with straight spokes and the driving wheel with its teeth cut in the
form of epicycloids, caused by rolling a circle with a diameter equal
to the radius of the pinion upon the driving wheel, we shall get a
uniform ratio of leverage one upon the other.
The circles with radii _a f_, _b f_, are called the “pitch circles,”
and these radii are in the ratio of the movement that is required for
the wheels, usually six to one or eight to one, as the case may be. The
sides of the teeth of the pinion wheels are straight lines radiating
from the centre, and rounded off at the ends so as to avoid accidental
jambing. The teeth of the cogwheel have epicycloidal sides. The tips
are cut off so as to be out of the way, and spaces are left between
them for the width of the leaves of the pinion wheel.
[Illustration: FIG. 81.]
Both pinion wheels and cogwheels are cut by cutters rotating at a
high speed, about 3,500 times in a minute, the cutters being carefully
shaped for the pinion wheels with straight edges, for the cogwheels
in epicycloids. It is a pretty thing to see a wheel-cutting engine at
work, the cutter flying round with a hum, cutting the rim of a brass
wheel into teeth, the brass coming off in flakes thinner than fine
hairs and falling in fine dust. When a tooth is cut, the wheel is moved
round one division of an apparatus called a “dividing plate,” so as to
present a new part of the wheel to the cutter. Of course, the cutter
and wheels must all be properly proportioned. Cutters are sold in sets
duly shaped for the work they have to do. Wheel-cutting is a special
branch of the clockmaking industry. The reason the speed of cutting is
so high is because it is desired to take off small portions of metal
at a time, and thus not strain the wheel and the cutting machinery. If
bigger cuts were made, then the machine would have to go slower, for
it is a principle in the construction of cutting machinery that the
speed of the cut must always be proportioned to the depth of it. If
you want to take deep cuts you must move the cutting edge slowly, and
_vice versâ_. The most modern method of making cogwheels of brass, and
the best, is to stamp them out of solid sheet metal at a single punch
of a punching machine, and cheap watches are always made in this way.
In fact, the whole method of watch and clock-making is undergoing a
transformation.
Before the time of the great engineering development which took place
towards the end of the eighteenth century, the making of machines was
a sort of fine art. Cogwheels were cut by hand. The circumference
was marked out by means of compasses. Then holes were drilled round
the rim, and teeth cut out leading into them, and shaped by means of
special files constructed for the purpose (Fig. 82). Big machinery was
all shaped out at the forge and by the file. The engineers complained
that you could not get big work made true even to the eighth of an
inch. But watches and clocks were beautifully made, though only at the
cost of hours of patient measuring and filing. The taste for ornament
still existed. The wheels and backs of watches were chased over with
the most beautiful patterns; the frames of the clocks were wrought
into beautiful figures and forms. Even astronomical instruments were
embellished.
[Illustration: FIG. 82.]
Then came the era of severe accuracy. Men of science took the
government of machine-making whose feelings were repugnant to art in
any form. They hated to see any effort expended in ornament. With
severely utilitarian aims, they banished all appearance of beauty from
instruments and tools of all sorts, so that our modern machines, from a
steam engine down to a watch, are now models of precise but perfectly
unornamented workmanship. They are the fitting implements of a nation
that wears trousers and tall hats. One has only to compare an old
vessel of war, with its sculptured prow and streamers, with a modern
ironclad to take note of the difference. The art of ornamentation
is now little more than a spasmodic imitation of the past, with a
historical interest only. As a living entity it has almost ceased to
exist.
But in precision of manufacture the present age is without a rival in
the history of the world. People believe no longer in the old methods
of scraping and filing, and hand-work directly exercised on metal is
rapidly falling into desuetude. It is possible, of course, with a file
and scraper and days of labour to get two flat surfaces of metal so
perfect that when put together one will lift the other like a sucker
on a stone, but it is waste labour. A small machine will do it as well
in a few minutes. No longer is a watch built up as one would build a
house, fitting part to part. By expensive machines thousands of watch
parts are stamped and cut out to pattern, and then a watch is made by
taking one of each indiscriminately and just putting them into their
places. Comparatively unskilled workmen can do this. Where the skill
is wanted is to design and make the machinery and watch the cutters,
measuring them with microscopic gauges from time to time, and at once
remedying them if an edge is found to be a ten-thousandth part of an
inch out of place. So that the labour of man is becoming more and more
a labour of design and of supervision. Machines are the slaves that do
the work, for in a good machine we have an eye and an arm that never
tires, and only needs to be kept in working order. But machines are not
artistic, and thus art is lost while precision is gained. At present
a desperate attempt is being made to supply by means of machinery
the craving of the human mind for art. But it is destined to failure.
Art of this kind is generally produced by the same brain that designs
machines, and therefore presents an appearance of rigid accuracy and
uniformity, which, while essential to an engine, is out of place in an
artistic product.
The great manufacturers of our Midlands do not seem to understand that
there is no object in making a towel-horse as geometrically accurate as
a turning lathe. It will apparently be years before they learn to put
art and precision each in the place where it is wanted—precision in the
works of the watch, art in the face and the case of it; machine work in
the inside of a watch, hand work on the outside. When the public taste
is educated so as to see the odious character of the jumble of Gothic,
Egyptian, and meaningless ornament on such an article as the case of
an American organ, one step will have been made towards the revival of
artistic taste.
But to propose as a means of reviving art that we should discontinue
the use of machinery or abandon our modern cutters of precision to go
back to a hack-saw and file is ridiculous, and could only be suggested
by men quite destitute of scientific ideas. Art and precision each has
its place: there is room for both; let neither intrude on the domain of
the other.
INDEX.
Acceleration, 73, 77
Almagest, 53
Anchor escapement, 120
Ancient science, 50
Aristotle’s ideas, 23, 52
Attwood’s machine, 83
Babylon, temple of, 24
Balance wheel, 159
Candles to measure time, 46
Chaldean day, 15
Chaucer, 56
Chronographs, 179
Chronometer, 165
Chronometer escapement, 166
Clock movement, 123
Copernicus, 56
Crossbow experiment, 183
Crown wheel, 115
Cycloid, the, 109
Dante’s Inferno, 54
Day, length of, 29
Dead beat escapement, 135
Density, 12
Driving weight, 127, 141
Earth, a sphere, 21
Earth’s motion, 57, 69
Earth not at rest, 67
Egg-boiler, 43
Electric clocks, 179
Epicycloidal wheels, 191
Escapements, anchor, 120
crown, 115
chronometer, 166
dead beat, 135
gravity, 169
Falling bodies, laws of, 62
Force, 76
Forces, revolution of, 89
Fusee, the, 117
Galileo’s “Dialogues,” 58
clock, 111
Grandfather’s clock, 119
Gravity, action of, 13, 65
Gravity escapement, 169
Greek day, 16
Harmonic motion, 97
Hooke’s law, 71
Isochronism of springs, 93
Lamps to measure time, 46
Latitude and longitude, 161
finding, 163
Mass, nature of, 10
Mercury clock, 45
Modern methods, 177, 197
Moments, 101
Moon’s appearance, 17
Motion, reliability of, 57
Musical notes, 95
North pole, days at, 33
Oscillations, law of, 151
Parabola, the, 87
Pendulum, the, 103, 145
suspension, 145
mercury, 147
gridiron, 149
theory of, 155
free, 133
Pisa, leaning tower of, 61
Planets, names of, 11
Pulse measurer, 99
Ratchet wheels, 129
Roman clocks, 40
Sand-glasses, 41
Space, nature of, 8
Speed of falling bodies, 79
Spring balance, 107
Stevinus’ theory, 81
Style of sun-dials, 35
Sun-dials, 27
to make, 48
Synchronous clocks, 175
Time, 13
Toothed wheels, 125, 137
Tuning fork, 94, 181
Velocities, composition of, 85
Water pressure, 37
Water clocks, 39
Watches, 156
Week days, names of, 24
Wheels, shape of teeth, 190
Wheel-cutting machines, 193
Winding drum, 131
Winter sun, 31
Zodiac, 18
BRADBURY, AGNEW, & CO. LD., PRINTERS, LONDON AND TONBRIDGE.
* * * * * *
Transcriber’s note:
Punctuation, hyphenation, and spelling were made consistent when a
predominant preference was found in this book; otherwise they were not
changed.
Simple typographical errors were corrected; occasional unpaired
quotation marks were retained.
Ambiguous hyphens at the ends of lines were retained.
Square roots are represented as √(values).
Index not checked for proper alphabetization or correct page references.
Page 16: “six o’clock” was printed as “six clock”; changed here.