screw B has twenty-one; during one revolution, the screw A will
descend through a space equal to the 20th part of an inch. If, during
this motion, the screw B did not turn within A, the board D would be
advanced through the 20th of an inch; but because the hollow screw
within A turns upon B, the screw B will, relatively to A, be raised in
one revolution through a space equal to the 21st part of an inch. Thus,
while the board D is depressed through the 20th of an inch by the screw
A, it is raised through the 21st of an inch by the screw B. It is,
therefore, on the whole, depressed through a space equal to the excess
of the 20th of an inch above the 21st of an inch, that is, through the
420th of an inch.
The power of this machine will, therefore, be expressed by the number
of times the 420th of an inch is contained in the circumference through
which the power moves.
(298.) In the practical application of this principle at present the
arrangement is somewhat different. The two threads are usually cut
on different parts of the same cylinder. If nuts be supposed to be
placed upon these, which are capable of moving in the direction of
the length, but not of revolving, it is evident that by turning the
screw once round, each nut will be advanced through a space equal to
the breadth of the respective threads. By this means the two nuts
will either approach each other, or mutually recede, according to the
direction in which the screw is turned, through a space equal to the
difference of the breadth of the threads, and they will exert a force
either in compressing or extending any substance placed between them,
proportionate to the smallness of that difference.
(299.) A toothed wheel is sometimes used instead of a nut, so that
the same quality by which the revolution of the screw urges the nut
forward is applied to make the wheel revolve. The screw is in this
case called an endless screw, because its action upon the wheel may be
continued without limit. This application of the screw is represented
in _fig. 143._ P is the winch to which the power is applied; and
its effect at the circumference of the wheel is estimated in the same
manner as the effect of the screw upon the nut. This effect is to be
considered as a power acting upon the circumference of the wheel; and
its proportion to the weight or resistance is to be calculated in the
same manner as the proportion of the power to the weight in the wheel
and axle.
(300.) We have hitherto considered the screw as an engine used to
overcome great resistances. It is also eminently useful in several
departments of experimental science, for the measurement of very
minute motions and spaces, the magnitude of which could scarcely be
ascertained by any other means. The very slow motion which may be
imparted to the end of a screw, by a very considerable motion in the
power, renders it peculiarly well adapted for this purpose. To explain
the manner in which it is applied--suppose a screw to be so cut as
to have fifty threads in an inch, each revolution of the screw will
advance its point through the fiftieth part of an inch. Now, suppose
the head of the screw to be a circle, whose diameter is an inch, the
circumference of the head will be something more than three inches:
this may be easily divided into a hundred equal parts distinctly
visible. If a fixed index be presented to this graduated circumference,
the hundredth part of a revolution of the screw may be observed, by
noting the passage of one division of the head under the index. Since
one entire revolution of the head moves the point through the fiftieth
of an inch, one division will correspond to the five thousandth of an
inch. In order to observe the motion of the point of the screw in this
case, a fine wire is attached to it, which is carried across the field
of view of a powerful microscope, by which the motion is so magnified
as to be distinctly perceptible.
A screw used for such purposes is called a _micrometer screw_. Such an
apparatus is usually attached to the limbs of graduated instruments,
for the purposes of astronomical and other observation. Without the
aid of this apparatus, no observation could be taken with greater
accuracy than the amount of the smallest division upon the limb. Thus,
if an instrument for measuring angles were divided into small arcs of
one minute, and an angle were observed which brought the index of the
instrument to some point between two divisions, we could only conclude
that the observed angle must consist of a certain number of degrees and
minutes, together with an additional number of seconds, which would
be unknown, inasmuch as there would be no means of ascertaining the
fraction of a minute between the index and the adjacent division of
the instrument. But if a screw be provided, the point of which moves
through a space equal to one division of the instrument, with sixty
revolutions of the head, and that the head itself be divided into
one hundred equal parts, each complete revolution of the screw will
correspond to the sixtieth part of a minute, or to one second, and each
division on the head of the screw will correspond to the hundredth part
of a second. The index being attached to this screw, let the head
be turned until the index be moved from its observed position to the
adjacent division of the limb. The number of complete revolutions of
the screw necessary to accomplish this will be the number of seconds;
and the number of parts of a revolution over the complete number of
revolutions will be the hundredth parts of a second necessary to be
added to the degrees and minutes primarily observed.
It is not, however, only to such instruments that the micrometer screw
is applicable; any spaces whatever may be measured by it. An instance
of its mechanical application may be mentioned in a steel-yard,
an instrument for ascertaining the amount of weights by a given
weight, sliding on a long graduated arm of a lever. The distance from
the fulcrum, at which this weight counterpoises the weight to be
ascertained, serves as a measure to the amount of that weight. When the
sliding weight happens to be placed between two divisions of the arm, a
micrometer screw is used to ascertain the fraction of the division.
Hunter’s screw, already described, seems to be well adapted to
micrometrical purposes; since the motion of the point may be rendered
indefinitely slow, without requiring an exquisitely fine thread, such
as in the single screw would be necessary.
CHAP. XVII.
ON THE REGULATION AND ACCUMULATION OF FORCE.
(301.) It is frequently indispensable, and always desirable, that the
operation of a machine should be regular and uniform. Sudden changes
in its velocity, and desultory variations in the effective energy
of its power, are often injurious or destructive to the apparatus
itself, and when applied to manufactures never fail to produce
unevenness in the work. To invent methods for insuring the regular
motion of machinery, by removing those causes of inequality which may
be avoided, and by compensating others, has therefore been a problem to
which much attention and ingenuity have been directed. This is chiefly
accomplished by controlling, and, as it were, measuring out the power
according to the exigencies of the machine, and causing its effective
energy to be always commensurate with the resistance which it has to
overcome.
[Illustration: _C. Varley, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
Irregularity in the motion of machinery may proceed from one or more
of the following causes:--1. irregularity in the prime mover; 2.
occasional variation in the amount of the load or resistance; and, 3.
because, in the various positions which the parts of the machine assume
during its motion, the power may not be transmitted with equal effect
to the working point.
The energy of the prime mover is seldom if ever regular. The force of
water varies with the copiousness of the stream. The power which impels
the windmill is proverbially capricious. The pressure of steam varies
with the intensity of the furnace. Animal power, the result of will,
temper, and health is difficult of control. Human labour is most of
all unmanageable; hence no machine works so irregularly as one which
is manipulated. In some cases the moving force is subject, by the very
conditions of its existence, to constant variation, as in the example
of a spring, which gradually loses its energy as it recoils. (255.) In
many instances the prime mover is liable to regular intermission, and
is actually suspended for certain intervals of time. This is the case
in the single acting steam-engine, where the pressure of the steam
urges the descent of the piston, but is suspended during its ascent.
The load or resistance to which the machine is applied is not less
fluctuating. In mills there are a multiplicity of parts which are
severally liable to be occasionally disengaged, and to have their
operation suspended. In large factories for spinning, weaving,
printing, &c. a great number of separate spinning machines, looms,
presses, or other engines, are usually worked by one common mover, such
as a water-wheel or steam-engine. In these cases the number of machines
employed from time to time necessarily varies with the fluctuating
demand for the articles produced, and from other causes. Under such
circumstances the velocity with which every part of the machinery is
moved would suffer corresponding changes, increasing its rapidity with
every augmentation of the moving power or diminution of the resistance,
or being retarded in its speed by the contrary circumstances.
But even when the prime mover and the resistance are both regular, or
rendered so by proper contrivances, still it will rarely happen that
the machine by which the energy of the one is transmitted to the other
conveys this with unimpaired effect in all the phases of its operation.
To give a general notion of this cause of inequality to those who have
not been familiar with machinery would not be easy, without having
recourse to an example. For the present we shall merely state, that the
several moving parts of every machine assume in succession a variety of
positions; that at regular periods they return to their first position,
and again undergo the same succession of changes. In the different
positions through which they are carried in every period of motion,
the efficacy of the machine to transmit the power to the resistance
is different, and thus the effective energy of the machine in acting
upon the resistance would be subject to continual fluctuation. This
will be more clearly understood when we come to explain the methods of
counteracting the defect or equalising the action of the power upon the
resistance.
Such are the chief causes of the inequalities incidental to the
motion of machinery, and we now propose to describe a few of the many
ingenious contrivances which the skill of engineers has produced to
remove the consequent inconveniences.
(302.) Setting aside, for the present, the last cause of inequality,
and considering the machinery, whatever it be, to transmit the power to
the resistance without irregular interruption, it is evident that every
contrivance, having for its object to render the velocity uniform,
can only accomplish this by causing the variations of the power and
resistance to be proportionate to each other. This may be done either
by increasing or diminishing the power as the resistance increases or
diminishes; or by increasing or diminishing the resistance as the power
increases or diminishes.
According to the facilities or convenience presented by the peculiar
circumstances of the case either of these methods is adopted.
The contrivances for effecting this are called _regulators_. Most
regulators act upon that part of the machine which commands the supply
of the power by means of levers, or some other mechanical contrivance,
so as to check the quantity of the moving principle conveyed to the
machine when the velocity has a tendency to increase; and, on the
other hand, to increase that supply upon any undue abatement of its
speed. In a water-mill this is done by acting upon the shuttle; in a
wind-mill, by an adjustment of the sail-cloth; and in a steam-engine,
by opening or closing, in a greater or less degree, the valve by which
the cylinder is supplied with steam.
(303.) Of all the contrivances for regulating machinery, that which is
best known and most commonly used is the _governor_. This regulator,
which had been long in use in mill-work and other machinery, has of
late years attracted more general notice by its beautiful adaptation
in the steam-engines of Watt. It consists of heavy balls B B,
_fig. 144._, attached to the extremities of rods B F.
These rods play upon a joint at E, passing through a mortise in the
vertical stem D D′. At F they are united by joints to the short
rods F H, which are again connected by joints at H to a ring
which slides upon the vertical shaft D D′. From this description
it will be apparent that when the balls B are drawn from the axis,
their upper arms E F are caused to increase their divergence in
the same manner as the blades of a scissors are opened by separating
the handles. These, acting upon the ring by means of the short links
F H, draw it down the vertical axis from D towards E. A contrary
effect is produced when the balls B are brought closer to the axis, and
the divergence of the rods B E diminished. A horizontal wheel W is
attached to the vertical axis D D′, having a groove to receive a
rope or strap upon its rim. This strap passes round the wheel or axis
by which motion is transmitted to the machinery to be regulated, so
that the spindle or shaft D D′ will always be made to revolve with
a speed proportionate to that of the machinery.
As the shaft D D′ revolves, the balls B are carried round it
with a circular motion, and consequently acquire a centrifugal force
which causes them to recede from the axle, and therefore to depress
the ring H. On the edge or rim of this ring is formed a groove, which
is embraced by the prongs of a fork I, at the extremity of one arm of
a lever whose fulcrum is at G. The extremity K of the other arm is
connected by some means with the part of the machine which supplies
the power. In the present instance we shall suppose it a steam-engine,
in which case the rod K I communicates with a flat circular valve
V, placed in the principal steam-pipe, and so arranged that, when K is
elevated as far as by their divergence the balls B have power over it,
the passage of the pipe will be closed by the valve V, and the passage
of steam entirely stopped; and, on the other hand, when the balls
subside to their lowest position, the valve will be presented with its
edge in the direction of the tube, so as to intercept no part of the
steam.
The property which renders this instrument so admirably adapted to
the purpose to which it is applied is, that when the divergence of
the balls is not very considerable, they must always revolve with the
same velocity, whether they move at a greater or lesser distance from
the vertical axis. If any circumstance increases that velocity, the
balls instantly recede from the axis, and closing the valve V, check
the supply of steam, and thereby diminishing the speed of the motion,
restore the machine to its former rate. If, on the contrary, that
fixed velocity be diminished, the centrifugal force being no longer
sufficient to support the balls, they descend towards the axle, open
the valve V, and, increasing the supply of steam, restore the proper
velocity of the machine.
When the governor is applied to a water-wheel it is made to act upon
the shuttle through which the water flows, and controls its quantity as
effectually, and upon the same principle, as has just been explained in
reference to the steam-engine. When applied to a windmill it regulates
the sail-cloth so as to diminish the efficacy of the power upon the
arms as the force of the wind increases, or _vice versâ_.
In cases where the resistance admits of easy and convenient change, the
governor may act so as to accommodate it to the varying energy of the
power. This is often done in corn-mills, where it acts upon the shuttle
which metes out the corn to the millstones. When the power which drives
the mill increases, a proportionally increased feed of corn is given
to the stones, so that the resistance being varied in the ratio of the
power, the same velocity will be maintained.
(304.) In some cases the centrifugal force of the revolving balls is
not sufficiently great to control the power or the resistance, and
regulators of a different kind must be resorted to. The following
contrivance is called the _water-regulator_:--
A common pump is worked by the machine, whose motion is to be
regulated, and water is thus raised and discharged into a cistern.
It is allowed to flow from this cistern through a pipe of a given
magnitude. When the water is pumped up with the same velocity as it is
discharged by this pipe, it is evident that the level of the water in
the cistern will be stationary, since it receives from the pump the
exact quantity which it discharges from the pipe. But if the pump
throw in more water in a given time than is discharged by the pipe,
the cistern will begin to be filled, and the level of the water will
rise. If, on the other hand, the supply from the pump be less than
the discharge from the pipe, the level of the water in the cistern
will subside. Since the rate at which water is supplied from the
pump will always be proportional to the velocity of the machine, it
follows that every fluctuation in this velocity will be indicated by
the rising or subsiding of the level of the water in the cistern, and
that level never can remain stationary, except at that exact velocity
which supplies the quantity of water discharged by the pipe. This pipe
may be constructed so as by an adjustment to discharge the water at
any required rate; and thus the cistern may be adapted to indicate a
constant velocity of any proposed amount.
If the cistern were constantly watched by an attendant, the velocity of
the machine might be abated by regulating the power when the level of
the water is observed to rise, or increased when it falls; but this is
much more effectually and regularly performed by causing the surface
of the water itself to perform the duty. A float or large hollow metal
ball is placed upon the surface of the water in the cistern. This ball
is connected with a lever acting upon some part of the machinery, which
controls the power or regulates the amount of resistance, as already
explained in the case of the governor. When the level of the water
rises, the buoyancy of the ball causes it to rise also with a force
equal to the difference between its own weight and the weight of as
much water as it displaces. By enlarging the floating ball, a force may
be obtained sufficiently great to move those parts of the machinery
which act upon the power or resistance, and thus either to diminish
the supply of the moving principle or to increase the amount of the
resistance, and thereby retard the motion and reduce the velocity to
its proper limit. When the level of the water in the cistern falls,
the floating ball being no longer supported on the liquid surface,
descends with the force of its own weight, and producing an effect upon
the power or resistance contrary to the former, increases the effective
energy of the one, or diminishes that of the other, until the velocity
proper to the machine be restored.
The sensibility of these regulators is increased by making the surface
of water in the cistern as small as possible; for then a small change
in the rate at which the water is supplied by the pump will produce a
considerable change in the level of the water in the cistern.
Instead of using a float, the cistern itself may be suspended from
the lever which controls the supply of the power, and in this case a
sliding weight may be placed on the other arm, so that it will balance
the cistern when it contains that quantity of water which corresponds
to the fixed level already explained. If the quantity of water in
the cistern be increased by an undue velocity of the machine, the
weight of the cistern will preponderate, draw down the arm of the
lever, and check the supply of the power. If, on the other hand, the
supply of water be too small, the cistern will no longer balance the
counterpoise, the arm by which it is suspended will be raised, and the
energy of the power will be increased.
(305.) In the steam-engine the self-regulating principle is carried
to an astonishing pitch of perfection. The machine itself raises in
due quantity the cold water necessary to condense the steam. It pumps
off the hot water produced by the steam, which has been cooled, and
lodges it in a reservoir for the supply of the boiler. It carries from
this reservoir exactly that quantity of water which is necessary to
supply the wants of the boiler, and lodges it therein according as it
is required. It breathes the boiler of redundant steam, and preserves
that which remains fit, both in quantity and quality, for the use of
the engine. It blows its own fire, maintaining its intensity, and
increasing or diminishing it according to the quantity of steam which
it is necessary to raise; so that when much work is expected from the
engine, the fire is proportionally brisk and vivid. It breaks and
prepares its own fuel, and scatters it upon the bars at proper times
and in due quantity. It opens and closes its several valves at the
proper moments, works its own pumps, turns its own wheels, and is only
not alive. Among so many beautiful examples of the self-regulating
principle, it is difficult to select. We shall, however, mention one or
two, and for others refer the reader to our treatise on this subject.[3]
[3] Lardner on the Steam-Engine, Steam-Navigation, Roads, and Railways.
8th edition. 1851.
It is necessary in this machine that the water in the boiler be
maintained constantly at the same level, and, therefore, that as
much be supplied, from time to time, as is consumed by evaporation.
A pump which is wrought by the engine itself supplies a cistern C,
_fig. 145._, with hot water. At the bottom of this cistern is a
valve V opening into a tube which descends into the boiler. This valve
is connected by a wire with the arm of a lever on the fulcrum D, the
other arm E of which is also connected by a wire with a stone float F,
which is partially immersed in the water of the boiler, and is balanced
by a sliding weight A. The weight A only counterpoises the stone float
F by the aid of its buoyance in the water; for if the water be removed,
the stone F will preponderate, and raise the weight A. When the water
in the boiler is at its proper level, the length of the wire connecting
the valve V with the lever is so adjusted that this valve shall be
closed, the wire at the same time being fully extended. When, by
evaporation, the water in the boiler begins to be diminished, the level
falls, and the stone weight F, being no longer supported, overcomes
the counterpoise A, raises the arm of the lever, and, pulling the
wire, opens the valve V. The water in the cistern C then flows through
the tube into the boiler, and continues to flow until the level be so
raised that the stone weight F is again elevated, the valve V closed,
and the further supply of water from the cistern C suspended.
In order to render the operation of this apparatus easily
intelligible, we have here supposed an imperfection which does not
exist. According to what has just been stated, the level of the water
in the boiler descends from its proper height, and subsequently returns
to it. But, in fact, this does not happen. The float F and valve V
adjust themselves, so that a constant supply of water passes through
the valve, which proceeds exactly at the same rate as that at which the
water in the boiler is consumed.