would be uniform, provided that the moving power of the engine be
always proportionate to the load which it drives. But in the
general application of the steam engine to manufactures it was
evident that the amount of the resistance to which any given
machine would be subject must be liable to variation. If, for
example, the engine drive a cotton-mill, it will have to impart
motion to all the spinning frames in that mill. The operation of
one or more of these may from time to time be suspended, and the
moving power would be relieved from a corresponding amount of
resistance. If, under such circumstances, the energy of the moving
power remained the same, the velocity with which the machines
would be driven would be subject to variation, being increased
whenever the operation of any portion of the machines usually
[Pg207] driven by it is suspended; and, on the other hand,
diminished when any increased number of machines are brought into
operation. In fine, the speed would vary nearly in the inverse
proportion of the load driven, increasing as the load is
diminished, and _vice versâ_.
On the other hand, supposing that no change took place in the
amount of the load driven by the engine, and that the same number
of machines of whatever kind would have to be continually driven,
the motion imparted to the main axle would still be subject to
variation by the changes inevitable to the moving power. The
piston of the engine being subject to an unvaried resistance, a
uniform motion could only be imparted to it, by maintaining a
corresponding uniformity in the impelling power. This would
require a uniform supply of steam from the boiler, which would
further imply a uniform rate of evaporation in the boiler, unless
means were provided in the admission of steam from the boiler to
the cylinder to prevent any excess of steam which might be
produced in the boiler from reaching the cylinder.
[Illustration: _Fig._ 39.]
[Illustration: _Fig._ 40.]
This end was attained by a contrivance afterwards called the
_throttle-valve_. An axis A B (_figs._ 39, 40.) was placed across
the steam pipe in a ring of cast-iron D E, of proper thickness. On
this axis was fastened a thin circular plate T, of nearly the same
diameter as the steam pipe. On the outer end B of this axle was
placed a short lever or handle B C, by which it could be turned.
When the circular plate T was turned into such a position as to be
at right angles to the length of the tube, it stopped the passage
within the tube altogether, so that no steam could pass from the
boiler to the engine. On the other hand, when the handle was
turned through a fourth of a revolution from this position, then
the circular plate T had its plane in the direction of the length
of the tube, so that its edge would be presented towards the
current of steam flowing from the boiler to the cylinder. In that
position the passage within the tube [Pg208] would be necessarily
unobstructed by the throttle-valve. In intermediate positions of
the valve, as that represented in _figs._ 39, 40., the passage
might be left more or less opened, so that steam from the boiler
might be admitted to the cylinder in any regulated quantity
according to the position given to the lever B C.
A view of the throttle-valve taken by a section across the steam
pipe is exhibited in _fig._ 40., and a section of it through the
axis of the steam pipe is represented in _fig._ 39. The form of
the valve is such, that, if accurately constructed, the steam in
passing from the boiler would have no effect by its pressure to
alter any position which might be given to the valve; and any
slight inaccuracy of form which might give a tendency to the steam
to alter the position would be easily counteracted by the friction
of the valve upon its axle. The latter might be regulated at
pleasure.
By this expedient, however the evaporation of water in the boiler
might vary within practical limits, the supply of steam to the
cylinder would be rendered regular and uniform. If the boiler became
too active, and produced more steam than was necessary to move the
engine with its load at the requisite speed, then the throttle-valve
was shifted so as to contract the passage and limit the supply of
steam. If, on the other hand, the process of evaporation in the
boiler was relaxed, then the throttle-valve was placed with its edge
more directed towards the steam. Independently of the boiler, if the
load on the engine was lightened, then the same supply of steam to
the cylinder would unduly accelerate the motion. In this case,
likewise, the partial closing of the throttle-valve would limit the
supply of steam and regulate the motion; and if, on the other hand,
the increase of load upon the engine rendered necessary an increased
supply of steam, then the opening of the throttle-valve would
accomplish the purpose. By these means, therefore, a uniform motion
might be maintained, provided the vigilance of the engine-man
was sufficient for the due management of the lever B C, and
provided that the furnace under the boiler was kept in sufficient
activity to supply the greatest amount of steam which would be
necessary [Pg209] for the maintenance of a uniform motion with the
throttle-valve fully opened.
(125.) Watt, however, soon perceived that the proper manipulation
of the lever B C would be impracticable with any degree of
vigilance and skill which could be obtained from the persons
employed to attend the engine. He, therefore, adapted to this
purpose a beautiful application of a piece of mechanism, which had
been previously used in the regulation of mill-work, and which has
since been well known by the name of the _Governor_, and has
always been deservedly a subject of much admiration.
The governor is an apparatus by which the axle of the fly-wheel is
made to regulate the throttle-valve, so that the moment that the
axle begins to increase its velocity, it shifts the position of
the throttle-valve, so as to limit the supply of steam from the
boiler, and thereby to check the increase of speed. And on the
other hand, whenever the velocity of the axle is diminished, the
lever B C is moved in the contrary direction, so as to open more
fully the passage for the steam, and accelerate the motion of the
engine.
A small grooved wheel A B (_fig._ 41.) is attached to a vertical
spindle supported in pivots or sockets C and D, in which it is
capable of revolving. An endless cord works in the groove A B, and
is carried over proper pulleys to the axle of the fly-wheel, where
it likewise works in a groove. When this cord is properly
tightened the motion of the fly-wheel will give motion to the
wheel A B, so that the velocity of the one will be subject to all
the changes incidental to the velocity of the other. By this means
the speed of the grooved wheel A B may be considered as
representing the speed of the fly-wheel, and of the machinery
which the axle of the fly-wheel drives.
[Illustration: _Fig._ 41.]
It is evident that the same end might be attained by substituting
for the grooved wheel A B a toothed wheel, which might be
connected by other toothed wheels, and proper shafts, and axles
with the axle of the fly-wheel.
A ring or collar E is placed on the upright spindle, so as to be
capable of moving freely upwards and downwards. To this ring are
attached by pivots two short levers, E F, the [Pg210] pivots or
joints at E allowing these levers to play upon them. At F these
levers are joined by pivots to other levers F G, which cross each
other at H, where an axle or pin passes through them, and attaches
them to the upright spindle C D. These intersecting levers are
capable, however, of playing on this axle or pin H. To the ends G
of these levers are attached two heavy balls of metal I. The
levers F G pass through slits in a metallic arch attached to the
upright spindle, so as to be capable of revolving upon it. If the
balls I are drawn outwards from the vertical axis, it is evident
that the ends F of the levers will be drawn down, and therefore
the pivots E likewise drawn down. In fact, the angles E F H will
become more acute, and the angle F E F more obtuse. By these means
the sliding ring E will be drawn down. To this sliding ring E, and
immediately above it, is attached a grooved collar, which slides
on the vertical spindle upwards and downwards with the ring E. In
the grooved collar are inserted the prongs of a fork K, formed at
the end of the lever K L, the fulcrum or pivot of the lever being
at L. By this arrangement, when the divergence of the balls I
causes the collar E to be drawn down, the fork K, whose prongs are
inserted in the groove of that collar, is likewise drawn down;
and, on the other hand, when, by reason of the balls I falling
towards the [Pg211] vertical spindle, the collar E is raised, the
fork K is likewise raised.
The ascent and descent of the fork K necessarily produce a
contrary motion in the other end N of the lever. This end is
connected by a rod, or system of rods, with the end M of the short
lever which works the throttle-valve T. By such means the motion
of the balls I, towards or from the vertical spindle, produces in
the throttle-valve a corresponding motion; and they are so
connected that the divergence of the balls I will cause the
throttle-valve to close, while their descent towards the vertical
spindle will cause it to open.
These arrangements being comprehended, let us suppose that, either
by reason of a diminished load upon the engine or an increased
activity of the boiler, the speed has a tendency to increase. This
would impart increased velocity to the grooved wheel A B, which
would cause the balls I to revolve with an accelerated speed. The
centrifugal force which attends their motion would therefore give
them a tendency to move from the axle, or to diverge. This would
cause, by the means already explained, the throttle-valve T to be
partially closed, by which the supply of steam from the boiler to
the cylinder would be diminished, and the energy of the moving
power, therefore, mitigated. The undue increase of speed would
thereby be prevented.
If, on the other hand, either by an increase of the load, or a
diminished activity in the boiler, the speed of the machine was
lessened, a corresponding diminution of velocity would take place
in the grooved wheel A B. This would cause the balls I to revolve
with less speed, and the centrifugal force produced by their
circular motion would be diminished. This force being thus no
longer able fully to counteract their gravity, they would fall
towards the spindle, which would cause, as already explained, the
throttle-valve to be more fully opened. This would produce a more
ample supply of steam to the cylinder, by which the velocity of
the machine would be restored to its proper amount.
[Illustration: _Fig._ 42.]
(126.) The principle which renders the governor so perfect a
regulator of the velocity of the machine is difficult to be
[Pg212] explained without having recourse to the aid of the
technical language of mathematical physics. As, however, this
instrument is of such great practical importance, and has
attracted such general admiration, it may be worth while here to
attempt to render intelligible the mechanical principles which
govern its operation. Let S (_fig._ 42.) be the point of
suspension of a common pendulum S P, and let P O P′ be the arch of
its vibration, so that the ball P shall swing or vibrate
alternately to the east and to the west of the lowest point O,
through the arches O P′ and O P. It is a property of such an
instrument that, provided the arch in which it vibrates be not
considerable in magnitude, the time of its vibration will be the
same whether the arch be long or short. Thus, for example, if the
pendulum, instead of vibrating in the arch P P′, vibrated in the
arch _p p′_, the time which it would take to perform its
vibrations would be the same. If, however, the magnitude of the
arch of vibration be increased, then a variation will take place
in the time of vibration; but unless the arch of vibration be
considerably increased, this variation will not be great.
Now let it be supposed that while the pendulum P P′ continues to
vibrate east and west through the arch P P′, it shall receive such
an impulse from north and south as would, if it were not in a
state of previous vibration, cause it to vibrate between north and
south, in an arch similar to the arch P P′. This second vibration
between north and south [Pg213] would not prevent the continuance
of the other vibration between east and west; but the ball P would
be at the same time affected by both vibrations. While, in virtue
of the vibration from east to west, the ball would swing from P to
P′, it would, in virtue of the other vibration, extend its motion
towards the north to a distance from the line W E equal to half a
vibration, and will return from that distance again to the
position P′. While returning from P′ to P, its second vibration
will carry it towards the south to an equal distance on the
southern side of W E, and it will return again to the position P.
If the combination of these two motions or vibrations be
attentively considered, it will be perceived that the effect on
the ball will be a circular motion, precisely similar to the
circular motion of the balls of the governor already described.
Now the time of vibration of the pendulum S P between east and
west will not in any way be affected by the second vibration,
which it is supposed to receive between north and south, and
therefore the time the pendulum takes in moving from P to P′ and
back again from P′ to P will be the same whether it shall have
simultaneously or not the other vibration between north and south.
Hence it follows that the time of revolution of the circular
pendulum will be equal to the time of similar vibrations of the
same pendulum, if, instead of having a circular motion, it were
allowed to vibrate in the manner of a common pendulum.
If this point be understood, and if it also be remembered that the
time of vibration of a common pendulum is necessarily the same
whether the arch of vibration be small or great, it will be easily
perceived that the revolving pendulum or governor will have nearly
the same time of revolution whether it revolve in a large circle
or a small one: in other words, whether the balls revolve at a
greater or a less distance from the central spindle or axis. This,
however, is to be understood only approximately. When the angle of
divergence of the balls is as considerable as it usually is in
governors, the time of revolution at different distances from the
axis will therefore be subject to some variation, but to a very
small one. [Pg214]
The centrifugal force (which is the name given in mechanics to
that influence which makes a body revolving in a circle fly from
the centre) depends conjointly on the velocity of revolution, and
on the distance of the revolving body from the centre of the
circle. If the velocity of revolution be the same, then the
centrifugal force will increase in the same proportion as the
distance of the revolving body from the centre. If, on the other
hand, the distance of the revolving body from the centre remain
the same, the centrifugal force will increase in the same
proportion as the square of the time of vibration diminishes, or,
in other words, it will increase in the same proportion as the
square of the number of revolutions per minute. It follows from
this, therefore, that the greater is the divergence of the balls
of the governor, and the more rapidly they revolve, the greater
will be their centrifugal force. Now this centrifugal force, if it
were not counterbalanced, would give the balls a constant tendency
to recede from the centre; but from the construction of the
apparatus, the further they are removed from the centre the
greater will be the effect of their gravitation in resisting the
centrifugal force.
It is evident that the ball at P will have a greater tendency to
fall by gravitation towards O than it would have at _p_, because
the acclivity of the arch descending towards O at P is greater
than its acclivity at _p_. The gravitation, therefore, or tendency
of the ball to fall towards the central axis being greater at P
than at _p_ it will be able to resist a greater centrifugal force.
This increased centrifugal force, which the ball would have
revolving at the distance P above what it would have at the
distance _p_, is produced partly by the greater distance of the
ball from the central axis, and partly by the greater velocity of
its motion. But it will be evident that the time of its revolution
may nevertheless be the same, or nearly the same, at both
distances. If it should appear that the actual velocity of its
motion of revolution at P be greater than its velocity at _p_, in
the same proportion as the circles in which they revolve, then it
is evident that the time of revolution would be as much increased
by the greater space which P will have to travel over, as it will
have to be [Pg215] diminished by the greater speed with which
that space is traversed. The time of revolution, therefore, may be
the same, or nearly the same, in both cases.
If this explanation be comprehended, it will not be difficult to
apply it to the actual case of the governor. If a sudden increase
of the energy of the moving power, or a diminution of the load,
should give the machine an increased velocity, then the increased
speed of the balls of the governor will give them an increased
centrifugal force, which for the moment will be greater than the
tendency of their gravitation to make them fall towards the
vertical axis. This centrifugal force, therefore, prevailing, the
balls will recede from the axis; but as they recede, their
gravitation towards the vertical axis will, as has been already
explained, be increased, and will become equal to the centrifugal
force produced by the increased velocity, provided that velocity
do not exceed a certain limit. When the balls, by diverging, get
such increased gravitation as to balance the centrifugal force,
then they will continue to revolve at a fixed distance from the
vertical axis. When this happens, the time of the revolution must
be nearly the same as it was before their increased divergence; in
other words, the proportion of the moving power to the load will
be so restored by the action of the levers of the governor on the
throttle-valve that the machine will move at its former velocity,
or nearly so.
The principle on which the governor acts, as just explained,
necessarily supposes temporary disarrangements of the speed. In
fact, the governor, strictly speaking, does not maintain a uniform
velocity, but restores it after it has been disturbed. When a
sudden change of motion of the engine takes place, the governor
being immediately affected will cause a corresponding alteration
in the throttle-valve; and this will not merely correct the change
of motion, but it will, as it were, overdo it, and will cause a
derangement of speed of the opposite kind. Thus if the speed be
suddenly increased to an undue amount, then the governor being
affected will first close the throttle-valve too much, so as to
reduce the speed below the proper limit. This second error will
again affect the governor in the contrary way, and the speed
[Pg216] will again be increased rather too much. In this way a
succession of alterations of effect will ensue until the governor
settles down into that position in which it will maintain the
engine at the proper speed.
To prevent the inconvenience which would attend any excess of such
variations, the governor is made to act with great delicacy on the
throttle-valve, so that even a considerable change in the
divergence of the balls shall not produce too much alteration in
the opening of that valve: the steam in the boiler should have at
least 2 lbs. per square inch pressure more than is generally
required in the cylinder. This excess is necessary to afford scope
for that extent of variation of the power which it is the duty of
the throttle-valve to regulate.
The governor is usually so adjusted as to make thirty-six
revolutions per minute, when in uniform motion; but if the motion
is increased to the rate of thirty-nine revolutions, the balls
will fly to the utmost extent allowed them, being the limitation
of the grooves in which their rods move; and if, on the other
hand, the speed be diminished to thirty-four revolutions per
minute, they will collapse to the lowest extent of their play. The
duty of the governor, therefore, is to correct smaller casual
derangements of the velocity; but if any permanent change to a
considerable extent be made either in the load driven by the
machine or in the moving power supplied to it from the boiler,
then a permanent change is necessary to be made in the connection
between the governor and the throttle-valve, so as to render the
governor capable of regulating those smaller changes to which the
speed of the machine is liable.
(127.) Having thus explained the principal mechanical contrivances
provided by Watt for the maintenance and regulation of the
rotatory motion to be produced by his double-acting steam engine,
let us now consider the machine as a whole, and investigate the
process of its operation. A section of this engine is represented
in _fig._ 43.
[Illustration: _Fig._ 43.]