resistance, then all that portion of the resistance which exceeds
the amount of the moving force will be expended in depriving the
mass of the body of momentum, and the body will therefore be moved
with continually diminished speed until it be brought to rest.
(88.) Whenever, therefore, a uniform motion is produced in a body,
it may be taken as an indication of the equality of the moving
force to the resistance; and, on the other hand, according as the
speed of the body is augmented or diminished, it may be inferred
that the energy of the moving force has been greater or less than
the resistance.
It is an error to suppose that rest is the only condition possible
for a body to assume when under the operation of two or more
mechanical forces which are in equilibrium. By the laws of motion
the state of a body which is not under the operation of any
external force must be either in a state of rest or of uniform
motion. Whichever be its state, it will suffer no change if the
body be brought under the operation of two or more forces which
are in equilibrium; for to suppose [Pg159] such forces to produce
any change in the state of the body, whether from rest to motion,
or _vice versâ_, or in the velocity of the motion which the body
may have previously had, would be equivalent to a supposition that
the forces applied to the body being in equilibrium were capable
of producing a dynamical effect, which would be a contradiction in
terms. This, though not always clearly understood by mere
practical men, or by persons superficially informed, is, in fact,
among the fundamental principles of mechanical science.
(89.) When the piston is at the top of the cylinder, and about to
commence its motion downwards, the steam acting upon it will have
not only to overcome the resistance arising from the friction of
the various parts of the engine, but will also have to put in
motion the whole mass of matter of the piston pump rods, pump
pistons, and the column of water in the pump barrels. Besides
imparting to this mass the momentum corresponding to the velocity
with which it will be moved, it will also have to encounter the
resistance due to the preponderance of the weight of the water and
pump rods over that of the steam piston. The pressure of steam,
therefore, upon the piston at the commencement of the stroke must,
in accordance with the mechanical principles just explained, have
a greater force than is equal to all the resistances which it
would have to overcome, supposing the mass to be moving at a
uniform velocity. The moving force, therefore, being greater than
the resistance, the mass, when put in motion, will necessarily
move with a gradually augmented speed, and the piston of the
engine which has been described in the last chapter would
necessarily move from the top to the bottom of the cylinder with
an accelerated motion, having at the moment of its arrival at the
bottom a greater velocity than at any other part of the stroke. As
the piston and all the matter which it has put in motion must at
this point come to rest, the momentum of the moving mass must
necessarily expend itself on some part of the machinery, and would
be so much mechanical force lost. It is evident, therefore,
independently of any consideration of the expansive principle, to
which we shall presently refer, that the action of the [Pg160]
moving power in the descent of the piston ought to be suspended
before the arrival of the piston at the bottom of the cylinder, in
order to allow the momentum of the mass which is in motion to
expend itself, and to allow the piston to come gradually to rest
at the termination of the stroke.
Thus, if we were to suppose that after the piston had descended
through three fourths of the whole length of the cylinder, and had
acquired a certain velocity, the steam above it were suddenly
condensed, so as to leave a vacuum both above and below it, the
piston, being then subject to no impelling force, would still move
downwards, in virtue of the momentum it had acquired, until the
resistance would deprive it of that momentum, and bring it to
rest; and if the remaining fourth part of the cylinder were
necessary for the accomplishment of this, then it is evident that
that part of the stroke would be accomplished without further
expenditure of the moving power.
In fact, this part of the stroke would be made by the expenditure
of that excess of moving power, which, at the commencement of the
stroke, had been employed in putting the machinery and its load in
motion, and in subsequently accelerating that motion.
Although under such circumstances the resistance, during the
operation of the moving power, shall not have been at any time
equal to the moving power, since while the motion was accelerated
it was less, and while retarded greater than that power, yet as
the whole moving power has been expended upon the resistance, the
mechanical effect which the moving power has produced under such
circumstances will be equal to the actual amount of that power. If
in an engine of this kind the steam was not cut off till the
conclusion of the stroke, a part of the moving power would be lost
upon those fixed points in the machinery which would sustain the
shock produced by the instantaneous cessation of motion at the end
of the stroke.
Independently, therefore, of any consideration of the expansive
principle, it appears that, in an engine of this kind, the steam
ought to be cut off before the completion of the stroke. [Pg161]
[Illustration: _Fig._ 28.]
(90.) To render the expansive action of steam intelligible, let A
B (_fig._ 28.) represent a cylinder whose area we will suppose,
for the sake of illustration, to be a square foot, and whose
length, A B, shall also be a foot. If steam of a pressure equal to
the atmosphere be supplied to this cylinder, it will exert a
pressure of about one ton on the piston; and if such steam be
uniformly supplied from the boiler, the piston will be moved from
A to B with the force of one ton, and that motion will be uniform
if the piston be opposed throughout the same space by a resistance
equal to a ton. When the piston has arrived at B, let us suppose
that the further supply of steam from the boiler is stopped by
closing the upper steam valve, and let us also suppose the
cylinder to be continued downwards so that B C shall be equal to A
B, and suppose that B C has been previously in communication with
the condenser, and is therefore a vacuum. The piston at B will
then be urged with a force of one ton downwards, and as it
descends the steam above it will be diffused through an increased
volume, and will consequently acquire a diminished pressure. We
shall, for the present, assume that this diminution of pressure
follows the law of elastic fluids in general; that it will be
decreased in the same proportion as the volume of the steam is
augmented. While the piston, therefore, moves from B downwards it
will be urged by a continually decreasing force. Let us suppose,
that by some expedient, it is also subject to a continually
decreasing resistance, and that this resistance decreases in the
same proportion as the force which urges the piston. In that case
the motion of the piston would continue uniform. When the piston
would arrive at P′, the middle of the second cylinder, then the
space occupied by the steam being increased in the proportion of 2
to 3, the pressure on the piston would be diminished in the
proportion of 3 to 2, and the pressure at B being one ton, it
would be two-thirds of a ton at P′. In like manner when the piston
would arrive at C, the space occupied by the steam being double
that which [Pg162] it occupied when the piston was at B, the
pressure of the steam would be half its pressure at B, and
therefore at the termination of the stroke, the pressure on the
piston would be half a ton.
If the space from B to C, through which the steam is here supposed
to act expansively, be divided into ten equal parts, the pressure
on the piston at the moment of passing each of those divisions
would be calculated upon the same principle as in the cases now
mentioned. After moving through the first division, the volume of
the steam would be increased in the proportion of 10 to 11, and
therefore its pressure would be diminished in the proportion of 11
to 10. The pressure, therefore, driving the piston at the end of
the first of these ten divisions would be 10/11ths of a ton. In
like manner, its pressure at the second of the divisions would be
10/12ths of a ton, and the third 10/13ths of a ton; and so on, as
indicated in the figure.
Now if the pressure of the steam through each of these divisions
were to continue uniform, and, instead of gradually diminishing,
to suffer a sudden change in passing from one division to another,
then the mechanical effect produced from B to C would be obtained
by taking a mean or average of the several pressures throughout
each of the ten divisions. In the present case it has been
supposed that the force on the piston at B was 2240 pounds. To
obtain the pressure in pounds corresponding to each of the
successive divisions, it will therefore only be necessary to
multiply 2240 by 10, and to divide it successively by 11, 12, 13,
&c. The pressures, therefore, in pounds, at each of the ten
divisions, will be as follows:—
1st 2036·3
2d 1866·6
3d 1723·1
4th 1600·0
5th 1493·3
6th 1400·0
7th 1317·6
8th 1244·4
9th 1179·0
10th 1120·0
If the mean of these be taken by adding them together [Pg163] and
dividing by 10, it will be found to be 1498 pounds. It appears,
therefore, that the pressures through each of the ten divisions
being supposed to be uniform (which however, strictly, they are
not,) the mechanical effect of the steam from B to C would be the
same as if it acted uniformly throughout that space upon the
piston with a force of about 1500 pounds, being rather less than
three-fourths of its whole effect from A to B.
But it is evident that this principle will be equally applicable
if the second cylinder had any other proportion to the first. Thus
it might be twice the length of the first; and in that case, a
further mechanical effect would be obtained from the expansion of
the steam.
The more accurate method of calculating the effect of the
expansion from B to C, would involve more advanced mathematical
principles than could properly be introduced here; but the result
of such a computation would be that the actual average effect of
the steam from B to C would be equal to a uniform pressure through
that space, amounting to one thousand five hundred and forty-five
pounds, being greater than the result of the above computation,
the difference being due to the expansive action through each of
the ten divisions, which was omitted in the above computation.
(91.) It is evident that the expansive principle, as here explained,
involves the condition of a variation in the intensity of the moving
power. Thus, if the steam act with a uniform energy on the piston so
long as its supply from the boiler continues, the moment that supply
is stopped, by closing the steam valve, the steam contained in the
cylinder will fill a gradually increasing volume by the motion of
the piston, and therefore will act above the piston with a gradually
decreasing energy. If the resistance to the moving power produced by
the load, friction, &c. be not subject to a variation corresponding
precisely to such variation in the moving power, then the
consequence must be that the motion imparted to the load will cease
to be uniform. If the energy of the moving power at any part of the
stroke be greater than the resistance, the motion produced will be
accelerated; if it be less, the motion will be retarded; and if it
be at one time greater, and another [Pg164] time less, as will
probably happen, then the motion will be alternately accelerated and
retarded. This variation in the speed of the body moved will not,
however, affect the mechanical effect produced by the power,
provided that the momentum imparted to the moving mass be allowed to
expend itself at the end of the stroke, so that the piston may be
brought to rest as nearly as possible by the resistance of the load,
and not by any shock on any fixed points in the machine. This is an
object which, consequently, should be aimed at with a view to the
economy of power, independently of other considerations connected
with the wear and tear of the machinery. So long as the engine is
only applied to the operation of pumping water, great regularity of
motion is not essential, and, therefore, the variation of speed
which appears to be an almost inevitable consequence of any
extensive application of the expansive principle, is of little
importance. In the patent which Watt took out for the application of
the expansive principle, he specified several methods of producing a
uniform effect upon a uniform resistance, notwithstanding the
variation of the energy of the power which necessarily attended the
expansion of the steam. This he proposed to accomplish by various
mechanical means, some of which had been previously applied to the
equalisation of a varying power. One consisted in causing the piston
to act on a lever, which should have an arm of variable length, the
length increasing in the same proportion as the energy of the moving
power diminished. This was an expedient which had been already
applied in mechanics for the purpose of equalising a varying power.
A well-known example of it is presented in the main-spring and fuzee
of a watch. According as the watch goes down, the main-spring
becomes relaxed, and its force is diminished; but, at the same time,
the chain by which it drives the fuzee acts upon a wheel or circle,
having a diameter increased in the same proportion as the energy of
the spring is diminished.
Another expedient consisted in causing the moving power, when
acting with greatest energy, to lift a weight which should be
allowed to descend again, assisting the piston when the energy of
the moving force was diminished. [Pg165]
Another method consisted in causing the moving force, when acting
with greatest energy, to impart momentum to a mass of inert
matter, which should be made to restore the same force when the
moving power was more enfeebled. We shall not more than allude
here to these contrivances proposed by Watt, since their
application has never been found advantageous in cases where the
expansive principle is used.
(92.) The application of the expansive principle in the engines
constructed by Boulton and Watt, was always very limited, by
reason of their confining themselves to the use of steam having a
pressure not much exceeding that of the atmosphere. If the
principle of expansion, as above explained, be attentively
considered, it will be evident that the extent of its application
will mainly depend on the density and pressure of the steam
admitted from the boiler. If the density and pressure be not
considerable when the steam is cut off, the extent of its
subsequent expansion will be proportionally limited. It was in
consequence of this, that this principle from which considerable
economy of power has been derived, was applied with much less
advantage by Mr. Watt than it has since been by others, who have
adopted the use of steam of much higher pressure. In the engines
of Boulton and Watt, where the expansive principle was applied,
the steam was cut off after the piston had performed from one half
to two thirds of the stroke, according to the circumstances under
which the engine was worked. The decreasing pressure produced by
expansion was, in this case, especially with the larger class of
engines, little more than would be necessary to allow the momentum
of the mass moved to spend itself, before the arrival of the
piston at the end of the stroke.
Subsequently, however, boilers producing steam of much higher
pressure were applied, and the steam was cut off when the piston
had performed a much smaller part of the whole stroke. The great
theatre of these experiments and improvements has been the mining
districts in Cornwall, where, instead of working with steam of a
pressure not much exceeding that of the atmosphere, it has been
found advantageous to use steam whose pressure is at least four
times as great as [Pg166] that of the atmosphere; and instead of
limiting its expansion to the last half or fourth of the stroke,
it is cut off after the piston has performed one fourth part of
the stroke or less, all the remainder of the stroke being
accomplished by the expansive power of the steam, and by momentum.
[Illustration: BRIDGE OVER THE CLYDE AT HAMILTON, DESIGNED BY
WATT.]
[Pg167]
[Illustration: DOUBLE-ACTING ENGINE, ZINC WORKS, CITY ROAD,
LONDON.]
CHAP. VII.
PROPERTIES OF STEAM. — COMMON STEAM. — SUPERHEATED STEAM. —
LAW OF DALTON AND GAY LUSSAC. — LAW OF MARIOTTE. — RELATION
BETWEEN TEMPERATURE AND PRESSURE OF COMMON STEAM. — EFFECTS OF
THE EXPANSION OF COMMON STEAM. — MECHANICAL EFFECTS OF STEAM.
— METHOD OF EQUALISING THE EXPANSIVE FORCE. — HORNBLOWER'S
ENGINE. — WOOLF'S ENGINE. — WATT'S ATTEMPTS TO EXTEND THE
STEAM ENGINE TO MANUFACTURES. — PAPIN'S PROJECTED APPLICATIONS
OF THE STEAM ENGINE. — SAVERY'S APPLICATIONS OF THE ENGINE TO
MOVE MACHINERY. — JONATHAN HULL'S APPLICATION TO WATER WHEELS.
— STEWART'S APPLICATION OF THE ENGINE TO MILL WORK. —
WASHBOROUGH'S APPLICATION OF THE FLY WHEEL AND CRANK. — WATT'S
SECOND PATENT. — DOUBLE-ACTION VALVES.
(93.) Since the application of the expansive action of steam
involves the consideration of its properties when it ceases to be
in contact with the water from which it was produced, and likewise
the variation of its pressure in different states of [Pg168]
density and at different temperatures, it is necessary here to
explain some of the most important of these properties of vapour.
Steam may exist in two states, distinguished from each other by
the following circumstances:—
1st. It may be such that the abstraction from it of any portion of
heat, however small, will cause its partial condensation.
2d. It may be such as to admit of the abstraction of heat from it
without undergoing any other change than that which air would
undergo under like circumstances, viz. a diminution of temperature
and pressure.
(94.) We shall call, for distinction, the former _Common Steam_,
and the latter _Superheated Steam_.
[Illustration: _Fig._ 29.]
To explain the circumstances out of which these properties arise,
let B (_fig._ 29.) be imagined to be a vessel filled with water,
communicating by a pipe and stopcock with another vessel A, which
in the commencement of the process may be conceived to be filled
with air. Let D be a pipe and stopcock at the top of this vessel.
If the vessel B be heated, and the two cocks be opened, the steam
proceeding from the water in B will blow the air out of the vessel
A through the open stopcock D, in the same manner as air is blown
from a steam engine. When the vessel A by these means has been
filled with pure steam, let both stopcocks be closed. If the steam
in A, under these circumstances, have a pressure of 15 lbs. per
square inch, its temperature will be found to be 213°. Now, if any
heat be abstracted from this steam, its temperature will fall, and
a portion of it will be reconverted into water.
Again, suppose the vessel A to be filled with pure steam which has
been produced from the heated water in B, the stopcock C being
open. Let the stopcock C be then closed, and the water in B be
heated to a higher temperature, the temperature and pressure of
the steam in A being observed. If the stopcock C be now opened,
the steam in A will be immediately observed to rise to the more
elevated temperature which has been imparted to the water in B,
and at the same time it will acquire an increased pressure.
[Pg169]
The increase of temperature which it has received would of itself
produce an increased pressure; but that this is not the sole cause
of the augmented pressure in the present case might be proved by
weighing the vessel A. It would be found to have increased weight,
which could only arise from its having received from the water in
B an additional quantity of vapour. The increased pressure
therefore, which the steam in A has acquired, is due conjointly to
its increased density and its increased temperature. In general,
if the water in the vessel B be raised or lowered in temperature,
the steam in the vessel A will rise and fall in temperature in a
corresponding manner, always having the same temperature as the
water in B. If the weight of the vessel A were observed, it would
be found to increase with every increase of temperature, and to
diminish with every diminution of temperature, proving that the
augmented temperature of the water in B produces an augmented
density of the steam in A. The same pressure would be found always
to correspond to the same temperature and density, so that if the
numerical amount of any one of the three quantities, the
temperature, the pressure, or the density, were known, the other
two must necessarily be determined, the same temperature always
corresponding to the same pressure, and _vice versâ_. And in like
manner, steam produced under these circumstances of the same
density cannot have different pressures. It must be observed that
the steam here produced receives all the heat which it possesses
from the water from which it is raised. Now it is easily
demonstrable, that this is the least quantity of heat which is
compatible with the steam maintaining the vaporous form; for if
the stopcock C be closed so as to separate the steam in A from the
water in B, and that any portion of heat, however small, be then
abstracted from the steam in A, some portion of the steam will be
reconverted into water.
This then, according to the definition already given, is _Common
Steam_.
(95.) Let us now suppose that the vessel A, being in communication
with the vessel B by the open stopcock, has been filled with pure
steam of any given temperature. The steam which it thus contains
will be common steam, and, as has been [Pg170] shown (94.), it
cannot lose any portion of heat, however small, without being
partially condensed; but let the stopcock C be closed, and let the
steam in A be then exposed to any source of heat by which its
temperature may be raised any required number of degrees. From the
steam thus obtained heat may be abstracted without producing any
condensation; and such abstraction of heat may be continued
without producing condensation, until the steam is cooled down to
that temperature at which it was raised from the water in B, when
the stopcock C was opened. Any further reduction of temperature
would be attended with condensation.
If after increasing the temperature of the steam in A, the
stopcock C being shut so as to render it superheated steam, its
pressure be observed, the pressure will be found to be increased,
but not to that amount which it would have been increased had the
steam in A been raised to the same temperature by heating the
water in B to that temperature, and keeping the stopcock open. In
fact, its present augmented pressure will be due only to its
increased temperature, since its density remains unchanged. But if
in these circumstances the stopcock C be suddenly opened, the
pressure of the steam in A will as suddenly rise to that pressure
which in common steam corresponds to its temperature; and if the
vessel A were weighed, it would be found to have increased in
weight, proving that the steam contained in it has received
increased density by an increased quantity of vapour proceeding
from the water in A. In fact, by opening the stopcock the steam
which was before superheated steam, has become common steam. It
has the greatest density which steam of that temperature can have;
and consequently, if any heat be abstracted from it, a partial
condensation will ensue.