the water will raise it through six perpendicular inches, and the
result so far will be equivalent to a ton raised half a foot; but if
the piston-rod be supposed also to act by a chain or cord over a
wheel, so as to pull a weight up, the steam which has just raised the
ton weight through six inches, may be condensed, and the piston will
descend with a force of one ton into the vacuum thus produced, and
another ton may be thus raised through half a foot. The total
mechanical power thus yielded by the steam, adding to its direct
action its effect by condensation, will then be one ton raised through
one foot, being an effect exactly equal to that obtained by the
condensation of atmospheric steam.
If the piston be loaded with two tons, its direct action will, as we
have shown, raise these two tons through four inches, which is
equivalent to two thirds of a ton raised a foot. By condensing this
steam a ton weight may be raised in the same manner, by the descent
of the piston through a third of a foot, which is equivalent to the
third of a ton raised through one foot.
By pursuing like reasoning, it will appear that, if the direct force
of high-pressure steam be combined with the indirect force produced by
its condensation, the total mechanical effect will be precisely equal
to the mechanical effect by the mere condensation of atmospheric
steam.
(134.) In applying the principle of expansion to the direct action of
high-pressure steam, advantages are gained analogous to those already
explained with reference to the method of condensation.
Let the piston be supposed to be loaded with three tons: the
evaporation of the water beneath it will raise this weight, including
the atmospheric pressure, through three perpendicular inches. Let one
ton be now removed, and the remaining two tons will be raised, by the
expansion of the steam, through another perpendicular inch. Let the
second ton be now removed, and the piston loaded with the remaining
ton will rise, by the expansion of the steam, to the height of six
inches from the bottom. These consequences follow immediately from the
principle that steam will expand in proportion as the pressure upon it
is diminished, observing that in this case the atmospheric pressure,
amounting to one ton, must always be added to the load. In this
process three separate effects are produced: one ton is raised through
three inches, which is equivalent to a quarter of a ton raised through
one foot; another ton is raised through four inches, which is
equivalent to a third of a ton through a foot, and the third ton is
raised through six inches, which is equivalent to half a ton raised
through a foot. The total of these effects amounts to one and
one-twelfth of a ton raised through one foot, while the same load,
raised by the high-pressure steam without expansion, would be
equivalent to only half a ton raised through one foot.
Again, let the load placed upon the piston be five tons: the
evaporation of the water will raise this through the sixth part of a
foot; if one ton be now removed, the other four tons will be raised to
a height above the bottom of the tube equal to a fifth part of a foot;
another ton being removed, the remaining three will be raised to a
height from the bottom equal to a fourth of a foot; and so on, the
last ton being raised through half a foot. To estimate the total
mechanical effect thus produced, we are to consider that the several
tons raised from their first position are raised through the sixth,
fifth, fourth, third, and half of a perpendicular foot, giving a total
effect equal to the sixth, fifth, fourth, third, and half of a ton
severally raised through one foot; these, therefore, added together,
will give a total of nineteen twentieths of a ton raised through one
foot.
In general, the expansive force applied to the direct action of
high-pressure steam, therefore, will increase its effect according to
the same law, and subject to the same principles as were shown with
respect to the method of condensation accompanied with expansion.
The expansive action of high-pressure steam may be accompanied with
condensation, so as considerably to increase the mechanical effect
produced; for, after the weights with which the piston is loaded have
been successively raised to the extent permitted by the elastic force
of the steam, and are removed from the piston, the steam will expand
until it balances the atmospheric pressure. It may afterwards be made
further to expand, by adding weights to the counterpoise W in the
manner already explained; and, the steam being subsequently condensed,
all the effects will be produced upon the descent of the piston which
we have before noticed. It is evident that by this means the
mechanical effect admits of very considerable increase.
(135.) We have hitherto considered the piston to be resisted by the
atmospheric pressure above it; but, as is shown in the preceding
chapters, in the modern steam engines, the atmosphere is expelled from
the interior of the machine by allowing the steam to pass freely
through all its cavities in the first instance, and to escape at some
convenient aperture, which, opening outwards, will effectually
prevent the subsequent re-admission of air. The piston-rod and other
parts which pass from the external atmosphere to the interior of the
machine, are likewise so constructed and so supplied with oil or other
lubricating matter that neither the escape of steam nor the entrance
of air is permitted. We are therefore now to consider the effect of
the action of steam against the piston P, when subjected to a
resistance which may be less in amount, to any extent, than the
atmospheric pressure.
In such machines the steam always acts both directly by its power, and
indirectly by its condensation. In calculating its effects, excluding
friction, &c., we have therefore only to estimate its total force upon
the piston, and to deduct the force of the uncondensed vapour which
will resist the motion of the piston.
Supposing, then, the total force exerted upon the piston, after
deducting the resistance from the uncondensed vapour, to be one ton,
and the length of the cylinder to be one foot, each motion of the
piston from end to end of the cylinder will produce a mechanical force
equivalent to a ton weight raised one foot high. If in this case the
magnitude of the piston be equivalent to one square foot, the pressure
of the steam will be equal to that of the atmosphere, and the quantity
of water in the form of steam which the cylinder will contain will be
a cubic inch, while the quantity of steam in it will be a cubic foot.
In proportion as the area of the piston is enlarged the pressure of
the steam will be diminished, if the moving force is required to
remain the same; but with every diminution of pressure the density of
the steam will be diminished in the same proportion, and the cylinder
will still contain the same quantity of water in the form of vapour.
In this way steam may be used, as a mechanical agent, with a pressure
to almost any extent less than that of the atmosphere, and at
temperatures considerably lower than 212°. To obtain the same
mechanical force, it is only necessary to enlarge the piston in the
same proportion as the pressure of the steam is diminished.
By a due attention to this circumstance, the expansive power of steam,
both in its direct action and by condensation, may be used with very
much increased advantage; and such is the principle on which the
benefits derived from Woolf's contrivances depend. If steam of a
high-pressure, say of three or four atmospheres, be admitted to the
piston, and allowed to impel it through a very small portion of the
descent, it may then be cut off and its expansion may be allowed to
act upon the piston until the pressure of the steam is diminished
considerably below the atmospheric pressure; the steam may then be
condensed and a vacuum produced, and the process repeated.
In the double-acting engines, commonly used in manufactures and in
navigation, and still more in the high-pressure engines used for
locomotion, the advantageous application of the principle of expansion
appears to have been hitherto attended with difficulties; for,
notwithstanding the benefits which unquestionably attend it in the
economy of fuel, it has not been generally resorted to. To derive from
this principle full advantage, it would be necessary that the varying
power of the expanding steam should encounter a corresponding, or a
nearly corresponding, variation in the resistance: this requisite may
be attained, in engines applied to the purpose of raising water, by
many obvious expedients; but when they have, as in manufactures, to
encounter a nearly uniform resistance, or, in navigation and
locomotion, a very irregular resistance, the due application of
expansion is difficult, if indeed it be practicable.
We have seen that the mechanical effect produced by steam when the
principle of expansion is not used, is always proportional to the
quantity of water contained in the steam, and is likewise in the same
proportion so long as a given degree of expansion is used. It is
apparent, therefore, that the mechanical power which is or ought to
be exerted by an engine is in the direct proportion of the quantity of
water evaporated. It has also been shown that the quantity of water
evaporated, whatever be the pressure of the steam, will be in the
direct proportion of the quantity of heat received from the fuel, and
therefore in the direct proportion of the quantity of fuel itself, so
long as the same proportion of its heat is imparted to the water.
(136.) The POWER of an engine is a term which has been used to express
the rate at which it is able to raise a given load, or overcome a
given resistance. The DUTY of an engine is another term, which has
been adopted to express the load which may be raised a given
perpendicular height, by the combustion of a given quantity of fuel.
When steam engines were first introduced, they were commonly applied
to work pumps or mills which had been previously wrought by horses. It
was, therefore, convenient, and indeed necessary, in the first
instance, to be able to express the performance of these machines by
reference to the effects of animal power, to which manufacturers,
miners, and others, had been long accustomed. When an engine,
therefore, was capable of performing the same work in a given time, as
any given number of horses of average strength usually performed, it
was said to be an engine of so many _horses' power_. This term was
long used with much vagueness and uncertainty: at length, as the use
of steam engines became more extended, it was apparent that confusion
and inconvenience would ensue, if some fixed and definite meaning were
not assigned to it, so that the engineers and others should clearly
understand each other in expressing the powers of these machines. The
term _horse-power_ had so long been in use, that it was obviously
convenient to retain it. It was only necessary to agree upon some
standard by which it might be defined. The performance of a horse of
average strength, working for eight hours a day, was, therefore,
selected as a standard or unit of steam-engine power. Smeaton
estimated the amount of mechanical effect which the animal could
produce at 22,916 pounds, raised one foot per minute; Desaguiliers
makes it 27,500 pounds, raised through the same height. Messrs. Bolton
and Watt caused experiments to be made with the strong horses used in
the breweries in London; and from the result of these they assigned
33,000 pounds raised one foot per minute, as the value of a horse's
power: this is, accordingly, the estimate now generally adopted; and,
when an engine is said to be of so many horses' power, it is meant
that, when in good working order and properly managed, it is capable
of overcoming a resistance equivalent to so many times 33,000 pounds
raised one foot per minute. Thus, an engine of ten-horse-power would
be capable of raising 330,000 pounds one foot per minute.
As the same quantity of water converted into steam will always produce
the same mechanical effect, whatever be the density of the steam
produced from it, and at whatever rate the evaporation may proceed, it
is evident that the _power_ of a steam engine will depend on two
circumstances: first, the rate at which the boiler with its appendages
is capable of evaporating water; and, secondly, the rate at which the
engine is capable of consuming the steam by its work. We shall
consider these two circumstances separately.
The rate at which the boiler produces steam will depend upon the rate
at which heat can be transmitted from the fire to the water which it
contains. Now this heat is transmitted in two ways: either by the
direct action of the fire radiating heat against the surface of the
boiler; or by the flame, and heated air which escapes from the fire,
passing through the flues, as already explained. The surface of the
boiler exposed to the direct radiation of the fire is technically
called _fire surface_; and that which takes heat from the flame and
air, on its way to the chimney, is called _flue surface_. Of these the
most efficient in the generation of steam is the former. In stationary
boilers, used for condensing engines, where magnitude and weight are
matters of little importance, it has been found that the greatest
effect has been produced in general by allowing four and a half square
feet of fire surface, and four and a half square feet of flue surface,
for every horse-power. By means of this quantity of fire and flue
surface, a cubic foot of water per hour may be evaporated.
It has been already shown that the total power exerted by a cubic inch
of water, converted into steam, will be equivalent to 2160 pounds
raised one foot. A cubic foot of water consists of 1728 cubic inches,
and the power produced by its evaporation will therefore be found by
multiplying 2160 by 1728; the product, 3,732,480, expresses the number
of pounds' weight which the evaporation of a cubic foot of water would
raise one foot high, supposing that its entire mechanical force were
rendered available: but to suppose this in practice, would be to
suppose the machine, through the medium of which it is worked, moved
without any power being expended upon its own parts. It would be, in
fact, supposing all its moving parts to be free from friction and
other causes of resistance. To form a practical estimate, then, of the
real quantity of available mechanical power obtained from the
evaporation of a given quantity of water, it will be necessary to
inquire what quantity of this power is intercepted by the engine
through which it is transmitted. In different forms of steam
engine--indeed, we may say in every individual steam engine--the
amount thus lost is different; nevertheless, an approximate estimate
may be obtained, sufficiently exact to form the basis of a general
conclusion.
Let us consider, then, severally, the means by which mechanical power
is intercepted by the engine.
_First_, The steam must flow from the boiler into the cylinder to work
the piston; it passes necessarily through pipes more or less
contracted, and is, therefore, subject to friction as well as cooling
in its passage.
_Second_, Force is lost by the radiation of heat from the cylinder
and its appendages.
_Third_, The friction of the piston in the cylinder must be overcome.
_Fourth_, Loss of steam takes place by leakage.
_Fifth_, Force is expended in expelling the steam after having worked
the piston.
_Sixth_, Force is required to open and close the several valves, to
pump up the water for condensation, and to overcome the friction of
the various axes.
_Seventh_, Force is expended upon working the air-pump.
In engines which do not condense the steam, and which, therefore, work
with steam of high-pressure, some of these sources of waste are
absent, but others are of increased amount. If we suppose the total
effective force of the water evaporated per hour in the boiler to be
expressed by 1000, it is calculated that the waste in a high-pressure
engine will be expressed by the number 392; or, in other words, taking
the whole undiminished force obtained by evaporation as expressed by
10, very nearly 4 of these parts will be consumed in moving the
engine, and the other 6 only will be available.
In a single-acting engine which condenses the steam, taking, as
before, 1000 to express the total mechanical power of the water
evaporated in the boiler, 402 will express the part of this consumed
in moving the engine, and 598, therefore, will express the portion of
the power practically available; or, taking round numbers, we shall
have the same result as in the non-condensing engine, viz. the whole
force of the water evaporated being expressed by 10, 4 will express
the waste, and 6 the available part.
In a double-acting engine the available part of the power bears a
somewhat greater proportion to the whole. Taking, as before, 1000 to
express the whole force of the water evaporated, 368 will express the
proportion of that force expended on the engine, and 632 the
proportion which is available for work.
In general, then, taking round numbers, we may consider that the
mechanical force of four tenths of the water evaporated in the boiler
is intercepted by the engine, and the other six tenths are available
as a moving force. In this calculation, however, the resistance
produced in the condensing engine by the uncondensed steam is not
taken into account: the amount of this force will depend upon the
temperature at which the water is maintained in the condenser. If this
water be kept at the temperature of 120°, the vapour arising from it
will have a pressure expressed by three inches seven tenths of
mercury; if we suppose the pressure of steam in the boiler to be
measured by 37 inches of mercury, then the resistance from the
uncondensed steam will amount to one tenth of the whole power of the
boiler; this, added to the four tenths already accounted for, would
show a waste amounting to half the whole power of the boiler, and
consequently only half the water evaporated would be available as a
moving power.
If the temperature of the condenser be kept down to 100°, then the
pressure of uncondensed steam will be expressed by two inches of
mercury, and the loss of power consequent upon it would amount to a
proportionally less fraction of the whole power.
The following example will illustrate the method of estimating the
effective power of an engine.
In a double-acting engine, in good working condition, the total power
of steam in the boiler being expressed by 1000, the proportion
intercepted by the engine, exclusive of the resistance of the
uncondensed steam, will be 368, and the effective part 632. Now,
suppose the pressure of steam in the boiler to be measured by a column
of 35 inches of mercury; the thousandth part of this will be seven two
hundredths of an inch of mercury, and 632 of these parts will express
the effective portion of the power. By multiplying seven two
hundredths by 632, we obtain 22 nearly. Now, suppose the temperature
in the condenser is 1200, the pressure of steam corresponding to that
temperature will be measured by 3-7/10 inches of mercury. Subtracting
this from 22, there will remain 18-3/10 inches of mercury, as the
effective moving force upon the piston; this will be equivalent to
about 7 lbs. on each circular inch.
If the diameter of the piston then be 24 inches, its surface will
consist of a number of circular inches expressed by the square of 24,
or 24 × 24 = 576; and, as upon each of these circular inches there is
an effective pressure of 7 lbs., we shall find the total pressure in
pounds by multiplying 576 by 7, which gives 4032 lbs.
We shall find the space through which this force works per minute, by
knowing the length of the cylinder and the number of strokes per
minute. Suppose the length of the cylinder to be 5 feet, and the
number of strokes per minute 21-1/2. In each stroke[51] the piston
will, therefore, move through 10 feet, and in one minute it will move
through 215 feet. The moving force, therefore, is 4032 lbs. moved
through 215 feet per minute, which is equivalent to 215 times 4032
lbs., or 866,880 lbs., raised one foot per minute.
[Footnote 51: By a stroke of the piston is meant its motion from one
end of the cylinder and back again.]
For every 33,000 lbs. contained in this, the engine has a horse-power.
To find the horse-power, then, of the engine, we have only to divide
866,880 by 33,000; the quotient is 26 nearly, and, therefore, the
engine is one of 26 horse power.
Let it be required to determine the quantity of water which a boiler
must evaporate per hour, for each horse-power of the engine which it
works.
It has been already explained that one horse-power expresses 33,000
lbs. raised one foot high per minute, or, 1,980,000 lbs. raised one
foot high per hour. The quantity of water necessary to produce this
mechanical effect by evaporation, will be found by considering that a
cubic inch of water, being evaporated, will produce a mechanical
force equivalent to 2160 lbs. raised a foot high. If we divide
1,980,000, therefore, by 2160, we shall find the number of cubic
inches of water which must be evaporated per hour, in order to produce
the mechanical effect expressed by one horse-power; the result of this
division will be 916,6, which is therefore the number of cubic inches
of water per hour, whose evaporation is equivalent to one horse-power.
But it has been shown that, for every 6 cubic inches of water
evaporated in the boiler which are available as a moving power, there
will be 4 cubic inches intercepted by the engine. To find, then, the
quantity of waste corresponding to 916 cubic inches of water, it will
be necessary to divide that number by 6, and to multiply the result by
4: this process will give 610 as the number of cubic inches of water
wasted. The total quantity of water, therefore, which must be
evaporated per hour, to produce the effect of one horse-power, will be
found by adding 610 to 916, which gives 1526.
This result, however, being calculated upon a supposition of a degree
of efficiency in the engines which is, perhaps, somewhat above their
average state, it has been customary with engineers to allow a cubic
foot of water per hour for each horse-power, a cubic foot being 1728
cubic inches, or above 11 per cent. more than the above estimate.
(137.) It has been stated, that to evaporate a cubic foot of water per
hour requires 9 square feet of surface exposed to the action of the
fire and heated air. This, therefore, is the quantity of surface
necessary for each horse-power, and we shall find the total quantity
of fire and flue surface necessary for a boiler of a given power, by
multiplying the number of horses in the power by 9; the product will
express, in square feet, the quantity of boiler surface which must be
exposed to the fire, one half of this being fire surface and the other
half flue surface.
Since the supply of heat to the boiler must be proportionate to the
quantity of fuel maintained in combustion, and the quantity of that
fuel must depend on the extent of grate surface, it is clear that a
determinate proportion must exist between the power of the boiler, and
the extent of grating in the fire place. The quantity of oxygen which
combines with the fuel varies with the quality of that fuel; for
different kinds of coal it varies from two to three pounds for each
pound of coal.
We shall take it an average of 2-1/2 pounds. Now 2-1/2 pounds of
oxygen will measure 30 cubic feet; also 5 cubic feet of atmospheric
air contain 1 cubic foot of oxygen; and consequently 150 cubic feet of
atmospheric air will be necessary for the combustion of 1 pound of
average coals. At least one third of the air, which passes through a
fire, escapes uncombined into the chimney. We must, therefore, allow
220 cubic feet of atmospheric air to pass through the grate-bars for
every pound of fuel which is consumed. Now since land boilers will
consume 15 pounds, and marine boilers 10 pounds, per hour per
horse-power, it follows that the spaces between the grate-bars, and
the extent of grate surface, must be sufficient to allow 3000 cubic
feet of air per hour in land boilers, and 2000 cubic feet in marine
boilers, to pass through them for each horse-power, or, what is the
same, for each foot of water converted into steam per hour. The
quantity of grate surface necessary for this does not seem to be
ascertained with precision; but, perhaps, we may take as an
approximate estimate for land boilers one square foot of grate surface
per horse-power, and for marine boilers two thirds of a square foot,
the spaces between the grate-bars being equal to their breadth.
It is evident that the capacity of a boiler for water and steam must
have a determinate relation to the power of the engine it is intended
to supply. For each horse-power of the engine, it has been shown that
a cubic foot of water must pass from the boiler in the form of steam
per hour. Now, it is evident that the steam could not be supplied of a
uniform force, if the quantity of steam contained at any moment in
the boiler were not considerably greater than the contents of the
cylinder. For example, if the volume of steam in the boiler were
precisely equal to the capacity of the cylinder, then one measure of
the cylinder would for the moment cause the steam to expand into
double its bulk and to lose half its force, supposing it to pass
freely from the boiler to the cylinder. In the same manner, if the
volume of steam contained in the boiler were twice the contents of the
cylinder, the steam would for a moment lose a third of its force, and
so on. It is clear, therefore, that the space allotted to steam in the
boiler must be so many times greater than the magnitude of the
cylinder, that the abstraction of a cylinder full of steam from it
shall cause a very trifling diminution of its force.
In the same manner, we may perceive the necessity of maintaining a
large proportion between the total quantity of water in the boiler,
and the quantity supplied in the form of steam to the cylinder. If,
for example (taking as before an extreme case,) the quantity of water
in the boiler were only equal to the quantity supplied in the form of
steam to the cylinder in a minute, it would be necessary that the
contents of the boiler should be replaced by cold water once in each
minute: and, under such circumstances, it is evident that the action
of the heat upon the water would be quite unmanageable. But,
independent of this, the quantity of water must be sufficient to fill
the boiler above the point at which the flue surface terminates,
otherwise the heat of the fuel would act upon the part of the boiler
containing steam and not water; and, steam receiving heat sluggishly,
the metal of the boiler would be gradually destroyed by undue
temperature.
The total quantity of space for water and steam in boilers is subject
to considerable variation in proportion to their power. Small boilers
require a greater proportion of steam and water-room, or a greater
capacity of boiler, in proportion, than large ones; and the same
applies to their fire surface and flue surface.
The general experience of engineers has led to the conclusion, that a
low-pressure boiler of the common kind requires ten cubic feet of
water-room, and ten cubic feet of steam-room in the boiler, for every
cubic foot which the engine consumes per hour, or, what is the
same, for each horse-power of the engine. Thus, an engine of
ten-horse-power, according to this rule, would require a boiler having
the capacity of 200 cubic feet which should be constantly kept half
filled with water. There are, however, different estimates of this.
Some engineers hold that a boiler should have twenty-five cubic feet
of capacity for each horse-power of the engine, while others reduce
the steam so low as eight cubic feet.
In a table of the capacities of boilers of different powers, and the
feed of water necessary to be maintained in them, Mr. Tredgold assigns
to a boiler of five-horse-power fourteen cubic feet of water per
horse-power; for one of ten-horse power, twelve and a half cubic feet;
and, for one of forty-horse, eleven cubic feet.
For engines of greater power it is generally found advantageous to
have two or more boilers of small power, instead of one of large
power. This method is almost invariably adopted on board steam boats,
and has the advantage of securing the continuance of the working of
the engine, in case of one of the boilers being deranged. It is also
found convenient to keep an excess of power in the boilers, above the
wants of the engine. Thus, an engine of sixty-horse-power may be
advantageously supplied with two forty-horse boilers, and an engine of
eighty-horse-power with two fifty-horse boilers, and so on.
(138.) The pressure of steam in the cylinder of an engine is always
less than the pressure of steam in the boiler, owing to the
obstructions which it encounters in its passage through the steam
pipes and valves. The difference between these pressures will depend
upon the form and magnitude of the passages: the straighter and wider
they are, the less the difference will be; if they are contracted and
subject to bends, especially to angular inflexions, the steam will be
considerably diminished in its pressure before it reaches the
cylinder. The throttle valve placed in the steam pipe may also be so
managed as to diminish the pressure of steam in the cylinder to any
extent: this effect, which is well understood by practical engineers,
is called _wire-drawing_ the steam. By such means it is evidently
possible for the steam in the boiler to have any degree of
high-pressure while the engine is worked at any degree of low
pressure. Since, however, the pressure of the steam in the cylinder is
a material element in the performance of the engine, the magnitude,
position, and shape of the steam pipe and of the valves are a matter
of considerable practical importance. But theory furnishes us with
little more than very general principles to guide us. One practical
rule which has been adopted is, to make the diameter of the steam pipe
about one fifth of that of the cylinder: by this means the area of the
transverse action of the pipe will be one twenty-fifth part of the
superficial magnitude of the piston; and, since the same quantity of
steam per minute must flow through this pipe as through the cylinder,
it follows that the velocity of the steam, in passing through the
steam pipe, will be twenty-five times the velocity of the piston.
(139.) Another rule which has been adopted is, to allow a square inch
of magnitude, in the section of the steam pipe, for each horse-power
of the engine.
The result of this and all similar rules is, that the steam should
always pass through the steam pipe with the same velocity, whatever be
the power of the engine.
In engines of the same power, the piston will have very different
velocities in the cylinder, according to the effective pressure of the
steam, and the proportions and capacity of the cylinder. It is clear
from what has been already explained, that, when the power is the
same, the same actual quantity of water, in the form of steam, must
pass through the cylinder per minute: but, if the steam be used with a
considerable pressure, being in a condensed state, the same weight of
it will occupy a less space; and consequently the cylinders of
high-pressure engines are smaller than those of the same power in
low-pressure engines: the magnitude of the cylinder and the piston
therefore, as well as the velocity of the latter, will depend first
upon the pressure of the steam.
But with steam of a given pressure, the velocity of the piston will be
different: with a given capacity of cylinder, and a given pressure of
steam, the power of the engine will determine the number of strokes
per minute. But the actual velocity of the piston will depend, in that
case, on the proportion which the diameter of the cylinder bears to
its length; the greater the diameter of the piston is with respect to
its length, the less will be its velocity. In case of stationary
engines used on land, that proportion of the diameter of the cylinder
to its length is selected, which is thought to contribute to the most
efficient performance of the machine. According to some engineers, the
length of the cylinder should be twice its diameter;[52] others make
the length equal to two diameters and a half; but there are
circumstances in which considerations of practical convenience render
it necessary to depart from these proportions. In marine engines,
where great length of cylinder would be inadmissible, and where, on
the other hand, considerable power is required, cylinders of short
stroke and great diameter are used. In these engines the length of the
stroke is often not greater than the diameter of the piston, and
sometimes even less.
[Footnote 52: This is the proportion under which the cylinder with a
given capacity will present the least possible surface to the cooling
effect of the atmosphere.]
The actual velocity which has been found to have the best practical
effect, for the piston in low-pressure engines, is about 200 feet per
minute. This, however, is subject to some variation.
(140.) A given weight or measure of fuel burnt under the boiler of an
engine is capable of producing a mechanical effect through the means
of that engine, which, when expressed in an equivalent number of
pounds' weight lifted a foot high, is called the _duty_ of the engine.
If all the heat developed in the combustion of the fuel could be
imparted to the water in the boiler, and could be rendered
instrumental in producing its evaporation; and if, besides, the steam
thus produced could be all rendered mechanically available at the
working point; then the duty of the engine would be the entire
undiminished effect of the heat of combustion; but it is evident that
this can never practically be the case. In the first place, the heat
developed by the combustion can never be wholly imparted to the water
in the boiler: some part of it will necessarily escape without
reaching the boiler at all; another portion will be consumed in
heating the metal of the boiler, and in supplying the loss by
radiation from its surface; another portion will be abstracted by the
various sources of the waste and leakage of steam; another portion
will be abstracted by the reaction of the condensed steam; and another
portion of the power will be consumed in overcoming the friction and
resistance of the engine itself. It is apparent that all these sources
of waste will vary according to the circumstances and conditions of
the machine, and according to the form and construction of the
furnace, flues, boilers, &c. The duty, therefore, of different engines
will be different; and when such machines are compared, with a view to
ascertain their economy of fuel, it has been found necessary carefully
to register and to compare the fuel consumed with the weight or
resistance overcome. In engines applied to manufactures generally or
navigation, it is not easy to measure the amount of resistance which
the engine encounters, but when the engine is applied to the pumping
of water, its performance is more easily determined.
In the year 1811, several of the proprietors of the mines in
Cornwall, suspecting that some of their engines might not be doing a
duty adequate to their consumption of fuel, came to a determination to
establish a uniform method of testing the performance of their
engines. For this purpose a counter was attached to each engine, to
register the number of strokes of the piston. All the engines were put
under the superintendence of Messrs. Thomas and John Lean, engineers;
and the different proprietors of the mines, as well as their directing
engineers, respectively pledged themselves to give every facility and
assistance in their power for the attainment of so desirable an end.
Messrs. Lean were directed to publish a monthly report of the
performance of each engine, specifying the name of the mine, the size
of the cylinder, the load upon the engine, the length of the stroke,
the number of pump lifts, the depth of the lift, the diameter of the
pumps, the time worked, the consumption of coals, the load on the
pump, and, finally, the duty of the engine, or the number of pounds
lifted one foot high by a bushel of coals. The publication of these
monthly reports commenced in August, 1811, and have been regularly
continued to the present time.
The favourable effect which these reports have produced upon the
vigilance of the several engineers, and the emulation they have
excited, both among engine-makers and those to whom the working of the
machines are intrusted, are rendered conspicuous in the improvement
which has gradually taken place in the performance of the engines, up
to the present time. In a report published in December, 1826, the
highest duty was that of an engine at Wheal Hope mine in Cornwall. By
the consumption of one bushel of coals, this engine raised 46,838,246
pounds a foot high, or, in round numbers, forty-seven millions of
pounds.
In a report published in the course of the present year (1835) it was
announced that a steam engine, erected at a copper mine near St.
Anstell, in Cornwall, had raised by its average work 95 millions of
pounds 1 foot high, with a bushel of coals. This enormous mechanical
effect having given rise to some doubts as to the correctness of the
experiments on which the report was founded, it was agreed that
another trial should be made in the presence of a number of competent
and disinterested witnesses. This trial accordingly took place a short
time since, and was witnessed by a number of the most experienced
mining engineers and agents: the result was, that for every bushel of
coal consumed under the boiler the engine raised 125-1/2 millions of
pounds weight one foot high.
(141.) It may not be uninteresting to illustrate the amount of
mechanical virtue, which is thus proved to reside in coals, in a more
familiar manner.
Since a bushel of coal weighs 84 lbs. and can lift 56,027 tons a foot
high, it follows that a pound of coal would raise 667 tons the same
height; and that an ounce of coal would raise 42 tons one foot high,
or it would raise 18 lbs. a mile high.
Since a force of 18 lbs. is capable of drawing 2 tons upon a railway,
it follows that an ounce of coal possesses mechanical virtue
sufficient to draw 2 tons a mile, or 1 ton 2 miles, upon a level
railway.[53]
[Footnote 53: The actual consumption of coal upon railways is in
practice about eight ounces per ton per mile. It is, therefore, worked
with sixteen times less effect than in the engine above mentioned.]
The circumference of the earth measures 25,000 miles. If it were
begirt by an iron railway, a load of one ton would be drawn round it
in six weeks by the amount of mechanical power which resides in the
third part of a ton of coals.
The great pyramid of Egypt stands upon a base measuring 700 feet each
way, and is 500 feet high; its weight being 12,760,000,000 lbs. To
construct it, cost the labour of 100,000 men for 20 years. Its
materials would be raised from the ground to their present position by
the combustion of 479 tons of coals.
The weight of metal in the Menai bridge is 4,000,000 lbs., and its
height above the level of the water is 120 feet: its mass might be
lifted from the level of the water to its present position by the
combustion of 4 bushels of coals.[54]
[Footnote 54: Some of these examples were given by Sir John Herschel,
in his Preliminary Discourse on Natural Philosophy; but since that
work was written an increased power has been obtained from coals, in
the proportion of 7 to 12-1/2.]
The enormous consumption of coals in the arts and manufactures, and in
steam navigation, has of late years excited the fears of some persons
as to the possibility of the exhaustion of our mines. These
apprehensions, however, may be allayed by the assurance received from
the highest mining and geological authorities, that, estimating the
present demand from our coal mines at 16 millions of tons annually,
the coal fields of Northumberland and Durham alone are sufficient to
supply it for 1700 years, and after the expiration of that time the
great coal basin of South Wales will be sufficient to supply the same
demand for 2000 years longer.
But, in speculations like these, the probable, if not certain,
progress of improvement and discovery ought not to be overlooked; and
we may safely pronounce that, long before a minute fraction of such a
period of time shall have rolled over, other and more powerful
mechanical agents will altogether supersede the use of coal.
Philosophy already directs her finger at sources of inexhaustible
power in the phenomena of electricity and magnetism. The alternate
decomposition and recomposition of water, by magnetism and
electricity, has too close an analogy to the alternate processes of
vaporisation and condensation, not to occur at once to every mind: the
development of the gases from solid matter by the operation of the
chemical affinities, and their subsequent condensation into the liquid
form, has already been essayed as a source of power. In a word, the
general state of physical science, at the present moment, the vigour,
activity, and sagacity with which researches in it are prosecuted in
every civilized country, the increasing consideration in which
scientific men are held, and the personal honours and rewards which
begin to be conferred upon them, all justify the expectation that we
are on the eve of mechanical discoveries still greater than any which
have yet appeared; and that the steam engine itself, with the gigantic
powers conferred upon it by the immortal Watt, will dwindle into
insignificance in comparison with the hidden powers of nature still to
be revealed; and that the day will come when that machine, which is
now extending the blessings of civilisation to the most remote skirts
of the globe, will cease to have existence except in the page of
history.
CHAPTER XIX.
PLAIN RULES FOR RAILWAY SPECULATORS.
(142.) For some time after the completion of the Liverpool and
Manchester railway, doubts were entertained of its ultimate success as
a commercial speculation; and, even still, after several years'
continuance, some persons are found, sceptical by temperament, who
have not acquired full confidence in the permanency of its advantages.
The possibility of sustaining a system of regular transport upon it,
with the unheard of speed effected at the commencement of the
undertaking, was, for a long period, questioned by a considerable
portion even of the scientific world; and, after that possibility was
established, by the regular performance of some years, the
practicability of permanently profitable work, at that rate of speed,
was still doubted by many, and altogether denied by some. The numerous
difficulties to be encountered, and the enormous expense of
locomotive power, have been fully admitted by the directors in their
semi-annual reports. Persons interested in canals and other rival
establishments, and others constitutionally doubtful of everything,
attributed the dividends to the indirect proceedings of the managers,
and asserted that when they appeared to be sharing their profit's,
they, in reality, were sharing their capital. This delusion, however,
could not long continue, and the payment of a steady semi-annual
dividend of 4-1/2 per cent. since the opening of the railway, together
with the commencement of a reserved fund of a considerable amount,
with a premium of above 100 per cent. on the original shares, has
brought conviction to understandings impenetrable to general
reasoning; and the tide of opinion, which, for a time, had turned
against railways, has now, by the usual reaction, set in so violently
in their favour, that it becomes the duty of those who professionally
devote themselves to such inquiries, to restrain and keep within
moderate bounds the public ardour, rather than to stimulate it.
The projects for the construction of great lines of internal
communication which have been announced would require, if realized, a
very large amount of capital. Considering that the estimated capital
is invariably less than the amount actually required, we shall not,
perhaps, overrate the extent of the projected investments if we
estimate them at fifty millions. The magnitude of this amount has
created alarm in the minds of some persons, lest a change of
investment so extensive should produce a serious commercial shock. It
should, however, be considered that, even if all the projected
undertakings should be ultimately carried into execution, a long
period must elapse, perhaps not less than fifteen or twenty years,
before they can be all completed: the capital will be required, not
suddenly, but by small instalments, at distant intervals of time. Even
if it were true, therefore, that, to sustain their enterprises, an
equivalent amount of capital must be withdrawn from other investments,
the transfer would lake place by such slow degrees as to create no
serious inconvenience. But, in fact, it is not probable that any
transfer of capital whatever will be necessary. Trade and
manufacturers are at the present moment in a highly flourishing
condition; and the annual accumulation of capital in the country is so
great, that the difficulty will probably be, not to find capital to
meet investments, but to find suitable investments for the increasing
capital. In Manchester alone, it is said that the annual increment on
capital is no less than three millions. In fifteen years, therefore,
this mart alone would be sufficient to supply all the funds necessary
for the completion of all the proposed railroads, without withdrawing
capital from any other investment.
The facilities which these Joint Stock Companies offer for the
investment of capital, even of the smallest amount, the temptations
which the prospect of large profits hold out, and the low interest
obtained on national stock of every description, have attracted a vast
body of capitalists, small and great, who have subscribed to these
undertakings with the real intention of investment. But, on the other
hand, there is a very extensive body of speculators who engage in them
upon a large scale, without the most distant intention, and, indeed,
without the ability, of paying up the amount of their shares. The loss
which the latter class of persons may sustain would, probably, excite
little commiseration, were it not for the consequences which must
result to the former, should a revolution take place, and the market
be inundated with the shares of these gambling speculators, who buy
only to sell again. Effects would be produced which must be ruinous to
a large proportion of the _bonâ fide_ subscribers. It may, therefore,
be attended with some advantage to persons who really intend to make
permanent investments of this nature, to state, in succinct and
intelligible terms, the principal circumstances on which the
efficiency and economy of railroads depend, so as to enable them, in
some measure, to form a probable conjecture of the prospective
advantages which the various projects hold out. In doing this, we
shall endeavour, as much as possible, to confine our statements to
simple facts and results, which can neither be denied nor disputed,
leaving, for the most part, the inferences to which they lead to be
deduced from them by others.
It may be premised, that persons proposing to engage in any railroad
speculation should obtain _first_ a table of _gradients_; that is, an
account of all the acclivities upon the line from terminus to
terminus, stating how many feet in a mile each incline rises or falls,
and its length. _Secondly_, it would also be advantageous to have a
statement of the lengths of the radii of the different _curves_ as
well as the lengths of the curves themselves. _Thirdly_, an account of
the actual intercourse which has taken place, for a given time, upon
the turnpike road connecting the proposed termini, stating the number
of coaches licensed, and the average number of passengers they carry;
also as near an account of the transport of merchandise as may be
obtained. The latter, however, is of less moment. An approximate
estimate may be made of the intercourse in passengers, by allowing for
each coach, upon each trip, half its licensed complement of load.
_Fourthly_, the water communication by canal or otherwise between the
places; and the amount of tonnage transported by it. With the
information thus obtained, the following succinct maxims will be found
useful:--
I.
No railroad can be profitably worked without a large intercourse of
passengers. Goods, merchandise, agricultural produce, &c., ought to be
regarded as of secondary importance.
II.
A probable estimate of the number of passengers to be expected upon a
projected line of railroad may be made by increasing the average
number of passengers for the last three years, by the common road, in
a twofold proportion.
The average number of passengers daily between Liverpool and
Manchester, before the formation of the railway, was about 450; the
present average number is above 1300. A short railroad of about five
miles is constructed between Dublin and Kingstown: on which the
average number of passengers daily between those places has increased
in nearly the same proportion.
III.
Passengers can be profitably transported by canal, at a speed not
exceeding nine miles an hour, exclusive of delays at locks, at the
rate of one penny per head per mile. The average fares charged upon
the Manchester railway are at the rate of 1-84/100_d._ per head per
mile, the average speed being twenty miles an hour.
To transport passengers at the rate of ten miles an hour on a railway,
would cost very little less than the greater speed of twenty miles an
hour, so that a railroad could not enter into competition on equal
terms with a canal by equalising the speed.
The canal between Kendal and Preston measures 57 miles: passengers are
transported upon it between these places at the average speed of a
mile in 6-1/2 minutes, or 9-1/4 miles an hour nearly, exclusive of
delays at locks. The fare charged is at the average rate of a penny a
mile. There are eight locks, rising 9 feet each, and a tunnel 400
yards long, through which the boat is tracked by hand; the tunnel
requires 5 minutes, and the locks from 25 to 28 minutes, in
descending, and 45 to 48 minutes in ascending.
Similar boats are worked on the Forth and Clyde, and the Union canals
in Scotland, and on the Paisley and Johnstone canal at nearly the
same fares.
IV.
At the fare of 1-84/100_d._ per head per mile, the profit on the
Manchester railroad is 100 per cent. on the disbursements for
passengers.
V.
Goods can be profitably transported by canal at a lower tonnage than
by railroads; the speed on the canal (for goods) being, however, but
one-fifth of the speed on the railroad.
VI.
Goods are transported on the Liverpool and Manchester railroad at
three-pence three farthings per ton per mile, with a profit of about
40 per cent. upon the disbursement, having the competition of a canal
between its termini.
VII.
A long railroad can be worked with greater relative economy than a
short one.
VIII.
Steam engines work with the greatest efficiency and economy, when the
resistance they have to overcome is perfectly uniform and invariable.
IX.
The variation of resistance on railroads depends, first, on
acclivities, secondly, on curves.
By curves are meant the changes of direction of the road to the right
or to the left. The direction of a railroad cannot be changed suddenly
by an angle, but must be effected gradually by a curve. Supposing the
curve to be (as it generally is) the arc of a circle, the radius of
the curve is the distance of the centre of the circle from the curve.
This radius is an important element in the estimate of the road.
X.
The more nearly a railroad approaches to an absolute level, and
perfect straightness, the more profitably will it be worked.
XI.
The total amount of mechanical power necessary to transfer a given
load from one extremity of a railroad to another is a matter of easy
and exact calculation, when the gradients and curves are known; and
the merits of different lines may be compared together in this
respect: but it is not the only test of their efficiency which must be
applied.
XII.
A railroad having gradients exceeding seventeen feet in a mile will
require more mechanical power to work it than it would were it level;
and the more of these excessive gradients there are upon it, and the
more steep they are, the greater will be this disadvantage.
XIII.
Although a railroad having no gradients exceeding seventeen feet in a
mile does not require more mechanical power than a level, yet the
mechanical power which it requires will not be so advantageously
expended, and, therefore, it will not be so economical.
XIV.
A railroad which has gradients above thirty feet in a mile will
require such gradients to be worked by assistant locomotive engines,
which will be attended with a waste of power, and an increase of
expenditure, more or less, according to the number and length of such
gradients.
XV.
A very long inclined plane cannot be worked by an assistant locomotive
without a wasteful expense. Gradients exceeding seventeen feet per
mile must, therefore, be short.
XVI.
Gradients exceeding fifty feet in a mile cannot be profitably worked
except by stationary engines and ropes, an expedient attended with so
many objections as to be scarcely compatible with a large intercourse
of passengers.
XVII.
Steep gradients, provided they descend from the extremities of a line,
are admissible provided they be short.
It is evident that in this case the inclined planes will help at
starting to put the trains in motion, at the time when, in general,
there would be the greatest strain upon the moving power; and, in
approaching the terminus, the momentum would be sufficient to carry
the train to the top of the plane, if its length were not great, since
it must, at all events, come to a stop at the extremity.
XVIII.
The effect of gradients in increasing the resistance during the
ascent may be estimated by considering that a gradient of seventeen
feet in a mile doubles the resistance of the level, thirty-four feet
in a mile triples it, and eight and a half feet in a mile adds one
half its amount, and so on.
XIX.
With the speed now attainable on railways, curves should be avoided
with radii shorter than a mile. Expedients may diminish the
resistance, but, through the negligence of engine drivers, they must
always be attended with danger. Curves are not objectionable near the
extremities of a line.
XX.
The worst position for a curve is the foot of an inclined plane,
because of the velocity which the trains acquire in the descent, and
the occasional impracticability of checking them.
XXI.
In proportion as the speed of locomotives is increased by the
improvements they are likely to receive, the objections and dangers
incident to curves will be increased.
XXII.
The difficulty which attends the use of long tunnels arises from the
destruction of the vital air which is produced by the combustion in
the furnaces of the engines. Tunnels on a level should, therefore, be
from twenty-five to thirty feet high, and should be ventilated by
shafts or other contrivances.
XXIII.
The transition from light to darkness, the sensation of humidity, and
the change in summer from a warm atmosphere to a cold one, will always
form an objection to long tunnels on lines of railroad intended for a
large intercourse of passengers.
XXIV.
All the objections to a tunnel are aggravated when it happens to be
upon an acclivity. The destruction of vital air in ascending it will
be increased in exactly the same proportion as the moving power is
increased. Thus, if it ascend 17 feet in a mile, the destruction of
vital air will be twice as great as on a level; if it ascend 34 feet
in a mile, it will be three times as great; 51 feet in a mile, four
times as great, and so on.
XXV.
If by an overruling necessity a tunnel is constructed on an acclivity,
its magnitude and means of ventilation should be greater than on a
level, in the same proportion as the resistance produced by the
acclivity is greater than the resistance upon a level.
XXVI.
Tunnels should be ventilated by shafts at intervals of not more than
200 yards.
XXVII.
While a train is passing through a tunnel, no beneficial ventilation
can be obtained from shafts. The engine will leave behind it the
impure air which it produces, and the passengers will be enveloped in
it before it has time to ascend the shafts. Sufficient magnitude,
however, may be given to the tunnel to prevent any injurious
consequences from this cause. A disagreeable and inconvenient odour
will be experienced.
XXVIII.
Tunnels on a level, the length of which do not exceed a third of a
mile, will probably not be objectionable. Tunnels of equal length upon
acclivities would be more objectionable.
I may observe generally that we have as yet little or no experience of
the effect of tunnels on lines of railroad worked by locomotive
engines, where there is a large intercourse of passengers. On the
Leicester and Swannington railroad, there is a tunnel of about a mile
long, on a part of the road which is nearly level; it is ventilated by
eight shafts, and I have frequently passed through it with a
locomotive engine. Even when shut up in a close carriage the annoyance
is very great, and such as would never be tolerated on a line of road
having a large intercourse in passengers. This railroad is chiefly
used to take coals from some collieries near Swannington, and there is
no intercourse in passengers upon it, except of the labouring classes
from the adjacent villages: the engines burn coal, and not coke; and
they consequently produce smoke, which is more disagreeable than the
gases which result from the combustion of coke. This tunnel also is of
small calibre.
On the Leeds and Selby railroad there is a tunnel, on a part which is
nearly level, the length of which is 700 yards, width 22 feet, height
17. It is ventilated by three shafts of about 10 feet diameter and 60
feet high. There is an intercourse of passengers amounting to four
hundred per day, upon this road, and, generally speaking, they do not
object to go through the tunnel with a locomotive engine. The fuel is
coke.
(_l_) In order to show the present state of railroad transportation in
the United States, and enable our readers to compare it with the
opinions and facts adduced by Dr. Lardner, we take the latest accounts
from the Charleston and Hamburgh Railroad. The engines drag a train of
cars which carry a load of 130 tons, and perform the distance (240
miles) in three days, travelling only by day-light. With these loads
they mount planes having inclinations of 37 feet per mile. The same
engines are capable of carrying passengers at the rate of 40 miles per
hour, and often perform 30, but their average speed is limited by
regulation to 20 miles per hour.
This railroad is remarkable for being the largest which has yet been
constructed, and is besides an object of just pride, in as much as it
was commenced at a time, when according to Dr. Lardner, the subject
was but imperfectly understood even in Europe, and all its
arrangements are due to native talent and skill, unassisted by
previous discoveries in Europe.--A. E.
INDEX.
A.
Atmospheric air, elastic force of, 23
Atmospheric pressure rendered available as a mechanic agent
by Denis Papin, 48
Atmospheric engine, first conception of by Newcomen, 61.
Description of, 63.
Advantage of over that of Savery, 69
B.
Barometer, the, 21
Barometer gauge, the, 123
Belidor, 133
Birmingham and London railroad, probable advantages to be derived
from, 206
Black, Dr., his doctrine of latent heat, 76
Blasco de Garay, his contrivance to propel vessels, 42
Blinkensop, Mr., constructs a locomotive engine, 161
Boiler, methods for showing the level of water in the, 118.
Its power and proportions, 297
Bolton, Matthew, his connexion with Watt, 88
---- and Watt, Messrs., immense expenditure of, in bringing their
engines into use, 91
Booth, Mr., his method of using tubes to conduct heated air through
locomotive boilers, 176.
His report to the directors of the Liverpool and Manchester railway
on the apparent discrepancies of Messrs. Walker and Rastrick's
estimate of locomotive power, 189
Braithwaite and Ericsson, Messrs., their "Novelty" described, 175
Branca, Giovanni, his machine for propelling a wheel by a blast of
steam, 45
Brewster, Dr., 79
Brunton, Mr., his improved furnace described, 130
C.
Canals, transport on, 208.
Experiments with boats on, 209,
Comparison of with railroads, 210
Cartwright, Rev. Mr., description of his improvements in the steam
engine, 142
Cawley, John, 61
"Century of Inventions" by the Marquis of Worcester, 46
Chapman, Messrs., obtain a patent for working a locomotive by means
of a chain, 162
Church, Dr., his steam carriage, 239
Cohesion, attraction of, 32
Condensation of solids, 28
Condensation by jet, accidental discovery of, 65
Cornwall, reports of duty of steam engines in, 303
Cotton, processes in the culture of, 18
Cylinder, its proportions, 300
D.
D valve, description of the, 113
Damper, the, 126
Duty of a steam engine, 291
Duty, reports of, in Cornwall, 303
E.
Eccentric; description of the, 111
Edelcrantz, the Chevalier, 127
F.
Farey, Mr., his statement respecting the variations in the work
of different steam engines, 133
Fluids, property of, 21
Fly-wheel, introduction of the, 104
Four-way cock, description of the, 115
Fuel, table of the consumption of, in different locomotives, 180
G.
Governor, description of the, 105
Guericke, Otto, inventor of the air-pump, 70
Gurney, Mr., his steam carriage, 216
H.
Hackworth, Mr., description of his engine, the "Sanspareil," 173
Hall, Mr. Samuel, his patent steam engine, 248.
Its advantages for navigation, 249.
Its successful application, 250
Hamilton, Duke of, 88
Hancock, Mr. Walter, his steam carriage, 235
Heat, phenomena of, 29
Hero of Alexandria, description of his machine, 41
Hopper, the, or apparatus for supplying the fire-place with coals, 131
Hornblower, Mr., his double-cylinder engine, 134
Horse power and steam power, comparison between, 202
Horse power of an engine, 291.
Method of calculating it, 293
Howard, Mr. Thomas, his patent steam engine, 253.
Its advantages in navigation, 256
Huskisson, Mr., 154
I.
Inclined planes, their injurious effects on railroads, 194.
Methods proposed to remedy these, 194
India, steam communication with, 271
K.
Kendal and Preston canal, speed of boats on, 209
L.
Leeds and Selby railroad, 317
Leicester and Swannington railroad, 317
Leupold, his "Theatrum Machinarum," 116.
His engine described, 147
Liquids converted into vapour by the application of heat, 27.
Difference of temperatures of, 35
Liverpool and Manchester railroad, effects of the introduction
of steam transport on, 152.
Want of experience in the construction of the engines, 154.
Proceedings of the directors, 167.
Premium offered by them for the best engine, 169.
Experiments made on, 183.
Passengers the chief source of profit to the proprietors, 204
Liverpool and London, supposed advantages from the connexion of
these places by railroad, 206
Llangennech coal, its economy, 267
Locomotive engines, description of the "Rocket," 171.
The "Sanspareil," 173.
The "Novelty," 175.
Mr. Booth's method of using tubes to conduct heated air through
boilers, 177.
Mr. Stephenson's method of subdividing the flue, 179.
Amount of fuel consumed in, 180.
Progressive improvement of, 180.
Description of an improved form of engine, 181.
Circumstances on which their efficiency depends, 183.
Experiments with, on Liverpool and Manchester railroad, 184.
Defects of, 186.
Improvement in the method of tubing, 188.
Proposed methods for working them on levels and inclined planes, 194.
Extraordinary speed and power of, 204.
Their introduction on turnpike roads, 213
Locomotive power, expense of, 188
Locomotive boilers, improved form of, 177
M.
Machines, definition of, 19
Manufactures, motions required in, 19
Morgan, Mr., his patent paddle-wheel, 259
Morland, Sir Samuel, his application of steam to raise water, 47
Motion, a primary agent in the cultivation of cotton, 18.
Variety of, 19
Murray, Mr., description of his suggested slide valve, 113
N.
Newcomen, Thomas, and John Cawley, turn their attention to the
practicability of applying steam engines to the drainage of
mines, 61
Newcomen, Thomas, his construction of the atmospheric engine, 63
"Novelty," description of the, 175
O.
Ogle, Mr., his steam carriage, 239
Oldham, Mr., his modification of the self-regulating furnace, 132
P.
Paddle-wheel, the common one, 257. Mr. Morgan's patent one, 259
Papin, Denis, his contrivance, by which atmospheric pressure is
rendered available as a mechanical agent, 48.
Description of his steam engine, 71
Parallel motion, description of the, 95
Piston, its velocity, 302
Post-office steam packets, their speed, 268
Potter, Humphrey, his contrivance for working the valves, 67
Power of a steam engine, how estimated, 291
R.
Railroads, first introduction of locomotives on, 151.
Important effects to be expected from their adoption, 155.
Imaginary difficulty respecting the progression of carriages on, 160.
Various methods resorted to, to remedy this supposed difficulty, 161.
One of these methods described, 162.
Comparative estimate of the expenses of locomotive and stationary
engines, 168.
Difficulties arising from changes of level, 192.
Their great extension, 206.
Comparison of, with turnpike roads, 213.
Inclined planes on, 194
Railway speculators, plain rules for, 307
Roads, their resistance to draft, 213.
Compared with railroads, 213
Robinson, Dr., 73
Roebuck, Dr., assistance rendered by him to Watt, 87.
His embarrassments, 88
"Rocket," description of the, 171
S.
Savery, Thomas, obtains a patent for an engine to raise water, 49.
His discovery of the principle of condensation, 49.
Constructs the first engine brought into operation, 50.
Description of, 51.
Inefficiency of, 57.
Great consumption of fuel necessary in his engines, 60.
Different purposes to which he proposed to apply the steam engine, 61.
Limited power of his engine, 69
"Sanspareil", description of the, 173
Smeaton turns his attention to the details of the atmospheric engines, 73
Solids converted into liquids by the application of heat, 27
Solomon De Caus, description of the apparatus of, 43
Somerset, Edward, Marquis of Worcester, invention of the steam engine
ascribed to him, 45.
Description of his contrivance, 45.
Similar to Savery's, 46. His "Century of Inventions," 46
Steam carriages, Mr. Gurney's, 216.
Mr. Hancock's, 235.
Mr. Ogle's, 238.
Dr. Church's, 239
Steam, its properties described, 30.
Its mechanical power in proportion to the water evaporated, 277.
Its volume, 279.
Its quantity of heat, 279.
Its power in respect of fuel, 280.
Its expansive action, how advantageous, 280.
Combination of expansion with condensation, 285.
High-pressure, its expansive action, 288.
Examples illustrative of its mechanical force, 305
Steam engine, first mover in, 19.
Physical effects connected with, 20.
Claims to the invention of, 38.
Efficacy of, as a mechanical agent, 39.
First brought into operation by Savery, 50.
Its inefficiency, 58.
First proposed to be applied to the drainage of mines, 61.
Accidental discovery of condensation by jet, 65.
Further improvements by Humphrey Potter and Beighton, 67, 68.
Description of Papin's engine, 71.
First experiments of Watt and subsequent improvements, 73.
Dr. Black's theory of latent heat, 76.
Watt's method of condensation, 76.
Further improvements of Watt, 77.
Description of Watt's single-acting engine, 80.
The cold water pump, 86.
The hot water pump, 86.
Erection of a specimen engine at Soho, and gradual demand for them, 89.
The single-acting engine inapplicable to manufactures, 91.
The double-acting engine, 92.
Invention of the parallel motion, 95.
Introduction of the rotatory motion, 100.
The fly-wheel, 104.
The governor, 105.
The throttle valve, 105.
The eccentric, 111.
The D valve, 113.
The four-way cock, 115.
Methods for ascertaining the level of water in the boiler, 118.
The engine made to feed its own boiler, 120.
Waste of water prevented, 121.
The steam gauge, 122.
Barometer gauge, 123.
The damper, 125.
Methods proposed for preventing the waste of fuel, 128.
Mr. Brunton's furnace described, 130.
Mr. Oldham's modification of the self-regulating furnace, 132.
Improvements by Hornblower and Woolf, 134.
Description of the improvements of Mr. Cartwright, 142.
High-pressure engines, 145.
Leupold's engine described, 147.
Construction of the first high-pressure engine by Messrs. Trevithick
and Vivian, 148.
First application of the steam engine to propel carriages on
railroads, 151.
How applied to navigation, 242.
Marine engine; its form and arrangement, 243.
Mr. Howard's patent engine described, 253.
Mr. Hall's engine described, 248
Steam gauge, the, 122
Steam navigation, incredulity which existed respecting, 159.
The limit of its present powers, 264
Steam vessels, their average speed, 265.
Their average consumption of fuel, 265.
Proportion of their power to their tonnage, 266.
Speed of post-office packets, 268.
Iron steam vessels, 269.
American vessel called the "Cigar Boat," its great speed, 270
Stephenson's, Mr., description of an engine constructed by him, 164.
Premium awarded to this engine by the Liverpool and Manchester
Railway Directors, 170.
His method of dividing the flues, 179
Stephenson and Lock, Messrs., appointed by the Directors of the
Liverpool and Manchester Railroad to make reports on the merits
of various railroads, 167
Sun and planet wheels, 101
T.
Thermometer, description of, 24
Throttle valve, use of, 104
Traction, force of, on a railroad, 192
Tredgold,70
Trevithick and Vivian, Messrs., construct the first high-pressure
engine used in this country, 148
U.
United States, steam communication with, 274
V.
Vacuum, production of, by experiment, 37
Vapour, elastic, force of, 35
Valves, Watt's method of working the, 109
W.
Walker and Rastrick, Messrs., apparent discrepancy of their estimated
expense of locomotive power, 189
Washborough takes out a patent for Watt's invention of the rotatory
motion, 100
Water, sea, injurious to marine boilers, 245.
How remedied by blowing out, 246
Watt, James, important discoveries of, 39.
His acquaintance with Dr. Robinson and first experiments on the steam
engine, 73.
His subsequent improvements, 75.
His method of condensation, 76.
His first introduction of the air-pump into the steam engine, 77.
Further improvements, 78.
His difficulties, 78.
Description of his single-acting engine, 80.
His introduction to Dr. Roebuck, 88.
Erects his first engine on the estate of the Duke of Hamilton, 88.
After further improvements, obtains a patent for this engine, in
conjunction with Roebuck, 88.
His difficulties owing to Dr. Roebuck's failure, and subsequent
connexion with Bolton, 88.
Obtains an extension of his patent, 89.
Ingenious invention of, to determine the rate of remuneration he
should receive, 89.
His invention of the parallel motion, 95.
His method for producing a rotatory motion anticipated by Washborough,
who takes out a patent for it, 101.
His contrivance of the governor, 104.
His method of working the valves, 109.
His suggestion of the D valve, 113
Wood, Mr. Nicholas, 168
Woolf, Mr., his improvements in the steam engine, 134.
Obtains a patent for the double-cylinder engine, 137
* * * * *
JUST PUBLISHED, IN ONE VOLUME, 8VO.
MATHEMATICS FOR PRACTICAL MEN;
BEING
A COMMON-PLACE BOOK
OF
PRINCIPLES, THEOREMS, RULES AND TABLES, IN VARIOUS DEPARTMENTS
OF
PURE AND MIXED MATHEMATICS,
With their applications; especially to the pursuits of Surveyors,
Architects, Mechanics, and Civil Engineers. With numerous
engravings.
BY OLINTHUS GREGORY, LL. D., F. R. A. S.
"Only let men awake, and fix their eyes, one while on the nature
of things, another while on the application of them to the use
and service of mankind."--_Lord Bacon._
SECOND EDITION, CORRECTED AND IMPROVED.
_Extract of a Letter from_ WALTER R. JOHNSON, _Professor of Mechanics
and Natural Philosophy in the Franklin Institute_.
"This treatise is intended and admirably calculated to supply the
deficiency in the means of mathematical instruction to those who
have neither time nor inclination to peruse numerous abstract
treatises in the same departments. It has, besides the claims of
a good elementary manual, the merit of embracing several of the
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to these the rules and principles embraced in the earlier
sections of the work.
"Questions in Statics, Dynamics, Hydrostatics, Hydrodynamics,
&c., are treated with a clearness and precision which must
increase the powers of the student over his own intellectual
resources by the methodical habits which a perusal of such works
cannot fail to impart.
"With respect to Engineering, and the various incidents of that
important profession, much valuable matter is contained, in this
volume; and the results of many laborious series of experiments
are presented with conciseness and accuracy."
_Letter from_ ALBERT B. DOD, _Professor of Mathematics in the College
of New Jersey_.
"MESSRS. CAREY & HART,
"Gentlemen,--I am glad to learn that you have published an
American edition of Dr. Gregory's 'Mathematics for Practical
Men.' I have for some time been acquainted with this work, and I
esteem it highly. It contains the best digest, within my
knowledge, of such scientific facts and principles, involved in
the subjects of which it treats, as are susceptible of direct
practical application. While it avoids such details of
investigation and processes of mathematical reasoning as would
render it unintelligible to the general reader, it equally avoids
the sacrifice of precision in its statement of scientific
results, which is too often made in popular treatises upon the
Mathematics and Natural Philosophy. The author has succeeded to a
remarkable degree in collecting such truths as will be found
generally useful, and in presenting them, in an available form,
to the practical mechanic. To such, the work cannot be too
strongly recommended; and to the student, too, it will often be
found highly useful as a book of reference.
"With much respect,
"Your obedient servant,
"ALBERT B. DOD,
"Professor of Mathematics in the College of New Jersey.
"_Princeton, Nov. 11, 1834._"
_Extract of a Letter from_ EDWARD H. COURTENAY, _Professor of
Mathematics in the University of Pennsylvania_.
"The design of the author--that of furnishing a valuable
collection of rules and theorems for the use of such as are
unable, from the want of time and previous preparation, to
investigate mathematical principles--appears to have been very
successfully attained in the present volume. The information
which it affords in various branches of the pure and mixed
Mathematics embraces a great variety of subjects, is arranged
conveniently, and is in general conveyed in accurate and concise
terms. To THE ENGINEER, THE ARCHITECT, THE MECHANIC--indeed to
all for whom _results_ are chiefly necessary--the work will
doubtless form a very valuable acquisition."
_Letter from_ CHARLES DAVIES, _Professor of Mathematics in the
Military Academy, West Point_.
"MILITARY ACADEMY, West Point, May 14th, 1835.
"_To Messrs. E. L. Carey & A. Hart_,--
"The 'Mathematics for Practical Men,' by Dr. Gregory, which you
have recently published, is a work that cannot fail to be
extensively useful.
"It embraces, within a comparatively small compass, all the rules
and formulas for mathematical computation, and all the practical
results of mechanical philosophy. It is, indeed, a collection of
the useful results of science and the interesting facts which
have been developed by experience. It may safely be said, that no
work, of the same extent, contains so much information, with the
rules for applying it to practical purposes.
"I have the honour to be,
"With great respect,
"Your obedient servant,
"CHARLES DAVIES,
"_Professor of Mathematics_."
_Extract from a Letter from_ J. A. MILLER, _Professor of Mathematics
in Mount St. Mary's College, Emmettsburg, Md._
"Since the London edition of Gregory's Mathematics for Practical
Men appeared in this country, it has been much used in this
institution. The accuracy of its definitions, its beautiful
systematic arrangement, the many simplified and facilitated
methods which it proposes, and its highly practical character,
must recommend it strongly to public patronage, as one of the
very best works which have lately issued from the press. I have
examined your edition of this valuable work sufficiently to say
with confidence that it is very accurately printed."
* * * * *
[Transcriber's note: Only obvious printer's errors have been corrected
(e.g.: 3 s instead of 2, etc.). The author's spelling has been
maintained and inconsistencies have not been standardised.
The advertisement page has been move from the front to the end of the
book.
Other corrections made:
--Page x: "the wealth of rations" has been replaced by "the wealth of
nations".
--Page 17: "Pressure of Rarified Air." has been replaced by "Pressure
of Rarefied Air."
--Page 98: "This beautiful contrivance, which is incontestibly" has
been replaced by "This beautiful contrivance, which is incontestably".
--Page 100: "the working beam no longer used" has been replaced by
"the working beam is no longer used".
--Page 223: "is attended with peliar difficulty" has been replaced by
"is attended with peculiar difficulty".
--Page 271: "The projecter is now employed in" has been replaced by
"The projector is now employed in".]