_Ft_ = _At_;
that is, the motive power produced would be found to be exactly
proportional to the fall of the caloric. This is the analytical
translation of what was stated on page 98.
NOTE F.—M. Dalton believed that he had discovered that the vapors of
different liquids at equal thermometric distances from the boiling-point
possess equal tensions; but this law is not precisely exact; it is only
approximate. It is the same with the law of the proportionality of the
latent heat of vapors with their densities (see Extracts from a Mémoire
of M. C. Despretz, _Annales de Chimie et de Physique_, t. xvi. p. 105,
and t. xxiv. p. 323). Questions of this nature are closely connected
with those of the motive power of heat. Quite recently MM. H. Davy and
Faraday, after having conducted a series of elegant experiments on the
liquefaction of gases by means of considerable pressure, have tried to
observe the changes of tension of these liquefied gases on account of
slight changes of temperature. They have in view the application of the
new liquids to the production of motive power (see _Annales de Chimie et
de Physique_, January, 1824, p. 80).
According to the above-mentioned theory, we can foresee that the use of
these liquids would present no advantages relatively to the economy of
heat. The advantages would be found only in the lower temperature at
which it would be possible to work, and in the sources whence, for this
reason, it would become possible to obtain caloric.
NOTE G.—This principle, the real foundation of the theory of
steam-engines, was very clearly developed by M. Clement in a memoir
presented to the Academy of Sciences several years ago. This Memoir has
never been printed, and I owe the knowledge of it to the kindness of the
author. Not only is the principle established therein, but it is applied
to the different systems of steam-engines actually in use. The motive
power of each of them is estimated therein by the aid of the law cited
page 92, and compared with the results of experiment.
The principle in question is so little known or so poorly appreciated,
that recently Mr. Perkins, a celebrated mechanician of London,
constructed a machine in which steam produced under the pressure of 35
atmospheres—a pressure never before used—is subjected to very little
expansion of volume, as any one with the least knowledge of this machine
can understand. It consists of a single cylinder of very small
dimensions, which at each stroke is entirely filled with steam, formed
under the pressure of 35 atmospheres. The steam produces no effect by
the expansion of its volume, for no space is provided in which the
expansion can take place. It is condensed as soon as it leaves the small
cylinder. It works therefore only under a pressure of 35 atmospheres,
and not, as its useful employment would require, under progressively
decreasing pressures. The machine of Mr. Perkins seems not to realize
the hopes which it at first awakened. It has been asserted that the
economy of coal in this engine was ⁹⁄₁₀ above the best engines of Watt,
and that it possessed still other advantages (see _Annales de Chimie et
de Physique_, April, 1823, p. 429). These assertions have not been
verified. The engine of Mr. Perkins is nevertheless a valuable
invention, in that it has proved the possibility of making use of steam
under much higher pressure than previously, and because, being easily
modified, it may lead to very useful results.
Watt, to whom we owe almost all the great improvements in steam-engines,
and who brought these engines to a state of perfection difficult even
now to surpass, was also the first who employed steam under
progressively decreasing pressures. In many cases he suppressed the
introduction of the steam into the cylinder at a half, a third, or a
quarter of the stroke. The piston completes its stroke, therefore, under
a constantly diminishing pressure. The first engines working on this
principle date from 1778. Watt conceived the idea of them in 1769, and
took out a patent in 1782.
We give here the Table appended to Watt’s patent. He supposed the steam
introduced into the cylinder during the first quarter of the stroke of
the piston; then, dividing this stroke into twenty parts, he calculated
the mean pressure as follows:
Portions of the descent from the top of the Decreasing pressure of the
cylinder. steam, the entire pressure
being 1.
Steam arriving
0.05 freely from the 1.000 Total pressure.
boiler.
0.10 „ 1.000 „
0.15 „ 1.000 „
0.20 „ 1.000 „
Quarter 0.25 „ 1.000 „
The steam being cut
off and the
0.30 descent taking 0.830
place only by
expansion.
0.35 „ 0.714
0.40 „ 0.625
0.45 „ 0.555
Half 0.50 „ 0.500 Half original
pressure.
0.55 „ 0.454
0.60 „ 0.417
0.65 „ 0.385
0.70 „ 0.375
0.75 „ 0.333 One third.
0.80 „ 0.312
0.85 „ 0.294
0.90 „ 0.277
0.95 „ 0.262
Bottom of cylinder 1.00 „ 0.025 Quarter.
Total, 11.583
Mean pressure (11.583)/(20) = 0.579.
On which he remarked, that the mean pressure is more than half the
original pressure; also that in employing a quantity of steam equal to a
quarter, it would produce an effect more than half.
Watt here supposed that steam follows in its expansion the law of
Mariotte, which should not be considered exact, because, in the first
place, the elastic fluid in dilating falls in temperature, and in the
second place there is nothing to prove that a part of this fluid is not
condensed by its expansion. Watt should also have taken into
consideration the force necessary to expel the steam which remains after
condensation, and which is found in quantity as much greater as the
expansion of the volume has been carried further. Dr. Robinson has
supplemented the work of Watt by a simple formula to calculate the
effect of the expansion of steam, but this formula is found to have the
same faults that we have just noticed. It has nevertheless been useful
to constructors by furnishing them approximate data practically quite
satisfactory. We have considered it useful to recall these facts because
they are little known, especially in France. These engines have been
built after the models of the inventors, but the ideas by which the
inventors were originally influenced have been but little understood.
Ignorance of these ideas has often led to grave errors. Engines
originally well conceived have deteriorated in the hands of unskilful
builders, who, wishing to introduce in them improvements of little
value, have neglected the capital considerations which they did not know
enough to appreciate.
NOTE H.—The advantage in substituting two cylinders for one is evident.
In a single cylinder the impulsion of the piston would be extremely
variable from the beginning to the end of the stroke. It would be
necessary for all the parts by which the motion is transmitted to be of
sufficient strength to resist the first impulsion, and perfectly fitted
to avoid the abrupt movements which would greatly injure and soon
destroy them. It would be especially on the working beam, on the
supports, on the crank, on the connecting-rod, and on the first
gear-wheels that the unequal effort would be felt, and would produce the
most injurious effects. It would be necessary that the steam-cylinder
should be both sufficiently strong to sustain the highest pressure, and
with a large enough capacity to contain the steam after its expansion of
volume, while in using two successive cylinders it is only necessary to
have the first sufficiently strong and of medium capacity,—which is not
at all difficult,—and to have the second of ample dimensions, with
moderate strength.
Double-cylinder engines, although founded on correct principles, often
fail to secure the advantages expected from them. This is due
principally to the fact that the dimensions of the different parts of
these engines are difficult to adjust, and that they are rarely found to
be in correct proportion. Good models for the construction of
double-cylinder engines are wanting, while excellent designs exist for
the construction of engines on the plan of Watt. From this arises the
diversity that we see in the results of the former, and the great
uniformity that we have observed in the results of the latter.
NOTE I.—Among the attempts made to develop the motive power of heat by
means of atmospheric air, we should mention those of MM. Niepce, which
were made in France several years ago, by means of an apparatus called
by the inventors a pyréolophore. The apparatus was made thus: There was
a cylinder furnished with a piston, into which the atmospheric air was
introduced at ordinary density. A very combustible material, reduced to
a condition of extreme tenuity, was thrown into it, remained a moment in
suspension in the air, and then flame was applied. The inflammation
produced very nearly the same effect as if the elastic fluid had been a
mixture of air and combustible gas, of air and carburetted hydrogen gas,
for example. There was a sort of explosion, and a sudden dilatation of
the elastic fluid—a dilatation that was utilized by making it act upon
the piston. The latter may have a motion of any amplitude whatever, and
the motive power is thus realized. The air is next renewed, and the
operation repeated.
This machine, very ingenious and interesting, especially on account of
the novelty of its principle, fails in an essential point. The material
used as a combustible (it was the dust of Lycopodium, used to produce
flame in our theatres) was so expensive, that all the advantage was lost
through that cause; and unfortunately it was difficult to employ a
combustible of moderate price, since a very finely powdered substance
was required which would burn quickly, spread rapidly, and leave little
or no ash.
Instead of working as did MM. Niepce, it would seem to us preferable to
compress the air by means of pumps, to make it traverse a perfectly
closed furnace into which the combustible had been introduced in small
portions by a mechanism easy of conception, to make it develop its
action in a cylinder with a piston, or in any other variable space;
finally, to throw it out again into the atmosphere, or even to make it
pass under a steam-boiler in order to utilize the temperature remaining.
The principal difficulties that we should meet in this mode of operation
would be to enclose the furnace in a sufficiently strong envelope, to
keep the combustion meanwhile in the requisite state, to maintain the
different parts of the apparatus at a moderate temperature, and to
prevent rapid abrasion of the cylinder and of the piston. These
difficulties do not appear to be insurmountable.
There have been made, it is said, recently in England, successful
attempts to develop motive power through the action of heat on
atmospheric air. We are entirely ignorant in what these attempts have
consisted—if indeed they have really been made.
NOTE J.—The result given here was furnished by an engine whose large
cylinder was 45 inches in diameter and 7 feet stroke. It is used in one
of the mines of Cornwall called Wheal Abraham. This result should be
considered as somewhat exceptional, for it was only temporary,
continuing but a single month. Thirty millions of lbs. raised one
English foot per bushel of coal of 88 lbs. is generally regarded as an
excellent result for steam-engines. It is sometimes attained by engines
of the Watt type, but very rarely surpassed. This latter product
amounts, in French measures, to 104,000 kilograms raised one metre per
kilogram of coal consumed.
According to what is generally understood by one horse-power, in
estimating the duty of steam-engines, an engine of ten horse-power
should raise per second 10 × 75 kilograms, or 750 kilograms, to a height
of one metre, or more, per hour; 750 × 3600 = 2,700,000 kilograms to one
metre. If we suppose that each kilogram of coal raised to this height
104,000 kilograms, it will be necessary, in order to ascertain how much
coal is burnt in one hour by our ten-horse-power engine, to divide
2,700,000 by 104,000, which gives ²⁷⁰⁰⁄₁₀₄ = 26 kilograms. Now it is
seldom that a ten-horse-power engine consumes less than 26 kilograms of
coal per hour.
APPENDIX C.
NOTE BY THE EDITOR.
All the preceding data are to-day subject to modification.
Thus a duty of 150,000,000 ft.-lbs. per 100 lbs. good coal is to-day
attainable, and two thirds that figure is extremely common. With engines
of large size the coal-consumption has fallen to one half, sometimes
even to one fourth, the figure in the text.
Hot air-engines are superseded by the gas-engine and the oil-vapor
engine; which even threaten, in the opinion of many engineers, to
ultimately displace the steam-engine.
Compound and other multiple-cylinder engines, with two, three, and even
four cylinders in series, are now always employed where fuel is costly.
The reason of their success is, in part, that given in Note H; but in
only small part. The real cause of their general adoption is the fact
that the internal thermal waste by “cylinder condensation”—which in
simple engines ordinarily amounts, according to size, to from 25 to 50
per cent, or more, of all heat supplied by the boiler—is reduced nearly
in proportion to the number of steam-cylinders in series.
For the applied thermodynamics of the steam-engine, following Carnot and
Thomson, see the pages of Rankine and of Clausius of 1850 to 1860, and
especially the treatise of Rankine on the Steam-engine. The editor has
adopted the methods of these great successors of Carnot in his “Manual
of the Steam-engine” (2 vols. 8vo; N. Y., J. Wiley & Sons), which may be
consulted in this connection, and especially for details of the theory
and the structure of this prime mover.
-----
Footnote 1:
Tait: Thermodynamics, p. 13.
Footnote 2:
Account of Carnot’s Theory of the Motive Power of Heat; Sir Wm.
Thomson; Trans. Roy. Soc. of Edinburgh, xvi. 1849; and Math. and Phys.
Papers, xli. vol. 1 (Cambridge, 1882), p. 113. In this paper the
corrections due to the introduction of the dynamic theory are first
applied.
Footnote 3:
See the Appendix for these memoranda, and for other previously
unpublished matter.
Footnote 4:
Sadi Carnot’s _Réflexions sur la puissance motrice du feu_ (Paris,
Bachelier 1824) was long ago completely exhausted. As but a small
number of copies were printed, this remarkable work remained long
unknown to the earlier writers on Thermodynamics. It was therefore for
the benefit of savants unable to study a work out of print, as well as
to render honor to the memory of Sadi Carnot, that the new publishers
of the _Annales Scientifique de l’École Normale supérieure_ (ii.
series, t. 1, 1872) published a new edition, from which this
translation is reproduced.
Footnote 5:
It may be said that coal-mining has increased tenfold in England since
the invention of the steam-engine. It is almost equally true in regard
to the mining of copper, tin, and iron. The results produced in a
half-century by the steam-engine in the mines of England are to-day
paralleled in the gold and silver mines of the New World—mines of
which the working declined from day to day, principally on account of
the insufficiency of the motors employed in the draining and the
extraction of the minerals.
Footnote 6:
We say, to lessen the dangers of journeys. In fact, although the use
of the steam-engine on ships is attended by some danger which has been
greatly exaggerated, this is more than compensated by the power of
following always an appointed and well-known route, of resisting the
force of the winds which would drive the ship towards the shore, the
shoals, or the rocks.
Footnote 7:
We use here the expression motive power to express the useful effect
that a motor is capable of producing. This effect can always be
likened to the elevation of a weight to a certain height. It has, as
we know, as a measure, the product of the weight multiplied by the
height to which it is raised.
Footnote 8:
We distinguish here the steam-engine from the heat-engine in general.
The latter may make use of any agent whatever, of the vapor of water
or of any other, to develop the motive power of heat.
Footnote 9:
Certain engines at high pressure throw the steam out into the
atmosphere instead of the condenser. They are used specially in places
where it would be difficult to procure a stream of cold water
sufficient to produce condensation.
Footnote 10:
The existence of water in the liquid state here necessarily assumed,
since without it the steam-engine could not be fed, supposes the
existence of a pressure capable of preventing this water from
vaporizing, consequently of a pressure equal or superior to the
tension of vapor at that temperature. If such a pressure were not
exerted by the atmospheric air, there would be instantly produced a
quantity of steam sufficient to give rise to that tension, and it
would be necessary always to overcome this pressure in order to throw
out the steam from the engines into the new atmosphere. Now this is
evidently equivalent to overcoming the tension which the steam retains
after its condensation, as effected by ordinary means.
If a very high temperature existed at the surface of our globe, as it
seems certain that it exists in its interior, all the waters of the
ocean would be in a state of vapor in the atmosphere, and no portion
of it would be found in a liquid state.
Footnote 11:
It is considered unnecessary to explain here what is quantity of
caloric or quantity of heat (for we employ these two expressions
indifferently), or to describe how we measure these quantities by the
calorimeter. Nor will we explain what is meant by latent heat, degree
of temperature, specific heat, etc. The reader should be familiarized
with these terms through the study of the elementary treatises of
physics or of chemistry.
Footnote 12:
We may perhaps wonder here that the body _B_ being at the same
temperature as the steam is able to condense it. Doubtless this is not
strictly possible, but the slightest difference of temperature will
determine the condensation, which suffices to establish the justice of
our reasoning. It is thus that, in the differential calculus, it is
sufficient that we can conceive the neglected quantities indefinitely
reducible in proportion to the quantities retained in the equations,
to make certain of the exact result.
The body _B_ condenses the steam without changing its own
temperature—this results from our supposition. We have admitted that
this body may be maintained at a constant temperature. We take away
the caloric as the steam furnishes it. This is the condition in which
the metal of the condenser is found when the liquefaction of the steam
is accomplished by applying cold water externally, as was formerly
done in several engines. Similarly, the water of a reservoir can be
maintained at a constant level if the liquid flows out at one side as
it flows in at the other.
One could even conceive the bodies _A_ and _B_ maintaining the same
temperature, although they might lose or gain certain quantities of
heat. If, for example, the body _A_ were a mass of steam ready to
become liquid, and the body _B_ a mass of ice ready to melt, these
bodies might, as we know, furnish or receive caloric without
thermometric change.
Footnote 13:
Note A, Appendix B.
Footnote 14:
We assume here no chemical action between the bodies employed to
realize the motive power of heat. The chemical action which takes
place in the furnace is, in some sort, a preliminary action,—an
operation destined not to produce immediately motive power, but to
destroy the equilibrium of the caloric, to produce a difference of
temperature which may finally give rise to motion.
Footnote 15:
This kind of loss is found in all steam-engines. In fact, the water
destined to feed the boiler is always cooler than the water which it
already contains. There occurs between them a useless re-establishment
of equilibrium of caloric. We are easily convinced, _à posteriori_,
that this re-establishment of equilibrium causes a loss of motive
power if we reflect that it would have been possible to previously
heat the feed-water by using it as condensing water in a small
accessory engine, when the steam drawn from the large boiler might
have been used, and where the condensation might be produced at a
temperature intermediate between that of the boiler and that of the
principal condenser. The power produced by the small engine would have
cost no loss of heat, since all that which had been used would have
returned into the boiler with the water of condensation.
Footnote 16:
The matter here dealt with being entirely new, we are obliged to
employ expressions not in use as yet, and which perhaps are less clear
than is desirable.
Footnote 17:
Note 13, Appendix B.
Footnote 18:
We tacitly assume in our demonstration, that when a body has
experienced any changes, and when after a certain number of
transformations it returns to precisely its original state, that is,
to that state considered in respect to density, to temperature, to
mode of aggregation—let us suppose, I say, that this body is found to
contain the same quantity of heat that it contained at first, or else
that the quantities of heat absorbed or set free in these different
transformations are exactly compensated. This fact has never been
called in question. It was first admitted without reflection, and
verified afterwards in many cases by experiments with the calorimeter.
To deny it would be to overthrow the whole theory of heat to which it
serves as a basis. For the rest, we may say in passing, the main
principles on which the theory of heat rests require the most careful
examination. Many experimental facts appear almost inexplicable in the
present state of this theory.
Footnote 19:
We will suppose, in what follows, the reader to be _au courant_ with
the later progress of modern Physics in regard to gaseous substances
and heat.
Footnote 20:
M. Poisson, to whom this figure is due, has shown that it accords very
well with the result of an experiment of MM. Clement and Desormes on
the return of air into a vacuum, or rather, into air slightly
rarefied. It also accords very nearly with results found by MM.
Gay-Lussac and Welter. (See note, p. 87.)
Footnote 21:
The law of Mariotte, which is here made the foundation upon which to
establish our demonstration, is one of the best authenticated physical
laws. It has served as a basis to many theories verified by
experience, and which in turn verify all the laws on which they are
founded. We can cite also, as a valuable verification of Mariotte’s
law and also of that of MM. Gay-Lussac and Dalton, for a great
difference of temperature, the experiments of MM. Dulong and Petit.
(See _Annales de Chimie et de Physique_, Feb. 1818, t. vii. p. 122.)
The more recent experiments of Davy and Faraday can also be cited.
The theories that we deduce here would not perhaps be exact if applied
outside of certain limits either of density or temperature. They
should be regarded as true only within the limits in which the laws of
Mariotte and of MM. Gay-Lussac and Dalton are themselves proven.
Footnote 22:
When the volume is reduced ¹⁄₁₁₆, that is, when it becomes ¹¹⁵⁄₁₁₆ of
what it was at first, the temperature rises one degree. Another
reduction of ¹⁄₁₁₆ carries the volume to (¹¹⁵⁄₁₁₆)^2, and the
temperature should rise another degree. After _x_ similar reductions
the volume becomes (¹¹⁵⁄₁₁₆)^{_x_}, and the temperature should be
raised _x_ degrees. If we suppose (¹¹⁵⁄₁₁₆)^{_x_} = ¹⁄₁₄, and if we
take the logarithms of both, we find
_x_ = about 300°.