CHAPTER
VII.
THE PHILOSOPHY OF THE STEAM ENGINE
THE HISTORY OF ITS GROWTH; ENERGETICS AMD THERMO-DYNAMICS
"OF all the features which characterize this progressive economical
movement of civilized nations, that which first excites attention, through
its intimate connection with the phenomena of production, is the perpetual
and, so far as human foresight can extend, the unlimited growth of man's
power over Nature. 0ur knowledge of the properties and laws of physical
objects shows no sign of approaching its ultimate boundaries; it is advancing
more rapidly, and in a greater number of directions at once, than in any
previous age or generation, and affording such frequent glimpses of unexplored
fields beyond as to justify the belief that our acquaintance with Nature
is still almost in its infancy."MILL.
THE growth of the philosophy of the steamcngine presents as interesting a study as that of the successive changes which have occurred in its mechanism.
In the operation of the steamengine we find illustrated many of the most
important principles and facts which constitute thc physical spinners.
The steamengine is an exceedingly ingenious, but, unfortunately, still
very imperfect, machine for transforming the heatenergy obtained by the
chemical combination of a combustible with the supporter of combustion
into mechanical energy. But the original sourer of all this energy is found
far back of its first appearance in the steamboiler. It had its origin
at the beginning, when all Nature came into existence. After the solar
system had been formed from the nebulous chaos of creation, the glowing
mass which is now called the sun was the depository of a vast store of
heatenergy, which was thence radiated into space and showered upon the
attendant worlds in inconceivable quantity and with unmeasured intensity.
During the past life of the globe, the heatenergy received from the sun
upon the earth's surface was partly expelled in the production of great
forests, and the storage, in the trunks, branches, and leaves of the trees
of which they were composed, of an immense quantity of carbon, which had
previously existed in the atmosphere, combined with oxygen, as carbonic
acid. The great geological changes which buried these forests under superincumbent
strata of rock and earth resulted in the formation of coalbeds, and the
storage, during many succeeding ages, of a vast amount of carbon, of which
the affinity for oxygen remained unsatisfied until finally uncovered by
the hand of man. Thus we owe to the heat and light of the sun, as was pointed
out George Stephenson, the incalculable store of potential energy upon
which the human race is so dependent for life and all its necessaries,
comforts, and luxuries.
This coal, thrown upon the grate in the steamboiler takes fire, and, uniting
again with the oxygen, sets free heat in precisely the same quantity that
it was received from the sun and appropriated during the growth of the
tree. The actual enelgy thus rendered available is transferred, by conduction
and radiation, to the water in the steamboiler, converts it into steam,
and its mechanical effect is seen in the expansion of the liquid into vapor
against the superincumbent pressure. Transferred from the boiler to the
engine, the steam is there permitted to expand doing work, and the heatenergy
with which it is charged becomes partly converted into mechanical energy,
and is applied to useful work in the mill or to driving the locomotive
or the steamboat.
Thus we may trace the store of energy received from the sun and contained
in our coal through its several changes until it is finally set at work;
and we might go still further and observe how, in each case, it is again
usually retransformed and again set free as heatenergy.
The transformation which takes place in the furnace is a chemical change;
the transfer of heat to the water and the subsequent phenomena accompanying
its passage through the engine are physical changes, some of which require
for their investigation abstruse mathematical operations. A thorough comprehension
of the principles govern ing the operation of the steamengine,
therefore, can only be attained after studying the phenomena of physical
science with sufficient minuteness and accuracy to be able to express with
precision the laws of which those sciences are constituted. The study of
the philosophy of the steam engine involves the study of chemistry and
physics, and of the new science of energeties, of which the now wellgrown
science of
thermodynamics is a brash. This sketch of the growth of the steamengine
may,
therefore, be very properly concluded by an outline of the growth of the
several sciences which together make up its philosophy, and especially
of the science of thermodynamics which is peculiarly the science of the
steam-engine and of the other heatengines.
These sciences, like the steamengine itself, have an origin which antedates
the commencement of the Christian era; but they grew with an almostimperceptible
growth for many centuries, and finally, only a century ago, started onward
suddenly and rapidly, and their progress has never since been checked.
They are now fullydeveloped and wellestablished systems of natural philosophy.
Yet, like that of the steamengine and of its companion heatengines, their
growth has by no means ceased; and, while the studentof science cannot
do more than indicate the direction of their progress, he can readily believe
that the beginning of the end is not yet reached in their movement toward
completeness, either in the determination of facts or in the modification
of their laws.
When Hero lived at Alexandria, the great "Museum" was a most
important centre, about which gathered the teachers of all then known philosophies
and of all the then recognized but unformed sciences, as well as of all
those technical branches of study which had already been so far developed
as to be capable of being systematically taught. Astronomical observations
had been made regularly and uninterruptedly by the Chaldean astrologers
for two thousand years, and records extending back many centuries had been
secured at Babylon by Calisthenes and given to Aristotle, the father of
our modern scientific method. Ptolemy had found ready to his hand the records
of Chaidean observers of eclipses extending back nearly 650 years, and
marvelously accurate.(1)
A rude method of printing with an engraved roller on plastic elay, afterward
baked, thus making up ceramic libraries, was practised long previous to
this time; and in the alcoves in which Hero worked were many of these books
of clay.
This great Library and Museum of Alexandria was founded three centuries
before the birth of Christ, by Ptolemy Soter, who established as his capital
that great Egyptian city when the death of his brother, the youthful but
famous conqueror whose name he gave it, placed him upon the throne of the
colossal successor of the then fallen Persian Empire. The city itself,
embellished with every ornament and provided with every luxury that the
wealth of a conquered world or the skill, taste, and ingenuity of the Greek
painters, sculptors, architects, and engineers could provide, was full
of wonders; it was a wonder in itself. This rich, populous, and magnificent
city was the metropolis of the then civilized world. Trade, commerce, manufactures,
and the fine arts were all represented in this
1 Their estimate of the length of the Saros, or cycle
of eclipscs - over 19 yearswas "within 19.5 minutes of the truth."Draper.
splendid exchange, and learning found its most acceptable home and noblest field within the walls of Ptolemy's Museum; its disciples found themselves welcomed and protected by its founder and his successors, Philadelphus and the later Ptolemies.
The Alexandrian Museum was founded with the declared object of collecting
all written works of authority, of promoting the study of literature and
art, and of stimulating and assisting experimental and mathematical scientific
investigation and research. The founders of modern libraries, colleges,
and technical schools have their prototype in intelligence, public spirit,
and liberality, in the first of the Ptolemics, who not only spent an immense
sum in establishing this great institution, but spared no expense in sustaining
it. Agents were sent out into all parts of the world, purchasing books.
A large staff of scribes was maintained at the museum, whose duty it was
to multiply copies of valuable works, and to copy for the library such
works as could not be purchased.
The faculty of the museum was as carefully organized as was the plan of
its administration. The four principal faculties of astronomy, literature,
mathematics, and medicine were subdivided into sections devoted to the
several branches of each department. The collections of the museum were
as complete as the teachers of the undeveloped skinners of the time could
make them. Lectures were given in all branches of study, and the number
of students was sometimes as great as twelve or thirteen thousand. The
number of books which were collected here, when the barbarian leaders of
the Roman troops under Csesar burned thc greater part of it, was stated
to be 700,000. Of these, 400,000 were within the museum itself, and were
all destroyed; the rest were in the temple of Serapis, and, for the time,
escaped destruction.
The greatest of all the great men who lived at Alexandria at the time of
the establishment of the museum was Aristotle, the teacher of Alexander
and the friend of Ptolemy. It is to Aristotle that we owe the systematization
of the philosophical ideas of Plato and the creation of the inductive method,
in which has originated all modern scicnce. It is to the learned men of
Alexandria that we are indebted for so effective an application of the
Aristotelian philosophy that all the then known sciences wele given form,
and were so thoroughly established that the work of modern science has
been purely one of development.
The inductive method, which built up all the older sciences, and which
has created all those of recent development, consists, first, in the discovery
and quantitative determination of facts; secondly, when a sufficient number
of facts have been thus observed and defined, in the grouping of those
facts, and the detection, by a study of their mutual relations, of the
natural laws which give rise to or regulate them. This simple method is
that and the only method by which science advances. By this method,
and by it only, do we acquire connected and systematic knowledge of all
the phenomena of Nature of which the physical sciences are cognizant. It
is only by the application of this Aristotelian method and philosophy that
we can hope to acquire exact scientific knowledge of existing phenomena,
or to become able to anticipate the phenomena which are to distinguish
the futures The Aristotelian method of observing facts, and of inductive
reasoning with those facts as a basis, has taught the chemist the properties
of the known elementary substances and their characteristic behavior under
ascertained conditions, and has taught him the laws of combination and
the effects of their union, enabling him to predict the changes and the
phenomena, chemical and physical, which inevitably follow their contact
under any specified set of conditions.
It is this process which has enabled the physicist to ascertain the methods
of molecular motion which give us light, heat, or electricity, and the
range of action and the laws which govern the transfer of energy from one
of these modes of motion to another. It was this method of study which
enabled James Watt to detect and to remedy the defects of the Newcomen
engine, and it is by the Aristotelian philosophy that thc engineer of today
is taught to construct the modern steamship, and to predict, before the
keel is laid or a blow struck in the workshop or the shipyard, what will
be the weight of the vessel, its cargo-carrying capacity, the necessary
size and power of its engines, the quantity of coal which they will require
per day while crossing the ocean, the depth at which the great hull will
float in the water, and the exact speed that the vessel will attain when
the engines arc exerting their thousand or their ten thousand horsepower.
It was at Alexandria that this mightv philosophy was first given a field
in which to work effectively. Here Ptolemy studied astronomy and "natural
philosophy; "Archimedes applied himself to the studies which attract
the mathematician and engineer; Euclid taught his royal pupil those elements
of geometry which have remained standard twentytwo centuries; Eratosthenes
and Hipparchus studies and taught astronomy, and inaugurated the existing
system of quantitative investigation, proving the spherical form of the
earth; and Ctesibius and Hero studied pneumatics and experimented with
the germs of the steam-engine and of less important machines.
When, seven centuries later, the destruction of this splendid institution
was signalized by the death of that brilliant scholar and heathen teacher
of philosophy, Hypatia, at the hands of the more heathenish fanaties who
tore her in pieces at the foot of the cross, and by the dispersion of the
library left by Caesar's soldiers in the Serapeum, a true philosophy had
been created, and the inductive method was destined to live and to overcome
every obstacle in the path of enlightenment and civilization. The fall
of the Alexandrian Muscum, sad as was the event, could not destroy the
new philosophical method. Its fruits ripened slowly but surely, and we
are today gathering a plentiful harvest.
Science, literature, and the arts, all remained dormant for several centuries after the catastrophe which deprived them of the light in which they had flourished so many centuries. The armies of the caliphs made complete the shameful work of destruction begun by the armies of Cae sar, and the Alexandrian Library, partly destroyed by the Romans, was completely dispersed by the Patriarchs and their ignorant and fanatical followers; and finally all the scattered remnants were burned by the Saracens. But when the thirst for conquest had become satiated or appeased, the followers of the caliphs turned their attention to intellectual pursuits, and the ninth century of the Christian era saw once more such a collection of philosophical writings, collected at Bagdad, as could only be gathered by the power and wealth of the later conquerors of the world. Philosophy once again resumed its empire, and another race commenced the study of the mathematics of India and of Greece, the astronomy of Chaldea, and of all the sciences which originated in Greece and in Egypt. By the conquest of Spain by the Saracens, the new civilization was imported into Western Europe and libraries were gathered together under the Moorish rulers, one of which numbered more than a halfmillion volumes. Wherever Saracen armies had extended Mohammedan rule, schools and colleges, libraries and collections of philosophical apparatus, were scattered in strange profusion; and students, teachers, phi losophers, of allthe speculative as well as the Aristo telianschools, gathered together at these intellectual ganglia, as enthusiastic in their work as were their Alex andrian predecessors. The endowment of colleges, that truest gauge of the intelligence of the wealthy classes of any community, became as commonperhaps more soas at the present time, and provision was made for the education of rich and poor alike. The mathematical sciences, and the wonderful and beautiful phenomena whichbut a thousand years laterwere afterward grouped into a science and called chemistry, were especially attractive to the Arabian scholars, and technical applications of diseovered facts and laws assisted in a wonderfully rapid development of arts and manufactures.
When, a thousand years after Christ, the centre of intellectual activity
and of material civilization had drifted westward into Andalusia, the foundation
of every modern physical seienee except that now just taking shapethe
allgrasping science of energeticshad been laid with experimentally
derived facts; and in mathematics there had been erected a symmetrical
and elegant superstructure. Even that underlying principle of all the sciences,
the principle of the persistence of energy, had been, perhaps unwittingly,
enunciated.
Distinguished historians have shown how the progress of civilization in
Europe resulted in the creation, during the middle ages, of the now great
middle class, whieh, holding the control of political power, governs every
civilized nation, and has come into power so gradually that it was only
after centuries that its influenee was seen and felt. This, which Buekle1
calls the intellectual class, first became active, independently of the
military and of the clergy, in the fourteenth century. In the two succeeding
centuries this class gained power and influence; and in the seventeenth
century we find a magnificent advance in all branches of science, literature,
and art, marking the complete emancipation of the intellect from the artificial
conditions which had so long repressed its every effort at advancement.
Another great social revolution thus occurred, following another period
of centuries of intellectual stagnation. The Salacen invaders were driven
from Europe; the Crusaders invaded Palestine, in the vain effort to recover
from the hands of the infidels the Holy Sepulchre and the Holy
1 "History of Civilization in England," vol.
i., p. 208. London, 1868.
Land; and intestine broils and interstate conflicts, as well as these greater social movements, withdrew the minds of men once Lore from the arts of peace and the pursuits of scholars. It is not, then, until the beginning of the seventeenth centurythe time of Galileo and of Newton that we find the nations of Europe sufficiently quiet and secure to permit general attention to intellectual vocations, although it was a halfcentury earlier (1543) that Copernicus left to the world that legacy which revolutionized the theories of the astronomers and established as correct the hypothesis which made the sun the centre of the solar system.
Galileo now began to overturn the speculations of the deductive philosophers,
and to proclaim the still disputed principle that the book of Nature is
a trustworthy commentary in the study of theological and revealed truths,
so far as they affect or are affected by science; He suffered martyrdom
when he proclaimed the fact that God's laws, as they now stand, had been
instituted without deference to the preconceived notions of the most ignorant
of men. Bruno had a few years earlier (l600) been burned at the stake for
a similar offense.
Galileo was perhaps the first, too, to combine invariably in application
the idea of Plato, the philosophy of Aristotle, and the methods of modern
experimentation, to form the now universal scientific method of experimental
philosophy. He showed plainly how the grouping of ascertained facts, in
natural sequence, leads to the revelation of the law of that sequence,
and indicated the existenee of a principle which is now known as the law
of continuitythe law that in all the operations of Nature there is
to be seen an unbroken chain of effect leading from the present back into
a known or all unknown past, toward a cause which may or may not be determinable
by science or known to history.
Galileo, the Italian, was worthily matched by Newton, the prince of English
philosophers. The scicnce of theorctieal mechanics was hardly beginning
to assume the position which it was afterward given among the scienees;
and the grand work of collating facts already ascertained, and of definitely
stating principles whieh had previously been vaguely recognized, was splendidly
done by Newton. The needs of physical astronomy urged this work upon him.
Da Vinci had, in the latter half of the fifteenth century, summarized as
much of the statics of mechanical philosophy as had, up to his time, been
given shape; he also rewrote and added very much to what was known on the
subject of friction, and enunciated its laws. He had evidently a good idea
of the principle of "virtual velocities," that simple ease of
equivalence of work, in a connected system, which has done such excellent
service since; and with his mechanical philosophy this versatile engineer
and artist curiously mingled much of physical science. Then Stevinus, the
"brave engineer of Bruges," a hundred years later (1586), alternating
office and field work, somewhat after the manner of the engineer of today,
wrote a treatise on mechanics, which showed the value of practical experience
and judgment in even scientific work. And thus the path had been cleared
for Newton.
Meantime, also, Kepler had hit upon the true relations of the distances
of the planets and their periodic times, after spending half a generation
in blindly groping for them, thus furnishing those great landmarks of fact
in the mechanics of astronomy; and Galileo had enunciated the laws of motion.
Thus the foundation of the science of dynamics, as distinguished from statics,
was laid, and the beginning was made of that later science of energetic
of which the philosophy of the steamengine is so largely constituted.
Hooke, Huyghens, and others, had already seen some of the principal consequences
of these laws; but it remained for Newton to enunciate them with the precision
of a true mathematician, and to base upon them a system of dynamieal laws,which,
complemented by his announcement of the existence of the force of gravitation,
and his statement of its laws, gave a firm basis for all that the astronomer
has since done in those quantitative determinations of size, weight, and
distance, and of the movements of the heavenly bodies, which compel the
wonder and admiration of mankind.
The Arabians and Greeks had noticed that the direction taken by a body
falling under the action of gravitation was directly toward the centre
of the earth, wherever its fall might occur; Galileo had shown, by his
experiments at Pisa, that the velocity of fall, second after second, varied
as the numbers l, 3, 5, 7, 9, etc., and that the distances varied as the
squares of the total periods of time during which the body was falling,
and that it was, in British feet, very nearly sixteen times the square
of that time in seconds. Kepler had proved that the movements of the heavenly
bodies were just such as would occur under the action of central attractive
forces and of centrifugal force.
Putting all these things together, Newton was led to believe that there
existed a " force of gravity," due to the attraction, by the
great mass of the earth, of its own particles and of neighboring bodies,
like the moon, of which force the influence extended as far, at least,
as the latter. He caleulated the motion of the earth's satellite, on the
assumption that his theory and the then accepted measurements of the earth's
dimensions were correct, and obtained a roughly approximate result. Later,
in l679, he revised his calculations, using Picard's more accurate detcrmination
of the dimensions of the earth, and obtained a result which preciscly tallied
with careful measurements, made by the astronomers of the moon's motion.
The science of mechanics had now, with the publication of Newton's "Principia," become thoroughly consistent and logically complete, so far as was possible without a known edge of the principles of energetic and Newton's enunciations of the laws of motion, concise and absolutely perfect as they still seem, were the basis of the whole seiene of dynamics, as applied to bodies moving freely under the action of applied forees, either constant or variable. They are as perfect a basis for that science as are the primary principles of geometry for the whole beautiful structure which is built up on them.
The three perfect qualitative expressions of dynamical law are:
1. Every free body continues in the state in which it may be, whether of
rest or of rectilinear uniform motion, until compelled to deviate from
that state by impressed forces.
2. Change of motion is proportional to the force impressed, and in the
direction of the right line in which that force acts.
3. Action is always opposed by reaction; action and reaction are equal,
and in directly contrary directions.
We may add to these principles a definition of a force, which is equally
and absolutely complete:
Force is that which produces, or tends to produce, motion, or change of
motion, in bodies. It is measured statically by the weight that will counterpoise
it, or by the pressure which it still produce, and dynamically by the velocity
which it will produce, acting in the unit of time on the unit of mass.
The quantitative determinations of dynamic effects of forces are always
readily made when it is remembered that the effect of a force equal to
its own weight, when the body is free to move, is to produce in one seeond
a velocity of 32.2 feet per second, which quantity is the unit of dynamic
measurement.
Work is the product of the resistance met in any instance of the exertion
of a force, into the distance through which that force overcomes the resistance.
Energy is the work which a body is capable of doing, by its weight or inertia,
under given conditions. The energy of a falling body, or of a flying shot,
is about .0125 its weight multiplied by the square of its velocity, or,
which is the same thing, the product of its weight into the height of fall
or height due its velocity. These principles and definitions, with the
longsettled definitions of the primary ideas of space and time, were all
that were needed to lead the way to that grandest of all physical generalizations,
the doctrine of the persistence or conservation of all energy, and to its
corollary declaring the equivalence of all forms of energy, and also to
the experimental demonstration of the transformability of energy from one
mode of existence to another, and its universal existence in the various
modes of motion of bodies and of their molecules.
Experimental physical science had hardly become acknowledged as the only
and the proper method of acquiring knowledge of natural phenomena at the
time of Newton; but it soon became a generally accepted principle. In physics,
Gilbert had made valuable investigations before Newton, and Galileo's experiments
at Pisa had been examples of similarly useful research. In chemistry, it
was only when, a century later, Lavoisier showed by his splendid example
what could be done by the skillful and intelligent use of quantitative
measurements, and mode the balance the chemist's most important tool, that
a science was formed comprehending all the facts and laws of chemical change
and molecular combination. We have already seen how astronomy and mathematics
together led philosophers to the creation and the study of what finally
became the science of mechanics, when experiment and observation were finally
brought to their aid. We can now see how, in all these physical sciences,
four primitive ideas are comprehended: matter, force, motion, and space
which latter two terms include all relations of position.
Based on these notions, the science of mechanics comprehends four sections,
which are of general application in the study of all physical phenomena.
These are:
Statics, which treats of the action and effect of forces.
Kinematics, which treats of relations of motion simply.
Dynamics, or kinetics, which treats of simple motion as an effect of the
action of forces.
Energetics, which treats of modifications of energy under the action of
forces, and of its transformation from one mode of manifestation to another,
and from one body to another.
Under the latter of these four divisions of mechanical philosophy is comprehended
that latest of the minor sciences, of which the heatengines, and especially
the steamengine, illustrate the most important applications Thermo-dynainics.
This science is simply a wider generalization of principles which, as we
have seen, have been established one at a time, and by philosophers widely
separated both geographically and historically, by both space and time,
and which have been slowly aggregated to form one after another of the
sciences, and out of which, as we now are beginning to see, we are slowly
evolving wider generalizations, and thus tending toward a condition of
scientific knowledge which renders more and more probable the truth of
Cicero's declaration: " One eternal and immutable law embraces all
things and all times." At the basis of the whole science of energetics
lies a principle which was enunciated before Science had a birthplace or
a name:
All that exists, whether matter or force, and in whatever form, is isdeslestructible,
except by the Infinite Power which has created it.
That matter is indestructible by finite power became admitted as soon as
the chemists, led by their great teacher Lavoisier, began to apply the
balance, and were thus able to show that in all chemical change there occurs
only a modification of form or of combination of elements, and no loss
of matter ever takes place. The "persistence" of energy was a
later discovery, consequent largely upon the experimental determination
of the convertibility of heat-energy into other forms and into mechanical
work, for which we are indebted to Rumford and Davy, and to the determination
of the quantivalence anticipated by Newton, shown and calculated approximately
by Cording and Mayer, and measured with great probable accuracy by Joule.
The great fact of the conservation of energy was loosely stated by Newton,
who asserted that the work of friction
Benjamin Thompson, Count Rumford.
and the vis viva of the system or body arrested by friction were equivalent.
In 1798, Benjamin Thompson, Count Rumford, an American who was then in
the Bavarian service, presented a paper1 to the Royal Society of great
Britain, in which he stated the results of an experiment which he had recently
made, proving the immateriality of heat and the transformation of mechanical
into heat energy.
l " Philosophical Transactions," 1798.
This paper is of very great historical interest, as the now accepted doctrine of the persistence of energy is a generalization which arose out of a series of investigations, the most important of which are those which resulted in the determination of the existence of a definite quantivalent relation between these two forms of energy and a measuremcnt of its value, now known as the "mechanical equivalent of heat." His experiment consisted in the determination of the quantity of heat produced by the boring of a cannon at the arsenal at Munich.
Rumford, after showing that this heat could not have been derived from
any of the surrounding objects, or by comression of the materials employed
or acted upon, says: " It appears to me extremely difficult, if not
impossible, to form any distinct idea of anything capable of being excited
and communicated in the manner that heat was excited and communicated in
these experiments, except it be motion."1 He then goes on to urge
a zealous and persistent investigation of the laws which govern this motion.
He estimates the heat produced by a power which he states could easily
be exerted by one horse, and makes it equal to the "combustion of
nine wax candles, each threequarters of an inch in diameter," and
equivalent to the elevation of "25.68 pounds of icecold water"
to the boilingpoint, or 4,784.4 heatunits.2 The time was stated at "150
minutes." Taking the actual power of Rumford's Bavarian "one
horse" as the most probable figure, 25,000 pounds raised one foot
high per minute,3 this gives the "mechanical equivalent" of the
footpound as 783.8 heatunits, differing but 1.5 percent from the now
accepted value.
l This idea was not by any means original with Rumford.
Bacon seems to have had the same idea; and Locke says, explicitly enough:
"Heat is a very brisk agitation of the insensible parts pf the object
.... so that what in our sensation is heat, in the object is nothing but
motion."
2 The British heatunit is the quantity of heat required to heat one pound
of water 1° Fahr. from the temperature of maximum density.
3 Rankine gives 25,920 footpounds per minuteor 432
per second for the average draughthorse in Great Britain, which is
probably too high for Bavaria. The engineer's "horse-power"-33,000
foot-pounds per minute-is far in excess of the average power of even a
good draught-horse, which latter is sometimes taken as two-thirds the former.
Had Rumford been able to eliminate all losses of heat by evaporation, radiation, and conduction, to which losses he refers, and to measure the power exerted with accuracy, the approximation would have been still closer. Rumford thus made the experimental discovery of the real nature of heat, proving it to be a form of energy, and, publishing the fact a halfcentury before the now standard determi nations were made, gave us a very close approximation to the value of the heatequivalent. Rumford also observed that the heat generated was "exactly proportional to the force with which the two surfaces are pressed together, and to the rapidity of the friction," which is a simple state ment of equivalence between the quantity of work done, or energy expended, and the quantity of heat produced. This was the first great step toward the formation of a Science of Thermodynamics. Rumford's work was the cornerstone of the science.
Sir Humphry Davy, a little later (1799), published the details of an experiment which conclusively confirmed these deductions from Rumford's work. He rubbed two pieces of ice together, and found that they were melted by the friction so produced. He thereupon concluded: "It is evident that ice by friction is converted into water.... Friction, consequently, does not diminish the capacity of bodies for heat."
Bacon and Newton, and Hooke and Boyle, seem to have anticipatedlong
before Rumford's timeall later philosophers, in admitting the probable
correctness of that modern dynamical, or vibratory, theory of heat which
considers it a mode of motion; but Davy, in 1812, for the first time, stated
plainly and precisely the real nature of heat, saying: " The immediate
cause of the phenomenon of heat, then, is motion, and the laws of its communication
are precisely the same as the laws of the communication of motion."
The basis of this opinion was the same that had previously been noted by
Rumford.
So much having been determined, it became at once evident that the determination
of the exact value of the mechanical equivalent of heat was simply a matter
of experiment; and during the succeeding generation this determination
was made, with greater or less exactness, by several distinguished men.
It was also equally evident that the laws governing the new science of
thermodynamics could be mathematically expressed.
Fourier had, before the date last given, applied mathematinal analysis in the solution of problems relating to the transfer of heat without transformation, and his "Theoriedo la Chaleur" contained an exceedingly beautiful treatment of the subject. Sadi Carnot, twelve years later (1824), published his " Reflexions sur la Puissance Motrice du Feu," in which he made a first attempt to express the principles involved in the application of heat to the production of mechanical effect. Starting with the axiom that a body which, having passed through a series of conditions modifying its temperature, is returned to " its primitive physical state as to density, temperature, and molecular constitution," must contain the same quantity of heat which it had contained originally, he shows that the efficiency of heat engines is to be determined by carrying the working fluid through a complete cycle, beginning and ending with the same set of conditions. Carnot was not a believer in the vibratory theory of heat, and consequently was led into some errors; but, as will be seen hereafter the idea just expressed is one of the most important details of a theory of the steam-engine.
Seguin, who has already been mentioned as one of the first to use the firetubular
boiler for locomotive engines, published in 1839 a work, " Sur l'Influence
des Chemins de Fer," in which he gave the requisite data for a rough
determination of the value of the mechanical equivalent of heat, although
he does not himself deduce that value.
Dr. Mayer, of Heilbronn, three years later (1842), pub lished the results
of a very ingenious and quite closely approximate calculation of the heatequivalent,
basing his estimate upon the work necessary to compress air, and on the
specific heats of the gas, the idea being that the work of compression
is the equivalent of the heat generated. Seguin had taken the converse
operation, taking the loss of heat of expanding steam as the equivalent
of the work done by the steam while expanding. The latter also was the
first to point out the fact, afterward experimentally proved by Hirn, that
the fluid exhausted from an engine should heat the water of condensation
less than would the same fiuid when originally taken into the engine.
A Danish engineer, holding, at about the same time (1843), published the results of experiments made to determine the same quantity; but the best sold most extended work, and that which is now .allnost universally accepted as standard, was done by a British investigator.
Joule, the physicist referred to, commenced the experimental investigations which have made him famous at some time previous to 1843, at which date he published, in the Philosophical Magazine, his earliest method. His first determination gave 770 footpounds. During the succeeding five or six years Joule repeated his work, adopting a considerable variety of methods, and obtaining very variable results. One method was to determine the heat produced by forcing air through tubes; another, and his usual plan, was to turn a paddlewheel by a definite power in a known weight of water. He finally, in 1819, concluded these rescarches.
The method of calculating the mechanical equivalent of heat which was adopted
by Dr. Mayer, of Heilbronn, is as beautiful as it is ingenious: Conceive
two equal portions of atmospheric air to be inclosed, at the same temperatureas
at the freezingpointin vessels eaeh capable of containing one cubic
foot; communicate heat to both, retaining the
PICT. P. 439
Joules Prescott Joule.
one portion at the original volume, and permitting the other to expand under a constant pressure equal to that of the atmosphere. In each vessel there will be inclosed 0.08073 pound, or 1.29 ounce, of air. When, at the same temperature, the one has doubled its pressure and the other has doubled its volume, each will be at a temperature of 525.2° Fahr., or 274° C., and each will have double the original temperature, as measured on the absolute scale from the zero of heatmotion. But the one will have absorbed but 6.75 British thermal units, while the other will have absorbed 9.5. In the first case, all of this heat will have been em ployed in simply increasing the temperature of the air; in the second case, the temperature of the air will have been equally increased, and, besides, a certain amount of work2,l16.3 footpoundsmust have been done in overcoming the resistance of the air; it is to this latter action that we must debit the additional heat which has disappeared. Now, 2,116.3/2.75 = 770 footpounds per heatunitalmost precisely the value derived from Joule's experiments. Had Mayer's measurement been absolutely accurate, the result of his calculation would have been an exact determination of the heatequivalent, provided no heat is, in this case, lost by internal work.
Joule's most probably accurate measure was obtained by the use of a paddlewheel
revolving in water or other fluid. A copper vessel contained a carefully
weighed portion of the fluid, and at the bottom was a step, on which stood
a vertical spindle carrying the paddlewheel. This wheel was turned by
cords passing over nieelybalanced grooved wheels, the axles of which were
carried on friction rollers. Weights hung at the ends of these cords were
the moving forces. Falling to the ground, they exerted an easily and accurately
determinable amount of work, W x H, which turned the paddlewheel a definite
number of revolutions, warming the water by the production of an amount
of heat exactly equivalent to the amount of work done. After the weight
had been raised and this operation repeated a sufficient number of times,
the quantity of heat communicated to the water was carefully determined
and compared with the amount of work expended in its development. Joule
also used a pair of disks of iron rubbing against each other in a vessel
of mercury, and measured the heat thus developed by friction, comparing
it with the work done. The average of forty experiments with water gave
the equivalent 772.692 footpounds; fifty with mercury gave 774.083; twenty
with castiron gave 774.987 the temperature of the apparatus being
from 55° to 60° Fahr.
Joule also determined, by experiment, the fact that the expansion of air
or other gas without doing work produces no change of temperature, which
fact is predicable from the now known principles of thermodynamics. He
stated the results of his researches relating to the mechanical equivalent
of heat as follows:
1. The heat produced by the friction of bodies, whether solid or liquid,
is always proportional to the quantity of work expended.
2. The quantity required to increase the temperature of a pound of water
(weighed in vacuo at 55° to 60° Fahr.) by one degree requires for
its production the expenditure of a force measured by the fall of 772 pounds
from a height of
one foot. This quantity is now generally called " Joule's equivalent."
During this series of experiments, Joule also deduced the position of the "absolute zero," the point at which heatmotion ceases, and stated it to be about 480° Fahr. below the freezingpoint of water, which is not very far from the probably true value,493.2° Fahr. (273° C.), as deduced afterward from more precise data.
The result of these, and of the later experiments of Hirn and others, has
been the admission of the following principle: Heatenergy and mechanical
energy are mutually con vertible and have a definite equivalence, the British
thermal unit being equivalent to 772 footpounds of work, and the metric
calorie, or, as usually taken, 424 kilogrammetres. The exact measure is
not fully determined, however.
It has now become generally admitted that all forms of energy due to physical
forces are mutually convertible with a definite quantivalence; and it is
not yet determined that even vital and mental energy do not fall wiihin
the same great generalization. This quantivalence is the sole basis of
the science of energetic
The study of this science has been, up to the present time, principally
confined to that portion which comprehends the relations of heat and mechanical
energy. In the study of this department of the science, thermodynamics,
Rankine, Clausius, Thompson, Hirn, and others have acquired great distinction.
In the investigations which been made by these authorities, the methods
of transfer of heat and of modification of physical state in gases and
vapors, when a change occurs in the form of the energy considered, have
been the subjects of especial study.
According to the law of Boyle and Marriotte, the expansion of such fluids
follows a law expressed graphically by the hyperbola, and algebraically
by the expression PVx = A, in which, with unchanging ternperature, x is
equal to l. One of the first and most evident deductions from the principles
of the equivalence of the several forms of energy is that the value of
x must increase as the energy expended in expansion increases. This change
is very masked with a vapor like steam which, expanded without doing
work, has an exponent less than unity and which, when doing work by expanding
behind a piston, partially condenses, the value of x increases to, in the
case of steam, l.111 according to Rankine, or, probably more correctly,
to 1.135 or more, according to Zeuner and Grashof. This fact has an important
bearing upon the theory of the steamengine, and we are indebted to Rankine
for the first complete treatise on that theory as thus modified.
Prof. Rankine began his investigations as early as 1819, at which time
he proposed his theory of the molecular constitution of matter, now well
known as the theory of molecular vortices. He supposes a system of whirling
rings or vortices of heatmotion, and bases his philosophy upon that hypothesis,
supposing sensible heat to be employed in changing the velocity of the
particles, latent heat to be the work of altering the dimensions of the
orbits, and considering the effort of each vortex to enlarge its boundaries
to be due to
PICT. P. 443
Prof. W. J. M. Rankine.
not of the nature of the working substancean assertion which is quite true where the material does not change its physieal state while working. Rankine now deduced that "general equation of thermodynamics" which expresses algebraically the relations between heat and mechanical energy, when energy is changing from the one state to the other, in which equation is given, for any assumed change of the fluids, the quantity of heat transformed. He showed that steam in the engine must be partially liquefied by the process of expanding against a resistance, and proved that the total heat of a perfect gas must increase with rise of temperature at a rate proportional to its specific heat under constant pressure.
Rankine, in 1850, showed the inaccuracy of the then accepted vahle, 0.2669
of the specific heat of air under constant pressure, and calculated its
value as 0.24. Three years later, the experiments of Regnault gave the
value 0.2379, and Rankine, recalculating it, made it 0.22377. In 1851,
Rankine continued his discussion of the subject, and, by his own theory,
corroborated Thompson's law giving the efficiency of a perfect heatengine
as the quotient of the range of working temperature to the temperature
of the upper limit, measured from the absolute zero.
During this period, Clausius, the German physicist, was working on the
same subject, taking quite a different method, studying the mechanical
effects of heat in gases, and deducing, almost simultaneously with Rankine
(1850), the general equation which lies at the beginning of the theory
of the equivalence of heat and mechanical energy. He found that the probable
zero of heatmotion is at such a point that the Carnot function must be
approximately the reciprocal of the "absolute" temperature, as
measured with the air thermometer, or, stated exactly, that quantity as
determined by a perfect gas thermometer. He confirmed Rankine's conclusion
relative to the liquefaction of saturated vapors when expanding against
resistance, and, in 1854, adapted Carnot's principle to the new theory,
and showed that his idea of the reversible engine and of the performance
of a cycle in testing the changes produced still held good, notwithstanding
Carnot's ignorance of the true nature of heat. Clausius also gave us the
extremely important principle: It is impossible for a selfacting machine,
unaided, to transfer heat from one body at a low temperature to an
other having a higher temperature.
Simultaneously with Rankine and Clausius, Prof. William Thomson was
engaged in researches in thermodynamics (1850). He was the first to express
the principle of Carnot as adapted to the modern theory by Clausius in
the now generally quoted propositions:(1)
1. When equal mechanical effects are produced by purely thermal action,
equal quantities of heat are produced or disappear by transformation of
energy.
2. If, in any engine, a reversal effects complete inversion of all the physical and mechanical details of its operation, it is a perfect engine, and produces maximum effect with any given quantity of heat and with any fixed limits of range of temperature.
William Thomson and James Thompson showed, among the earliest of their
deductions from these principles, the fact, afterward confirmed by experiment,
that the meltingpoint of ice should be lowered by pressure 0.0135°
Fahr. for each atmosphere, and that a body which contracts while being
heated will always have its temperature decreased by sudden compression.
Thomson applied the principles of ener getics in extended investigations
in the department of electricity, while Helmholtz carried some of the same
methods into his favorite study of acoustics.
The application of now wellsettled principles to the physics of gases
led to many interesting and important deductions:
l Vide Tait's admirable "Sketch of Thermodynamics," second edition, Edinburgh, 1877.
Clausius explained the relations between the volume, density, temperature, and pressure of gases, and their modifications; Maxwell reestablished the experimentally determined law of Dalton and Charles, known also as that of GayLussac (1801), which asserts that all masses of equal pressure, volume, and temperature, contain equal numbers of molecules. On the Continent of Europe, also, Hirn, Zelmer, Grashof, Tresea, Laboulaye, and others have, during the same period and since, continued and greatly extended these theoretical researches.
During all this time, a vast amount of experimental work has also been
done, resulting in the determination of important data without which all
the preceding labor would have been fruitless. Of those who have engaged
in such work, Cagniard de la Tour, Andrews, Regnault, Hirn, Fairlrairn
and Tate, Laboulaye, Tresea, and a few others have directed their researches
in this most important direction with the special object of aiding in the
advancement of the newborn sciences. By the middle of the present eentury,
the time which we are now studying, this set of data was tolerably complete.
Boyle had, two hundred years before, discovered and published the law,
which is now known by his name1 and by that of Marriotte,2 that the pressure
of a gas varies inversely as its volume and directly as its density; Dr.
Black and James Watt discovered, a hundred years later (1760), the latent
heat of vapors, and Watt determined the method of expansion of steam; Dalton,
in England, and GayLussac, in France, showed, at the beginning of the
nineteenth eentury, that all gaseous fluids are expanded by equal fractions
of their volume by equal increments of temperature; Watt and Robison had
given tables of the elastic force of steam, and Gren had shown that, at
the temperature
l "New Experiments, Physico-Mechanical, etc., touching
the Spring of Air," 1662.
2 "De la Nature de l'Air" 1676.
of boiling water, the pressure of steam was equal to that of the atmosphere;
Dalton, Ure, and others proved (18001818) that the law connecting temperatures
and pressures of steam was expressed by a geometrical ratio; and
Biot had already given an approximate formula, when Southern introduced another, which is still in use.
The French Government established a commission in 1823 to experiment with
a view to the institution of legislation regulating the working of steamengines
and boilers; and this commission, M M. de Prony, Arago, Girard, and Dulong,
determined quite accurately the temperatures of steam under pressures running
up to twentyfour atmospheres, giving a formula for the calculation of
the one quantity, the other being known. Ten years later, the Government
of the United States instituted similar experiments under the direction
of the Franklin Institute.
The marked distinction between gases like oxygen and hydrogen and condensible vapors, like steam and carbonic acid, hall been, at this time, shown by Cagniard de la Tour, who, in 1822, studied their behavior at high temperatures and under very great pressures. He found that, when a vapor was confined in a glass tube in presence of the same substance in the liquid state, as where steam and water were confined together, if the temperature was increased to a certain definite point, the whole mass suddenly became of uniform character, and the previously existing line of de markation vanished, the whole mass of fluid becoming, as he inferred, gaseous. It was at about this time that Fara day made known his then novel experiments, in which gases which hall been before supposed permanent were liquefied, simply by subjecting them to enormous pressures. He then also first stated that, above certain temperatures, liquefaction of of vapors was impossible, however great the pressure.
Farraday's conclusion was justified by the researches of Dr. Andrews, who has since most successfully extended the investigation commenced by Cagniard
de la Tour, and who has shown that, at a certain point, which he calls
the "critical point," the properties of the two states of the
fluid fade into each other, and that, at that point, the two become continuous.
With carbonic acid, this occurs at 75 atmospheres, about 1,125 pounds per
square inch, a pressure which would counterbalance a column of mercury
60 yards, or nearly as many metres, high. The temperature at this point
is about 90° Fahr., or 31° Cent. For ether, the temperature is
370° Fahr., and the pressure 38 atmospheres; for alcohol, they are
498° Fahr., and 120 atmospheres; and for disulphide of carbon, 505°
Fahr., and 67 atmospheres. For water, the pressure is too high to be determined;
but the temperature is about 775° Fahr., or 413° Cent.
Donny and Dufour have shown that these normal properties of vapors and
liquids are subject to modification by certain conditions, as previously
(1818) noted by Gay-Lussac, and have pointed out the bearing of this fact
upon the safety of steamboilers. It was discovered that the boiling-point
of water could be elevated far above its ordinary temperature of ebullition
by expedients which deprive the liquid of the air usually condensed within
its mass, and which prevent contact with rough or metallic surfaces. By
suspension in a mixture of oils which is of nearly the same density, Dufour
raised drops of water under atmospheric pressure to a temperature of 356°
Fahr.180° Cent. the temperature of steam of about 150 pounds
per square inch. Prof. James Thompson has, on theoretical grounds, indicated
that a somewhat similar action may enable vapor, under some conditions,
to be cooled below the normal temperature of condensation, without liquefaction.
Fairbairn and Tate repeated the attempt to determine the volume and temperature
of water at pressures extending beyond those in use in the steam engine,
and incomplete determinations have also been made by others.
Regnault is the standard authority on these data. His experiments (1847)
were made at the expense of the French Government, and under the direction
of the French Acad emy. They were wonderf ully accurate, and extended
through a very wide range of temperatures and pressures. The results remain
standard after the lapse of a quarter of a century, and are regarded as
models of precise physical work.(1)
Regnault found that the total heat of steam is not constant, but that the latent heat varies, and that the sum of the latent and sensible heats, or the total heat, increases 0.305 of a degree for each degree of increase in the sensible heat, making 0.305 the specific heat of saturated steam. He found the specific heat of superheated steam to be 0.4805.
Regnault promptly detected the fact that steam was not subject to Boyle's
law, and showed that the difference is very marked. In expressing his results, he not only tabulated them but also laid them down graphically; he further
determined exact constants for Biot's algebraic expression.
1 See Porter on the SteamEngine Indicator for the best set of Regnault's tables generally accessible.
Since Regnault's time, nothing of importance has been done in this direction.
There still remains much work to be done in the extension of the research
to higher pressures, and under conditions which obtain in the operation
of the steamengine. The volumes and densities of steam require further
study, and the behavior of steam in the engine is still but little known,
otherwise than theoretically. Even the true value of Joule's equivalent
is not undisputed.
Some of the most recent experimental work bearing directly upon the philosophy
of the steamengine is that of Hirn, whose determination of the value of
the mechanical equivalent was less than two per cent. below that of Joule.
Hirn tested by experiment, in 1853, and repeatedly up to 1876, the analytical work of Rankine, which led to the conclusion that steam doing work by expansion
must become gradually liquefied. Constructing a glass steam engine cylinder,
he was enabled to see plainly the clouds of mist which were produced by
the expansion of steam behind the pistols where Regnault's experiments
prove that the steam should become drier and superheated, were no heat
transformed into mechanical energy. As will be seen hereafter, this great
discovery of Rankine is more important in its bearing upon the theory of
the steamengine than any made during the century. Hirn's confirmation
stands, in value, beside the original discovery. In 1858 Hirn confirmed
the work of Mayer and Joule by determining the work done and the carbonic
acid produced, as well as the increased temperature due to their presence,
where men were set at walk in a treadmill; he found the elevation of temperature
to be much greater in proportion to gas produced when the men were resting
than when they were at work. He thus proved conclusively the conversion
of heatenergy into mechanical work. It was from these experiments that
Helmholtz deduced the "modulus of efficiency" of the human machine
at onefifth, and concluded that the heart works with eight times the efficiency
of a locomotive engine, thus confirming a statement of Rumford, who asserted
the higher efficicency of the animal.
Hirn's most important experiments in this department were made upon
steamengines of considerable size, includ ing simple and compound engines,
and using steam sometimes saturated and sometimes superheated to temperatures
as high, on some occasions, as 340° Cent. He determined the work done,
the quantity of heat entering, and the amount rejected from, the steamcylinder,
and thus obtained a coarse approximation to the value of the heatequivalent.
His figure varied from 296 to 337 kilogrammetres. But, in all cases, the
loss of heat due to work done was marked, and, while these researches could
not, in the nature of the case, give acurate quantitative results, they
are of great value as qualitatively confirming Mayer and Joule, and proving
the transformation of energy.
Thus, as we have seen, experimental investigation and analytical research
have together created a new science, and the philosophy of the steamengine
has at last been given a complete and welldefined form, enabling the intelligent
engineer to comprehend the operation of the machine, to perceive the conditions
of effieicncy, and to look forward in a wellsettled direction for further
advances in its improvement and in the increase of its efficiency.
A very concise resume of the principal facts and laws bearing upon the philosophy of the steamengine will form a fitting conclusion to this historical sketch.
The term "energy" was first used by Dr. Young as the equivalent
of the work of a moving body, in his hardly yet obsolete " Lectures
on Natural Philosophy.''
Energy is the capacity of a moving body to overcome resistance offered
to its motion; it is measured either by the product of the mean resistance
into the space through which it is overcome, or by the halfproduct of
the mass of the body into the square of its velocity. Kinetic energy is
the actual energy of a moving body; potential energy is the measure of
the work which a body is capable of doing under certain conditions which,
without expending energy, may be made to affect it, as by the breaking
of a cord by which a weight is suspended, or by firing a mass of explosive
material. The British measure of energy is the footpound; the metric measure
is the kilogrammetre.
Energy, whether kinetic or potential, may be observable and due to massmotion;
or it may be invisible and due to molecular movements. The energy of a
heavenly body or of a cannonshot, and that of heat or of electrical action,
are illustrations of the two classes. In Nature we find utilizable potential
energy in fuel, in food, in any available head of water, and in available
chemical affinities.. We find kinetic energy in the motion of the winds
and the flow of running water, in the heatmotion of the sun's rays, in
heatcurrents on the earth, and in many intermittent movements of bodies
acted on by applied forces, natural or artificial. The potential energy
of fuel and of food has already been seen to have been derived, at an earlier
period, from the kinetic energy of the sun's rays, the fuel or the food
being thus made a storehouse or reservoir of energy. It is also seen that
the animal system is simply a mechanism of transmission " for energy,
and does not create but simply diverts it to any desired direction of application.
All the available forms of energy can be readily traced back to a common
origin in the potential energy of a universe of nebulous substance (chaos),
consisting of infinitely diffused matter of immeasurably slight density,
whose "energy of position" had been, since the creation, gradually
going through a process of transformation into the several forms of kinetic
and potential energy above specified, through intermediate methods of action
which are usually still in operation, such as the potential energy of chemical
affinity, and the kinetic forms of energy seen in solar radiation, the
rotation of the earth, and the heat of its interior.
The measure of any given quantity of energy, whatever may be its form,
is the product of the resistance which it is capable of overcoming into
the space through which it can move against that resistance, i. e., by
the product RS. Or it is measured by the equivalent expressions .5MV2,
in
which W is the weight, M is the " mass " of matter in motion,
V the velocity, and g the dynamic measure of the force of gravity, 32.2
feet, or 9.8 metres, per second.
There are three great laws of energetics:
1. The sum total of the energy of the universe is in variable.
2. The several forms of energy are interconvertible, and possess an exact
quantitative equivalence.
3. The tendency of all forms of kinetic energy is continually toward reduction
to forms of molecular motion, and to their final dissipation uniformly
throughout space.
The history of the first two of these laws has already been traced. The
latter was first enunciated by Prof. Sir William Thomson in 1853. Undissipated
energy is called " Entropy."
The science of thermo-dynamics is, as has been stated, a branch of the
seienee of energeties, and is the only branch of that science in the domain
of the physicist which has been very much studied. This branch of science,
which is restricted to the consideration of the relations of heatenergy
to mechanical energy, is based upon the great fact determined by Rumford
and Joule, and considers the behavior of those fluids which are used in
heatengines as the media through which energy is transferred from the
one form to the other. As now accepted, it assumes the correctness of
the hypothesis of the dynamic theory of fluids, which supposes their expansive
force to be due to the motion of their molecules.
This idea is as old as Lucretius, and was distinctly expressed by Bernouilli,
Le Sage and Prevost, and Herapath. Joule recalled attention to this idea,
in 1848, as explaining the pressure of gases by the impact of their molecules
upon the sides of the containing vessels. Helmholtz, ten years later, beautifully
developed the mathematics of media composed of moving, frictionless particles,
and Clausius has carried on the work still further.
The general conception of a gas, as held today, including the vortexatom
theory of Thomson and Rankine, supposes all bodies to consist of small
particles called molecules, each of which is a chemical aggregation of
its ultimate parts or atoms. These molecules are in a state of continual
agitation, which is known as heatmotion. The higher the temperature, the
more violent this agitation; the total quantity of motion is measured as
vis viva by the half-product of the mass into the square of the velocity
of molecular movement, or in heatunits by the same product divided by
Joule's equivalent. In solids, thc range of motion is circumscribed, and
change of form cannot take place. In fluids, the motion of the molecules
has become sufficiently violent to enable them to break out of this range,
and their motion is then no longer definitcly restricted.
The laws of thermodynamics are:
1. Heatenergy and mechanical energy are mutually convertible, one British
thermal unit being the equivalent in heatcncrgy of 772 footpounds of
mechanical energy, and one metric calorie equal to 423.55 kilogrammetres
of work.
2. The energy due to the heat of each of the several equal parts into which
a uniformly hot substance may be divided is the same; and the total heatenergy
of the mass is equal to the sum of the energies of its parts.(1)
It follows that the work performed by the transformation of the energy
of heat, during any indefinitely small
l This uniformity is not seen where a substance is changing
its physical state while developing its heat-energy, as occurs with steam
doing work while expanding.
variation of the state of a substance as respects temperature, is measured
by the product of the absolute temperature into the variation of a "
function,'' which function is the rate of variation of the work so done
with temperature. This function is the quantity called by Rankine the "
heat-potential " of the substance for the given kind of work. A similar
function, which comprehends the total heat-variation, including both heat
transformed and heat needed to effect accompanying physical changes, is
ealled the " thermodynamic function." Rankine's expression for
the general equation of thermodynamics includes the latter, and is given
by him as follows:
J d h = d H = k d + d F = d
in which J is Joule's equivalent, dh the variation of total heat in the substance, kd the product of the "dynamic specific heat" into the variation of temperature, or the total heat demanded to produce other changes than a transformation of energy, and dF is the work done by the transformation of heatenergy, or the product of the absolute temperature, T. into the differential of the heatpotential. ¢> is the thermodynamie function, and Sb measures the whole heat needed to produce, simultaneously, a eertain amount of work or of meehanieal energy, and, at the same time, to change the temperature of the working substance.
Studying the behavior of gases and vapors, it is found that the work done
when they arc used, like steam, in heat-engines, consists of three parts:
(a.) The change effected in the total actual heatmotion of the fluid.
(b.) That heat which is expended in the production of internal work.
(c.) That heat which is expended in woek, the external work of expansion.
In any case in which the total heat expended exceeds that due the production
of work on external bodies, the ex cess so supplied is so much added to
the intrinsic energy of the substance absorbing it. The application of
these laws to the working of steam in the engine is a comparatively recent
step in the philosophy of the steamengine, and we are indebted to Ranking
for the first, and as yet only, extended and in any respect complete treatise
embodying these now accepted principles.
It was fifteen years after the publication of the first logical theory
of the steamengine, by Pambour,1 before Rankine, in 1859, issued the most
valuable of all his works, " The SteamEngine and other Crime Movers."
The work is far too abstruse for the general reader, and is even difficult
reading for many accomplished engineers. It is excellent beyond praise,
however, as a treatise on the thermodynamics of heatengines. It will be
for his successors the work of years to extend the application of the laws
which he has worked out, and to place the results of his labors before
students in a readily comprehended form.
William J. Macquorn Rankine, the Scotch engineer and philosopher, will
always be remembered as the author of the modern philosophy of the steamengine,
and as the greatest among the founders of the science of thermodynamics.
His death, while still occupying the chair of engineering at the University
of Glasgow, December 24, 1872, at the early age of fiftytwo, was one of
the greatest losses to science and to the profession which have occurred
during the century.
l " Theorie de la Machine a Vapeur," par le Chevalier F. M. G. de Pambour, Paris, 1844.