History of the Conservation of Energy: Booms, Blood, and Beer (Part 3)

The final long-awaited conclusion of a trilogy of posts describing the history of the discovery of conservation of energy, inspired by my research on “Falling Felines and Fundamental Physics.” Part 1 can be read here, and part 2 can be read here.

NOTE: Be prepared this is a long post! James Joule did a lot.

In 1798, Count Rumford had noted that there was a problem with the accepted caloric theory of heat. In 1842, Julius Robert Mayer presented a theory of conserved “forces,” basically laying out for the first time a theory of what we now call conservation of energy, in which energy is neither created nor destroyed, but only changes form. Mayer furthermore gave a quantitative estimate of the mechanical equivalent of heat, viewing heat as a form of motion (as we now know today to be true).

James Joule, circa 1863. Taken from the Memoir of James Prescott Joule (1892).

But neither Rumford nor Mayer pursued their investigations with enough rigor to convince the scientific community to embrace such a radical new vision of physics. Such work would instead be done by a third unlikely researcher: James Prescott Joule (1818-1889), the son of a wealthy brewer and a remarkably young man when he made his key breakthroughs in the 1840s.  Starting from simple investigations into the efficiency of engines, Joule would eventually, almost ruthlessly, demonstrate the energy equivalence of a variety of different types of natural phenomena — mechanical work, heat, electricity, and chemical reactions.  His studies would transform our understanding of the universe and connect different aspects of it in ways previously almost undreamed of.

 

James Joule was the second-eldest of five children of Benjamin Joule, who ran the Salford Brewery established by his own father, William Joule.  James Joule was a rather frail child, with spinal issues, but was very inquisitive and encouraged in his curiosity by his elder brother Benjamin St. J.B. Joule. Brother Benjamin kept a diary of his early years¹, from which one finds many interesting indications of James’ burgeoning interest in science and technology.  From the earliest entry mentioning James, on September 15, 1830, we have:

into a field near Eccles to see the first trains which travelled between Liverpool and Manchester, and to their riding on several Saturday afternoons to a place between Eccles and Patricroft to watch the two trains (one on each set of rails) passing and repassing for the amusement of passengers to Newton-in-the- Willows and back.

Lithograph of the railway opening, by A.B. Clayton. Via Wikipedia.

They had, in fact, attended the opening of the very first entirely locomotive-powered public transportation system, often referred to as the Grand British Experimental Railway; its success or failure would determine the future of all other such projects.  Obviously, it was a success, and James’ early encounter with it likely guided his future studies in a way that would lead to his revolutionary research.

One other example from Benjamin’s diary illustrates James’ curiosity and enthusiasm, from much later in 1842:

May 24, Lake Windermere.—After breakfast our party were rowed by James and myself to one of the islands. I then rowed James a short distance away to let them hear a very good echo which we had discovered. I was not observing what James was doing, though I thought he was unusually long in loading the pistol (a large old-fashioned cavalry weapon, used by my father when he belonged to the Manchester Mounted Volunteers), when I was suddenly startled by a tremendous report, and on looking round found that the pistol had disappeared. The ” knock ” had been so violent that the weapon had been wrested out of James’ hand and had fallen into the lake. He told me that he wished to produce the loudest report possible, and had used three charges of powder.

John Dalton in 1834, via Wikipedia.

By that time, Benjamin and James had both received extensive private tutoring, often from very distinguished scientists.  In 1834, for example, after having a series of at-home teachers, they began studies under the famed chemist John Dalton, a Fellow of the Royal Society of London.  This training was evidently in preparation for the two of them to take over the operations of the brewery, where some knowledge of chemistry was essential. Unfortunately, Dalton’s health took a severe turn for the worse in 1837, before the brothers had hardly begun to learn chemistry, cutting short their tutelage — though they remained friends with Dalton for the rest of his life.  But even in that short time, James was able to learn a lot about experimental studies and become proficient with some of the tools that were used at the time.  By 1838, Joule had set up a laboratory in his father’s house at Broom Hill to perform his own experiments in electricity, while his brother handled affairs for their father’s business.

William Sturgeon, via Wikipedia.

In 1839, the brothers acquired another teacher, the chemistry lecturer John Davies. Under his direction, James became further intrigued with the phenomena of electricity and “galvanism,” the electrical stimulation of biological tissue. By this time, the Joule family was apparently on very close terms with many members of the Royal Society, even having them over for dinner. One significant guest was William Sturgeon, a physicist and inventor who in 1832 had developed the first electric motor capable of turning machinery.  In 1841, the brothers went on an outing to see Sturgeon fly an electric kite, similar to that experiment first done by Benjamin Franklin almost a century earlier.

It was Sturgeon’s motor that truly started Joule down the path to fundamental discoveries. Joule had been entranced by the possibilities of the electric motor, and set himself the goal of improving it to the point that it would be far superior than the steam-driven engines that had captivated him in his childhood. As he later wrote², “I can hardly doubt that electro-magnetism will ultimately be substituted for steam to propel machinery.”  Joule was, perhaps, even more ahead of his time than anyone realized, because essentially the same strategy is currently being implemented in automobiles, with electric motors replacing internal combustion engines.

To understand how Joule’s research proceeded from this point, it is worthwhile to jump ahead and discuss a bit of the physics of engines, as we now understand it. One measure of an engine is the amount of force it can produce at a given moment. If you’re trying to lift up a heavy object, for example, the force of lifting has to be greater than the weight of the object (the force of gravity on it). But an equally important measure of an engine is the power: how fast can you lift the heavy object? This is force times speed or, equivalently, energy per unit time.  In the case of an electric motor, the power provided by the motor will have an upper limit equal to the amount of power the battery can provide.  One takeaway: for a given battery, force and speed are inversely related: make an engine that provides a lot of force, it will move slowly, make an engine that moves quickly, it won’t provide much force.  Both quantities are important in practice: a locomotive that can pull 100 cars but only move 2 miles an hour or a locomotive that can move 100 miles an hour but only pull two cars are equally limiting.

Joule dove into the problem of electric motors in earnest. Already by 1838 he had published his first paper³ on the improvement of the electric motor in Sturgeon’s journal Annals of Electricity, where most of his early work would go. He was only 19 years old at the time.

Joule’s first improved engine.

Joule’s sketch of his engine is shown to the left, which provides an nice image of the general working principles of all such motors. The workhorse, so to speak, of the motor is two arrays of electromagnets: U-shaped iron bars wrapped in wire. One array is visible in this picture as the ring of dark ovals, fixed to the board abc, while the second array is free to rotate and out of sight on the back of the device.  When a current is applied at inputs hi, the two sets of magnets are magnetically drawn into alignment, with north and south poles opposite. This would be a very small rotation, indeed, except that a device known as a commutator, g, switches the direction of current as it rotates. The magnets cannot ever perfectly match up north and south poles, and it ends up rotating endlessly in one direction trying to do so.

In Joule’s first paper, he focused entirely on improving the force produced by an electric motor. Considerations of speed, or power, and the properties of the battery were evidently not on his mind.  In his second paper of December 1, 1838, he explicitly notes that the power of his new engine was not what he had hoped,

It weighs 7 1/2 lb. ; and the greatest power I have been able to develop with a battery of forty-eight Wollaston four-inch plates was to raise 15 lb. 21. foot high per minute, in which estimate the friction of the working parts, which was very considerable, was reckoned as the load.

The result shows that the advantages of a close arrangement of electro-magnets are not such as I anticipated.

Joule then made an effort to speed up his motor, but met with little success. A third paper, in March of 1839, involved different designs of the magnets, but made no significant improvements. But he had been comparing the power of his different engines by connecting them to the same battery, and somewhere along the way he realized that it might be the limiting factor in his researches.  In his fourth letter, of May, 1839, he described the construction of a galvanometer — a device to measure electric current — and used it discover a precise mathematical relationship between the currents used in his motor and the force of attraction between his electromagnets.

The attractive force of two electro-magnets for one another is directly proportional to the square of the electric force to which the iron is exposed ,- or, if E denote the electric current, W the length of wire, and M the magnetic attraction, M=E²W².

This was really Joule’s first foray into physics proper: the development of a general law from which he could predict some behaviors of his motors without even building them.

We noted in previous posts that both Rumford and Mayer attempted to build perpetual motion machines at some point early in their careers; we can, in fact, add Joule to this list. At the end of his fourth paper, emboldened by his new law, he states,

If the power of the engine is in proportion to the attractive force of its magnets, and if this attraction is as the square of the electric force, the economy will be in the direct ratio of the quantity of electricity, and the cost of working the engine may be reduced ad infinitum. It is, however, yet to be determined how far the effects of magnetic electricity may disappoint these expectations.

That reduction “ad infinium” is the hope of effectively getting power for nothing, the dream of perpetual motion. It is striking that all of the major researchers involved in energy conservation dreamed of the possibility at one point or another, perhaps being driven to their inevitable discoveries by their failure.

Joule would publish a lot of papers on the subject, going forward. One common factor of these papers, however, is the discovery of new limitations on the power output of an electric motor. Among them, he calculates the amount of work (energy) created per pound of zinc consumed in his battery, thus somewhat unknowingly providing a quantitative measure of the chemical energy of the zinc.  He also discovered that the resistance of his motor to an electrical current increases as the motor speeds up, which he recognizes as a consequence of Faraday’s law: time-varying magnetic fields produce an electrical resistance. At the same time, he further improved the design of his electric motors and also came up with more precise measurements of all quantities associated with them, including a determination of the amount of electricity produced in the consumption of zinc.

A Joule motor of 1840.

Here he ran into a problem that is hard to imagine in modern times: there were no standard units for electricity! Today the standard unit of charge is called the Coulomb, and the standard unit of current is the Ampere, but in Joule’s time electrical measurements were much more qualitative. So Joule came up with his own definition of a fundamental unit of electricity, which he then used in all his later experiments (and he would go on to help define the standard electrical units which we know today, but that is another blog post).

By April of 1841, Joule had pushed his studies of the efficiency of the electric motor as far as he could and, it is fair to say, his studies had ended in failure. Instead of improving the motor’s abilities without limit by increasingly careful design, he found that there were fundamental limits to its operation, which he did not fully understand.  But he had already begun to approach the problem from a different angle, which would turn out to be much more fruitful, from a purely philosophical standpoint: the relationship between electricity and heat.

On December 17, 1840, Joule presented his first paper on the subject to the Royal Society of London,4 “On the production of heat by voltaic electricity.”  This oral presentation apparently did not make any strong impression on the Royal Society at the time, and they declined to publish the paper in full in their Philosophical Transactions. Joule ended up publishing it in the Philosophical Magazine the next year5, with a longer title.

In this research, his first major task was to determine a mathematical relationship between heat and electrical current. We have all seen that a wire carrying electrical current heats up, and is hotter with more current, but in Joule’s time there was no experimental measurement of this phenomenon.  Joule set up a simple and straightforward arrangement to measure this, as shown on the left. Wires of different conducting materials were passed through and coiled around a long glass tube A, and the whole arrangement submerged in a flask of water B, with a thermometer T to measure temperature.  Both thick and thin wires were used, as well as wires of copper, iron, and a U-shaped tube of mercury.

Through his experiments, Joule found a law that is now referred to as Joule’s first law, describing what is now called Joule heating: the power P of heating created by an electrical current is proportional to the resistance R of the wire and the square of the current I running through it, which may be written as

P = I²R.

But this was just the necessary precursor to the true work of interest.  Joule investigated the amount of heat generated in electrolysis — the driving of a chemical reaction using an electrical current.  Plates of zinc and platinum-plated iron were submerged in sulfuric acid to form the electrolytic battery, as shown on the left.  In his first experiment, he used this arrangement as a simple battery. When the circuit was completed, a current would flow. Now that he had a definite relationship between heating power, current, and resistance, he was able to use his law of Joule heating to determine, for the first time, the effective electrical resistance of the electrolytic cell.

He then reversed the process, and ran a current through the system to reverse the chemical process and produce electrolysis.  He found that the heat produced and the current still followed the general law determined earlier — P = I²R — making it independent of the nature of the electrical or chemical process involved.

Joule ended up drawing at least one important direct conclusion, and an even more profound indirect one from his research.  The direct conclusion, from his law, is that the heat generated from a chemical battery is directly proportional to the number of atoms involved in the reaction. To a modern eye, this immediately draws to mind the idea of conservation of energy — the heat produced is equal to the energy released in the chemical reaction.

Jons Jacob Berzelius.

The indirect conclusion he reached was perhaps even more significant.  The Swedish chemist Jöns Jacob Berzelius (1779-1848) had speculated (correctly) that the heat and light of combustion comes from the electrical interaction of hydrogen and oxygen, and had determined how much heat is released from a given quantity of hydrogen. Since the chemical processes being studied by Joule also function on the interaction of hydrogen and oxygen, Joule was able to determine how much heat is produced in his electrolytic experiments for a given quantity of hydrogen — and arrived at nearly the same result as Berzelius.

Here was a great hint of some sort of unifying principle: that the heat released does not depend on the specific process of combination, but on the inherent properties of the chemical constituents. As Osborne Reynolds describes in the Memoir of James Prescott Joule,

Had this paper been published in 1840, with the guarantee of the Royal Society, it is impossible to doubt that it would have caught the attention of some of the numerous philosophers who were at the time studying these subjects. And had the facts it reveals become generally known at that time, the effect on the course of Joule’s subsequent discoveries would in all probability have been great. The revelations that the heat developed by the union of two chemical elements effected in the battery is the same as that developed by combustion, and that the heat has a definite equivalent in the electromotive force between these elements, are so pregnant with suggestions, that had others entered this field of enquiry, Joule’s attention might well have been diverted from the line it subsequently followed, and the completion of his work taken out of his hands.

But his first paper on the subject was met with little attention, and Joule pursued further an investigation on the relationship between electricity and the heat of combustion, and presented a paper6 to the Manchester Literary and Philosophical Society on November 2nd, 1841. Here he began to receive some attention. As his brother Benjamin wrote in his diary,

I accompanied James to hear his first paper before the Literary and Philosophical Society—Rev. J. J. Taylor in the chair; Dalton was present, and for the first time in his life moved the thanks of the meeting (and G. W. Wood seconded) to the author of the paper.

Joule was made a member of the Society in January of 1842.  For the next couple of years, he continued this line of investigation with a intensive series of experiments — and one paper7,  “On the Heat Evolved During the Electrolysis of Water,”  resulted in a groundbreaking prediction.

Though the quantity of heat released in combustion and in electrolysis for a given amount of material was strikingly similar, the electrolysis number was consistently lower. At first Joule had ascribed this to experimental error, but the difference was consistent in his experiments, and he soon decided that it was due to the fact that some amount of the electrical force produced by his battery is lost in separating water into hydrogen and oxygen. In the terminology of his day, he said that the heat had become “latent,” though in modern terms we would say that part of the power of the battery is lost in breaking the chemical bonds of water.

This really set Joule on the path of recognizing that electrical force can be converted into many forms.  He then remarked,

The magnetic electrical machine enables us to convert mechanical power into heat by means of the electric currents which are induced by it, and I have but little doubt that by interposing an electro-magnetic engine in the circuit of a battery a diminution of the heat evolved per equivalent of chemical change would be the consequence, and this in proportion to the mechanical power obtained.

The “magnetic electrical machine” he is referring to is the reverse of the electric motors — “electro-magnetic engine” — he began his research on years earlier. An electric motor takes electrical force from a battery and turns it into mechanical force. In a magnetic electrical machine, one can take mechanical motion — like turning a hand crank on the machine — and convert it into current.  Now Joule had recognized that, if one puts an electric motor in the circuit of a battery, the amount of heat produced must be less, because some of that electrical force is being converted into mechanical force instead of heat.

To quote again from Osborne Reynolds,

Joule had now discovered and described all the equivalences but one on which the conservation of energy is founded; the heat, and the chemical equivalents of electrical effect, and the heat equivalents of chemical effects. He has not yet generalized, because he has not realized, that the under lying principle is mechanical effect.

Basically, Joule had shown that heat, electricity, and chemical reactions all have definite relations to one another, and one can be converted into another. He was still missing the final piece of the puzzle — that all have a definite relationship to mechanical force — but that was his inevitable path now that he had become curious about how an electric motor would affect the relations.

He still needed to prove his assertions about the electricity and mechanical force, however.  Though it seems obvious today that the mechanical energy gets converted into electricity and then to heat in a magnetic electrical machine, in Joule’s era the caloric theory of heat was still preeminent. Existing experiments had demonstrated that heat appears in the wires when the magnetic electrical machine is operated, but had not shown that this heat comes from the mechanical operation.  In the caloric theory, it was just as plausible that the mechanical motion transferred the caloric fluid from the machine to the wires, leaving the machine itself colder.

The results of Joule’s efforts to investigated these possibilities culminated in his greatest work8, read before the Chemical Section of Mathematical and Physical Science of the British-Association meeting at Cork on the 21st of August, 1843, “On the Calorific Effects of Magneto-Electricity, and on the Mechanical Value of Heat.”  Here he would finally connect mechanical force to heat, more or less filling in the last piece of the puzzle leading to a general theory of the conservation of energy.

His first step was to ascertain whether heat is in fact generated by mechanical motion in a magnetic electrical machine, or simply transferred from one place to another. To study this, he constructed the device shown below.

The tube held in the wooden bracket “a” contained a wired electromagnet and was filled with water. It could be removed quickly to have the temperature of the water tested. The hand crank “b” sets the electromagnet in motion. Not pictured above, deliberately on Joule’s part for clarity, are two stationary electromagnets, which can be actively connected to a battery or not. When the stationary electromagnets are powered, the whole system works as a magnetic electrical machine, generating electricity that runs out through the wires to the left; when unpowered, there are no electrical effects present.

Joule compared how the temperature of the water changed when the electromagnets were powered versus unpowered; he found that the temperature went up when they were powered, and went down when unpowered. This proved that the electrical heat was not simply being transferred from the electromagnet to the wires, as the wire temperature should otherwise have gone down. Evidently, the mechanical motion itself was resulting in the heat created.

In these experiments, Joule was measuring temperature differences of 1/100th of a degree, something that was simply considered impossible by most researchers at the time!  Joule had spent years perfecting the art of temperature measurement, however, and could do things others had never even tried. This led to some resistance in accepting his results.

Next in Joule’s tasks was testing his hypothesis that the heat generated would be affected by the presence of a electro-magnetic engine.  Here, he simply put a battery into the circuit of his magnetic electrical machine pictured above. The crank of the machine could be turned in either direction: in one direction, it would add to the current produced by the battery, and in the other direction, it would resist the current produced by the battery. In the latter case, the battery ends up, in effect, doing mechanical work to resist the action of the hand crank. In Joule’s hypothesis, less heat should be generated because the electrical action is going towards mechanical action.  This hypothesis was confirmed; as Joule stated it, “We have therefore in magneto-electricity an agent capable by simple mechanical means of destroying or generating heat.”

This led to his groundbreaking measure of the mechanical equivalent of heat.  Joule describes his goal as follows,

Having proved that heat is generated by the magneto-electrical machine, and that by means of the inductive power of magnetism we can diminish or increase at pleasure the heat due to chemical changes, it became an object of great interest to inquire whether a constant ratio existed between it and the mechanical power gained or lost.

He was in the home stretch at this point, so to speak, because all he needed to do was modify his existing hand-cranked apparatus so that he could also measure in a quantitative way how much mechanical effort he put into using it.  For this purpose, he wrapped string around the axle of the crank, as pictured below, and this string was attached to weights.

Basically, the weights will spin the axle, and the heavier the weights, the faster the axle will spin; by making a table of weight versus rotation speed, he could determine how much mechanical force was required to turn the device at any desired speed.  Since he had already measured how much heat and electricity was produced for any rotation speed, he now had a direct relation between mechanical force and heat generated for the various configurations.

Skipping all of the calculations, we come to the groundbreaking conclusion,

The quantity of heat capable of increasing the temperature of a pound of water by one degree of Fahrenheits scale is equal to, and may be converted into, a mechanical force capable of raising 838 lb. to the perpendicular height of one foot.

Of course, we noted in the previous part of this series of blog posts that Julius Robert Mayer had made a similar estimate and observations a full year earlier.  But Mayer’s work was largely philosophical; Joule had the force of detailed experiments to back up his assertions.

In the short term, however, Joule fared no better than Mayer; his presentation to the British Association that August 21st was met with silence.

But the intellectual floodgates had been opened, even if it would take some time for the effects to be felt. Joule, though, like Mayer before him, suddenly found his perspective opened to new possibilities and unifying principles. In a postscript to his seminal paper, he begins,

We shall be obliged to admit that Count Rumford was right in attributing the heat evolved by boring a cannon to friction and not (in any considerable degree) to any change in the capacity of the metal.

Joule seems to be announcing the death of the caloric theory of heat, albeit indirectly! In accepting Rumford’s hypothesis, he is suggesting that heat is motion, and that frictional heat is the transfer of macroscopic (visible) motion to microscopic (atomic, and invisible) motion.

Joule continues, like Mayer before him, in seeing the application of his insights to biological processes,

On conversing a few days ago with my friend Mr. John Davies, he told me that he had himself, a few years ago, attempted to account for that part of animal heat which Crawford’s theory had left unexplained, by the friction of the blood in the veins and arteries, but that, finding a similar hypothesis in Haller’s ‘Physiology’, he had not pursued the subject further. It is unquestionble that heat is produced by such friction, but it must be understood that the mechanical force expended in the friction is a part of the force of affinity which causes the venous blood to unite with oxygen ; so that the whole heat of the system must still be referred to the chemical changes. But if the animal were engaged in turning a piece of machinery, or in ascending a mountain, I apprehend that in proportion to the muscular effort put forth for the purpose, a diminution of the heat evolved in
the system by a given chemical action would be experienced.

This is another impressive leap forward: recognizing that the same processes that govern physics and chemistry and can be used to understanding living creatures.

Finally, Joule revises some of his earlier thoughts on combustion, which he had previously thought of as entirely an electrical phenomenon. Now, he sees it as also a result of mechanical forces at play,

I now venture to state more explicitly, that it is not precisely the attraction of affinity, but rather the mechanical force expended by the atoms in falling towards one another, which determines the intensity of the current, and consequently the quantity of heat evolved ; so that we have a simple hypothesis by which we may explain why heat is evolved so freely in the combination of gases, and by which, indeed, we may account “latent heat ” as a mechanical power prepared for action as a watch-spring is when wound up.

This explanation of “latent heat” is a crude description of what we now call potential energy, i.e. energy bound up in a system that can be released under the right circumstances.

Despite the profound nature of Joule’s discoveries, or perhaps because of it, several years would pass before he received any recognition whatsoever for them. As Osborne Reynolds somewhat ironically put it,

The fact that these early papers of Joule were, at the time, apparently ignored by the many eminent physicists then living, though apt to inspire the present reader with a feeling of astonishment, if not of indignation, at the generation for their prejudice and neglect, was, in truth, the highest tribute that could be paid to the greatness of the advance in philosophy which he had made.

In short: Joule’s work was so groundbreaking that nobody understood its significance! Or, if they did, it was so revolutionary that many researchers did not want to take the risk of wandering into such uncharted territory.

Joule, undaunted, continued his flurry of experiments and publications. Along the way, he became a bigger proponent for the kinetic theory of heat, and also did experiments to measure how much heat is generated in compressing a gas. The inverse of this experiment, showing that temperature goes down when a gas expands, was of practical importance for the development of steam engines, as it suggests fundamental limits on engine efficiency.  In discussing such engines, he also became more confident in expressing a principle of conservation of… something, not yet given a definite name.

Believing that the power to destroy belongs to the Creator alone, I entirely coincide with Roget and Faraday in the opinion that any theory which, when carried out, demands the annihilation of force, is necessarily erroneous.

This was also thinking very much in the line of Mayer: a “cause” always produces an “effect,” and every physical phenomenon has some sort of influence on what happens next.  Physicists at the time were still using the concept of “vis viva” (living force) to describe what we now call kinetic energy, and without recognizing heat as a form of motion, they were forced to accept the notion that vis viva could simply disappear. Joule, however, had demonstrated that it did not disappear, but manifested instead as heat.

It was finally in 1847 that Joule started to receive the recognition that he deserved. Part of it can be said to be due to his own aggressive self-promotion, and in hindsight historians are all glad that he took that approach! On April 28, 1847, Joule gave a popular lecture on his ideas in Manchester, at St. Ann’s Church Reading Room, with the title, “On Matter, Living Force, and Heat.” This is the only time that he gave a big picture view of his ideas on conservation, and it is a beautiful lecture that is well-worth reading in its entirety. Here we provide a few simple excerpts.

A body may be endowed with living force in several ways. It may receive it by the impact of another body. Thus, if a perfectly elastic ball be made to strike another similar ball of equal weight at rest, the striking ball will communicate the whole of its living force to the ball struck, and, remaining at rest itself, will cause the other ball to move in the same direction and with the same velocity that it did itself before the collision. Here we see an instance of the facility with which living force may be transferred from one body to another. A body may also be endowed with living force by means of the action of gravitation upon it through a certain distance. If I hold a ball at a certain height and drop it, it will have acquired when it arrives at the ground a degree of living force proportional to its weight and the height from which it has fallen. We see, then, that living force may be produced by the action of gravity through a given distance or space. We may, therefore, say that the former is of equal value, or equivalent, to the latter.

In the preceding passage, Joule gives an introduction to the convention thinking about vis viva; next, though, he criticizes some other conventions:

You will at once perceive that the living force of which we have been speaking is one of the most important qualities with which matter can be endowed, and, as such, that it would be absurd to suppose that it can be destroyed, or even lessened, without producing the equivalent of attraction through a given distance of which we have been speaking. You will therefore be surprised to hear that until very recently the universal opinion has been that living force could be absolutely and irrevocably destroyed at any one’s option. Thus, when a weight falls to the ground, it has been generally supposed that its living force is absolutely annihilated, and that the labour which may have been expended in raising it to the elevation from which it fell has been entirely thrown away and wasted, without the production of any permanent effect whatever. We might reason, a priori, that such absolute destruction of living force cannot possibly take place, because it is manifestly absurd to suppose that the powers with which God has endowed matter can be destroyed any more than that they can be created by man’s agency; but we are not left with this argument alone, decisive as it must be to every unprejudiced mind.

He then makes a qualitative argument for conservation:

We have reason to believe that the manifestations of living force on our globe are, at the present time, as extensive as those which have existed at any time since its creation, or, at any rate, since the deluge —that the winds blow as strongly, and the torrents flow with equal impetuosity now, as at the remote period of 4000 or even 6000 years ago; and yet we are certain that, through that vast interval of time, the motions of the air and of the water have been incessantly obstructed and hindered by friction.

This is quite an elegant argument — a little too elegant, because it ignores the fact that we are constantly getting energy from the Sun, and constantly losing energy by radiation to space! But this was outside Joule’s experience at the time, and it is perhaps fair to note that one would expect things to have wound down a LOT more over the years if vis viva simply disappeared at every instance of friction.

But the bulk of Joule’s arguments are simply beautiful and insightful:

How comes it to pass that, though in almost all natural phenomena we witness the arrest of motion and the apparent destruction of living force, we find that no waste or loss of living force has actually occurred ? Experiment has enabled us to answer these questions in a satisfactory manner ; for it has shown that, wherever living force is apparently destroyed, an equivalent is produced which in process of time may be reconverted into living force. This equivalent is heat. Experiment has shown that wherever living force is apparently destroyed or absorbed, heat is produced. The most frequent way in which living force is thus converted into heat is by means of friction. Wood rubbed against wood or against any hard body, metal rubbed against metal or against any other body—in short, all bodies, solid or even liquid, rubbed against each other are invariably heated, sometimes even so far as to become red-hot. In all these instances the quantity of heat produced is invariably in proportion to the exertion employed in rubbing the bodies together—that is to the living force absorbed. By fifteen or twenty smart and quick strokes of a hammer on the end of an iron rod of about a quarter of an inch in diameter placed upon an anvil an expert blacksmith will render that end of the iron visibly red-hot.

As he continues, he touches on practical aspects…

The converse of this proposition is also true, namely, that heat cannot be lessened or absorbed without the production of living force, or its equivalent attraction through space. Thus, for instance, in the steam-engine it will be found that the power gained is at the expense of the heat of the fire,— that is, that the heat occasioned by the combustion of the coal would have been greater had a part of it not been absorbed in producing and maintaining the living force of the machinery.

… and recognizes other forms of living force…

All three, therefore—namely, heat, living force, and attraction through space (to which I might also add light, were it consistent with the scope of the present lecture)—are mutually convertible into one another. In these conversions nothing is ever lost.

… and even touches upon some astrophysics, providing an accurate explanation of shooting stars!

On the other hand, our safety equally depends in some instances upon the conversion of living force into heat. You have, no doubt, frequently observed what are called shooting-stars as they appear to emerge from the dark sky of night, pursue a short and rapid course, burst, and are dissipated in shining fragments. From the velocity with which these bodies travel, there can be little doubt that they are small planets which, in the course of their revolution round the sun, are attracted and drawn to the earth. Reflect for a moment on the consequences which would ensue, if a hard meteoric stone were to strike the room in which we are assembled with a velocity sixty times as great as that of a cannonball. The dire effects of such a collision are effectually prevented by the atmosphere surrounding our globe, by which the velocity of the meteoric stone is checked and its living force converted into heat, which at last becomes so intense as to melt the body and dissipate it into fragments too small probably to be noticed in their fall to the ground.

Weather can be explained by this conservation principle, as well,

The motion of air which we call wind arises chiefly from the intense heat of the torrid zone compared with the temperature of the temperate and frigid zones. Here we have an instance of heat being converted into the living force of currents of air. These currents of air, in their progress across the sea, lift up its waves and propel the ships ; whilst in passing across the land they shake the trees and disturb every blade of grass. The waves by their violent motion, the ships by their passage through a resisting medium, and the trees by the rubbing of their branches together and the friction of their leaves against themselves and the air, each and all of them generate heat equivalent to the diminution of the living force of the air which they occasion. The heat thus restored may again contribute to raise fresh currents of air ; and thus the phenomena may be repeated in endless succession and variety.

And, finally, Joule touches briefly upon the human implications,

When we consider our own animal frames, ‘ fearfully and wonderfully made,’ we observe in the motion of our limbs a continual conversion of heat into living force, which may be either converted back again into heat or employed in producing an attraction through space, as when a man ascends a mountain.

There are oversights and mistakes in Joule’s presentation, but these are overshadowed by the beauty of seeing nature’s grandest principle of conservation expressed elegantly and even poetically for one of the first times.

Joule was eager for his lecture to be put into print for wider dissemination to the public. As his brother Benjamin wrote,

James was very anxious that this lecture should be published in its entirety as soon as possible. One paper refused to give even a notice of it. After some discussion the Manchester Guardian would, as a favour, print extracts to be selected by themselves. This of course would not satisfy my brother. I returned to the Manchester Courier, and, after a long debate, they promised to insert the whole as a special favour to myself.

So it is thanks to Joule and his brother that we have the ability to read how Joule himself viewed the implications of his work.

Later that year, Joule’s work finally started to be recognized by scientific societies. In what would turn out to be an incredible stroke of luck, Joule presented his ideas again to the British Association on the 23rd of June, 1847. His earlier presentation in 1843 had gone almost unnoticed. In this case, though, things were different, as Joule himself recalled in 1885:

With the exception of some eminent men, among whom I recollect with pride, Dr. Apjohn, the president of the section, the Earl of Rosse, Dr. Eaton Hodgkinson, and others, the subject did not excite much general attention [in 1843], so that when I brought it forward again at the meeting in 1847 the chairman suggested that, as the business of the Section pressed, I should not read my paper but confine myself to a short verbal description of my experiments. This I endeavoured to do, and a discussion not being invited the communication would have passed without comment if a young man had not risen in the section, and by his intelligent observations created a lively interest in the new theory. The young man was William Thomson, who had two years previously passed the University of Cambridge with the highest honour, and is now probably the foremost scientific authority of the age.

Lord Kelvin.

William Thomson, later titled Lord Kelvin, ended up one of the most important physicists of his age. At that 1847 meeting of the British Association, Thomson was first convinced that Joule was wrong, but as Joule continued to talk, became more fascinated by his work and its implications. They talked at length during the meeting, and became fast friends. It so happened that Joule was married that very next week to Amelia Grimes, and in a fun bit of serendipity Thomson ended up meeting the couple again soon after, as Thomson himself later recalled,

However, he did not tell me he was to be married in a week or so, but about a fortnight later, I was walking down from Chamounix to commence the tour of Mont Blanc, and whom should I meet walking up but Joule, with a long thermometer in his hand, and a carriage with a lady in it not far off. He told me that he had been married since we parted at Oxford ! and he was going to try for elevation of temperature in waterfalls. We trysted to meet a few days later at Martigny, and look at the Cascade de Sallanches, to see if it might answer. We found it too much broken into spray. His young wife, as long as she lived, took complete interest in his scientific work, and both she and he showed me the greatest kindness during my visits to them in Manchester, for our experiments on the thermal effects of fluid in motion, which we commenced a few years later.

(What were they trying to measure? The water falling from the top of a waterfall has a high potential energy, which converts to kinetic energy as it falls. When it hits the base of the waterfall, that energy must be converted to heat, so one would expect that the temperature at the base of the waterfall must be higher than that at the top.)

It seems that Thomson’s support helped turn the tide in favor of Joule’s theory and ideas. Of course, the power of the ideas themselves and the simple elegance and truth of them also made their recognition inevitable. Also in 1847, Joule managed to publish an account of his work in the esteemed French journal Comptes Rendus, which marked the first time a major scientific society recognized its significance.

The work was not without bitter controversy and rivalry, of course. As we noted in Part II of this series, Joule ended up in a nasty feud with Mayer over priority. This, to me, tarnishes the reputation of Joule slightly, though I am a little sympathetic to the panic Joule must have felt at the possibility that a decade of painstaking experimental work might be overshadowed by the theoretical speculations of a German doctor. Today, both Mayer and Joule are recognized as having played important roles in the discovery of what we call conservation of energy.

But who coined the term “energy?” Joule used “living force” to describe the conserved quantity he had recognized, and others simply used “force” to describe it, though this terminology was impractical — force, of course, had already long been used to describe a very different quantity in physics.  It appears that the Scottish engineer William John Macquorn Rankine was the first to use the term “energy,” in an 1853 paper which lays out explicitly the idea of a law of transformation of energy,

In this investigation the term energy is used to comprehend every affection of substances which constitutes or is commensurable with a power of producing change in opposition to resistance, and includes ordinary motion and mechanical power, chemical action, heat, light, electricity, magnetism, and all other powers, known or unknown, which are convertible or commensurable with these. All conceivable forms of energy may be distinguished into two kinds ; actual or sensible, and potential or latent.

And with this, we can say that the theory of the conservation of energy was well and full established. It took several hundred years from the first recognition of “vis viva” by Gottfried Leibniz for this theory to develop, which is a strong testament to the intellectual prowess of the three researchers highlighted in this series — Count Rumford the cannon-maker, Julius Robert Mayer the doctor, and James Joule the brewer.

It is quite remarkable that the history of the conservation of energy can really be boiled down to booms, blood, and beer.

William Rankine.

**************************************

¹ Osborne Reynolds, Memoir of James Prescott Joule (Manchester Literary and Philosophical Society, 1892).

² J.P. Joule, “Investigations in Magnetism and Electro-magnetism,” Annals of Electricity 4 (1839), 131.

³ J.P. Joule, “Description of an Electro-Magnetic Engine,” Annals of Electricity 2 (1838), 122.

4 J.P. Joule, “On the production of heat by voltaic electricity,” Proc. Roy. Soc. Lond. 4 (1840), 280.

5 J.P. Joule, “On the Heat evolved by Metallic Conductors of Electricity, and in the Cells of a Battery during Electrolysis,” Phil. Mag. 19 (1841), 260.

6 J.P. Joule, “On the Electric Origin of the Heat of Combustion,” Phil. Mag. 20 (1841), 98.

7 J.P. Joule, “On the Heat Evolved During the Electrolysis of Water,” Memoirs of the Manchester Literary and Philosophical Society 7 (1843), 87.

8 J.P. Joule, “On the Calorific Effects of Magneto-Electricity, and on the Mechanical Value of Heat,” Phil. Mag. 23 (1843), 263, 347, and 435.

9 W.J.M. Rankine, “On the General Law of the Transformation of Energy,” Proceedings of the Philosophical Society of Glasgow 3 (1853), 276.

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2 Responses to History of the Conservation of Energy: Booms, Blood, and Beer (Part 3)

  1. Blake Stacey says:

    It is really remarkable how long after Newton’s time were finally established many of the concepts we teach as “Newtonian” physics. “Vis viva” as distinct from momentum, energy as a conserved quantity that can change from one form to another… and vectors are even more recent than that! Since Wilson’s Vector Analysis wasn’t published until 1901, you might even say that “classical physics” didn’t get the shape that our undergraduate curriculum typically gives it until after quantum physics had begun.

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