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

Part 2 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.

In 1798, Count Rumford presented the first significant challenge to the caloric theory of heat, arguing that the seemingly endless amount of heat that could be generated by boring cannons was inconsistent with the idea that heat is a fluid that lies latent in all materials — and can therefore be exhausted.  Rumford subscribed to the alternative, and it turns out correct, theory: that heat is the observable effect of random motion of particles.

But Rumford did not significantly shift the scientific consensus. In the view of most researchers, the evidence still strongly favored the caloric theory, and Rumford’s results were viewed by some as actually bolstering that theory.

It would be a number of years before the next true milestone in the idea of conservation of energy, and it would also come from an unlikely source: a physician, serving as a doctor on a ship sailing to the Dutch East Indies.  Julius Robert Mayer would introduce the first formal statement of what we now know as the conservation of energy — by making an amazingly astute observation about blood.  His discovery, however, would cost him dearly in the long run.

William Herschel (1738-1822), via Wikipedia.

Before discussing Mayer and his work, it is worthwhile to explain how the caloric theory had become even stronger in the years after Rumford, ironically due to the misinterpretation of another important scientific discovery.  Early in the year 1800, the famed astronomer William Herschel was making observations of sunspots through a telescope. Obviously, due to the amount of light being put out by the sun, it had to be heavily filtered before viewing.  But Herschel noticed that a red filter (designed to block red light) would absorb heat very quickly compared to other colored filters, and would even crack and break due to the heat in a short time.   This made him curious about the relative heating powers of different colors of light, and he undertook a systematic experiment to measure them.  Using a prism to separate the colors, like on the cover of Pink Floyd’s Dark Side of the Moon, he then placed a thermometer in the path of each one, and measured the amount that the temperature rose. He found that light on the violet end of the spectrum had the smallest heating power, and that this power increased all the way to the red end of the spectrum, where it was seemingly greatest.

Pink Floyd’s Dark Side of the Moon album cover, showing the principle by which the spectrum of light is generated.

I’ve found conflicting accounts of what happened next, though the result is the same.  Either out of curiosity or by accident, Herschel placed a thermometer slightly outside of the visible spectrum, on the red side. Even though there was no visible light hitting the thermometer, the temperature rose even more than it had when red light hit it!

Eventually, it would be recognized that Herschel had discovered infrared light, another part of the electromagnetic spectrum that has a longer wavelength than red light but a shorter wavelength than microwaves, and which is invisible to the naked eye.  But the wave theory of light had not yet even been accepted by science — and would not be until 1817, when the diffraction of light was successfully explained by the wave theory.  So, at the time, Herschel’s observation seemed instead to say something profound about the nature of heat.

We have noted that the heating power of light is greatest on the red end of the visible spectrum, and increases further beyond, where there is no visible light present.  In contrast, visible light is brightest in the middle of the spectrum, giving the sun its yellow appearance.  For researchers in Herschel’s time, this discrepancy was very odd — to them, it seemed that the amount of heat induced by light should be proportional to its brightness.

Today, we know that different types of radiation are more or less effective at heating due to the complicated way they interact with matter. In 1800, however, a decent theory of light-matter interactions was over 100 years away, and the calorists came to a different conclusion from the evidence. The discrepancy between brightness and heating power, to them, indicated that there must be two different types of rays being emitted by the sun: visible light rays and invisible caloric rays¹.

This appeared at the time as strong evidence for the existence of the substance they called caloric. Nobody doubted the existence of light as a real substance, and Herschel’s experiments seemed to show that heat acted very much like light — it could be refracted by a prism, for instance, and filtered.  The caloric theory had to be modified — again — to take into account this new behavior, but it seemed like science was closer than ever to solving the mystery of caloric.

Julius Robert Mayer, from a 1905 German biography by Dr. S. Friedlaender.

Into this state of affairs would come Julius Robert Mayer (1814-1878).  Mayer was born in the town of Heilbronn, in what is now Germany, as the son of an apothecary².  His father’s business apparently set Julius on an early course towards medicine, though he also showed an aptitude towards mechanical devices.  It is ironic, and perhaps a bit of foreshadowing, that he, like Rumford before him, apparently tried to construct a perpetual motion machine in his youth.  He received his early education in Heilbronn, but at age 15 moved to the seminary in Schönthal to prepare him for university.  There, he earned the nickname of “Geist” (spirit, or ghost) due to the scientific tricks he used to entertain his classmates.

In 1832, Mayer went to the Eberhard Karls University of Tübingen to pursue his medical degree.  His tenure there seems to have been largely unremarkable, except for one significant incident in 1837 that also foreshadowed later psychological troubles. Due to his membership in a forbidden organization on campus, he was expelled from the school for a full year.   His initial reaction to this decision was to undergo a six-day hunger strike.  The doctor supervising him noted that his mental health was being severely harmed by the interruption of his academic goals. He recuperated from this illness, though, and traveled to Munich and Vienna during his time off, returning to university in 1838.  He passed his doctoral examination that same year, and received his medical degree.

Perhaps due to the trials and tribulations in his education, Mayer did not immediately settle into private practice, as most would have done. Instead, against his parents’ wishes, he resolved to travel the world a bit first.  He secured a medical license in the Netherlands, which made him eligible to travel as a ship’s doctor on a trip to the East Indies. In February of 1840, he boarded the three-masted sailing ship Java, bound for Batavia (now called Jakarta) in Indonesia.  It was this trip, and the observations that Mayer made on it, that would secure his place in the history of science.

The trip took 101 days of sailing, 67 of which were completely out of sight of land.  There was not much day to day work for a doctor on board, and the officers of the ship largely ignored him. Mayer spent most of his time reading scientific books, pondering nature, and chatting with the sailors.

The ship arrived in Batavia in June of 1840. Right after arrival, a number of the crew came down with an affliction of the lungs, and — it being the 1800s — Mayer determined that a bloodletting was the proper treatment.  This involved releasing the blood from the sailor’s veins, and Mayer was astonished to see that this blood was bright red, more like arterial blood than venous blood.  He consulted with other doctors in Batavia, and found that this was common in the hot climate of Indonesia.

This was the key to Mayer’s revelation about what would become known as the conservation of energy.  It was already known that the heat of the human body was created through the consumption of oxygen in the blood; Mayer realized that less oxygen was being consumed, leaving the blood redder, because it was not necessary to heat the body as much in the tropics.  This set him pondering the nature of heat and chemical reactions, and this pondering would occupy him for the rest of his time in Indonesia.

It is a bit odd that this was the trigger for Mayer’s discovery, as it seems that the heating of the body could just as readily be explained via the caloric theory. But, apparently, the recognition that there was some sort of balance between the heat released in the body and the heat already in the atmosphere set him along a path of thinking about the transformation of intangible things from one form to another, with none of it being lost.  Perhaps even more important, though not as often discussed in reviews of Mayer’s work: Mayer now recalled that the sailors on the Java had told him that the sea is always warmer after a storm.  It then seemed clear to him that the motion of the storm — the wind and the waves — had in the end been converted into heat. The physical truth was suddenly revealed to him: heat and mechanical motion are just two aspects of the same fundamental, conserved quantity.  A quantity that we now refer to as energy.

A quantitative connection between heat and motion was the main obstacle to developing a law of conservation of energy throughout the history of physics. As we have noted, many had suggested that heat is motion, but it appears that few had suggested that they are, in essence, interchangeable.  And Julius Robert Mayer was the first to quantify this change.

Johann Christian Poggendorff, via Wikipedia. A bit of a jerk.

Mayer returned to his hometown of Heilbronn in early 1841, and set up a medical practice there; this would be his main profession for the rest of his life. But he realized that he had discovered something profound about nature, and immediately began writing up his work for publication.  On June 16, 1841, he submitted his first paper to the famed journal Annalen der Physik, run by the German physicist Johann Christian Poggendorff.  Mayer very humbly asked Poggendorff to publish the paper if he felt it was suitable, and return it if not. Incredibly, Poggendorff never returned the manuscript, even after several requests to do so; this must have been an incredible burden to Mayer in 1841, when it was not so easy to duplicate papers. (After Poggendorff died, the manuscript was found in his home, confirming that he did have it.)

Mayer, via Wikipedia.

Mayer was a novice in physics, and must have recognized — especially after the frosty reception at Annalen der Physik — that he would need his paper to be much more precise.  He consulted professors of physics in Tübingen and Heidelberg for advice, and was told that he should come up with some sort of conclusive experimental test to validate his work.  Recalling the observations of the sailors about the ocean temperature, Mayer tested whether a bottle of water can be warmed by shaking it; he found that it was true.

By 1842, not having received his manuscript back from Poggendorff, Mayer opted to write and submit a second paper to a different journal.  He was quite concerned at this point about being scooped in his discovery — which was prescient, as it turned out.  His second paper went to Annalen der Chemie und Pharmacie, and was published in May of 1842. The paper, whose title translates to “Remarks upon the Forces of Inanimate Nature,” was the first statement of a principle of conservation of energy, and gave the first quantitative measurement of a key quantity: the relationship between heat and mechanical work.

A few passages from this paper will give an inkling of the beauty of it³.  Before starting, we should note that the word “energy” does not appear at all in this paper, nor in any of Mayer’s papers on the subject: it was not yet a concept! Mayer used the word “Kraft,” or “Force”; in reading the excerpts below, think “energy” when you read “force.”

The following pages are designed as an attempt to answer the questions, What are we to understand by “Forces”? and how arc different forces related to each other? Whereas the term matter implies the possession, by the object to which it is applied, of very definite properties, such as weight and extension; the term force conveys for the most part the idea of something unknown, unsearchable, and hypothetical. An attempt to render the notion of force equally exact with that of matter, and so to denote by it only objects of actual investigation, is one which, with the consequences that flow from it, ought not to be unwelcome to those who desire that their views of nature may be clear and unencumbered by hypotheses.

Mayer begins with a compelling analogy: he notes that we have long been able to quantify material bodies with definite properties (most notably mass, or weight), and that something similar must be true of those forces of nature. Left unsaid, but strongly implied, is that mass is something that, in physics of the 19th century, is conserved.  Chemical reactions may take place to change different chemical compounds into each other, but their total mass remains unchanged.  This would be undeniable to even proponents of the caloric theory, as its founder — Antoine Lavoisier — popularized the concept.  So if mass is a definite quantity conserved, surely “force” — in the vague sense of the word — must have some associated conserved quantity?

Forces are causes : accordingly, we may in relation to them make full application of the principle — causa æquat effectum. If the cause c has the effect e, then c = e; if, in its turn, e is the cause of a second effect f, we have e = f, and so on: c = e = f … = c. In a chain of causes and effects, a term or a part of a term can never, as plainly appears from the nature of an equation, become equal to nothing. This first property of all causes we call their indestructibility.

In the above, Mayer is largely discussing philosophy, but it is a reasonable and even beautiful chain of reasoning, given that we know where it is leading. In short: he is saying that every physical effect has another effect, or a collection of effects. No physical phenomenon has no consequences — if it did, it would not be a measurable physical phenomenon.

If the given cause c has produced an effect e equal to itself, it has in that very act ceased to be: c has become e; if, after the production of e, c still remained in whole or in part, there must be still further effects corresponding to this remaining cause: the total effect of c would thus be > e, which would be contrary to the supposition c = e. Accordingly, since c becomes e, and e becomes f, &c., we must regard these various magnitudes as different forms under which one and the same object makes its appearance. This capability of assuming various forms is the second essential property of all causes. Taking both properties together, we may say, causes are (quantitatively) indestructible and (qualitatively) convertible objects.

Here, Mayer now further elaborates upon this idea of a chain of causes, noting that the two key qualities of causes are that they are not only indestructible, but convertible.  At this point, the similarity to a principle of conservation of energy is undeniable.

Finally, Mayer again makes the analogy between matter and forces, noting their similarities and differences:

Two classes of causes occur in nature, which, so far as experience goes, never pass one into another. The first class consists of such causes as possess the properties of weight and impenetrability; these are kinds of matter : the other class is made up of causes which are wanting in the properties just mentioned, namely Forces, called also Imponderables, from the negative property that has been indicated. Forces are therefore indestructible, convertible, imponderable objects.

This is a really interesting way of looking at physics as a whole, and a sort of “grand unified theory” of its own: everything in nature can be divided into matter and forces. The former are tangible, the latter intangible, but both can be converted from one form into another. This, in fact, isn’t so, so far from where we are in the modern Standard Model of Physics, where particles are divided into matter, such as electrons and quarks, versus mediators of forces, such as the photon and gluon.

Mayer next discusses some chemistry to illustrate the ideas he has put forth, in particular talking about the relationship between hydrogen and oxygen gas on the one hand and water on the other.  He gets into physics specifics again several paragraphs later:

A cause which brings about the raising of a weight is a force; its effect (the raised weight) is, accordingly, equally a force; or, expressing this relation in a more general form, separation in space of ponderable objects is a force; since this force causes the fall of bodies, we call it falling force. Falling force and fall, or, more generally still, falling force and motion, are forces which are related to each other as cause and effect—forces which are convertible one into the other—two different forms of one and the same object. For example, a weight resting on the ground is not a force : it is neither the cause of motion, nor of the lifting of another weight; it becomes so, however, in proportion as it is raised above the ground : the cause—the distance between a weight and the earth—and the effect—the quantity of motion produced— bear to each other, as we learn from mechanics, a constant relation.

It may be difficult to understand what Mayer is getting at in the preceding paragraph, but he is really laying out a definition of what is known in physics as potential energy.  Basically, when one lifts an object in a gravitational field, one imparts upon it potential energy — in modern terms, we may think of it as energy “stored” in the gravitational field.  If the object is allowed to fall freely, that gravitational energy becomes energy of motion — kinetic energy — but Mayer argues that none is lost, only converted from one form to another.  He also correctly notes that this “falling force” is proportional to the height the object is raised, and he even gives the explicit formula a few paragraphs later, to remove all doubt.

Mayer’s next paragraph may again be considered a rather profound philosophical statement for the time:

Gravity being regarded as the cause of the falling of bodies, a gravitating force is spoken of, and so the notions of property and of force are confounded with each other : precisely that which is the essential attribute of every force—the union of indestructibility with convertibility—is wanting in every property : between a property and a force, between gravity and motion, it is therefore impossible to establish the equation required for a rightly conceived causal relation. If gravity be called a force, a cause is supposed which produces effects without itself diminishing, and incorrect conceptions of the causal connexion of things are thereby fostered. In order that a body may fall, it is no less necessary that it should be lifted up, than that it should be heavy or possess gravity ; the fall of bodies ought not therefore to be ascribed to their gravity alone.

Mayer is arguing here that physicists need to take a different view of the world in order to properly understand the motion and interactions of objects. To me, he is saying that physicists have been so focused on gravity as the cause of motion that they have failed to notice that such motion requires an object to be lifted up first — the true cause of motion.  In short: they have missed the fact that the kinetic energy of falling objects only exists because we have imbued them with potential energy by lifting them up.  But what happens to that motion once the object hits the ground?  Mayer then gets to the key connection between heat and motion:

In numberless cases we see motion cease without having caused another motion or the lifting of a weight ; but a force once in existence cannot be annihilated, it can only change its form; and the question therefore arises, What other forms is force, which we have become acquainted with as falling force and motion, capable of assuming? Experience alone can lead us to a conclusion on this point. In order to experiment with advantage,
we must select implements which, besides causing a real cessation of motion, are as little as possible altered by the objects to be examined. If, for example, we rub together two metal plates, we see motion disappear, and heat, on the other hand, make its appearance, and we have now only to ask whether motion is the cause of heat. In order to come to a decision on this point, we must discuss the question whether, in the numberless cases in which the expenditure of motion is accompanied by the appearance of heat, the motion has not some other effect than the production of heat, and the heat some other cause than the motion.

The emphasis in this case is mine. Following his earlier reasoning, Mayer argues that it simply makes no sense to assume that the motion in frictional activities has simply disappeared, and that heat should be viewed as a consequence of stopped motion.  He then points out his simple experiment of shaking water:

Water undergoes, as was found by the author, a rise of temperature when violently shaken. The water so heated (from 12° to 13° C.) has a greater bulk after being shaken than it had
before; whence now comes this quantity of heat, which by repeated shaking may be called into existence in the same apparatus as often as we please ? The vibratory hypothesis of heat is an approach towards the doctrine of heat being the effect of motion, but it does not favour the admission of this causal relation in its full generality; it rather lays the chief stress on uneasy oscillations (unbehagliche Schwingungen).

Here Mayer outlines an important point: authors had previously argued that heat is the result of atomic and molecular motions, but had not fully connected that the quantity of heat (and microscopic motion) created is directly related to the macroscopic motions that produce it.

After a bit more discussion, Mayer then makes one more important connection — the idea that heat can, in turn, be turned back into motion.

But just as little as the connexion between falling force and motion authorizes the conclusion that the essence of falling force is motion, can such a conclusion be adopted in the case of heat. We are, on the contrary, rather inclined to infer that, before it can become heat, motion—whether simple, or vibratory as in the case of light and radiant heat, &c.—must cease to exist as motion.

If falling force and motion are equivalent to heat, heat must also naturally be equivalent to motion and falling force. Just as heat appears as an effect of the diminution of bulk and of the cessation of motion, so also does heat disappear as a cause when its effects are produced in the shape of motion, expansion, or raising of weight.

This is a big deal, and really completes a statement of conservation of energy.  If motion and “falling force” can be turned into heat, then heat must be able to be returned into these forms.  He provides obvious examples:

In water-mills, the continual diminution in bulk which the earth undergoes, owing to the fall of the water, gives rise to motion, which afterwards disappears again, calling forth unceasingly a great quantity of heat ; and inversely, the steam-engine serves to decompose heat again into motion or the raising of weights. A locomotive engine with its train may be compared to a distilling apparatus ; the heat applied under the boiler passes off as motion, and this is deposited again as heat at the axles of the wheels.

Almost the entirety of Mayer’s paper up to this point has been a qualitative discussion of this idea of conservation of forces.  Mayer himself, however, recognized that he needed something quantitative to give his argument weight. To conclude, he comes up with the key ingredient for connecting heat to motion: the mechanical equivalent of heat.

The solution of the equations subsisting between falling force and motion requires that the space fallen through in a given time, e. g. the first second, should be experimentally determined; in like manner, the solution of the equations subsisting between falling force and motion on the one hand and heat on the other, requires an answer to the question, How great is the quantity of heat which corresponds to a given quantity of motion or falling force? For instance, we must ascertain how high a given weight requires to be raised above the ground in order that its falling force may be equivalent to the raising of the temperature of an equal weight of water from 0° to 1° C.

Without doing experiments, Mayer was able to answer this question in an ingenious way, using existing measurements.  In studies of heat, it was already known that one can heat a quantity of gas in two ways: by either keeping the gas at a constant volume or keeping it at a constant pressure. The heat capacity — amount of heat required to raise the temperature — of a gas under constant pressure is higher than that under constant volume, in a ratio known at the time to be 1.421:1. Mayer recognized that this difference in heat capacity was due to the gas doing work to expand the volume of the container in the first case. But measurements had already been done showing how much mechanical work needed to be done to expand a gas at constant pressure, and the amount of heat used in doing so was also known.  From these numbers, Mayer was able to estimate that:

the warming of a given weight of water from 0° to 1° C. corresponds to the fall of an equal weight from the height of about 365 metres.

This was the first calculated estimate of the mechanical equivalent of heat; his number would later be found to be somewhat off, but this was due to insufficiently precise measurements of the heat capacities, not due to his mathematics.  Mayer was nevertheless the first to quantify, in print, the equivalence between mechanical effort and heat.

His work would not, however, earn him accolades, due to a combination of bad luck, politics, and institutional prejudices. Mayer was not a physicist, and his paper was published in a journal that was not really a good audience for the research; it therefore remained unknown at this key point in history when others were coming to similar conclusions. On August 21, 1843, a full year after Mayer’s paper appeared, the British scientist James Prescott Joule (to be discussed in Part 3 of this series of posts) presented his own independent results on the mechanical theory of heat before the British Association in Cork. Though Joule’s work was also initially met with stony silence, his persistence and rigorous work led to broad recognition for his labors, and an appreciation that this was a truly new and fundamental discovery in physics.

Mayer, meanwhile, continued to labor on his own ideas in obscurity.  By 1845, he had written an extremely lengthy paper titled, “Motion in organisms and its connection with metabolism. A contribution to natural science,” which described all of his earlier work in greater quantitative detail and further extended his ideas to physiology and the motion of living creatures. Mayer could not find a journal to publish his work, however, so he printed a small number of copies at his own expense for circulation. It is worth just providing one snippet to give an idea of how far his vision had extended (translation from R.B. Lindsey’s book):

If we now combine the results of all these investigations into a single general law, we once more obtain the axiom originally set up. This is:

In all physical and chemical processes the energy involved remains constant.

The following scheme provides a summary of the principal forms of energy already considered.

I. Potential energy (due to gravity) (fall-force)
II. Energy of motion
A. Simple
B. Vibrational
III. Heat
IV. Magnetism
Electricity (galvanic current)
V. Chemical separation of certain materials
Chemical combination of certain other materials

But as his ideas flourished, Mayer’s life began to fall apart. In 1847, James Joule finally published a detailed account of his own work in the prestigious journal Comptes Rendus.  Joule had in the meantime learned of Mayer’s work, and apparently felt threatened by it, because he added a critique to his own paper arguing that Mayer’s calculations were unjustified and, in fact, could only be proven through Joule’s results (which was untrue, in fact).  This compelled Mayer to respond in print with a defense of his own labors in 1848, and this led to a back-and-forth dispute over who could claim the priority of discovery.

By itself, this might have not been a catastrophic turn of events, but on August 19, 1848, Mayer’s daughter Anna died, and only six days later his younger daughter Julie died as well. Thus Mayer was defending his life’s work at a time when his personal life had been struck with the deepest tragedy.

This was followed up by even harsher criticisms on Mayer’s methodology.  In 1849, a young German physicist named Otto Seyffer published a brutal attack on Mayer’s work, declaring it to be a collection of unfounded speculations about forces of nature. More researchers piled on in other journals, no doubt leaving Mayer to feel himself besieged and rejected by the scientific community.

This took a devastating toll on his psyche.  In the early morning of May 28, 1850, he fell into a delirium and threw himself from his bedroom window thirty feet to the street below.  He was severely injured and spent weeks incapacitated, and walked with a severe limp for a year afterwards; he never fully recovered from his injury.  His beloved father passed away in September of that same year, compounding his misery.

His mental faculties degraded further over the next couple of years until, in July of 1852, he was confined to a straight jacket and taken to an asylum for psychiatric treatment. As one can imagine from the era, the treatment he received was cruel and punishing, and Mayer himself would later refer to it as unscientific and barbarous.  He was finally released in September of 1853, and returned to limited medical practice.  His psychological problems persisted, on and off, for the rest of his life.  He fortunately was able to visit an asylum in Kennenberg on a strictly volunteer basis where he received better treatment.  But he had fallen completely silent on matters of science, and would remain so for many years.

John Tyndall: hero.

He may have been completely forgotten for the rest of his life if not for the almost heroic efforts of other physicists. In 1862, the Irish physicist John Tyndall was preparing a treatise on the phenomenon of heat and, like any good physicist, wanted to know everything that he possibly could on the subject. He had heard of Mayer’s work, and asked a pair of German colleagues if they could send him any and all of it that they could find.  Both colleagues replied, and one of them, Rudolf Julius Emanuel Clausius, an extremely important physicist in his own right, sent copies of Mayer’s papers along.

Clausius first wrote to Tyndall announcing that he would be forwarding the memoirs, but commented that he doubted that Tyndall would find anything useful in them. But before passing them along, he read them himself, and he reversed course entirely. He wrote to Tyndall, “I must here retract the statement, in my last letter, that you would not find
much matter of importance in Mayer’s writings; I am astonished at the multitude of beautiful and correct thoughts which they contain.”

Tyndall was in turn also greatly impressed, and reintroduced Mayer’s thoughts to the world in a spectacular fashion.  On June 6, 1862, he gave a lecture to the Royal Institution on the subject of “Force” (i.e. energy). In his concluding remarks, he said (taken from the Popular Science Monthly):

To whom, then, are we indebted for the striking generalizations of this evening’s discourse? All that I have laid before you is the work of a man of whom you have scarcely ever heard. All that I have brought before you has been taken from the labors of a German physician, named Mayer. Without external stimulus, and pursuing his profession as town physician in Heilbronn, this man was the first to raise the conception of the interaction of natural forces to clearness in his own mind. And yet he is scarcely ever heard of in scientific lectures, and even to scientific men his merits are but partially known. Led by his own beautiful researches, and quite independent of Mayer, Mr. Joule published his first paper on the ‘ Mechanical Value of Heat,’ in 1843 ; but in 1842 Mayer had actually calculated the mechanical equivalent of heat from data which a man of rare originality alone could turn to account. From the velocity of sound in air, Mayer determined the mechanical equivalent of heat.

These statements led to a vehement backlash in the British scientific community, which had up to that point proudly proclaimed that the theory of energy and heat was in its entirety a British invention. Tyndall, however, was up to the challenge, and met each of their objections in turn; he also, wisely, made it very clear that he was not discounting the importance of Joule’s work, but simply pointing out that there was more credit to be shared. The whole history of this fight is worth exploring in detail in another post, but suffice to say that important physicists on the European continent backed up Tyndall, and the whole controversy served largely to draw even more attention to the important work of Mayer.  It was a 19th century example of the Streisand effect!

The Copley Medal of 1902, awarded to Joseph Lister, via Wikipedia.

It should be noted that recognition had started to come to Mayer in small but definite ways before Tyndall’s efforts.  The German-Swiss chemist Christian Friedrich Schönbein apparently recognized the significance of Mayer’s work in the late 1850s, and visited and befriended him. In 1858, possibly due to this friendship, Mayer was given a diploma of membership in a Swiss natural science association. But the attention brought by Tyndall and colleagues truly opened the door at last for success.  In 1869, he received the Poncelet Prize of the French Academy of Science, in the second year of its existence, an award given for distinguished work in pure or applied mathematics and mechanics. In 1871, he was awarded the Copley Medal of the Royal Society of London, “For his researches on the mechanics of heat; including essays on: – 1. The force of inorganic nature. 2. Organic motion in connection with nutrition. 3. Fever. 4. Celestial dynamics. 5. The mechanical equivalent of heat.” The medal was delivered to Mayer while he was recuperating in the asylum again, along with a letter from Tyndall, which reportedly made the struggling scientist beam. And honorary degrees were awarded him from numerous cities such as Munich, Vienna, Tunis, Halle, and Frankfurt, as well as from his alma mater in Tübingen.

The mention of “celestial dynamics” is worth addressing. In 1848, he published a paper with this title, further elaborating on his ideas of energy conservation. He estimated how long the sun would continue to burn in the absence of any additional source of energy, and found that it should expire in 5000 years. Considering this, he postulated that it gained new energy from the impact of meteorites. He was wrong, of course, but such calculations were the first steps in investigating and understanding the true nuclear source of the sun’s energy.

So fortunately, Mayer was able to get recognition for his groundbreaking efforts in his lifetime, although they came only after Mayer had suffered greatly.  Mayer himself is said to have never truly recovered from his illness and tragedy, though he did publish a number of short papers once he had been accepted into the scientific community. One wonders, though, how much different, and perhaps more beautiful, the history of the subject would have been had he been treated justly from the beginning.

Mayer passed away after an extended illness on March 20, 1878. He daughter stated that he was cheerful and happy in his last moments, a final respite in a turbulent and often unfair life.

But one thing that can never be taken away from Mayer is the priority of his discovery.  And it is amazing how this entire epic was sparked by a simple observation by a doctor about a patient’s blood.

A bust of Mayer that was erected in the garden of the Polytechnic Academy in Stuttgart in 1889, by the Association of German Civil Engineering.  From the September, 1891 issue of “Industrial Refrigeration.”


Robert Mayer memorial, in Heilbronn. By Gabriele Delhey.


¹ This discussion is based on a description given in Thomas Thomson’s A System of Chemistry, published in 1818.

² I used a trio of sources for the history of Mayer’s life.  “Julius Robert Mayer,” The Locomotive 26 (1906), 206; “Julius Robert Mayer,” The Popular Science Monthly 15 (1879), 397; R.B. Lindsey, Julius Robert Mayer (Pergamon, Oxford, 1973).

³ Mayer’s original paper was in German, but it was reprinted with an English translation in the Philosophical Magazine, November 1862, 371.


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