1 “THE GREATEST OF ALL GENERALIZATIONS”
One morning in late August 1847, James Prescott Joule, a wealthy Manchester brewer but also a distinguished physicist, was walking in Switzerland, near Saint-Martin, beneath the Col de la Forclaz, in the south of the country, not too far from the Italian border. On the road between Saint-Martin and Saint-Gervais he was surprised to meet a colleague, William Thomson, a fellow physicist, later even more distinguished as Lord Kelvin. Thomson noted in a letter the next day to his father—a professor of mathematics—that Joule had with him some very sensitive thermometers and asked if Thomson would assist him in an unusual experiment: he wanted to measure the temperature of the water at the top and bottom of a local waterfall. The request was particularly unusual, Thomson suggested in his letter, because Joule was then on his honeymoon.
The experiment with waterfalls came to nothing. There was so much spray and splash at the foot of the local cataract that neither Joule nor Thomson could get close enough to the main body of water to make measurements. But the idea was ingenious and it was, moreover, very much a child of its time. Joule was homing in on a notion that, it is no exaggeration to say, would prove to be one of the two most important scientific ideas of all time, and a significant new view of nature.
He was not alone. Over the previous few years as many as fifteen scientists, working in Germany, Holland, and France as well as in Britain, were all thinking about the conservation of energy. The historian of science Thomas Kuhn says that there is “no more striking instance of the phenomenon known as simultaneous discovery than conservation of energy.” Four of the men—Sadi Carnot in Paris in 1832, Marc Seguin in Lyon in 1839, Carl Holtzmann in Mannheim in 1845, and Gustave-Adolphe Hirn in Mulhouse in 1854—had all recorded their independent convictions that heat and work are quantitatively interchangeable. Between 1837 and 1844, Karl Mohr in Koblenz, William Grove and Michael Faraday in London, and Justus von Liebig in Giessen all described the world of phenomena “as manifesting but a single ‘force,’ one which could appear in electrical, thermal, dynamical, and many other forms but which could never, in all its transformations, be created or destroyed.”1
And between 1842 and 1847, the hypothesis of energy conservation was publicly announced, says Kuhn, by four “widely scattered” European scientists—Julius von Mayer in Tübingen, James Joule in Manchester, Ludwig Colding in Copenhagen, and Hermann von Helmholtz in Berlin, all but the last working in complete ignorance of the others.
Joule and his waterfalls apart, perhaps the most romantic of the different stories was that of Julius von Mayer. For the whole of 1840, starting in February, Julius Robert von Mayer served as a ship’s physician on board a Dutch merchantman to the East Indies. The son of an apothecary from Heilbronn, Württemberg, he was a saturnine, bespectacled man who, in the fashion of his time, wore his beard under—but not actually on—his chin. Mayer’s life and career interlocked in intellectually productive yet otherwise tragic ways. While a student he was arrested and briefly imprisoned for wearing the colors of a prohibited organization. He was also expelled for a year and spent the time traveling, notably to the Dutch East Indies, a lucky destination for him, as it turned out. Mayer graduated in medicine from the University of Tübingen in 1838, though physics was really his first love, and
that was when he enlisted as a ship’s doctor with the Dutch East India Company. The return to the East was to have momentous consequences.
On the way there, in the South Atlantic, off South Africa, he observed that the waves that were thrown about during some of the wild storms that the three-master encountered were warmer than the calm seas. That set him thinking about heat and motion. Then, during a stopover in Jakarta in the summer of 1840, he made his most famous observation. As was then common practice, he let the blood of several European sailors who had recently arrived in Java. He was surprised at how red their blood was—he took blood from their veins (blood returning to the heart) and found it was almost as red as arterial blood. Mayer inferred that the sailors’ blood was more than usually red owing to the high temperatures in Indonesia, which meant their bodies required a lower rate of metabolic activity to maintain body heat. Their bodies had extracted less oxygen from their arterial blood, making the returning venous blood redder than it would otherwise have been.2
Heat and Motion Are the Same
Mayer was struck by this observation because it seemed to him to be self-evident support for the theory of his compatriot, the chemist and agricultural specialist Justus von Liebig, who argued that animal heat is produced by combustion—oxidation—of the chemicals in the food taken in by the body. In effect, Liebig was observing that chemical “force” (as the term was then used), which is latent in food, was being converted into (body) heat. Since the only “force” that enters animals is their food (their fuel) and the only form of force they display is activity and heat, then these two forces must always—by definition—be in balance. There was nowhere else for the force in the food to go.
Mayer originally tried to publish his work in the prestigious Annalen der Physik und Chemie. Founded in 1790, the Annalen der Physik
was itself a symptom of the changes taking place. By the 1840s it was the most important German journal of physics, though many new journals proliferated in that decade. The Annalen’s editor since 1824, Johann Christian Poggendorff, a “fact-obsessed experimentalist and scientific biographer,” had a very firm idea of what physics was. By the middle of the century, there had emerged “a distinctive science of physics that took quantification and the search for mathematical laws as its universal aims.” (This, it will be recalled, is what drew Mary Somerville to the subject.) Poggendorff could make or break scientific careers. All the more so because he edited the Annalen for fifty-two years, until he died in 1877.
Owing to a number of basic mistakes, however, due to his poor knowledge of physics, Mayer’s paper was rejected by Poggendorff. Disappointed but undeterred, he broached his ideas to the physics professor at Tübingen, his old university, who disagreed with him but suggested some experiments he might do to further develop his ideas. If what Mayer was proposing was true, the professor said, if heat and motion are essentially the same, water should be warmed by vibration, the same thought that had occurred to Joule.
Mayer tried the experiment, and found not only that water is warmed by vibration (as he had spotted, months before, aboard the merchantman), but that he was able to measure the different forces—vibration, kinetic energy, and heat. These results, “Remarks on the Forces of Inanimate Nature,” were therefore published in the Annalen der Chemie und Pharmacie in 1842, and it was here that he argued for a relationship between motion and heat, that “motion and heat are only different manifestations of one and the same force [which must] be able to be converted and transformed into one another.” Mayer’s ideas did not have much impact at the time, no doubt because he was not a “professional” physicist, though obviously enough the editor of the Annalen der Chemie und Pharmacie thought them worth printing. That editor was none other than Justus von Liebig.3
“Interwoven into One Great Association”
These experiments, ideas, and observations of Mayer and Joule did not come quite out of the blue. Throughout the early nineteenth century, and apart from Liebig’s observations, provocative experimental results had been obtained for some time. In 1799, Alessandro Volta, in Como, north Italy, had stunned the world with his invention of the battery, in which two different metals, laid alternately together in a weak solution of salt, like a multilayered sandwich, generated an electric current. In 1820 Hans Christian Ørsted, in Copenhagen, had noticed that a magnetized compass needle was deflected from magnetic north when an electric current from a battery was switched on and off and passed through a wire near the needle. Five months later, in September that same year, in London, Michael Faraday, working in his basement laboratory in the Royal Institution in Albemarle Street, repeated Ørsted’s experiment, and found the same result. Then he moved on to new ground. He brought together a cork, some wire, a glass jar, and a silver cup. He inserted the wire into the cork and put some water in a jar with mercury lying at the bottom. Then he floated the cork in the water, in such a way that the end of the wire in the cork made contact with the mercury. Faraday next fixed the top of the wire into an inverted silver cup with a globule of mercury held under its rim. When connected to a battery, this comprised a circuit that would allow the wire to flex without breaking the flow of electricity. Next, he brought up a magnet near the wire—and it moved. He repeated the action on the other side of the wire, with the same result.
Now came a crucial adjustment. He fixed the magnet in a glass tube and arranged the other contents so that the wire on its cork in the mercury could revolve around it when the current was switched on. Then he joined the circuit and—flick-flick-flick—the wire did a jig around the magnet. Faraday, we are told, did a jig of his own around the workbench.4
In Volta’s battery, chemical forces produced electricity, Ørsted
had demonstrated a link between electricity and magnetism, and in Faraday’s experiments, electricity and magnetism together produced movement. On top of this, the new technology of photography, invented in the 1830s, used light to produce chemical reactions. Above all, there was the steam engine, a machine for producing mechanical force from heat. Steam technology would lead to the most productive transformations of all, at least for a time. During the 1830s and 1840s the demand for motive power soared. In an age of colonial expansion, the appetite for railways and steamships was insatiable, and these needed to be made more efficient, with less and less leakage of power, of energy.
But Thomas Kuhn also observed that, of these twelve pioneers in the conservation of energy, five came from Germany itself, and a further two came from Alsace and Denmark—areas of German influence. He put this preponderance of Germans down to the fact that “many of the discoverers of energy conservation were deeply predisposed to see a single indestructible force at the root of all natural phenomena.” He suggested that this root idea could be found in the literature of Naturphilosophie. “Schelling, for example [and in particular], maintained that magnetic, electrical, chemical and finally even organic phenomena would be interwoven into one great association.” Liebig studied for two years with Schelling.5
A final factor, according to science historian Crosbie Smith, was the extreme practical-mindedness of physicists and engineers in Scotland and northern England, who were fascinated by the commercial possibilities of new machines. All of this comprised the “deep background” to the ideas of Mayer, Joule, and the others. But the final element, says John Theodore Merz (1840–1922) in his four-volume History of European Thought in the Nineteenth Century (1904–12), was that the unification of thought that was brought about by all those experiments and observations “needed a more general term . . . a still higher generalisation, a more complete unification of knowledge . . . this greatest of all exact generalisations [was] the conception of energy.”6
Nature’s Currency System: “Continual Conversion”
The other men who did most, at least to begin with, to explore the conservation of energy—Joule and William Thomson in Britain, Hermann von Helmholtz and Rudolf Clausius in Germany—fared better than Mayer, though there were interminable wrangles in the mid-nineteenth century as to who had discovered what first.
Joule (1818–89), born into a brewing family from Salford, had a Victorian—one might almost say imperial—mane, hair which reached almost as far down his back as his beard did down his front: his head was awash in hair. He is known for just one thing, but it was and is an important thing and was one for which he conducted experiments over a number of years to provide an ever more accurate explanation.
As a young man he had worked in the family’s brewery, which may have ignited his interest in heat. This interest was no doubt fanned all the more when he was sent to study chemistry in Manchester with John Dalton. Dalton was famous for his atomic theory—the idea that each chemical element was made up of different kinds of atoms, and that the key difference between different atoms was their weight. Dalton thought that these “elementary elements” could be neither created nor destroyed, based on his observations which showed that different elements combined to produce substances which contained the elements in set proportions, with nothing left over.
With his commercial background, Joule was always interested in the practical end of science—in the possibility of electric motors, for instance, which might take over from steam. That didn’t materialize, not then anyway, but his interest in the relation between heat, work, and energy did eventually pay off. “Eventually,” because Joule’s early reports, on the relationship between electricity and heat, were turned down by the Royal Society—just as Mayer’s ideas had been turned down by Poggendorff—and Joule was forced to publish in the less prestigious
Philosophical Magazine. But he continued his experiments, which, by stirring a container of water with a paddle wheel, sought to show that work—movement—is converted into heat. Joule wrote that “we consider heat not as substance but as a state of vibration.” (This implicit reference to movement echoes his idea about the different temperatures of water at the top and bottom of waterfalls, and Mayer’s observation that storm waves were warmer than calm seas.) Over his lifetime, Joule sought ever more accurate ways to calculate just how much work was needed to raise the temperature of a pound of water by one degree Fahrenheit (the traditional definition of “work”). Accuracy was vital if the conservation of energy was to be proved.7
And gradually people were won over. For example, Joule addressed several meetings of the British Association for the Advancement of Science, in 1842, and again in 1847. In between these meetings, Mayer published his observations, about body heat and blood color, but Joule had the momentum and, in the BAAS, the stage. The BAAS was well established then, having been founded in 1831, in York, modeled on the German Gesellschaft Deutscher Naturforscher und Ärzte. It held annual meetings in different British cities each year. But Joule needed only one individual in his BAAS audience to find what he had to say important, and that moment came in the 1847 meeting, when his ideas were picked up on by a young man of twenty-one. He was then named William Thomson but he would, in time, become better known as Lord Kelvin.
Just as Joule befriended the older Dalton, so he befriended the younger Thomson. In fact, he worked with Thomson on the theory of gases and how they cool and how all that related to Dalton’s atomic theory. Joule was in particular interested in nailing the exact average speed at which molecules of gas move (movement that was of course related to their temperature). He focused on hydrogen and treated it as being made up of tiny particles bouncing off one another and off the walls of whatever container they were held in. By manipulating the temperature
and the pressure, which affected the volume in predictable ways, he was able to calculate that, at a temperature of sixty degrees Fahrenheit and a pressure of thirty inches of mercury (more or less room temperature and pressure), the particles of gas move at 6,225.54 feet per second. Similarly, with oxygen, the molecules of which weigh sixteen times those of hydrogen, and since the inverse-square lawI
applies, in ordinary air the oxygen molecules move at a quarter of the speed of hydrogen molecules, or 1,556.39 feet per second. To pin down such infinitesimal activity was an amazing feat, and Joule was invited to address the Royal Society and elected a fellow, more than making up for his earlier rejection.
Joule shared a lot with Thomson, including his religious beliefs, which played an important part in the theory for some people. The principle of continual conversions or exchanges was established and maintained by God, he argued, as a basis for “nature’s currency system,” guaranteeing a dynamic stability in “nature’s economy.” “Indeed the phenomena of nature, whether mechanical, chemical, or vital, consist almost entirely in a continual conversion of attraction through space, living force, and heat into one another. Thus it is that order is maintained in the universe—nothing is deranged, nothing ever lost . . . the whole being governed by the sovereign will of God.”8
Thomson followed on where Joule left off. Born in Belfast in June 1824, he spent almost all his life in university environments. His father was professor of mathematics at the Royal Belfast Academical Institution, a forerunner of Belfast University, and
William and his brother were educated at home by their father (his brother James also became a physicist). Their mother died when William was six, and in 1832 their father moved to Glasgow, where again he became professor of mathematics. As a special dispensation, both his sons were allowed to attend lectures there, matriculating in 1834, when William was ten. After Glasgow, William was due to go to Cambridge, but there were concerns that graduating in Glasgow might “disadvantage” his prospects down south, so although he passed his finals and the MA exams a year later, he did not formally graduate. At the time, he therefore signed himself as William Thomson BATAIAP (Bachelor of Arts To All Intents And Purposes).
William transferred to Cambridge in 1841, graduating four years later, having won a number of prizes and publishing several papers in the Cambridge Mathematical Journal. He then worked for a while in Paris, familiarizing himself with the work of the brilliant French physicist Sadi Carnot (who had died tragically young), and then joined his father in Glasgow, as professor of natural philosophy. James Thomson Senior, who had worked tirelessly to bring his son to Glasgow, died shortly afterwards from cholera. But William remained at Glasgow from when he was appointed professor (in his mid-twenties) until he retired at seventy-five, when, “to keep his hand in,” he enrolled as a student all over again. This, as historian John Gribbin rejoices in saying, made him “possibly both the youngest student and the oldest student ever to attend the University of Glasgow.”9
Thomson was much more than a scientist. He had a hand in the first working transatlantic telegraph, between Great Britain and the USA (after other attempts had failed), which transformed communication almost as much as, and maybe more than, the Internet of today. He made money from his scientific and industrial patents, to such an extent that he was, first, knighted in 1866 and then made Baron Kelvin of Largs in 1892 (the River Largs runs through the campus of Glasgow University).
“A Principle Pervading All Nature”
Thomson echoed Joule in his theology as well as his science. “The fact is,” he wrote, “it may I believe be demonstrated that work is lost to man irrecoverably [when conduction occurs] but not lost in the material world.” Employing the word “energy” for the first time since 1849, says Crosbie Smith, Thomson expressed his analysis in theological and cosmological terms. “Although no destruction of energy can take place in the material world without an act of power possessed only by the supreme ruler, yet transformations take place which remove irrecoverably from the control of man sources of power which, if the opportunity of turning them to his own account had been made use of, might have been rendered available.”10
God, as “supreme ruler,” had established this law of “energy conservation,” but nonetheless there were sources of energy in nature (such as waterfalls) that could be made use of—in fact, it was a mistake for Thomson if they were not made use of, because that implied waste, the Presbyterian’s abiding sin. Finally, nature’s transformations had a direction which only God could reverse: “The material world could not come back to any previous state without a violation of the laws which have been manifested to man.”
In purely scientific terms, however, Kelvin’s most important contribution was to make thermodynamics (as the conservation of energy became more formally known) a consolidated scientific discipline by the middle of the century. Together with Peter Guthrie Tait, another Scot, their joint work, Treatise on Natural Philosophy (1867), was both an attempt to rewrite Newton and to place thermodynamics and the conservation of energy at the core of a new science—nineteenth-century physics. Kelvin may even have been the first person to use the word “energy” in this new sense. In 1881 he said, “The very name energy, though first used in the present sense by Dr. Thomas Young about the beginning of this century, has only come into use practically after the doctrine which defines it had . . . been raised from a mere formula of
mathematical dynamics to the position it now holds of a principle pervading all nature and guiding the investigator in every field of science.”11
Tait and Kelvin planned a second volume of their book, never written, which would have included “a great section on ‘the one law of the Universe’, the Conservation of Energy’.”
On top of all this, Kelvin established the absolute scale of temperature, which also stems from the idea that heat is equivalent to work (as Joule had spent his lifetime demonstrating) and that a particular change in temperature is equivalent to a particular amount of work. This carries the implication that there is in fact an absolute minimum possible temperature: –273° Fahrenheit, now written as 0°K (for Kelvin), when no more work can be done and no more heat can be extracted from a system.
“The Human Engine Is Little Different from the Steam Engine”
Thomson’s ideas were being more or less paralleled in Germany by the work of Hermann von Helmholtz and Rudolf Clausius. With hindsight, everything can be seen as pointing toward the theory of the conservation of energy, but it still required someone to formulate these ideas clearly, and that occurred in the seminal memoir of 1847 by von Helmholtz (1821–94). In On the Conservation of Force he provided the requisite mathematical formulation, linking heat, light, electricity, and magnetism by treating these phenomena as different manifestations of “energy.”
Like Kelvin, von Helmholtz had many fingers in many pies. He was born in Potsdam when it was “a one-class” garrison town, and von Helmholtz’s parents were part of the intellectual middle class (his father was a high school teacher) and no fewer than twenty-three godparents graced Hermann’s baptism. His early studies were funded by a Prussian Army scholarship in the course of which he studied physiology. In return for his education being paid for, von Helmholtz served as a medical officer before becoming, in 1849, associate professor of physiology at
the University of Königsberg. In 1850 he invented the ophthalmoscope, which allows the far wall of the eye to be inspected, and contributed many papers on optics and the physiology of stereoscopic perception, as well as such subjects as fermentation. But von Helmholtz fits in here because of his 1847 pamphlet, “On the Conservation of Force.”12
Like Mayer, he had sent his paper to Poggendorff at the Annalen der Physik but was rebuffed, and he chose to publish his pamphlet privately. And, like Mayer, von Helmholtz approached the problem of energy from a medical perspective. His previous physiological publications had all been designed to show how the heat of animal bodies and their muscular activity could be traced to the oxidation of food—that the human engine was little different from the steam engine. He did not think there were forces entirely peculiar to living things but insisted instead that organic life was the result of forces that were “modifications” of those operating in the inorganic realm. He had parallel ideas not just with Mayer and Kelvin, but with Liebig too.
In the purely mechanical universe envisaged by von Helmholtz there was an obvious connection between human and machine work. For him, Lebenskraft, as the Germans called the life force, was no more than an expression of “organisation” among related parts which carried no implication of a vital force.13
“The idea of work is evidently transferred to machines from comparing their performances with those of men and animals, to replace which they were applied. We still reckon the work of steam engines according to horse power.” Which led him to the principle of the conservation of force: “We cannot create mechanical force, but we may help ourselves from the general storehouse of Nature. . . . The possessor of a mill claims the gravity of the descending rivulet, or the living force of the moving wind, as his possession. These portions of the store of Nature are what give his property its chief value.” His idea of the “store” of nature complemented Joule’s notion of the “currency” of nature.
In making his case without any experimental evidence (which
the members of the Berlin Academy noticed, while being impressed by his presentation), von Helmholtz “first established a clear distinction between theoretical and experimental physics.”
The Tendency Toward Increasing Disorder
While Mayer and von Helmholtz, being doctors, came to the science of work through physiology, von Helmholtz’s fellow Prussian Rudolf Clausius approached the phenomenon, like his British and French contemporaries, via the ubiquitous steam engine.
In later life Clausius had a rather forbidding appearance: a very high forehead, rather hard, piercing eyes, a thin, stern mouth, and a white beard fringing his cheeks and chin. In fairness to him, this sternness may have reflected nothing more than the pain he was in continuously after suffering a wound in the Franco-Prussian War of 1870–71. At the same time he was a fervent nationalist and that may also have been a factor.
He was born in January 1822, in Köslin, Prussia (now Koszalin, Poland), where his father was a pastor with his own private school. The sixth of his father’s sons, Rudolf attended the family school for a few years, before transferring to the gymnasium at Stettin (now Szczecin, Poland) and then going on to the University of Berlin in 1840. To begin with he was drawn to history and studied under the great Leopold von Ranke, which may have had something to do with his subsequent nationalism. But Clausius switched to math and physics. In 1846, two years after graduating from Berlin, he entered August Böckh’s seminar at Halle, and worked on explaining the blue color of the sky. The theory Clausius came up with about the blue of the sky, and its redness at night and morning, was based on faulty physics. He thought it was caused by reflection and refraction of light, whereas John Strutt, later Lord Rayleigh, was able to show it was due to the scattering of light.14
But Clausius’s special contribution was to apply mathematics
far more deeply than any of his predecessors, and his work was an important stage in the establishment of thermodynamics and theoretical physics. His first paper on the mechanical theory of heat was published in 1850. This was his most famous work and we shall return to it in just a moment. He advanced rapidly in his career, at least to begin with, being invited to the post of professor at the Royal Artillery and Engineering School at Berlin in September 1850 on the strength of his paper, then moving on to the Polytechnikum in Zurich, where he remained for some time despite being invited back to Germany more than once. He eventually accepted a chair at Würzburg in 1869, moving on to Bonn after only a year, when the Franco-Prussian War intervened. A “burning nationalist,” as someone described him, Clausius volunteered, despite being just short of his fiftieth birthday, and was allowed to assume the leadership of an ambulance corps, which he formed from Bonn students, helping to carry the wounded at the great battles of Vionville and Gravelotte—the Germans suffered twenty thousand casualties at the latter battle. During the hostilities, Clausius was wounded in the leg, which caused him severe pain and disability for the rest of his life.15
He was awarded the Iron Cross in 1871.
Unlike Mayer and von Helmholtz, Clausius did succeed in having his first important paper, “On the Moving Force of Heat, and the Laws Regarding the Nature of Heat That Are Deducible Therefrom,” accepted by the Annalen. It appeared in 1850 and its importance was immediately recognized. In it he argued that the production of work resulted not only from a change in the distribution of heat, as Sadi Carnot—the French physicist and military engineer—had argued, but also from the consumption of heat: heat could be produced by the “expenditure” of work. “It is quite possible,” he wrote, “that in the production of work . . . a certain portion of heat may be consumed, and a further portion transmitted from a warm body to a cold one: and both portions may stand in a certain definite relation to the quantity of work produced.” In doing this he stated two fundamental principles,
which would become known as the first and second laws of thermodynamics.
The first law may be illustrated by how it was later taught to Max Planck, the man who, at the turn of the twentieth century, would build on Clausius’s work. Imagine a worker lifting a heavy stone onto the roof of a house. The stone will remain in position long after it has been left there, storing energy until at some point in the future it falls back to earth. Energy, says the first law, can be neither created nor destroyed. Clausius, however, pointed out in his second law that the first law does not give the total picture. In the example given, energy is expended by the worker as he lifts the stone into place, and is dissipated in the effort as heat, which among other things causes the worker to sweat. This dissipation, which Clausius was to term “entropy,” was of fundamental importance, he said, because although it did not disappear from the universe, this energy could never be recovered in its original form. Clausius therefore concluded that the world (and the universe) must always tend towards increasing disorder, must always add to its entropy.16
Clausius never stopped refining his theories of heat, becoming in the process interested in the kinetic theory of gases, in particular the notion that the large-scale properties of gases were a function of the small-scale movements of the particles, or molecules, which comprised the gas. Heat, he came to think, was a function of the motion of such particles—hot gases were made up of fast-moving particles, colder gases of slower particles. Work was understood as “the alteration in some way or another of the arrangement of the constituent molecules of a body.”
This idea that heat was a form of motion was not new. In addition to the ideas of Joule and Mayer, the American Benjamin Thompson had observed that heat was produced when a cannon barrel was bored, and in Britain Sir Humphry Davy had likewise noted that ice could be melted by friction. What attracted Clausius’s interest was the exact form of motion that comprised heat. Was it the vibration of the internal particles, was
it their “translational” motion as they moved from one position to another, or was it because they rotated on their own axes?
Clausius’s second seminal paper, “On the Kind of Motion That We Call Heat,” was published in the Annalen in 1857. He argued that the heat of a gas must be made up of all three types of movement and that therefore its total heat ought to be proportional to the sum of these motions. He assumed that the volume occupied by the particles themselves was vanishingly small and that all the particles moved with the same average velocity, which he calculated as being hundreds—if not thousands—of meters per second (building on Joule). This prompted the objection from several others that his assumptions and calculations could not be right, since otherwise gases would diffuse far more quickly than they were known to do. He therefore abandoned that approach, introducing instead the concept of the “mean free path”—the average distance that a particle could travel in a straight line before colliding with another one.17
The Unification of Electricity, Magnetism, and Light
Clausius was elected a fellow of the Royal Society in 1868, and awarded its Copley Medal in 1879. Others were attracted by his efforts, in particular James Clerk Maxwell in Britain, who published “Illustrations of the Dynamical Theory of Gases” in the Philosophical Magazine in 1860, making use of Clausius’s idea of the mean free path.
According to one of his biographers, James Clerk Maxwell had a scientific idea “that was as profound as any work of philosophy, as beautiful as any painting, and more powerful than any act of politics or war. Nothing would be the same again.” These are big things to say, but, in a nutshell, Maxwell conceived four equations that, at a stroke, united electricity, magnetism, and light and in so doing showed that visible light was only a small band in a vast range of possible waves, “which all travelled at the same speed but vibrated at different frequencies.”18
Physicists, says the same
biographer, honor Maxwell alongside Newton and Einstein, yet among the general public “for some reason he is much less well known.” This was all carried through while Mary Somerville was still alive and, in effect, helped make Connexions out of date.
Maxwell was brought up for the first eight years of his life on his father’s estate at Glenlair, in the Galloway region of southwest Scotland. His family were well connected—his grandfather was a composer, as well as having various official municipal jobs, and a fellow of the Royal Society. An uncle was a friend of James Hutton and had illustrated Hutton’s seminal work, Theory of the Earth (see chapter 2). Maxwell’s parents had married late; their first child had died in infancy, and James’s mother was almost forty when he was born.
His late arrival made his parents indulgent. It became plain soon enough that he was an exceptional child, intent on finding out how everything worked and having an explanation for everything. As a result, as a boy he learned how to knit, bake, and weave baskets. Like Humphry Davy and Michael Faraday he shared the nineteenth-century scientist’s fascination with writing poetry, though none was published in his lifetime, and it is not hard to see why. One read:
Then Vn/Vt the tangent will equal
Of the angle of starting worked out in the sequel.
Another poem actually had a graph in it.
The Vale of Urr, where Glenlair was situated, was known to its residents as Happy Valley, but, when she was forty-seven, Maxwell’s mother, Frances, contracted abdominal cancer and died soon after undergoing an operation (performed without anesthetic). The loss brought father and son together, but there was a problem with James’s education. It had been planned that he would be educated at home until he was thirteen, but now his father had too many calls on his time. An aunt who lived in the
capital came to the rescue and took him in, which enabled him to attend Edinburgh Academy, one of the best schools in Scotland.19
It was not, at first, a success. Because the school was almost full, James was obliged to enter a class of boys a year older than he was, who had all been at the school for months, and had established their own conventions and cliques. On top of which they mostly came from well-heeled Edinburgh families—when they saw his rough-hewn country clothes and heard his rural accent, they picked on him mercilessly. He wore (to begin with) a loose tweed tunic, with a frilly collar, and square-toed shoes with brass buckles. No one had ever seen clothing like this in Edinburgh, where the pupils wore close-fitting tunics and slim shoes. The boys nicknamed him “Dafty.”
School continued difficult for a while, not helped by a hesitancy of speech verging on, but not quite, a stutter. And it contrasted strongly with his aunt’s house, which he loved. It was full of books, drawings, and paintings, and his cousin—his aunt’s daughter—was a rising artist, who even Landseer had complimented.
Then things started to improve. In his second year, the speed with which he mastered geometry impressed his teachers and, no less, his classmates. In the academy at that time, boys sat in order of ability, so he was now moved forward to sit with more congenial company, and began to make friends. Among them was Peter Guthrie Tait—P. G. Tait was to become one of Scotland’s finest physicists and, as we have seen, coauthor, with William Thomson, of the Treatise on Natural Philosophy.20
At the age of fourteen Maxwell published his first paper. It was about how to draw an oval. Everyone knows that if you attach string to a pin and a pencil to the other end, you can draw a perfect circle. Maxwell observed that if you have two pins, with one piece of string attached to each, and then push a pencil against the string, so that it remains taut, you can draw a perfect oval. Then he undid one end of the string and looped it around the free pin, and got another oval, egg-shaped. He played with more curves
and studied their mathematical relationships, coming up with some formulas to describe what he had found. Some of this had been worked out earlier by no less a figure than René Descartes, but Maxwell’s system was simpler and was judged good enough to be read before the Royal Society of Edinburgh. Because he was so young, the paper had to be read for him.
He was a devout Christian, of the austere Presbyterian kind, something that paid off when he visited other Presbyterian relatives in Glasgow. One of his cousins, Jemima, had married Hugh Blackburn, professor of mathematics at Glasgow and a great friend of William Thomson, the new professor of natural philosophy there. Maxwell and Thomson struck up a friendship that would continue for years.
As mentioned in the Introduction, in mid-nineteenth-century Britain the word “scientist” had not yet come into common use. Physicists and chemists called themselves “natural philosophers” and biologists called themselves “natural historians.” Maxwell decided to enroll at Edinburgh University, to study mathematics, natural philosophy, and logic. He matriculated at sixteen.
This was when Maxwell himself began to experiment, aided by the practice of the Scottish universities of closing from late April to early November to allow students home to help with the farming. He read and read and read and carried out his first experiments at Glenlair, developing an interest in electromagnetism and polarized light. These DIY adventures did more than develop his experimental skill, though that was important. They helped give him a deep feeling for nature’s materials and processes that later pervaded his theoretical work. While in Edinburgh he produced two more papers for the Royal Society there. So, when he left for Cambridge at the age of nineteen, he had a solid body of knowledge, a handful of publications to his name, and some valuable and potentially influential friends in the world of academia and science.
He started at Peterhouse but found it dull and moved to Trinity, which was more congenial and much more mathematically
minded (the master at the time being William Whewell). In Cambridge Maxwell joined the class of the famous (in mathematical circles) “senior wrangler maker,” William Hopkins—wranglers being those who gained first-class degrees in the mathematical tripos, which all had to take. The reward for wranglers was lifelong recognition in whatever field they chose. The tripos was an arduous seven-day affair, six hours a day, and James came second, after E. J. Routh, who went on to be a remarkable mathematician, with a function named after him, the routhian. (P. G. Tait, Maxwell’s erstwhile Edinburgh Academy friend, had been senior wrangler two years before.)21
With the tripos out of the way, Maxwell was now free to give rein to the ideas that had been brewing in his mind over his two stints as an undergraduate. There were two aspects of the physical world he wanted to explore. One was the process of vision, particularly the way we see colors, and the other was electricity and magnetism.
In his color research he had an early breakthrough, finding that there is a fundamental difference between mixing pigments, as one does with paints or dyes, and mixing lights, as one does when spinning a multicolored disc. Pigments act as extractors of color, so that the light you see after mixing two paints is whatever color the paints have failed to absorb. In other words, mixing pigments is a subtractive process, whereas mixing lights is additive—so that, for instance, blue and yellow do not make green, as they do with pigments, but pink. And by experiment he was able to show that there are, in light terms, three primary colors—red, blue, and green—and that it is possible to mix them in different proportions to obtain all the colors of the rainbow. This was a major advance and is the theory behind the colors in color television, for example.
At the same time, he was getting to grips with electricity and magnetism, and in 1855 the first of his three great papers appeared. Michael Faraday had thought of lines of force as discrete tentacles (analogous to the lines of iron filings that form
around a magnet). Maxwell now conceived them as merged into one continuous essence, which he called “flux”—the higher the density of flux at any particular location, the stronger the electrical or magnetic force there. And he grasped moreover that the electric and magnetic forces between bodies vary inversely as the square of their distance apart—much as Newton had said of gravity.22
In this way, lines of force became the “field,” and this was the concept that set Maxwell apart and put him on a par with Newton and Einstein. More than that, he would build on it six years later with his concept of electromagnetic waves.
In between times, his father fell ill, and James was forced to spend time nursing him. But it wasn’t enough: he needed a post nearer home. This cropped up when he was offered the position as professor of natural philosophy at Marischal College in Aberdeen, one of the colleges that would, not much later, become Aberdeen University. The post buoyed both father and son, but it had its drawbacks. James later wrote to a friend, “No jokes of any kind are understood here. I have not made one for 2 months, and if I feel one coming on I shall bite my tongue.” But it wasn’t all hopeless, as James found the daughter of the college principal exactly to his taste, proposed, and was accepted.23
In June 1858 he and Katherine were married and then, a few months later, he read the paper by Clausius about the diffusion of gases. The problem, which several people had pointed out, was that, to explain the pressure of gases at normal temperatures, the molecules would have to move very fast—several hundred meters a second, as Joule had calculated. Why then do smells—of perfume, say—spread relatively slowly about a room? Clausius proposed that each molecule undergoes an enormous number of collisions, so that it is forever changing direction—to carry a smell across a room the molecule(s) would actually have to travel several kilometers.
Clausius had assumed that, at any given moment, all the molecules would travel at the same speed. He knew that couldn’t
be the correct answer, but he couldn’t think of anything better. Maxwell was also stymied at first, but then he had a brain wave. At a stroke, says Basil Mahon, it “opened the way to huge advances in our understanding of how the world works.”
Maxwell saw that what was needed was a way of representing many motions in a single equation, a statistical law. He devised one that said nothing about individual molecules but accounted for the proportion that had the velocities within any given range. This was the first-ever statistical law in physics, and the distribution of velocities turned out to be bell-shaped, the familiar normal distribution of populations about a mean. But its shape varied with the temperature—the hotter the gas, the flatter the curve and the wider the bell.
This was a discovery of the first magnitude, which would in time lead to statistical mechanics, a proper understanding of thermodynamics, and to the use of probability distributions in quantum mechanics. This alone was enough to put Maxwell in the first rank of scientists. The Royal Society certainly thought so, awarding him the Rumford Medal, its highest award for physics. No less important in the long run, King’s College London was looking for a professor of natural philosophy—James entered his name and was appointed. And he still had more than one breakthrough in him.
King’s, in the Strand, just north of the Thames, had been founded in 1829 as an Anglican alternative to the nonsectarian University College, a mile further north, which was itself intended as an alternative to the strictly Church of England Oxbridge universities. Unlike the traditional courses, to be found at Aberdeen and Cambridge, King’s’ courses were much more modern.
Being in London meant that Maxwell could attend the meetings of the Royal Society, and the Royal Institution, where he was able to cement his friendship with Faraday. They had corresponded a great deal, but now at last met and struck up a genial friendship. And Maxwell homed in on his final great insight.
In his paper, “On Faraday’s Lines of Force,” he showed how he
had found a way of representing the lines of force mathematically as continuous fields, and had made a start towards forming a set of equations governing the way electrical and magnetic fields interact with one another. But that was still only part of the picture. Picture is in fact the wrong word here, because it is at this point that physics began to enter a world where the familiar visual analogies break down. The image of a “field” is easy enough to imagine in itself, but what Maxwell was struggling to explain, in his equations, could only be explained with difficulty in ordinary language, and this came home to him—and then to everyone—in his 1862 paper, where he concluded, dramatically, and using the mathematics that he had himself created, that light is also a form of electromagnetic disturbance and, moreover, could be understood as both a wave and a beam of particles. This was unheard of, inexplicable when put into language, but made sense in mathematics.24
In fact, Maxwell derived four equations that between them “summed up everything that it is possible to say about classical electricity and magnetism.” Which is why, among physicists, if not yet the general public, Maxwell is placed on a par with Newton. “Between them, Newton’s laws and his theory of gravity and Maxwell’s equations explained everything known to physics at the end of the 1860s.” Maxwell’s achievement was the greatest breakthrough since Newton’s Principia Mathematica in 1687.25
As if all this were not enough, Maxwell’s equations contained within them the implication that there must be other forms of electromagnetic waves with much longer wavelengths than those of visible light. Their discovery would not be long in coming.
The final chapter in Maxwell’s extraordinary career arrived when he was invited to accept an important new professorship at Cambridge. The duke of Devonshire, who was chancellor of the University, had offered a large sum of money to build a new laboratory for teaching and research, which was to compete with the best of what then existed on the Continent, especially in Germany. Cambridge was being left behind in experimental
science, not just in France and Germany, but by many of the new British universities as well.
Maxwell was not over keen to accept Cambridge’s offer. His theories were so new that not everyone understood them and he couldn’t be certain of his reception more generally. But many of the younger physicists at Cambridge, who had kept up with his work, implored him to come, and that settled it.26
Time Becomes a Property of Matter
Clausius had assumed that every particle in a gas traveled at the same average velocity. Maxwell relied on the new science of statistics to calculate a random distribution of particle velocities, arguing that the collisions between particles would result in a distribution of velocities about a mean rather than an equalization. (Just what these particles were was never settled, not then, though Maxwell was convinced they were “proof of the existence of a divine manufacturer.”)
The statistical—probabilistic—element introduced into physics in this way was a very controversial and yet fundamental advance. In his 1850 paper, Clausius had drawn attention in the second law of thermodynamics to the “directionality” of the heat flow—heat tends to pass from a hotter to a colder body. He had not at first bothered with the implications of the irreversibility or otherwise of processes, but in 1854 he argued that the transformation of heat into work and the transformation of heat from a higher temperature into heat of a lower temperature were in effect equivalent and that in some circumstances they could be counteracted—reversed—by the conversion of work into heat, where heat would flow from a colder to a warmer body. This, for Clausius, only emphasized the difference between reversible (man-made) and irreversible (natural) processes: a decayed house never puts itself back together, a broken bottle never spontaneously reassembles.27
It was only later, in 1865, that Clausius proposed the term
“entropy” (from the Greek word for “transformation”) for the irreversible processes. The tendency for heat to pass from warmer to colder bodies could now be described as an instance of the increase in entropy. In doing this, Clausius emphasised the directionality of physical processes. Entropy was a counterpart of energy “because the two concepts had analogous physical significance.” Clausius set out the two laws of thermodynamics as follows: “The energy of the universe is constant” and “The entropy of the universe tends to a maximum.” Time, in some mysterious way, had become a property of matter.
For some people, the second law had a much greater significance than even Clausius understood. William Thomson thought that the irreversibility that was such a feature of the second law—the dissipation of energy—also implied a “progressivist cosmogony,” one that moreover underlined the biblical view about the transitory character of the universe. In particular, Thomson drew the implication from the second law that the universe, known by then to be cooling, would “in a finite time” run down and become uninhabitable. Von Helmholtz had also noticed this implication of the second law. It was only in 1867 that Clausius himself, who had by then moved back to Germany from Zurich, acknowledged the “heat death” of the universe.28
The Marriage of Mathematics and Physics
The statistical notions aired by Clausius and Maxwell attracted the attention of the Austrian physicist Ludwig Boltzmann. Boltzmann (1844–1906) was born in Vienna during the night of the Mardi Gras Ball, between Shrove Tuesday and Ash Wednesday, a coincidence which, he half-jokingly complained, helped to explain the frequent and rapid mood swings that tossed him between unalloyed happiness and deep depression. The son of a tax official, he was short and stout, with curly hair that made him look younger than he was. His fiancée called him her “sweet fat darling.”
He took his doctorate at the University of Vienna, then taught
at Graz before moving to Heidelberg and afterward Berlin, where he studied under Bunsen, Kirchhoff, and von Helmholtz. In 1869, at the age of twenty-five, he was appointed to the chair of theoretical physics in Graz. After that, Boltzmann had a very unsettled career—he changed professorships numerous times, more than once because he couldn’t get on with colleagues. The constant arguments depressed Boltzmann and he attempted suicide for the first time.
Finally, in 1901, after all this chopping and changing, Boltzmann returned to Vienna to the chair he had vacated in one of his arguments with colleagues and which had not been filled in the meantime. In addition he was given a course to teach on the philosophy of science, which quickly became very popular, so much so that he was invited to the palace of Emperor Franz Joseph.
This was impressive, but Boltzmann’s main achievement lay in two famous papers that described in mathematical terms the velocities, spatial distribution, and collision probabilities of molecules in a gas, all of which determined its temperature (heat and motion again). The mathematics were statistical, showing that—whatever the initial state of a gas—Maxwell’s velocity distribution law would describe its equilibrium state. This became known as the Maxwell-Boltzmann distribution. Boltzmann also produced a statistical description of entropy.29
In 1904 Boltzmann went to the United States and visited the World’s Fair at St. Louis, where he gave some lectures before going on to visit Berkeley and Stanford. While there he behaved oddly—people couldn’t make out whether his elevated manner was an illness or pretentiousness. He returned home and went on vacation with his family to Duino, near Trieste. While his wife and daughter were swimming he hanged himself. No one can be certain whether his general instability was the cause of his suicide, or the continual attacks on his ideas. What is certain, unfortunately, is that he couldn’t have been aware, at the time of his death, that his ideas would very soon receive experimental confirmation.
What is important about the work of Mayer, Joule, and von Helmholtz, and in particular Clausius, Maxwell, and Boltzmann, is that—whether one can follow the mathematics or not—they brought probability into physics. How can that be? Matter definitely exists, transformations (as when water freezes, say) obey invariant laws. What can probability have to do with it? This was the first appearance of “strangeness” in physics, heralding the increasingly weird twentieth-century quantum world. These early physicists also made “particles” (atoms, molecules, or something else, not yet clearly understood) integral to the behavior of substances.30
The understanding of thermodynamics was the high point of nineteenth-century physics, and of the early marriage between physics and mathematics, building richly on Mary Somerville’s previous ideas. It signaled an end to the strictly mechanical Newtonian view of nature. It would prove decisive in leading to a spectacular new form of energy: nuclear power. This all stemmed, ultimately, from the concept of the conservation of energy. I
. The inverse-square law applies when some force or energy is radiated evenly from a point source into three-dimensional space, like a lightbulb, say. Since the surface area of a sphere is proportional to the square of the radius, the emitted radiation (light in this example) is spread out over an area that is increasing in proportion to the square of the distance from the source. When you sit next to a light to read by, the phenomenon shows itself. If you move your chair so that you are twice as distant from the source of light as you were initially, the light diminishes by the square of that—i.e., 22: it is four times as dim.