Faraday, Maxwell, and the Electromagnetic Field

by Nancy Forbes

  Sessions with Fawcett no doubt took Maxwell back to the hours spent with his father mulling over plans for the extension to Glenlair. The current project was on a far grander scale, but the design process—outline sketches, discussion, fuller sketches, and, eventually, detailed drawings—was probably much the same. The outcome of these sessions was a fine building, plain and functional yet in keeping with the much-older buildings of the rest of the university. It seemed to exude confidence about its place in the scheme of things and went on to serve Cambridge well for over one hundred years, becoming the site of many important discoveries, such as those of the electron and the structure of DNA.

  Plans were agreed and work got under way. Meanwhile, there were lectures to give and Maxwell had nowhere to call his own. He wrote to Lewis Campbell:

  I have no place to erect my chair, but move about like the cuckoo, depositing my notions in the Chemical lecture room 1st term; in the Botanical in lent, and in Comparative Anatomy in Easter.*

  There was also, of course, the customary inaugural lecture, Maxwell's third. Through some misunderstanding, a group of senior professors came to his first ordinary lecture to undergraduates, believing it to be the formal one, and Maxwell, with a twinkle in the eye, solemnly explained to them the difference between the Fahrenheit and Centigrade scales of temperature. In the real inaugural lecture, he developed themes that he had already expounded in Aberdeen and London: his job was to teach students to think for themselves, to seek out truth, and to recognize and expose falsity in all its forms. He also emphasized once more the essential role of practical work in science. One passage clearly evokes Faraday:

  When we shall be able to employ in scientific education, not only the trained attention of the student, and his familiarity with symbols, but the keenness of his eye, the quickness of his ear, the delicacy of his touch, and the adroitness of his fingers, we shall not only extend our influence over a class of men who are not fond of cold abstractions, but, by opening at once all the gateways of knowledge, we shall ensure the association of the doctrines of science with those elementary sensations which form the obscure background of all our conscious thoughts, and which lend a vividness and relief to ideas, which, when presented as mere abstract terms, are apt to fade entirely from the memory.

  And, in a further passage that might have been composed by Faraday himself, Maxwell said:

  We may find illustrations of the highest doctrines of science in games and gymnastics, in travelling by land and by water, in storms of the air and of the sea, and wherever there is matter in motion.

  Building progress was reasonable but seemed frustratingly slow to everyone waiting to get experiments under way. Even Maxwell's patience was tested by the gas men, whom he described as “the laziest and the most permanent of the gods that have been hatched under heaven.” At last all was ready and the laboratory opened in the spring of 1874. It was to have been called the Devonshire, after its founder, but shortly before the inauguration a decision was made to call it instead the Cavendish Laboratory. This way, the name would commemorate not only the duke, whose family name was Cavendish, but also his great uncle Henry Cavendish, one of the greatest British scientists. Henry Cavendish was a very strange character. Extremely shy, he had lived as a recluse, venturing out only occasionally to scientific meetings and communicating with his domestic staff by written notes. Women servants were fired if they allowed themselves into his sight. He rarely spoke. An acquaintance said: “He probably uttered fewer words in the course of his life than any man who lived to four score years, not at all excepting the monks of La Trappe.” His genius lay in performing amazingly accurate experiments using simple but brilliantly effective apparatus of his own design. With his faithful servant Richard as laboratory assistant, he had achieved remarkable experimental results, for example, proving that water was not an element but a compound, and measuring the density of Earth to within 2 percent of its correct value. He had also played an important, though indirect, part in establishing the career of Michael Faraday—along with Count Rumford he had been one of the founding fathers of the Royal Institution.

  Henry Cavendish had been shy even of publishing. Some of his work had been published, but much had not, and at around the time of the laboratory's inauguration the duke handed Maxwell a great pile of papers—his great uncle's accounts of electrical experiments from 1781 to 1791—with a request to edit them for belated publication. No doubt Maxwell's heart sank—he already had more than enough to do—but he undertook to look through the papers. He could hardly refuse the university's great benefactor, but it wasn't entirely a forced decision. He had a high regard for the duke, who, like himself, had been second wrangler and first Smith's Prize man, and they shared a deeper bond—both felt passionately about the importance of practical work in scientific education. The duke's generous gift of a new laboratory had not been hailed with unalloyed joy in the country, or even in Cambridge. Skeptics and cynics abounded. Even the progressive scientific journal Nature commented disparagingly that, with luck, the laboratory might in ten years reach the standard of a provincial German university. And many thought that although scientific research was a necessary activity, demonstration experiments were pointless. Among them was the celebrated Cambridge tutor Isaac Todhunter. One day, Maxwell bumped into Todhunter in the street outside the laboratory and asked him to come in to see an example of conical refraction, a phenomenon that was much talked about but rarely witnessed because it was so hard to set up. Todhunter replied: “No thank you. I've been teaching it all my life and I don't want my ideas upset by seeing it now.”

  Maxwell was no politician but saw clearly how important it was for the laboratory to establish a reputation with some early successes. From our distant perspective it may seem surprising that he didn't straightaway set about trying to verify his own theory of electromagnetism by detecting displacement currents or electromagnetic waves, but such experiments were too difficult and risky for the purpose. He set up instead a research program focused mainly on high-precision measurements of fundamental physical quantities. This was unspectacular but important work and it brought in solid results. One such experiment was to verify Ohm's law, which said that no matter what amount of current flowed in a conductor, the ratio of current to voltage remained constant. Maxwell's student, George Chrystal from Aberdeen, vanquished the doubters by demonstrating that the law held true for a vast range of currents within one part in a million million.

  Political considerations aside, Maxwell saw his job as helping science to advance on a broad front. He had many interests besides electromagnetism and, in any case, had no thought of establishing a “Maxwell school.” Defying the gloomy predictions, he had no difficulty in attracting a highly talented set of young researchers, some of whom had left good jobs elsewhere to come and work with him. His style was not at all dictatorial—everyone was encouraged to come up with his own ideas and solve his own problems—but Maxwell kept a fatherly eye on progress, and advice from one of the greatest scientific minds of all time was dispensed with unfailing generosity and humor. His students loved him, and many went on to have distinguished careers elsewhere. For example, Richard Glazebrook was the first director of the National Physical Laboratory of Great Britain; Donald MacAlister became president of the General Medical Council and principal of Glasgow University; William Napier Shaw became known as the father of modern meteorology; and Ambrose Fleming became Guglielmo Marconi's right-hand man and invented the thermionic valve. There was also John Henry Poynting, who, as we'll see, made an important contribution to the theory of electromagnetism. Funds were tight, but Maxwell donated his own equipment to the laboratory and bought several hundred pounds’ worth of new apparatus from his own pocket during his tenure.

  Maxwell's Treatise on Electricity and Magnetism was published in 1873. Still in print, it is probably, after Newton's Principia Mathematica, the most renowned book in physics. Before the Treatise, students and scholars had no substantial books to help with thei
r studies, just scattered writings. Now they had a book that covered everything. In a thousand crisply written pages, Maxwell set out all that he knew. At first sight, it looks like a textbook—and, indeed, most modern textbooks are derived from it—but it was drawn up many years before its subject matter became standard in university courses, and it was really more of an explorer's report, written for those who wanted not only to follow but to venture further. This audience included himself: Maxwell was still exploring and was partway through an extensive revision of the book at the time of his death. The subject matter was complex, difficult, and new, so it is not surprising that early readers found it hard going. Like all of Maxwell's work, it was thorough: it covered not only theory but also practical applications, for example, setting out how to make galvanometers and the procedure to be followed when correcting compass readings on iron ships. It was emphatically not a showcase for Maxwell's own theory of electromagnetism. The theory was there, but you had to hunt for it. The topic of electromagnetism is not introduced until article 475 in volume 2, and the sublime creation on which his whole theory depends, the displacement current, is slipped in with no fanfare in article 610. This can be fairly interpreted as an example of Maxwell's excessive modesty, but it is also a reminder to us that the Treatise, even now a wonderfully authoritative text on electricity and magnetism, was written at a time when Maxwell's own theory was only a contender, generally less favored than Weber's action-at-a-distance theory. And although the theory was wholly encapsulated in its equations, it was then like a vehicle chassis without a body—for example, it predicted electromagnetic waves but gave no indication of how they might be produced or detected in a laboratory. We'll see in the next chapter how a few men from the next generation were able to see the latent power and beauty of the theory, to take it further, and to cast it in a cogent form that came to command universal assent.

  Only after several decades did the Treatise begin to achieve the acclaimed status it holds today. Its early readers faced more obstacles than those inherent in Maxwell's own theory of the electromagnetic field. To many, the whole of electricity and magnetism was an arcane topic on the fringes of known science, and they had to wrestle with what seems today to be an idiosyncratic selection and arrangement of topics. For example, as early as article 8 on page 7, the reader is faced with the heading “Discontinuity of a Function of More Than One Variable” and presented with a difficult equation. And most of the first third of the book is taken up with a minutely detailed and highly mathematical account of electrostatics. What really brought the Treatise to prominence were the rapid advances in electrical communications and in electrical power and machines in the late nineteenth and early twentieth centuries. Technology had forged ahead: it needed trained scientists and engineers, and those charged with the training found a superb text in Maxwell's Treatise. They didn't need the long chapters on such things as spherical harmonics, but Maxwell had already set out very clearly much of what they did need. The Treatise was ahead of its time.

  Henry Cavendish had also been ahead of his time. When Maxwell looked through Cavendish's accounts of electrical experiments performed a hundred years earlier, he was astonished. It was like finding a dozen unpublished plays by Shakespeare. Among a string of stupendous results, Cavendish had demonstrated the inverse-square law for the force between electrical charges more effectively than Coulomb, after whom the law was named. He had also discovered Ohm's law fifty years before Ohm and twenty years before Volta produced the first electric battery. His method was simple and painful. He connected two wires to the oppositely charged parts of a Leyden jar and grasped both wires in one hand. He then repeated the procedure with various circuit arrangements, each time judging the strength of the current by measuring how far up his arm he could feel the shock. One day, a distinguished American, Samuel Pierpoint Langley, visited the Cavendish and was horrified to find Maxwell and some of the students with sleeves rolled up, repeating the experiment. He declined an invitation to join in and remarked: “When an English man of science comes to the United States we do not treat him like that.”

  Maxwell could have delegated the huge task of editing Cavendish's papers, but he decided to take on the job himself, “walking the plank” with them, as he put it to William Thomson. In retrospect, it seems extraordinary that Maxwell chose to spend time on this work when he could have spent it on his own research. He, of course, saw it differently. His own ideas on electromagnetism and other topics were still developing—“decocting” in the subconscious—and he didn't know that he had only five years to live. Cavendish's work was an important part of scientific history, and it needed to be presented in a proper way. Maxwell went to great trouble to write an interesting and informative narrative, even checking such details as whether the Royal Society premises in the 1770s had a garden.

  As always, Maxwell took everything in his stride. Along with editing the Cavendish papers and repeating many of the experiments, he took on the scientific editorship of the ninth edition of the Encyclopaedia Britannica jointly with T. H. Huxley. He also wrote some brilliant and original papers, refereed many more by other authors, reviewed books, and wrote another of his own. Matter in Motion is a pedagogical gem. In only 122 pages, it explains the principles of dynamics with crystal clarity in plain language with no more than a few equations. Yet nothing is dumbed down: the reader is required to think. In contrast, his paper “On Boltzmann's Theorem on the Average Distribution of a Number of Material Points” contained some of his most complex mathematics. It laid the foundations for the development by Ludwig Boltzmann and Josiah Willard Gibbs of statistical mechanics, a difficult but useful set of methods by which the properties of a substance can be deduced from the behavior, en masse, of its molecules.

  Though still shy with strangers, Maxwell left an impression on everyone he met. Lewis Campbell described the effect:

  One great charm of Maxwell's society was his readiness to converse on almost any topic with those he was accustomed to meet…no one talked to him for five minutes without having some perfectly new ideas set before him; some so startling as to confound the listener, but always such as to repay a thoughtful examination.

  The only direct record we have of Maxwell's spoken words is from the text of his formal lectures, and most of these, by their nature, give us only the faintest hint of what his companions enjoyed every day. Perhaps one extract can take us a little closer. When giving a public lecture about Alexander Graham Bell's new invention, the telephone, he talked of Bell's father, who had lived in Edinburgh and was an expert in elocution. In his still strong Galloway accent, Maxwell told his audience:

  His whole life had been employed in teaching people to speak. He brought the art to such perfection that, though a Scotchman, he taught himself in six months to speak English. I regret extremely that when I had the opportunity in Edinburgh I did not take lessons from him.1

  Maxwell was rarely seen in Cambridge without a dog, and his terrier Toby was quite at home in the laboratory. Lewis Campbell reports that Toby always became uneasy when he heard electric sparks, but when Maxwell called him to his station, he would sit down between his master's feet and allow the sparks to be applied to his back, growling all the time in an odd manner but not showing any real signs of discomfort. There wasn't an ounce of cruelty here—Campbell reports elsewhere in his book of his friend's way with animals and love of all creatures.2

  Maxwell enjoyed Cambridge life, just as he had done as a student. When time allowed, he attended an essay club that was like a senior version of the Apostles. In one essay he challenged the widely held belief that scientific laws implied a mechanical universe whose whole future is predictable, given sufficient knowledge of its present state. In doing so, he gave a remarkable outline of chaos theory—a hundred years before mathematicians began to develop the subject:

  When the state of things is such that an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some futu
re time, the condition of the system, whether at rest or in motion, is said to be stable; but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the condition of the system is said to be unstable.

  It is manifest that the existence of unstable conditions renders impossible the prediction of future events, if our knowledge of the present state is only approximate and not accurate.3

  Maxwell was a relative newcomer to the senior ranks at the university, but his influence soon spread well beyond his own department. People who were at first hostile or indifferent to the new laboratory began to recognize its achievements in research and were won over by Maxwell's enthusiasm and unaffected charm. In only a few years, the Cavendish had established itself, and science at Cambridge had entered a new age and set an example for other universities to follow in experimental physics.

  The Maxwells lived in a comfortable house in Scroope Terrace, close to the laboratory. Katherine began to suffer from poor health and was for a while seriously ill, though the condition was never properly diagnosed. It was James's turn to be the nurse; he slept in a chair at her bedside for three weeks, yet carried on his work at the laboratory with apparently undiminished vigor. Perhaps because of her illness, Katherine wasn't always welcoming to Maxwell's colleagues and students, so he sometimes conducted business at the laboratory that might have been done more congenially over a cup of tea at home. One can see how Katherine acquired her reputation as a “difficult” woman. We will never have the full picture, but it is clear that, whatever the tensions, James and Katherine remained unswervingly devoted to one another.