Faraday, Maxwell, and the Electromagnetic Field

by Nancy Forbes

  Four months of every year were spent at Glenlair. Maxwell wrote many of his articles and reviews there and kept in touch with those working in the laboratory during the vacations. For some of the short summer courses, he allowed female students to attend—a remarkable departure for Cambridge. When the Maxwells were at Glenlair, the postman from the Kirkpatrick Durham post office was kept busy, as usual, and many of the packages contained proofs to be checked and corrected. Publishers became the second occupational group, after gas men, to arouse Maxwell's wrath. They seemed determined to economize by cutting every corner, and he reckoned their maxim must be “a stitch in nine save time.”

  In 1877, Maxwell had begun to suffer from heartburn. For a year and a half, the problem was no more than a nuisance—he ran the laboratory, gave his lectures, and wrote his articles, all with his usual sparkle. But then colleagues began to notice a loss of spring in his step and Maxwell did something he had never done before. He turned down a request to write an article for T. H. Huxley's English Men of Science, pleading overwork. In 1879, he and Katherine went to Glenlair as usual for the summer, hoping that he would recover with rest. By September, Maxwell was getting violent pains, but he insisted that a visit by his assistant William Garnett and his wife should go ahead as planned. Garnett was shocked at the change in Maxwell's appearance but marveled at the care he still gave to his guests and at the way he still conducted prayers each evening for the whole household. Maxwell showed Garnett the oval curves and other memorabilia from his childhood, and walked with him down to the river, pointing out where he used to swim and to sail in the washtub. This was the longest walk he had taken for weeks. When Katherine took the guests for a drive, he couldn't go with them because the shaking of the carriage was unbearably painful.

  Maxwell suspected that he had contracted the same type of abdominal cancer that had killed his mother at the same age. They sent for a specialist, Dr. Sanders, from Edinburgh. He arrived on October 2 and confirmed the worst: Maxwell couldn't expect to live much longer than a month. Sanders suggested he travel to Cambridge, where Dr. Paget, an expert in palliative care, would be able to make his last few weeks as bearable as possible for both Katherine and James. Fortunately, Katherine was having a respite from her own illness and was able to organize packing and travel. On arrival at Cambridge, Maxwell was barely able to walk the few yards from the train to a carriage, but once in the care of Dr. Paget, his pain was much relieved and for a few days he felt better. Word spread among friends and colleagues, and there was even some hope that he might recover. Such hopes were soon dashed. His remaining strength began to ebb, and it was clear to all that he was dying. Dr. Paget later described this time:

  As he had been in health, so was he in sickness and in the face of death. The calmness of his mind was never once disturbed. His sufferings were acute for some days after his return to Cambridge, and, even after their mitigation, were still of a kind to try severely any ordinary patience and fortitude. But they were never spoken of by him in a complaining tone. In the midst of them his thoughts and consideration were rather for others than for himself. Neither did the approach of death disturb his habitual composure…. A few days before his death he asked me how much longer he could last. This inquiry was made with the most perfect calmness. He wished to live until the expected arrival from Edinburgh of his friend and relative Mr. Colin Mackenzie. His only anxiety seemed to be about his wife, whose health had for a few years been delicate and had recently become worse….

  His intellect also remained clear and apparently unimpaired to the last. While his bodily strength was ebbing away to death, his mind never wandered or wavered, but remained clear to the very end. No man ever met death more consciously or more calmly.

  Maxwell's local doctor at Glenlair, Dr. Lorraine, had written to Dr. Paget with notes on the patient's condition. This, of course, was standard practice, but there was more. Dr. Lorraine had such admiration for his patient that he included a spontaneous tribute.

  I must say he is one of the best men I have ever met, and a greater merit than his scientific achievements is his being, so far as human judgement can discern, a most perfect example of a Christian Gentleman.

  He was, indeed, one of the best men that anyone could meet, a genius without vanity, someone who made people feel good about themselves and the world in general. His own reflections on his life were characteristically modest. He told his friend and Cambridge colleague Professor Hort:

  What is done by what I call myself is, I feel, done by something greater than myself in me…. I have been thinking how very gently I have always been dealt with. I have never had a violent shove in all my life. The only desire which I can have is like David to serve my own generation by the will of God, and then fall asleep.

  James Clerk Maxwell died on the November 5, 1879. Katherine and his friend and cousin Colin Mackenzie were at his bedside. The next Sunday, a memorial service was held at St. Mary's Church in Cambridge. The task of giving a voice to the all-pervading sense of loss fell to the Reverend H. M. Butler, one of Maxwell's friends from his student days, who was now headmaster of Harrow School. He chose his metaphor well:

  It is not often, even in this great home of thought and knowledge, that so bright a light is extinguished as that which is now mourned by many illustrious mourners, here chiefly, but also far beyond this place.

  Maxwell's old schoolfellow P. G. Tait echoed this thought, adding a typically combative touch of his own. He wrote in Nature,

  I cannot adequately express in words the extent of the loss which his early death has inflicted not merely on his personal friends, on the University of Cambridge, on the whole scientific world, but also, and most especially, on the cause of common sense, of true science, and of religion itself, in these days of much vain-babbling, pseudo-science, and materialism. But men of his stamp never live in vain; and in one sense at least they cannot die. The spirit of Clerk Maxwell still lives with us in his imperishable writings, and will speak to the next generation by the lips of those who have caught inspiration from his teachings and example.

  Maxwell's body was taken to Glenlair and buried next to those of his father and mother in Parton churchyard. Katherine was buried there seven years later, and the four share a headstone. A simple plaque by the roadside in front of the church now describes his life and achievements, and it concludes:

  A good man, full of humour and wisdom, he lived in this area and is buried in the ruins of the old Kirk in this Churchyard.

  A few miles away, the ruin of the house of Glenlair stands with empty windows and roofless gables, having been destroyed by fire in 1929.4

  Butler and Tait had not exaggerated the sense of loss inflicted by Maxwell's early death. He had been in full flow, and who knows what else he might have gone on to do. But he has been an inspiration to physicists and engineers ever since. Perhaps more than any other scientist's, his personality comes over in his work: he seems to elicit a unique blend of wonder and affection. An editorial in the Times Educational Supplement in 1925 summed this aspect up very well. It said:

  To scientists, Maxwell is easily the most magical figure of the 19th century.

  In the story of the electromagnetic field, Maxwell was a lone actor in his time, just as Faraday had been in his. Not until the following generation did anyone else truly understand what Faraday and Maxwell had been trying to tell them. The way was then led by a small band of individuals with disparate but complementary talents who came to be called the “Maxwellians.” Oliver Heaviside was one of these. As we will see, he was a prickly individual whose criticism could be withering, but when he wrote of Maxwell he seemed to have joy in his heart:

  A part of us lives after us, diffused through all humanity, more or less, and all through nature. This is the immortality of the soul. There are large souls and small souls…. That of a Shakespeare or Newton is stupendously big. Such men live the best part of their lives after they are dead. Maxwell is one of these men. His soul will grow for long to
come, and hundreds of years hence will shine as one of the bright stars of the past, whose light takes ages to reach us.5

  “One scientific epoch ended and another began with James Clerk Maxwell.”

  —Albert Einstein

  “From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell's discovery of the laws of electrodynamics.”

  —Richard P. Feynman

  Einstein's and Feynman's words aptly convey the momentous effect that James Clerk Maxwell's theory of the electromagnetic field has had on science and technology, and indeed on human history. But scientific theories rarely spring fully formed from the minds of their originators. It often happens that a following generation of scientists has to refine and codify a theory before it becomes assimilated into the common body of scientific knowledge—a process that can take decades. So it was with Maxwell's theory.

  Although Maxwell had set out the theory as clearly as he could in his paper “A Dynamical Theory of the Electromagnetic Field” and later in his Treatise on Electricity and Magnetism, almost nobody understood it during his lifetime. Not only was the mathematics difficult, but its whole approach was based on Michael Faraday's theoretical vision, which still seemed bizarre to most physicists. Maxwell's seminal work on another topic—the statistical properties of matter—was being taken forward by two men of genius, Ludwig Boltzmann and Josiah Willard Gibbs, but when Maxwell died, his theory of electromagnetism sat for a while like an exhibit in a glass case, admired by some but out of reach.

  Maxwell himself made no attempt to verify the theory experimentally while at the Cavendish. This is often attributed, with good grounds, to his self-effacing modesty, but, as we have seen, there was a further reason: the new laboratory needed to establish a reputation with some early successes, and experiments to find displacement currents or electromagnetic waves would have been too risky for the purpose. By the end of the 1870s, the laboratory's reputation had been secured, and one might have expected Maxwell's successor, Lord Rayleigh, to take up the challenge—he was a great admirer of Maxwell, and ten years earlier, as John William Strutt, he had been one of the young fellows who had begged Maxwell to accept the post. Rayleigh, though, had his own priorities as director of the laboratory. The first was to set the enterprise on a sound financial footing. Maxwell had been reluctant to pump the duke for more money, but Rayleigh, a hardheaded man of business as well as a scientist, had no such compunction. At length, the duke agreed, Rayleigh put in some money of his own, and the laboratory acquired the equipment it needed to build on its early successes. Rayleigh also introduced systematic training in laboratory techniques, moving on from Maxwell's laissez-faire approach, and he needed what time was left for his own research—among other outstanding achievements, he discovered argon and explained how scattering of light makes the sky appear blue. Whether from want of interest or from want of ideas, neither Rayleigh nor any of his researchers at the Cavendish made a serious and sustained attempt to confirm or develop Maxwell's theory. When the advance came, it was not from Cambridge.

  Oliver Heaviside was born in 1850, the youngest of four sons in a respectable but poor family living in London. Scarlet fever at the age of eight left him partially deaf, and he found himself excluded from street games because he couldn't hear what the other boys were saying. He was thrown on his own resources and began to build a defense against the barbs of the world. A stubborn independence took hold of him, almost against his will, and held its grip until the day he died. He did well at school, despite defying its rote-teaching methods, but university was beyond the family's resources, and instead he spent two years studying on his own at home, reading everything he could find on scientific topics. This privilege hadn't been extended to his brothers, who were working and contributing to the household income: Oliver's uncle by marriage, Charles Wheatstone, had interceded on his behalf. This is the same Wheatstone who, twenty years before, had fled from giving a lecture at the Royal Institution, and thereby caused Faraday to give his impromptu talk on “Ray-vibrations.” Wheatstone had also, with his partner William Fothergill Cooke, built the first commercial telegraph in Britain and expanded the business at a prodigious rate. With Wheatstone's recommendation, Oliver got his first (and only) job, at the age of eighteen as a telegraph operator with the Danish-Norwegian-English Telegraph Company at the excellent salary of £150 a year.

  The company had just laid its first North Sea cable, and Heaviside was posted to its main Danish operating station at Fredericia. He was soon enraptured by the telegraph and the mystery of how it worked. The equipment used visual cues rather than sound, so his partial deafness was no handicap. He quickly mastered Morse code, but the part of the job he really enjoyed was fixing faults. Suboceanic telegraphers were the technological elite of the day; operators were free to experiment with advanced equipment like rheostats, bridges, shunts, and condensers; indeed, they had to, simply to keep the traffic flowing. Heaviside became a star troubleshooter, though for him each problem was not merely something to be fixed but a means of probing the strange ways of electricity, which often baffled even the most experienced of his colleagues. At the age of twenty, he was posted to the company's English headquarters at Newcastle, given an increase in salary, and promoted to chief operator.

  He continued to shine, on one occasion saving the company money by accurately locating a mid-ocean fault by some deft measurements and calculations before the cable-repair ship left shore. In his free time, he continued his studies into electricity and mathematics, and he began to write scientific papers. One day, he opened a book in Newcastle's public library and was captivated. From that moment, the course of his life was set. Many years later, he recalled the experience:

  I remember my first look at the great treatise of Maxwell's when I was a young man. Up to that time there was not a single comprehensive theory, just a few scraps; I was struggling to understand electricity in the midst of a great obscurity. When I saw on the table in the library the work that had just been published (1873) I browsed through it and was astonished! I read the preface and the last chapter, and several bits here and there; I saw that it was great, greater and greatest, with prodigious possibilities in its power. I was determined to master the book and set to work.1

  Heaviside's vocation was to find out all he could about electricity and spread the word. It would be a full-time job. His work for the telegraph company was now becoming routine and tiresome, with long hours spent sending and receiving telegrams, so at the age of twenty-four he resigned his post and returned to his parent's house in London to work as a full-time unpaid researcher. He could expect only a pittance from writing articles and books, but that didn't bother him. He was doing what he saw as his duty: if society chose to reward him generously for his work, that would be fine; if not, his parents and brothers would be doing their duty by supporting him. It was a near-solitary life, but he had no feeling of loneliness. As he later explained:

  There was a time indeed in my life when I was something like old Teufelsdröckh in his garret, and was in some measure satisfied with a mere subsistence. But that was when I was making discoveries. It matters not what others think of their importance. They were meat and drink and company to me.2

  One question in particular fascinated him: exactly how do electrical signals travel along wires? The transmission line became a lifetime study, and he made it his own—the theory of transmission lines today is more or less where Heaviside left it. The line could be anything from an iron wire slung on wooden poles with an earth return to a sophisticated suboceanic cable; today it would be a fiber-optic cable. Early telegraphers thought of a line simply as an inert conduit along which a battery pumped a kind of fluid called electricity, but they were puzzled at the way pulses became smeared-out when sent along suboceanic cables, requiring the signaling speed to be slowed so that each pulse could be distinguished from the ne
xt. Faraday had explained that this happened because the cable acted as a giant electrical store, or capacitor, and William Thomson had encapsulated this principle in a formula. Thomson had intended his formula to apply only to long suboceanic cables worked at low speed, but telegraphers who didn't understand the mathematics had misapplied it to high-speed land lines, with sometimes bizarre results. Tact was never in Heaviside's repertoire—he mocked the ignorance of the senior post-office engineers unmercifully in his papers and soon became their bête noire. Luckily, he found a friend in C. H. W. Biggs, the editor of the weekly trade journal the Electrician. Biggs knew he was running a risk by taking on this enfant terrible. He also knew that scarcely any of his readers could follow Heaviside's increasingly abstruse mathematical papers, but, although no mathematician himself, he sensed that here was something new and important. His support for the maverick writer eventually cost Biggs his job, but meanwhile, Heaviside forged ahead. In his hands, the transmission line became a complex piece of equipment with properties—capacitance and inductance—that corresponded to elasticity and inertia in mechanical systems, and resistance, which was akin to friction. Using these quantities, Heaviside generalized Thomson's result to produce what is still called the “telegrapher's equation.”

  Articles in the Electrician were also an outlet for Oliver's puckish sense of fun. His satirical sallies must have raised a chuckle in the editorial office because Biggs published many passages that more cautious editors would have cut out. The first paragraph of Heaviside's first article must have given Biggs some idea of what he was getting himself into.