Faraday, Maxwell, and the Electromagnetic Field Page 17
Life wasn't all work. One summer he enjoyed a memorable holiday in the Lake District, where he had been asked to join his uncle Robert's family. Robert Dundas Cay was his mother Frances's younger brother, and he had five children. Maxwell was very fond of all his Cay cousins, especially Lizzie, and this time they fell in love. She was only fourteen, but they planned to marry when she was sixteen; such marriages were not uncommon in those days. After the holiday, Maxwell walked the fifty miles home to Glenlair from the Carlisle railway station with a joyful heart, but the euphoria didn't last. Fearful of consanguinity, the family persuaded them to abandon any thought of getting married. It was a deeply wounding experience for them both, but they got on with their lives and eventually married other people.
In 1855, Maxwell was elected a fellow of Trinity College. He would now need to look for a professorship because the university required fellows to be ordained into the Church of England within seven years of election. There was no hurry, but a chance came sooner than expected. In January 1856, a letter came from James Forbes to tell him that the chair of natural philosophy at Marischal College, Aberdeen, was vacant, and to suggest that he apply. Maxwell discussed the matter at length with his father and mulled things over. It would be a jolt, after five happy years, to leave the center of the academic world for a distant northern outpost. On the other hand, he had observed the narrowing tendencies of college life at Cambridge, and it would be good to be out, feeling “the rubs of the world,” as he put it to Campbell.13 He would need to seek a job in the next few years anyway, and opportunities like this one didn't come up often. Besides, the shorter terms at a Scottish University would allow him to spend more time at Glenlair with his now-ailing father. He decided to apply. At first he had no idea how to go about it, but he soon learned that he needed to ask “swells” for testimonials. This presented no problem, but he was surprised to be asked to supply one himself for a less well-connected acquaintance who had applied for the same post.14 He did. Another candidate was his old friend P. G. Tait, who was now professor of mathematics at Belfast University but wanted to return to Scotland.
John Clerk Maxwell was buoyed by the prospect of seeing more of his son. For a while, his health, which had been declining, seemed to improve, but it took a turn for the worse during the Easter vacation, and he died peacefully early one morning after Maxwell had nursed him through a troubled night. Maxwell had lost his closest companion—he and his father had been constantly in each other's thoughts and had written almost daily when apart—but sorrow was mixed with pride. He saw the love and respect that so many people had felt for his father, and he knew how fortunate he was to have had wise and loving parents. He wrote to relations and friends, organized the funeral, and assumed his father's mantle as laird, a role he took to heart.
To the casual observer, he would have appeared little changed after his father's death. He saw to estate business, kept up his correspondence, and carried on with his scientific pursuits. But inwardly he was devastated, and those close to him could see the pain beneath the surface. Lewis Campbell later recalled the great depth of feeling that underlay Maxwell's quiet demeanor at this time. As was his way at times of great joy or sadness, Maxwell expressed his emotions in a poem. Nothing could show more plainly the love of a son for his departed parents.
I have leapt the bars of distance—left the life that late I led—
I remember years and labors as a tale that I have read,
Yet my heart is hot within me, for I feel the gentle power
Of the spirits that still love me, waiting for this sacred hour
Yes—I know the forms that meet me, but are phantoms of the brain,
For they walk in mortal bodies, and they have not ceased from pain.
Oh! those signs of human weakness, left behind for ever now,
Dearer far to me than glories round a fancied seraph's brow.
Oh! the old familiar voices! Oh! the patient waiting eyes!
Let me live with them in dreamland, while the world in slumber lies.15
Back at Cambridge, he heard that his application had been successful. At the end of the summer term, he packed up his papers, color top, magnets, prisms, and the rest of his experimental paraphernalia, and, with fond memories, left Cambridge for Glenlair. It was the first time he had returned home without his father being there to welcome him. He spent much of the summer dealing with the estate, learning its detailed workings, and planning how he might fulfill his father's wish for more improvements when funds allowed. From time to time he entertained relations and Cambridge friends, but it was the loneliest episode in his life. In seven months, he left Glenlair only once; that was to make a short trip to Belfast to arrange for his cousin William Dyce Cay to study engineering under William Thomson's brother James. He managed to fit in a little scientific work and built a version of his color box rugged enough to withstand the journey to Aberdeen. The time for that journey approached, and part of his preparation was to draft what he called “a solemn manifesto to the Natural Philosophers of the North,”16 his inaugural speech, something that was then expected of all new professors. In November 1856, he left for the Granite City.
In the space of a few months, twenty-five-year-old Maxwell had acquired two weighty responsibilities, and he was determined to discharge both of them to the best of his ability. He had taken care to make a good start as laird of Glenlair but no doubt felt a mixture of excitement and anxiety as he journeyed north, not being sure what awaited him in Aberdeen. It wasn't unusual for professors to be appointed young—Thomson had taken his chair in Glasgow at twenty-two, and Tait his in Belfast at twenty-three—but at this time Marischal College had a rather elderly collection: the youngest of Maxwell's colleagues was forty and their average age was fifty-five. The new professor must have seemed to them a mere boy, but they made him welcome—he was invited out so often that he rarely dined at his lodgings. They seemed to be pleased to have somebody young to talk to, but there was none of the free banter that Maxwell had expected. Aberdeen felt a long way from Cambridge. He wrote to Lewis Campbell:
No jokes of any kind are understood here. I have not made a joke for 2 months, and if I feel one coming on I shall bite my tongue.1
Education was, indeed, serious business and Maxwell buckled down to it alongside his rather dour colleagues. Like other Scottish universities, Marischal College aimed to provide a broad and accessible education. Its staple four-year MA course was very broad indeed, taking in Greek, Latin, mathematics, natural philosophy, natural history, moral philosophy, and logic. Like the other professors, Maxwell had complete charge not only of the lectures but also of the syllabus and the exams. Avoiding any attempt at a joke, he set out his intentions in his inaugural address:
My duty is to give you the requisite foundation and to allow your thoughts to arrange themselves freely. It is best that every man be settled in his own mind, and not be led into other men's ways of thinking under the pretence of studying science. By a careful and diligent study of natural laws I trust that we shall at least escape the dangers of vague and desultory modes of thought and acquire a habit of healthy and vigorous thinking which will enable us to recognise error in all the popular forms in which it appears and hold fast truth whether it be old or new.2
And, to be able to think for themselves, the students would need to see for themselves by doing experiments:
I have no reason to believe that the human intellect is able to weave a system of physics out of its own resources without experimental labor. Whenever the attempt had been made it has resulted in an unnatural and self-contradictory mass of rubbish.
He carefully planned his course of lectures and agreed to give extra weekly evening classes at the Mechanics’ Institution. We'll see shortly how well he succeeded.
In February 1857, he decided to send a copy of his paper “On Faraday's Lines of Force” to the great man. No doubt, he did so with some trepidation. After having read the Experimental Researches in Electricity, he felt t
remendous empathy for Faraday, but he couldn't be sure that the feeling would be returned. He was, after all, an electrical novice—in the paper he had admitted that electricity was “a science in which I have hardly made a single experiment”—yet he had marched boldly into territory that Faraday had spent much of his life studying.3 He needn't have worried. As we've seen, Faraday's response was grateful, gracious, and charming. The two had at once formed a rare bond.
A sign of the respect and trust that Faraday immediately felt for his young colleague was that he sent a paper of his own, asking for an opinion. It was the one that tentatively proposed gravitational lines of force, an idea generally thought outrageous. Faraday was aware that he was exposing himself to possible criticism by sending perhaps his most speculative paper, but he need not have worried. Busy with other work, Maxwell took his time replying but then offered a thought that must have surprised even Faraday—the idea could work if the lines of force were not attractive but repulsive. They would emanate from all the matter in the universe and two bodies in relative proximity, such as Earth and the sun, would be, as it were, in each other's shadow, and so would be pushed together. So they would appear to be attracted to one another. Moreover, the force of apparent attraction would follow an inverse-square law, and so would be indistinguishable from Newton's law of direct gravitational attraction. Faraday was impressed and grateful, but he replied apologizing for his own presumption in pressing Maxwell for a view.
It was very wrong; for I do not think any one should be called upon for the expression of their thoughts before they are prepared, and wish to give them. I have often enough to decline giving an opinion because my mind is not ready to come to a conclusion.4
Questions of professional etiquette aside, it is clear that any reserve arising from differences in age and status had been swept aside.
Maxwell took up his work on colors again, but most of his spare time in the first few months in Aberdeen was taken up by Saturn's rings. The planet Saturn with its bizarre-seeming flat rings was the most mysterious object in the night sky and St. John's College, Cambridge, had chosen it as the theme for their prestigious Adams Prize, a biennial competition that had been founded to commemorate John Couch Adams's discovery of the planet Neptune. They had asked: under what conditions (if any) would the rings be stable if they were (1) solid, (2) fluid, or (3) composed of many separate pieces of matter? It was a fearsomely difficult problem that had defeated many mathematical astronomers, including the great Pierre Simon Laplace—it seemed the examiners had set it more in hope than in expectation.
Maxwell was, like everyone, intrigued by the rings, and to him they seemed to pose a giant, real-life version of the kind of problem he had tackled in the Smith's Prize examination. By a triumph of determination as much as skill, he managed to prove that solid rings would inevitably break up, and that the same would happen to fluid ones as the tidal waves grew bigger and bigger. He had thus shown that although the rings appear to be continuous, they must consist of many separate bodies orbiting independently—exactly the structure we have now seen on fly-past pictures from the Voyager and Cassini space probes. He tidied up his mass of calculations, posted off an essay weighing 12 ounces, and hoped for the best. It turned out that his was the only entry: the problem was so difficult that no one else got far enough to make it worth sending one in. He was awarded the Adams Prize, and the name James Clerk Maxwell began to be mentioned in high academic circles. The Astronomer Royal, Sir George Airy, described Maxwell's essay as “one of the most remarkable applications of mathematics to physics that I have ever seen.”* It was, indeed, a triumph. All the mathematical methods that Maxwell used had been known for years—what was new was the combination of boldness, imagination, ingenuity, and sheer persistence that he had brought to the task.
Maxwell's jokes were, for the present, confined to letters, and Thomson, by now well established as professor of natural philosophy at Glasgow University, was one of his many correspondents. Thomson was now also a technical consultant on the Atlantic telegraph-cable project and came in for some gentle ribbing from Maxwell when the cable-laying ran into difficulties. On a visit to Glasgow by train, Maxwell wrote “The Song of the Atlantic Telegraph Company”—prompted, it seems, by the clickety-clack rhythm of the train wheels going over joints in the track. One of its verses runs:
Under the sea, under the sea,
No little signals are coming to me
Under the sea, under the sea,
Something has surely gone wrong,
And it's broke, broke, broke;
What is the cause of it does not transpire
But something has broken the telegraph wire
With a stroke, stroke, stroke,
Or else they've been pulling too strong.5
There wasn't an ounce of schadenfreude here; Maxwell was a great admirer of the project and thought the cable layers were doing a heroic job. He just couldn't resist having a little fun at their expense.
Romance was probably the last thing Maxwell expected to find in Aberdeen, but it happened. His partner in love was Katherine, daughter of the college principal, the Reverend Daniel Dewar. An invitation to dinner at the house led to many more, and the Dewars began to treat him as one of the family, even asking him to join them on a vacation. There, he proposed and Katherine accepted. It was an unusual match. Katherine Dewar was seven years his senior and appears to have taken little part in the intellectual life he enjoyed with his friends—we can even wonder whether she shared in his jokes. She has come in for harsh judgment from most writers, who report that she could be difficult and even jealous at times, but some of these impressions have originated from people who didn't know her very well, or who had their own axes to grind. As we shall see, there are points in her favor and points against. What is certain is that both had been lonely and shared the joy, and perhaps relief, in having found a lifetime companion. As was his way, Maxwell expressed his feelings in verse:
Trust me spring is very near
All the buds are swelling
All the glory of the year
In those buds is dwelling
What the open buds reveal
Tells us—life is flowing;
What the buds, still shut, conceal,
We shall end in knowing.
Long I lingered in the bud,
Doubting of the season
Winter's cold had chilled my blood—
I was ripe for treason.
Now no more I doubt or wait
All my fears are vanished,
Summer's coming dear, though late,
Fogs and frosts are banished.6
It was truly a joyful time, as is evident from the way metaphors fly even more exuberantly than usual in his letters. He had recently been best man at the wedding of Lewis Campbell, who was now an Anglican parish priest in Brighton, and naturally wanted his closest friend to do the same for him. Here, he tells Campbell of the engagement and the approximate date of the wedding, and invites him to bring his wife to visit Glenlair:
We had done with the eclipse today, the next calculation was about the conjunction. The rough approximations bring it out early in June…The first part of May I shall be busy at home. The second part I may go to Cambridge, to London, to Brighton, as may be devised. After which we concentrate ourselves at Aberdeen by way of concerted tactics. This done, we steal a march, and throw our forces into the happy valley, which we shall occupy without fear, and we only await your signals to be ready to welcome reinforcements from Brighton.
After a month's honeymoon of “sun, wind and streams” at Glenlair, Maxwell got back to work. One might be forgiven for thinking that he had abandoned electricity and magnetism, but the subject was never far from his mind and ideas were, as he put it, “fermenting and decocting.” Meanwhile, on quite a different topic, he made a discovery that was truly a stroke of genius. Had he done nothing else, it alone would have been enough to set his mark on scientific history. His thoughts were set racing wh
en he picked up a paper by the German physicist Rudolf Clausius on the rate of diffusion in gases—exemplified by the time it takes for the smell of perfume to cross a room when a bottle is opened. Clausius was a follower of the kinetic theory of gases, originally proposed by the Swiss physicist and mathematician Daniel Bernoulli, which attributed properties like temperature and pressure to the motion of molecules in the gas. Atmospheric pressure, for example, could be explained this way, but only if the air molecules moved very fast—hundreds of meters per second. Why, then, did the smell of perfume take several seconds to cross a room? Clausius had an explanation that was convincing yet mind-boggling. The molecules are forever colliding and changing direction—by the time it crossed a room, a single molecule would actually have traveled several kilometers. The astounding rapidity of molecular movements was becoming apparent for the first time. Maxwell described it this way:
If you go at 17 miles a minute and take a totally new course 17,000,000,000 times in a second, where will you be in an hour?7
Kinetic theory was becoming plausible and had won converts, even though no one could be sure that molecules even existed. But there was a sticking point. Temperature was thought to depend on the speed of the molecules—the faster, the hotter—but, at a given temperature, did all the molecules travel at the same speed? This seemed unlikely, but, if not, what was the distribution of speeds, and how on earth could you work it out? Maxwell solved the problem in a few short paragraphs in what seemed almost like a conjuring trick and showed the distribution to have the shape of a lopsided bell. This was the Maxwell distribution of molecular speeds—the first ever statistical law in physics.8 He had opened the door to great new regions of scientific knowledge—in particular to a proper understanding of thermodynamics, to statistical mechanics, and to the use of probability distributions in quantum mechanics.
Maxwell wrote up his new law and in the same paper made the important and surprising prediction that the viscosity of a gas, its internal friction, was independent of pressure. This happened because, at higher pressure, the dragging effect on a moving body of being surrounded by more molecules was exactly counteracted by the screening effect they provided. It was vital for the prediction to be tested by experiment—a verdict of false would demolish the whole kinetic theory, but a verdict of true would greatly strengthen it. As we will see, Maxwell later managed to do the experiment at home, with much help from Katherine. Elsewhere in the paper Maxwell made mistakes; he was off by a factor of 8,000 in one calculation because he had forgotten to convert kilograms to pounds and hours to seconds! Despite the flaws, his paper “Illustrations of the Dynamical Theory of Gases” drew gasps of admiration and put Maxwell in the first rank of physicists. However, the first person to recognize Maxwell's full achievement in bringing statistics into physics was at that time a schoolboy in Vienna, and he didn't see the paper until five years later. Ludwig Boltzmann was then so inspired by Maxwell's work on kinetic theory that he spent most of his career developing the subject further. The two began a kind of tennis match that lasted all of Maxwell's life; each in turn would be inspired by the other's work and counter with a further extension of the theory. Though they never thought of themselves as such, they were, in effect, a magnificent partnership, and it is pleasing that their names are linked in the Maxwell-Boltzmann distribution of molecular energies.