Faraday, Maxwell, and the Electromagnetic Field Page 14
Another characteristic of Maxwell's work, no doubt strengthened by his study of philosophy, was the way he could give full rein to his imagination, using the most surprising analogies, yet at the same time apply strict skepticism to his own results, even when they were brilliantly successful. This way, he was often able to return to a subject after a long interval and take it to new heights using a completely different approach.
James Forbes inspired Maxwell in a different and still more profound way. He was a true mentor, and their relationship stands comparison with that between Michael Faraday and Humphry Davy. Forbes's special passion was for Earth science—he pioneered the study of glaciers—but he was a consummate all-round scientist whose fascination with the physical world bound Maxwell in its spell. The two developed a rare rapport, and Forbes would let his pupil stay long after hours in the laboratory, making whatever investigation took his fancy. He could also be a hard task-master when required. When Maxwell submitted a poorly drafted paper to the Royal Society of Edinburgh and a colleague was asked to referee it, Forbes chose to deliver the sharp reproof himself. This was an act of kindness, and Maxwell knew it. Maxwell went on to develop the distinctive and crystal-clear writing style so admired by scholars—the beautifully written papers express not only his scientific ideas but his love for the literary tradition of the English language.
In a book review written many years later for the journal Nature, Maxwell gave what is clearly a sketch of Forbes.
If a child has any latent talent for the study of nature, a visit to a real man of science in his laboratory may be a turning point in his life. He may not understand a word of what the man of science says to explain his operations, but he sees the operations themselves, and the pains and patience which are bestowed on them; and when they fail he sees how the man of science, instead of getting angry, searches for the cause of failure among the condition of the operation.
When his mentor died in 1868, Maxwell told a friend “I loved James Forbes.”
Inspiration from Hamilton and Forbes was one of three factors from Maxwell's Edinburgh years that helped to form his character as a scientist. The second was the enormous amount of reading he did on all manner of topics—far more than most people accomplish in a lifetime. And he didn't just read; he analyzed, appraised, and remembered. This meant that he always had a vast store of knowledge to draw on for comparisons and analogies. The third factor, and the most important, was the free-wheeling experimenting he carried out during the holidays in an improvised workshop-cum-laboratory that he set up in a little room over the washhouse at Glenlair. He described it in a letter to Lewis Campbell.
I have an old door set on two barrels, and two chairs, one of which is safe, and a skylight above, which will slide up and down.
On the door (or table) there is a lot of bowls, jugs, jam pigs [jars], etc., containing water, salt, soda, sulphuric acid, blue vitriol, plumbago ore; also broken glass, iron, and copper wire, copper and zinc plate, bees’ wax, sealing wax, clay, rosin, charcoal, a lens, a Smee's Galvanic apparatus [an electrical kit], and a countless variety of little beetles, spiders and woodlice, which fall into the different liquids and poison themselves.
He tried all the chemical experiments possible within his resources and, when visited by the estate children, let them spit on a mixture of two white powders to turn it green. Among countless other experiments, he copper-plated jam jars and made simple electromagnetic devices, including a model telegraph. But the most important equipment in the laboratory turned out to be the pieces of broken glass.
He had heard that if you shone plane polarized light through glass that was under strain, you would see colored patterns, so he set out to investigate. He cut the bits of broken window glass into geometric shapes, heated them to red heat, and cooled them rapidly, so that the outer parts would cool faster than the inner, leaving internal strains “frozen” into the glass. To get polarized light from ordinary sunlight, he made a polarizing apparatus from a large matchbox, a small sheet of mica, and two pieces of glass, cut to shape and stuck in with sealing wax at the correct angles. Results exceeded expectations. Each of the geometrically shaped specimens revealed its own beautiful pattern of colored lines. They mapped out perfectly the state of strain in the glass because each of the colored lines was a “contour,” connecting points of equal strain.
To record his findings, he improvised a camera lucida, which made a virtual image of the patterns appear on a piece of paper so that he could copy them in watercolor. He sent the results to William Nicol, the famous Edinburgh optician. Nicol was so impressed that he sent Maxwell a pair of his prized Iceland spar polarizing prisms, the very kind that Faraday had used when detecting the effect of magnetism on light. Now that he had a readymade source of polarized light, Maxwell extended his investigation by passing the light through various jellies made using gelatin from the kitchen. He twisted the jellies to put them under torsional stress, observed the patterns of strain revealed by the colored lines, and copied them in watercolor and crayon. This was an early demonstration of the technique of photoelasticity that became tremendously useful to structural engineers. When they made a scale model of, say, their bridge, in a transparent material, put it under various loads, and shone polarized light through it, the patterns of strain would show up as colored lines, indicating any weak points where the structure might need strengthening.
All these DIY adventures not only honed Maxwell's experimental skill but also gave him a commanding insight into nature's processes and helped develop his uncanny intuition—Maxwell's guesses always seemed to be right. And along with the experimental work went his mathematical propositions, or “props” as he called them. Two were published by the Royal Society of Edinburgh. One was geometrical, on the paths traced out by a point on one kind of curve when rolled on another. The other was a remarkable achievement for a nineteen-year-old working almost entirely on his own. Called “On the Equilibrium of Elastic Solids,” it was a theoretical accompaniment to his experimental work with polarized light and gave the full mathematical theory of photoelasticity based on strain functions. Both papers were read out for him as he was still too young to be allowed to do it himself.
Life was full, but Maxwell was missing the stimulating company of his close friends who had by now left Edinburgh University for Oxford or Cambridge. He filled long letters to Lewis Campbell with lighthearted accounts of his thoughts and researches at Glenlair, but it was no substitute for conversation and he implored his friend to visit. Campbell was at Oxford, but P. G. Tait and another friend, Allan Stewart, had gone to Cambridge. He began to worry that a matchless opportunity was slipping by. Cambridge was the place for aspiring scientists, and Forbes tried to persuade John Clerk Maxwell that James should go there too. John was reluctant—he would see less of his son as the university terms in England were longer, and there was the danger that James might fall under the influence of undesirable rich English students with their dissipated way of life. The decision was repeatedly put off and James was bracing himself to prepare for life at the Scottish Bar when events took a happy turn. He wrote to Campbell:
I have notions of reading the whole of Corpus Juris and Pandects in no time at all; but these are getting dim as the Cambridge scheme has been howked up from its repose in the region of abortions, and is as far forward as an inspection of the Cambridge Calendar and a communication with Cantabs.
His father had at last agreed that he should go to Cambridge. Forbes was delighted and took the unusual step of writing to William Whewell, master of Trinity College, to tell him what to expect. (This was the same man whom Faraday had consulted on terminology.) Forbes wrote of Maxwell,
He is not a little uncouth in manners, but withal one of the most original young men I have met…. He is a singular lad, and shy [but] very clever and persevering…. I am aware of his exceeding uncouthness, as well mathematical as in other respects…. I thought the Society and Drill of Cambridge the only chance of taming him and much advi
sed his going…I should think he might be a discoverer.
Uncouth? Forbes was probably indulging in some donnish argot with Whewell, whom he knew well. Certainly Maxwell lacked sophistication; his manners did not match those of the polished products of Eton and Harrow that made up much of the Cambridge student population, and his accent was strange to the English ear. Even within the family he was censured for his want of social poise—when, at dinner, his attention was drawn to an interesting reflection in a glass or a swaying of a candle flame, Aunt Jane would recall him to the company with a sharp “Jamesie, you're in a prop.” But he was strikingly good-looking and always neatly, though not fashionably, dressed—he hated starched collars and wore no gloves, even in the winter. He cared nothing for any kind of luxury, even traveling third class on the railway, saying that he preferred a hard seat. Lewis Campbell's mother summed him up very well:
His manners are very peculiar; but having good sense, sterling worth, and good humour, the intercourse with a college will rub off his oddities. I doubt not of his being a distinguished man.
At nineteen he was already an experienced scientific experimenter who had accumulated a vast amount of knowledge and had published three mathematical papers. Yet he had never worked under the slightest pressure; there was tremendous power in reserve. In the autumn of 1850, he packed his Nicol prisms and as much as he could manage of his experimental paraphernalia into a trunk. The society and drill of Cambridge were about to do their work.
After reporting to his tutor in St. Peter's College, known as Peterhouse, Maxwell was delighted to be given rooms with good light, just what he needed for his optical experiments. At peace with the world, he invited his old school friend Tait in for tea and they caught up with a long chat. The next day, there was a tour of the colleges, including homage at the tombs of Isaac Newton and Francis Bacon in Trinity College Chapel. The aura of scholarship seemed to be everywhere. But the lectures were a great disappointment at first—he found himself “spelling out Euclid” and “monotonously parsing a Greek play.”* And his fellow students at Peterhouse seemed to be a snobby crowd, unreceptive to his attempts at genial discourse. His elation began to fade, and beneath it was an undercurrent of unease and restlessness. But all turned out for the best, thanks in large part to quite another factor.
His father had chosen Peterhouse, a small and elite college, but was now having second thoughts. An assiduous networker, he had discovered that one of James's fellow students, E. J. Routh, was a formidable mathematician who was likely to take one of the rare Peterhouse fellowships. Other colleges were better endowed and had more fellowships. The outcome was that after a term Maxwell moved to Trinity, the large and sociable college that Forbes had recommended all along.
Life at Trinity was a joy. Under William Whewell's aegis, the college had become a fertile ground for ideas and debate on just about any topic. Maxwell was in his element, and in a short time had a troop of friends. He joined in any discussion that was going on and relished the camaraderie and badinage. On some evenings he walked about looking for someone to bandy ideas with, and he met others doing the same. He acted as a kind of general factotum to the other students, nursing those who were sick and bucking up those who were depressed. When a friend had eye trouble and couldn't read, Maxwell spent an hour each evening reading out the man's bookwork for the next day. Meanwhile, his private reading went on apace and, when time allowed, he tinkered with his odd miscellany of scientific apparatus, getting ideas for proper investigation later. He even managed to write two scientific articles, one of which reported his remarkable proposal for a flat lens with a variable refractive index that would give perfect imaging. It became known as the fish-eye lens, and was reputedly inspired by close examination of a breakfast kipper.
It wasn't easy to fit all this in along with lectures and the work set by the lecturers and tutors, so he tried unusual daily routines—even jogging in the middle of the night to make sure he got enough exercise. A fellow student reports:
From 2 to 2.30 am he took exercise by running along the upper corridor, down the stairs, along the lower corridor, then up the stairs, and so on until the inhabitants of the rooms along his track got up and lay perdus behind their sporting doors to have shots at him with boots, hair-brushes, etc., as he passed.1
Not all of Maxwell's experiments worked!
He gave full vent to his poetic muse, writing everything from translations of classic Greek odes to irreverent trifles dashed off to amuse his friends. In one of these he takes the part of the hypothetical “rigid body,” beloved of lecturers in applied mathematics, in a parody of Burns's Comin’ through the Rye.
Gin a body meet a body
Flyin’ through the air
Gin a body hit a body,
Will it fly? And Where?
Ilka impact has its measure
Ne'er a ane hae I,
But all the lads they measure me,
Or, at least, they try.
Gin a body meet a body
Altogether free,
How they travel afterwards
We do not always see,
Ilka problem has its method
By analytics high;
For me, I ken na ane o’ them,
But what the waur am I?
He was invited to join an elite discussion group called the Apostles. Initially founded by twelve students as a secret society in 1820, the group had perpetuated itself by electing a new member to replace each man who left. At first the society was a forum for discussing progressive ideas on religion, politics, and education that had been resolutely ignored by the university. By Maxwell's time, thanks in part to the Apostles themselves, the university had become much freer, but the society was still a breeding ground for ideas that transcended conventional ways of thinking. Over the years, it has included among its ranks many who went on to make outstanding contributions to human thought and its expression—for example: Alfred Lord Tennyson, Rupert Brooke, Bertrand Russell, Ludwig Wittgenstein, Lytton Strachey, the theologian and social reformer F. D. Maurice, the mathematician G. H. Hardy, E. M. Forster, and John Maynard Keynes.
Meetings were traditionally held on Saturday evenings, when one member would read an essay on a preannounced topic which he would then throw open for discussion. Maxwell's contributions show that his thoughts ranged far beyond mathematics—he was, in the language of Plato, “taking a survey of the universe of things.” It was a wonderful opportunity to present his brimming ideas to people with creative minds who would respond with ideas of their own, and he took it to the full. Among his essays were “Is Autobiography Possible?” “Has Everything Beautiful in Art Its Original in Nature?” “Morality; Language and Speculation,” and “Are There Any Real Analogies in Nature?”
Maxwell's studies of philosophy came to the fore in his “Analogies” essay, which, some say, holds the key to his seminal thinking in theoretical physics. Certainly, if one wants insight into how Maxwell was able to make progress where others were becalmed, this is a good place to look. At the heart of the essay was the Kantian philosophy that all human knowledge is of relations rather than things. As he put it:
Whenever [men]…see a relation between two things they know well and think there must be a similar relation between things less known, they reason from one to the other. This supposes that although pairs of things may differ widely from each other, the relation in the one pair may be the same as that in the other. Now, as in a scientific point of view, the relation is the most important thing to know, a knowledge of one thing leads us a long way towards a knowledge of the other.
But not, of course, all the way—analogy was simply an aid to understanding, and he warned of the dangers of confusing it with identity. One needs to explore issues from all sides, as he made clear in a passage that provides us with a fine forty-nine-word summary of his scientific philosophy:
The dimmed outlines of phenomenal things all merge into one another unless we put on the focusing glass of theory, and screw
it up sometimes to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world.2
A fellow member of the Apostles remembered that Maxwell always took part animatedly in the conversations, but that his tendency to speak in parables and his strange accent made it hard sometimes to get his meaning. It wasn't easy for newcomers to tune in to Maxwell's wavelength—to use an appropriate metaphor—but the effort was worth it. One of his fellow students remarked:
Maxwell as usual is showing himself acquainted with every subject upon which the conversation turned. I never met a man like him. I do believe there is not a single subject on which he cannot talk, and talk well too, displaying the most out of the way information.3
At Cambridge, the bachelor's degree course took four years and was known as the Tripos, reputedly after the type of three-legged stool that candidates used to sit on when taking oral exams. By Maxwell's time, oral exams had given way to written ones and there were several of these at stages during the course, culminating in the fearsome Mathematical Tripos exam in the final year, which everybody had to pass to get a degree of any kind. The Mathematical Tripos had become an important institution in nineteenth-century Britain and served as a model for the introduction of competitive examinations throughout the country.
The exam took place in chilly January, and its setting was the Senate House, a building in the style of a Greek temple that had no fires or stoves. Students arrived in greatcoats and mufflers, sometimes to find their ink frozen in the inkwells. Every man had to take the first three days of exams, doing his best to solve problems against the clock for five and a half hours each day. Those who wanted an honors degree, even classics students, then came back for another four days of exams that were even more difficult. Those who gained first-class honors were awarded the title of wrangler, which brought lifelong recognition and gave a substantial boost to a career in any field. Wranglers were ranked in order, and to become senior wrangler was like winning an Olympic gold medal. The Mathematical Tripos was, indeed, treated by the press like a national sporting event, and large sums were bet on the outcome. After it, the best students sat an even harder set of papers for the Smith's Prize.