Table of Contents
Title Page
Copyright Page
Table of Figures

Table of Figures
Figure 1 Maxwell’s colour triangle
Figure 2a . Switch open
Figure 2b . Switch first closed
Figure 2c . Shortly after switch closed
Figure 2d . Switch opened again

James Clerk Maxwell. From a bronze bust by Charles D’Orville Pilkington Jackson. Courtesy of the University of Aberdeen


To Ann

I fell under Maxwell’s spell when I was about 16 but for more than 40 years he was a man of mystery. His name cropped up in all the popular accounts of twentieth century discoveries such as relativity and quantum theory, and when I became an engineering student I learnt that his equations were the fount of all knowledge in electromagnetism. They seemed to work by magic—something I attributed, with good grounds, to imperfect understanding. But now that I understand the equations a little better they seem even more magical.
Over the years the spell tightened its grip. My extensive, if desultory, reading on scientific matters served to deepen the mystery. Usually introduced as ‘the great James Clerk Maxwell’, his influence on the physical sciences seemed to be all-pervasive. Yet he was scarcely known in the wider world; most of my friends and colleagues had never heard of him, although all knew of Newton and Einstein and most knew of Faraday. What is more, nothing in what I had read revealed much about Maxwell’s life beyond the bare facts that he was Scottish and lived in the mid-nineteenth century.
The time had come to unravel the mystery. A few years ago I looked him up in all the reference books I could find, starting in the local library. The Encyclopaedia Britannica had a helpful 2000 word entry and a short bibliography. It was like finding the way to a store of buried treasure. Maxwell was not only one of the most brilliant and influential scientists who ever lived but an altogether fine and engaging man. And he seemed to inspire in writers a unique combination of wonder and affection; a Times Literary Supplement editorial of 1925, preserved in Trinity College Library, sums it up by saying that Maxwell was ‘to physicists, easily the most magical figure of the nineteenth century’.
I have tried to tell the story simply and directly, putting the reader at Maxwell’s side, seeing the world from his perspective as his life unfolds. Hence the main narrative contains few references to sources and no more background or detail than is needed for the story. The separate Notes section attends to these aspects and gives some interesting sidelights.
To his friends, and he had many, Maxwell was the warmest and most inspiring of companions. I hope this book will leave readers glad that they, too, know him a little.

Anyone who writes, or indeed reads, about Maxwell owes a great debt to Lewis Campbell, who gave us an affectionate yet penetrating picture of his lifelong friend in The Life of James Clerk Maxwell, co-written with William Garnett and published 3 years after Maxwell’s death. Campbell and Garnett’s book has been the principal source of information for all subsequent biographies and I would like to add my tribute and my thanks to those given by other authors.
I am also much indebted to the more recent biographers Francis Everitt, Ivan Tolstoy and Martin Goldman for their added insights, to Daniel Siegel and Peter Harman for their scholarly but reader-friendly analyses of Maxwell’s work, and to the other authors listed in the bibliography. Several patient friends have kindly read drafts and suggested improvements; among these I am particularly grateful to Harold Allan and Bill Crouch. John Bilsland supplied excellent line drawings for the figures, and David Ritchie and Dick Dougal located many of the sources for the illustrations.
The Royal Societies of London and Edinburgh gave valuable help, as did the Royal Institution of Great Britain, King’s College London, the University of Aberdeen, Trinity College Cambridge, the University of Cambridge Department of Physics, Cambridge University Library, the Institution of Civil Engineers, the Institution of Electrical Engineers and Clifton College.
A visit to Maxwell’s birthplace at 14 India Street, Edinburgh, is a moving experience for anyone with an interest in Maxwell. It is possible only because the trustees of the James Clerk Maxwell Foundation service acquired the house in 1993 and have with trouble and care created a small but evocative museum. I should like to thank them for this service.
I am especially grateful to Sam Callander and to David and Astrid Ritchie for their generous encouragement and kindness.
The final words of thanks go to Wiley for publishing the book, and especially to my editor Sally Smith and her assistant Jill Jeffries for their friendly and expert help and guidance.

Principal events in Maxwell’s life
1831Born at 14 India Street, Edinburgh, 13 June. Grew up at Glenlair
1839His mother, Frances, died
1841Started school, Edinburgh Academy
1846Published his first paper, on oval curves
1847Started at University of Edinburgh
1848Published paper On Rolling Curves
1850Published paper On the Equilibrium of Elastic Solids Started at Cambridge University, Peterhouse for one term, then Trinity
1854Finished undergraduate studies at Cambridge: second wrangler, joint winner of Smith’s Prize: started post-graduate work
1855Published paper Experiments on Colour as Perceived by the Eye
Published first part of paper On Faraday’s Lines of Force, second part the following year Elected Fellow of Trinity
1856His father, John, died Appointed Professor of Natural Philosophy at Marischal College, Aberdeen
1858Awarded Adams’ Prize for essay On the Stability of the Motion of Saturn’s Rings, paper published 1859
1858Married Katherine Mary Dewar, daughter of Principal of Marischal College
1860Published papers Illustrations of the Dynamical Theory of Gases and On the Theory of Compound Colours and the Relations of the Colours of the Spectrum
Made redundant from Marischal College Failed in application for Chair of Natural Philosophy at University of Edinburgh
Severely ill from smallpox
Appointed Professor of Natural Philosophy at King’s College, London
Awarded Rumford Medal by the Royal Society of London for his work on colour vision
1861Produced world’s first colour photograph Published first two parts of paper On Physical Lines of Force, the remaining two parts the following year
Elected FRS
1863Published recommendations on electrical units and results of experiment to produce a standard of electrical resistance in his Committee’s report to the British Association for the Advancement of Science
1865Published paper On Reciprocal Figures and Diagrams of Force Published paper A Dynamical Theory of the Electromagnetic Field
Severely ill from infection from cut sustained in riding accident
Resigned chair at King’s College London; returned to live at Glenlair
1866Published paper On the Viscosity or Internal Friction of Air and Other Gases
1867Published paper On the Dynamical Theory of Gases Visited Italy
1868Published paper On Governors
Carried out experiment to measure the ratio of the electrostatic and electromagnetic units of charge, which by his theory was equal to the speed of light
Applied for but failed to get post of Principal of St Andrews University
1870Published paper On Hills and Dales Awarded Keith Medal by the Royal Society of Edinburgh for work on reciprocal diagrams for engineering structures
1871Published book The Theory of Heat, in which he introduced Maxwell’s demon
Appointed Professor of Experimental Physics at Cambridge University
Supervised design and construction of Cavendish Laboratory building (fully operational 1874)
1873Published book A Treatise on Electricity and Magnetism
1876Published book Matter and Motion
1879Published paper On Boltzmann’s Theorem on the Average Distribution of a Number of Material Points
Published paper On Stresses in Rarefied Gases Arising from Inequalities in Temperature
Published book Electrical Researches of the Honourable Henry Cavendish
Died at Cambridge 5 November; buried at Parton
Note: Maxwell published five books and about 100 papers. Those of his writings that are described in the narrative are listed here and are available, with others, under titles listed in the Bibliography.

Maxwell’s relations and close friends
Blackburn, Hugh: Professor of Mathematics at Glasgow University, husband of Jemima.
Blackburn, Jemima (née Wedderburn): James’ cousin, daughter of Isabella Wedderburn
Butler, Henry Montagu: student friend at Cambridge, afterwards Headmaster of Harrow School and, later, Master of Trinity College, Cambridge
Campbell, Lewis: schoolfriend, afterwards Professor of Greek at St Andrews University
Campbell, Robert: younger brother of Lewis
Cay, Charles Hope: James’ cousin, son of Robert
Cay, Jane: James’ aunt, younger sister of Frances Clerk Maxwell
Cay, John: James’ uncle, elder brother of Frances Clerk Maxwell
Cay, Robert: James’ uncle, younger brother of Frances Clerk Maxwell
Cay, William Dyce: James’ cousin, son of Robert
Clerk, Sir George: James’ uncle, elder brother of John Clerk Maxwell
Clerk Maxwell, Frances (née Cay): James’ mother
Clerk Maxwell, John: James’ father
Clerk Maxwell, Katherine Mary (née Dewar): James’ wife
Dewar, Daniel: James’ father-in-law, Principal of Marischal College, Aberdeen
Dunn, Elizabeth (Lizzie) (née Cay): James’ cousin, daughter of Robert Cay
Forbes, James: friend and mentor, Professor of Natural Philosophy at Edinburgh University, afterwards Principal of St Andrew’s University
Hort, Fenton John Anthony: student friend at Cambridge, afterwards a professor at Cambridge
Litchfield, Richard Buckley: student friend at Cambridge, afterwards Secretary of the London Working Men’s College
Mackenzie, Colin: James’ cousin once removed, son of Janet Mackenzie
Mackenzie, Janet (née Wedderburn): James’ cousin, daughter of Isabella Wedderburn
Monro, Cecil James: student friend at Cambridge, afterwards a frequent correspondent with James, particularly on colour vision
Pomeroy, Robert Henry: student friend at Cambridge who joined the Indian Civil Service and died in his 20s during the Indian Mutiny
Tait, Peter Guthrie: schoolfriend, afterwards Professor of Natural Philosophy at Edinburgh University
Thomson, William, later Baron Kelvin of Largs: friend (and mentor in early stages of James’ career), Professor of Natural Philosophy at Glasgow University
Wedderburn, Isabella (née Clerk): James’ aunt, younger sister of John Clerk Maxwell
Wedderburn, James: James’ uncle by marriage, husband of Isabella
Note: The list shows those of Maxwell’s relations and close friends who are mentioned in the narrative, and two more who are included to explain relationships. His work colleagues and associates are not listed here, apart from Forbes, Tait and Thomson.

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 Feynmann
In 1861, 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.
In the middle of the nineteenth century the world’s best physicists had been searching long and hard for a key to the great mystery of electricity and magnetism. The two phenomena seemed to be inextricably linked but the ultimate nature of the linkage was subtle and obscure, defying all attempts to winkle it out. Then Maxwell found the answer with as pure a shaft of genius as has ever been seen.
He made the astounding prediction that fleeting electric currents could exist not only in conductors but in all materials, and even in empty space. Here was the missing part of the linkage; now everything fitted into a complete and beautiful theory of electromagnetism.
This was not all. The theory predicted that every time a magnet jiggled, or an electric current changed, a wave of energy would spread out into space like a ripple on a pond. Maxwell calculated the speed of the waves and it turned out to be the very speed at which light had been measured. At a stroke, he had united electricity, magnetism and light. Moreover, 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.
Maxwell’s ideas were so different from anything that had gone before that most of his contemporaries were bemused; even some admirers thought he was indulging in a wild fantasy. No proof came until a quarter of a century later, when Heinrich Hertz produced waves from a spark-gap source and detected them.
Over the past 100 years we have learnt to use Maxwell’s waves to send information over great and small distances in tiny fractions of a second. Today we can scarcely imagine a world without radio, television and radar. His brainchild has changed our lives profoundly and irrevocably.
Maxwell’s theory is now an established law of nature, one of the central pillars of our understanding of the universe. It opened the way to the two great triumphs of twentieth century physics, relativity and quantum theory, and survived both of those violent revolutions completely intact. As another great physicist, Max Planck, put it, the theory must be numbered among the greatest of all intellectual achievements. But its results are now so closely woven into the fabric of our daily lives that most of us take it wholly for granted, its author unacknowledged.
What makes the situation still more poignant is that Maxwell would be among the world’s greatest scientists even if he had never set to work on electricity and magnetism. His influence is everywhere. He introduced statistical methods into physics; now they are used as a matter of course. He demonstrated the principle by which we see colours and took the world’s first colour photograph. His whimsical creation, Maxwell’s demon—a molecule-sized creature who could make heat flow from a cold gas to a hot one—was the first effective scientific thought experiment, a technique Einstein later made his own. It posed questions that perplexed scientists for 60 years and stimulated the creation of information theory, which underpins our communications and computing. He wrote a paper on automatic control systems many years before anyone else gave thought to the subject; it became the foundation of modern control theory and cybernetics. He designed the Cavendish Laboratory and, as its founding Director, started a brilliant revival of Cambridge’s scientific tradition which led on to the discoveries of the electron and the structure of DNA.
Some of his work gave direct practical help to engineers. He showed how to use polarised light to reveal strain patterns in a structure and invented a neat and powerful graphical method for calculating the forces in any framework; both techniques became standard engineering practice. He was also the first to suggest using a centrifuge to separate gases.
Maxwell was born in 1831 and lived for 48 years. A native Scotsman, he spent about half of his working life in England. From his earliest days he was fascinated by the world and determined to find out how it worked. Like all parents, his were assailed with questions, but to be interrogated by 3 year-old James must have been an experience of a different order. Everything that moved, shone or made a noise drew the question ‘What’s the go o’ that?’ and, if he was not satisfied, the follow-up ‘but what’s the particular go of it?’. A casual comment about a blue stone brought the response ‘but how d’ye know it’s blue?’. Maxwell’s childish curiosity stayed with him and he spent most of his adult life trying to work out the ‘go’ of things. At the task of unravelling nature’s deep secrets he was supreme.
Those in the know honour Maxwell alongside Newton and Einstein, yet most of us have never heard of him. This is an injustice and a mystery but most of all it is our own great loss. One excellent reason for telling this story is to try to gain Maxwell a little of the public recognition he so clearly deserves, but a much better one is to try to make good the loss. His was a life for all of us to enjoy. He was not only a consummate scientist but a man of extraordinary personal charm and generous spirit: inspiring, entertaining and entirely without vanity. His friends loved and admired him in equal measure and felt better for knowing him. Perhaps we can share a tiny part of that experience.

Glenlair 1831-1841
When they had their first glimpse of the newcomer, the boys of the second year class could scarcely contain their hostile curiosity. He was wearing an absurd loose tweed tunic with a frilly collar and curious square-toed shoes with brass buckles, the like of which had never been seen at the Edinburgh Academy. At the first break between lessons they swarmed around the new boy, baiting him unmercifully, and when he answered their taunts in a strange Galloway accent they let out whoops of jubilant derision. At the end of a long day he arrived home with clothes in tatters. He seemed to be dull in class and soon acquired the nickname ‘Dafty’. The rough treatment went on, yet he bore it all with remarkable good humour until one day, when provoked beyond endurance, he turned on his tormentors with a ferocity that astonished them. They showed him more respect after that, but the name ‘Dafty’ stuck. So started the academic career of one of the greatest scientists of all time, James Clerk Maxwell.
The first 8 years of his life had been wonderfully happy. He was born in Edinburgh1 but brought up at Glenlair, his father’s estate in the gently rolling Vale of Urr in the Galloway region of south-west Scotland2. His parents, John and Frances Clerk Maxwell, had married late and their first child, Elizabeth, had died in infancy. Frances was almost 40 when James was born. She and John adored their son and watched over his development with indulgent devotion. As soon as he could walk and talk a little it became plain that he was a remarkable boy. Like all children he was curious about everything around him, but his curiosity was of a different order and reached into places rarely explored. For example, it was not enough for him to discover how to ring the house bells; he had to find out which of the bell-pulls around the house rang which bell in the kitchen and where all the wires ran. And he could turn everyday objects to surprising uses. One day his nurse Maggy gave him a tin plate to play with. Perhaps he first tried banging it with a spoon or rolling it across the floor but soon he was excitedly calling his mother and father to come and see how he had brought the sun into the house by reflecting its image off the plate on to a wall.
As he grew, he played rough-and-tumble games with the local children, climbed trees, explored the fields and woods and watched the animals and birds with rapt attention. He enjoyed the morning chore of fetching water from the river by cart. Nothing that went on in the house escaped his attention. Nobody could do anything without having young James appear, demanding a full explanation and insisting on having a go himself. He knitted, made baskets, took a hand in the baking and helped his father design and plan improvements to the estate. Like all boys he could be a little monkey at times. One evening, just after dark, he blew out the candle as Maggy was approaching with the tea tray and lay down in the doorway.
He quickly learnt to read and, under his mother’s guidance, began to understand the wider world. He enjoyed history and geography and, especially, literature. Before long he was reading everything within reach. Milton and Shakespeare were particular favourites. What is more, he seemed to remember most of what he had read.
For entertainment, the family would often read novels or poetry aloud or act out a play. And religion was an important part of the domestic routine: every day the household, including servants, met for prayers and every Sunday they went to Parton church, five miles to the west. His father’s background was Presbyterian, his mother’s Episcopalian, but both took a tolerant view of doctrinal matters. The Clerk Maxwells played their full part in the social life of the area; there were fairs and dances and visits exchanged with other leading families. There were also visits to and from relations in Edinburgh and Penicuik, the estate of James’ uncle.
Life at Glenlair was harmonious, stimulating and gently bustling. It was also full of jokes and banter. There was no pomposity whatever—no person, institution or topic was above some gentle debunking. The spirit of these times stayed with James all his life. We shall see this demonstrated time and again but, even so, let us cheat a little by taking a glimpse now at a poem he wrote when he was 26, teasing his friend William Thomson, who was consultant to the Atlantic Telegraph Company, when its cable-laying ran into difficulties.
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.3
No Schadenfreude here. Maxwell admired the transatlantic cable project immensely and even suggested how they might lay the cable more smoothly and economically by using an underwater kite. He just couldn’t resist poking a little fun.
James’ parents were fairly new arrivals in the Happy Valley, as the Vale of Urr was known to its residents. John Clerk Maxwell was an advocate who had lived most of his life in Edinburgh. He had an adequate private income and it did not matter much to him that his practice never flourished. John’s heart lay elsewhere —in his hobby, which was what we would now call technology. He had built up a wide range of friends in industry, agriculture and universities and enjoyed keeping abreast of new ideas. His life ticked away pleasantly but ineffectively until events took a turn when he was in his late 30s. A long-standing acquaintance with the sister of a friend blossomed into romance and she agreed to marry him. Frances Cay was a spirited and resolute woman who supplied the get-up-and-go he had so far lacked. Both their lives were transformed and Glenlair was the focus. John had inherited the estate some years before and had toyed with the idea of going to live there and applying his ideas on farming. Now the day-dreams changed into hard and purposeful activity—they resolved on setting up home at Glenlair.
Previous owners of the estate had been absentee landlords and there was no suitable dwelling there. But to John this was an advantage: the prospect of designing and building his own family house was irresistible. The house he designed was a modest one for a country gentleman of that time—he planned to extend it later. Impatient to start their new life, he and Frances moved to Glenlair soon after building started and lived in one of the estate cottages until the house was habitable. They launched themselves wholeheartedly into country life, then endured the anguish when their first child died. When Frances became pregnant for the second time they decided to go to Edinburgh for the birth, to be near relations and hospital if needed. Soon after James was born they returned home and family life began.
Glenlair had belonged to John’s family for only three generations. It was the 1500 acre residue of a much larger estate called Middlebie, which had been the seat of the fierce Maxwell clan. John’s family name was Clerk: by the normal reckoning he was not really a Maxwell at all; neither was James. The Clerks had acquired the Middlebie estate by marriage in addition to their own baronetcy of Penicuik, 10 miles south of Edinburgh. They arranged that Penicuik would be passed on to the senior heir and Middlebie to the second, and that whoever inherited Middlebie would add Maxwell to the family name. When John’s grandfather lost a fortune in mining investments most of Middlebie had to be sold, leaving only Glenlair. So it came about that James’ father was John Clerk Maxwell of Glenlair while his uncle was Sir George Clerk of Penicuik.
John and Frances came from exceptionally talented families—previous generations of Clerks and Cays had distinguished themselves in many fields4. To do justice to this point would take us too far from our story, but two examples from the Clerk line will give an idea.
James’ great-great-grandfather, Sir John Clerk, was the kind of man whose easy brilliance at everything he did makes most of us despair of our own efforts. As well as being a Baron of the Exchequer of Scotland and a Commissioner of the Union he wrote good music that is still performed today. He was a Fellow of the Royal Society and an influential authority in archaeology, architecture, history, astronomy, geology and medicine.
One of Sir John’s sons, another John Clerk, was a spectacularly successful businessman as well as a gifted artist and geologist. He worked with his friend James Hutton and illustrated a volume of Hutton’s seminal work, Theory of the Earth. But his masterpiece was an essay on naval tactics. It is extraordinary that a landlubber —he never went to sea—should even think of writing such a book, but what is more remarkable is that it became the standard work on the subject. Nelson used several sentences straight from the essay in his orders for the battle of Trafalgar.
There was little evidence in John and Frances’ homely house at Glenlair of their illustrious antecedents. No grand family silver, no portrait gallery. Their one prized heirloom was a battered set of bagpipes which James’ grandfather, a captain in the British East India Company’s Navy, had used to keep afloat when he was shipwrecked. The lack of formal trappings made it a wonderful home for their son. James had a much closer relationship with his parents than was usual among the gentry; his mother became his tutor and his father often took him along when dealing with estate business. This still left him plenty of time to run around with the local children. He learnt their Galloway speech and acquired a local accent that he would never entirely lose. No child could have been happier, but sadness was to come.
Frances became ill and abdominal cancer was diagnosed. She decided to have an operation without anaesthetic. The chances of success were slim but she wanted to live longer if possible for the sake of her husband and son and so chose to undergo this excruciating treatment. But the operation was not successful and Frances died soon afterwards. She was 47 years old.
Frances had been the hub of the family; without her the house at Glenlair must have been a desolate place for a while. Heavy of heart, John and James were glad, at least, that her suffering was over. The loss brought them even closer together and the father enjoyed his son’s lively companionship. There was, however, the problem of schooling. The plan had been for James to be educated at home until he was 13, when he would go straight to university. But John was too busy with the estate and with various county boards and committees to teach the boy himself. There was no suitable school within daily travelling distance and he dreaded the loneliness that would follow if he sent James away.
He decided to engage a private tutor and chose a 16 year-old boy from the neighbourhood. The lad had done well in exams at school but delayed going to university so he could take the post. No-one then or since has been able to fathom how John Clerk Maxwell came to make such an ill-judged choice. Knowing he had an exceptionally gifted son, how could he entrust his education to a youth with little knowledge and no experience of life beyond school? Whatever the reasons, the results were disastrous.
The tutor used the methods by which he had himself been taught: rote learning encouraged by physical chastisement. The lessons became a moral and physical ordeal. James wanted to please his father but saw no sense in the mechanical recitation of words and numbers divorced from any meaning. No amount of ear pulling and cuffing about the head could persuade him to learn in that fashion. His local friends had no doubt suffered similar treatment at school, so perhaps he thought it was simply something that had to be endured. But eventually, after more than a year of torment, he rebelled.
Beside a duck pond near the house was a large washtub that James used to use as an improvised boat. In the middle of a lesson, his tolerance exhausted, he ran out, pushed the tub into the water, jumped in and paddled himself to the deepest part of the pond. Ignoring the tutor’s urgings, he refused to come in. Although reproved by his father for this act of rebellion, James had made his point.
His Aunt Jane, Frances’ younger sister, who lived in Edinburgh, was quick to understand what had been going on and persuaded John that it was high time that 10 year-old James had proper schooling. John’s widowed sister, James’ Aunt Isabella, who also lived in Edinburgh, agreed. The Edinburgh Academy5, one of the best schools in Scotland, was only a short walk from her house; James could stay with her during term time and return to Glenlair for the holidays. Much as he hated the thought of parting from his son, John could see that Jane and Isabella were right and agreed to the plan.
Unfortunately, the first year class was full, so James had to enrol in the second. There he would be joining a class of 60 older boys who had already spent more than a year in the school, long enough to have absorbed its conventions and developed their own schoolboy culture. They were mostly from smart Edinburgh families and spoke with refined accents. Clearly, life was not going to be easy for the newcomer. What made things even harder was that his father had designed and made special clothes for him. From a logical standpoint, they were excellent: warm, hard-wearing and comfortable, with a loose tunic and square-toed shoes. But John seemed oblivious to the human factor: to the boys in James’ new class, in their conventional tight jackets and slim shoes, the newcomer looked like a ridiculous peasant from a foreign land.
So it was that James arrived for his first day at the city school, a country boy with a strange accent and wearing peculiar clothes. As we have seen, he was tough enough to ride out his rough reception and parry the taunts. A hard time lay ahead, but in the end the attitude of his classmates was to turn from ridicule to acceptance, and finally to admiration.

Edinburgh Academy 1841-1847
Aunt Isabella and Aunt Jane promptly saw to it that James was kitted out in the same style as the other boys, but he did not think or behave like them. He rarely joined in formal sports and, although he enjoyed playground games with marbles and tops, he still insisted on calling them ‘bools’ and ‘pearies’ as he had done at Glenlair. He brought along crude mechanical contraptions and drew curious diagrams but none of his fellows could make head or tail of them. Often he went alone to a corner of the play area which had some trees and a grassy bank where he watched the bees and beetles or improvised gymnastic exercises on the branches.
His mind was a-whirr with impressions, thoughts and part-formed ideas. For a long while these found no expression at school. He was, as a classmate later put it, like a locomotive under full steam but with the wheels not gripping the track. More than a year went by before he made a real friend. But he showed himself to be strong and brave and these qualities commanded respect. He sought no quarrels and bore no grudges: for all his odd ways it became plain to everyone that he was good-natured and generous.
Two things held him back in class at first. One was the numbing effect of the repetitive exercises in Greek and Latin, harking back to the time with his tutor. The other was a hesitancy of speech, the words coming in spates between long pauses. This defect remained with him to some extent all his life and may also have stemmed from his time under the tutor. He eventually managed to overcome the worst of the problem by projecting a mental image of answers to the master’s anticipated questions on to the classroom windows, so he could simply read them out when needed.
At Aunt Isabella’s house1 there were no such problems. Life there was congenial and stimulating. The library was even better stocked than that at Glenlair and he was soon reading Swift and Dryden.
He loved to draw and had the example of his cousin Jemima, who had often brought her sketchbook to Glenlair and was now a rising young artist. Landseer had said that ‘in portraying animals he had nothing to teach her’ and she was soon to have pictures exhibited in the Royal Academy2. Jemima was also learning woodcutting and let James borrow her tools. His artistic efforts displayed more gusto than skill but had a rugged charm that made them his own.
Sometimes he and Jemima combined their talents by producing ‘wheels of life’ for parlour entertainment. A series of pictures, like an animated cartoon film, was set on a spinning wheel or cylinder so that one saw the images in rapid succession and got the impression of movement. James designed and made the machines and sketched sequences of pictures, which Jemima would then draw—a favourite sequence showed a rider doing acrobatic tricks on the back of a galloping horse.
His father came to Edinburgh whenever he could. When he was in town on a Saturday the two would walk up the rocky hill, Arthur’s Seat, or visit other local attractions. Every new experience fed James’ probing and retentive mind. One of these Saturday treats was to see an exhibition of ‘electromagnetic machines’. The sight of these primitive devices—nothing like the generators and motors we know today—started in the boy’s mind a process of thought that would ultimately transform the way physicists think about the world, a change that Einstein called ‘the most profound and useful that physics has experienced since the time of Newton’.
When they were apart, father and son wrote to one another frequently. James’ letters were full of childish jokes in which his father clearly took delight. He signed them with anagrams of his name, such as Jas Alex McMerkwell, and addressed some of them to Mr John Clerk Maxwell, Postyknowswhere, Kirkpatrick Durham, Dumfries. One letter, just after his 13th birthday, gives a tiny hint of things to come. After fulsome accounts of a minstrel show and a trip to the beach, he asks about events and people at Glenlair and finally mentions ‘I have made a tetrahedron and a dodecahedron and two more hedrons that I don’t know the right names for’. He had not yet learnt any geometry in school but had somehow found out about what mathematicians call the regular polyhedra: solid figures whose faces are all identical polygons and whose vertex angles are all equal. There are only five of them: the most familiar is the cube, which has six faces; the others have four, eight, 12 and 20. James quickly worked out how to make them out of pasteboard and went on to make other symmetrical solids derived from the basic ones.
We do not know what triggered his thoughts on this topic: he may have read something but it is unlikely to have been a mathematical account. Whatever the stimulus, James’ response showed an intuitive grasp of symmetry and a flair for exploring different forms of it, qualities that later shone through his scientific work.
At first, the method of teaching in James’ class was not very different from that of his old tutor. The boys spent long hours reciting Greek verbs and doing routine arithmetical exercises, and the class master, Mr Carmichael, was free with the tawse —a fearsome leather strap cut into strips at the end. But gradually the rote-based drudgery gave way to more appealing work and James began to take interest and be noticed. From somewhere near the bottom of the class in his first year, he rose to 19th overall in the second and won the prize for scripture biography.
He came to see that Greek and Latin were worth learning and his position in class improved. As the boys had to sit in places corresponding to their rank in the class, he now found himself in more sympathetic company. His knowledge of the Bible, which probably exceeded that of the masters, helped him to win the scripture biography prize in his second year, but it was in the third year that things really started to happen. Mathematics lessons began and ‘Dafty’ astonished his classmates by the ease and speed with which he mastered geometry. His confidence boosted, he became less reticent in the other lessons; he began to shine in English and was soon in the top group in all subjects.
By a stroke of luck, Lewis Campbell’s family moved to a house almost next door to Aunt Isabella’s. Lewis was the star of James’ class, a very clever boy who was well liked and usually came top. He and James had just begun to strike up a friendship before the move. Now they walked home together, often continuing the conversation by an open front door until voices from inside complained of the draught. The world opened up for James. For the first time he could share his teeming ideas with someone of his own age. Geometry was their first common ground but soon the topics ranged over the full sweep of their experiences and thoughts. It became a lifelong friendship. When Maxwell died at the age of 48, Campbell wrote a moving biography.
James’ friendship with Lewis Campbell put an end to his social isolation in school. Soon he found himself among a group of boys with lively minds who enjoyed his whimsical chatter and his unending flow of thought-provoking ideas. Among them was another who was to become a lifelong friend, Peter Guthrie Tait3.
P. G. Tait became one of Scotland’s finest physicists. As we shall see, the careers of Maxwell and Tait ran closely in parallel: more than once they found themselves competing for the same post. But friendship far outstripped rivalry and they continued the practice, begun as schoolboys, of bouncing ideas off one another. At school the two of them were always challenging each other with ‘props’, mathematical propositions or problems4. One was to find the shape of a mirror that would show a person his image the right way round. When both were senior professors, their letters, or more often postcards, were still written in a kind of schoolboy argot, more polished than that of 25 years earlier but just as exuberant.
We now come to James’ first publication. He was 14. It was about the kinds of curves that can be drawn on a piece of paper using pins, string and a pencil. Everyone knows that if you (1) stick in a pin, (2) tie one end of a piece of string to it and the other end to a pencil and (3) draw a curve by moving the pencil with the string taut, then the curve will be a circle. Groundsmen use the same method to mark out the circles in the middle of football pitches. People who have studied a little geometry will know that the construction can be modified in an interesting way. If you use two pins instead of one, tie one end of the string to each, push the pencil against the string and move the pencil while keeping the string taut, you get an oval-shaped curve called an ellipse. Each pin is at one of the two focal points of the ellipse (just as the sun is at one focal point of the earth’s elliptical orbit). If you put the pins close together the ellipse will be almost like a circle; the further you put them apart, the flatter the oval shape becomes.
For most people this would be the end of the matter. Not so for James. He untied one end of the string from its pin and tied it to the pencil instead. Then he looped the string around the free pin, pushed the pencil against it to make it taut, and drew another curve. It was a pleasing but lop-sided oval, like the outline of an egg. This was just the beginning. He reasoned that the simple ellipse could be defined as the locus of a movable point from which the sum of the distances to the two focal points (pins) was constant (the length of the string). As an equation:
p + q = s
where p is the distance to one focal point, q is the distance to the other and s is the length of the string. When drawing his new oval he had doubled the string between the pencil and one of the two focal points, so the equation was:
2p + q = s
He drew more curves, varying the number of times he looped the string around each pin, and got various egg-shaped ovals with different degrees of pointedness. He saw that, in principle, he could loop the string any number of times around either pin and thus generate a whole family of ovals:
mp + nq = s
where m and n are any integers. He then went on to draw curves with three, four and five focal points.
It was not unusual for James to produce geometrical propositions. He was doing it all the time. But his father decided to show this set to James Forbes, a friend who was professor of natural philosophy at Edinburgh University. He and his mathematical colleague Philip Kelland were struck by the boy’s ingenuity.
They combed the mathematical archives to see if anything at all similar had been done before. Sure enough, it had—by no less a person than René Descartes, the famous seventeenth century French mathematician and philosopher. Descartes had discovered the same set of bi-focal ovals but James’ results were more general and his construction method simpler. What is more, his equation for bi-focal curves turned out to have a practical application in optics.
Here was James’ debut on the scientific stage. Forbes read the paper5 to the Royal Society of Edinburgh because James was deemed too young to do it himself. It generated a lot of interest. Among those interested was D. R. Hay, a printer and an artist whose attempts to create pleasing shapes by mathematical means were well known in Edinburgh. It was his quest for ‘the perfect oval’ that had prompted James to experiment with pins and string. It transpired that Hay had also tried pins and string and had eventually had some success using three pins. But he used just a simple loop. This gave an oval made up from three part-ellipses joined together, neat but not very beautiful. The question ‘Why didn’t I think of that?’ comes to all of us at some time but rarely as emphatically as it must have struck Mr Hay when he saw James’ solution.
Level-headed as he was, James enjoyed the celebrity. His father was pleased as Punch. But the ovals paper marked the start of James’ scientific career in another, far more significant, way. It introduced him to the work of René Descartes, one of the great creators of mathematics. As it happens, he soon found a small mistake in the great man’s calculations, but the overwhelming feeling he had was one of fellowship. He went on in later years to read the work of all the pioneers in each area of science to which he turned his hand.