The Man Who Changed Everything

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.

The great men became his friends; he appreciated their struggles, knowing that most discoveries come only after a period of stumbling and fumbling. By also studying philosophy he gained a deeper insight into the processes of scientific discovery than any other man of his time. Nobody understood better than Maxwell the broad sweep of historical development in science. Set alongside this knowledge was his own extraordinary originality and intuition. Together, these components produced what the great American physicist Robert Millikan described as ‘one of the most penetrating intellects of all time’.

One of the things Maxwell learned from his reading was the fallibility of men’s efforts to understand the world. All of the great scientists had made mistakes. He was acutely aware of his own tendency to make errors in calculation. ‘I am quite capable of writing a fancy formula’, he once wrote to a friend, meaning a wrong formula. In fact, his intuition often led him to correct results even when he had made mistakes along the way. When reading the work of fellow scientists, past or present, he was tolerant of mistakes but sharply critical of any failure to be honest and open with the reader. Poisson is rebuked for ‘telling lies about the way people make barometers’ and Ampère for describing only polished demonstrations of his law of the force between wires carrying electric currents and hiding the rougher experiments by which he had originally discovered the law.

James enjoyed his last 2 years in school despite several periods of sickness: although strong and athletic he was prone to spells of ill-health. His achievements in English matched those in mathematics: he seemed to have no trouble recalling anything he had read and showed an amazing facility for composing verse on any topic in impeccable rhyme and metre. He also won school prizes for history, geography and French, and came second overall in his class in the final year. He entertained his fellows with whimsical poems and discussed all manner of things with Lewis Campbell, P. G. Tait and other boys with a serious turn of mind. One of them later recalled how the school governors, no doubt wishing to impress parents of future pupils, decided to add the new subject of ‘physical science’ to the curriculum without too much concern over who would teach it. All he could remember of the lessons was that Maxwell and Tait knew a lot more than the master did.

Sometimes James would stay for a while in his Aunt Jane’s house in a nearby part of the town⁶. As his mother’s sister, and with no children of her own, Aunt Jane did her best to give the boy the sort of guidance she felt Frances would have done. Kind-hearted but sharp of tongue, she could have been a character model for David Copperfield’s Aunt, Betsy Trotwood. She tried to soften James’ eccentricities and improve his social poise: when his thoughts were distracted by the pattern of light in a table glass or the swaying of a candle flame he would be recalled to the company by a sharp ‘Jamesie, you’re in a prop’.

She also saw to it that he attended the Episcopal church every Sunday as well as the Presbyterian one, and arranged for him to go to her friend Dean Ramsay’s catechism classes. Ramsay was good with young people and used to caution them against being carried away by the breakaway Presbyterian Free Church movement or any of the zealous new religious groups. In fact, James needed no such warning. His faith was the guiding principle of his life but it was an intensely reflective personal faith which could not be contained within the rules of a sect. Institutional politics, whether of the church, the state or the university, was a topic that never engaged his interest.

Another favourite relation was Uncle John. John Cay was his mother’s and Aunt Jane’s elder brother, and his father’s long-standing friend. Like John Clerk Maxwell he was a lawyer, but a more successful one who became a judge. The two Johns shared an enthusiasm for technology. In their younger days they had tried without success to make and market useful inventions; one project was for a bellows that would produce a continuous, even blast. One day he took James and Lewis Campbell to visit William Nicol, the celebrated experimental optician, who had invented a way of polarising light using prisms made from carefully cut Iceland spar. Prisms like these later became known simply as nicols, part of the standard toolkit. James was fascinated by all he saw in Nicol’s workshop and the visit was to have an important sequel.

The best times of all were holidays at Glenlair. James kept up his local friendships and joined in the Happy Valley social life. There was riding, walking the hills, picnics and archery in the summer, and curling in the winter. He helped the farm workers bring in the harvest. The one pastime James avoided was shooting. He did not condemn others; it was simply that he could not bring himself to do it. He loved animals of all kinds and seemed to have an easy rapport with them: he could ride the most wilful horse and teach any dog to do tricks.

He made himself useful by helping his father with estate business. The property had been in a poor state when his parents moved there. The building of the house had taken up most of what John could afford and the rest had to go into basic land improvements like stone clearance, drainage and fencing. Gradually, more was done and John was able to put up the outbuildings he had planned from the start. Plans to extend the house and replace the ford across the river Urr by a bridge still had to wait.

Not all holidays were taken at Glenlair. Christmases were generally spent with James’ uncle Sir George Clerk at Penicuik, where skating was a big attraction. After a busy political career, Sir George was at this time Master of the Royal Mint. He was also an accomplished amateur zoologist who later became President of the Zoological Society. His political skills were needed there; two of his Vice Presidents were renowned swashbucklers who held opposing views on just about everything. Their most famous clash was at a meeting at Oxford in 1860, where Bishop ‘Soapy Sam’ Wilberforce set out to smash Darwin’s theory of the Origin of Species but was himself demolished by Thomas Henry Huxley.

There were visits to Glasgow to see James’ cousin Jemima, who was by now living there. She had fallen in love with and married Hugh Blackburn, Professor of Mathematics at Glasgow University. Hugh was friendly with the ebullient new Professor of Natural Philosophy, William Thomson. Appointed professor at the age of 22, Thomson was a brilliant and inspirational man. In the course of 53 years in the same post he became, as Lord Kelvin, the patriarch of British science. He could see at once that the boy had a rare gift and the two struck up a friendship which lasted throughout Maxwell’s life. Thomson was a man from whom ideas flew like sparks. He and Faraday were the two people whose work most influenced Maxwell’s own.

Every minute of James’ day was occupied. When on his own at home he would read, write letters, work at his ‘props’, or try experiments in an improvised laboratory. His only frivolous diversion was to practise tricks with the devil on two sticks^a—a kind of top which could be spun, thrown and caught using a string tied to two hand-held sticks—on which he soon became a virtuoso. Even then he was no doubt sharpening his insight into the theory of angular momentum.

In mid nineteenth century Britain the word ‘scientist’ had not yet come into common use. Physicists and chemists called themselves ‘natural philosophers’ and biologists called themselves ‘natural historians’. Many people who did scientific work were gentlemen of independent means. Others were clergymen or doctors or lawyers or businessmen for whom science was a hobby. Several members of the Clerk and Cay families were just such men. There were a few professional posts, in universities and in organisations like the Royal Observatory and the Royal Institution, but they were poorly paid and rarely became vacant because their holders tended to remain for life. Competition for the best posts was very stiff. Science was thought of as interesting but not particularly useful. There had been rapid advances in industry and transport but these had mostly been brought about by practical engineers with little formal scientific background. The problem of finding longitude at sea had been solved not by the mathematical astronomers but by John Harrison and his clocks. Some ingenious physicists, like Charles Wheatstone and William Thomson, were turning their talents to inventing devices for the new telegraph but, with this exception, little of the work of Faraday and others on electricity and magnetism had yet fed through to practical application. In short, science was a splendid hobby for a gentleman but a poor profession.

John may also have reflected on his own failure as an advocate and hoped that his son would make amends. James felt the tension between his father’s wish and his own bent for science. But he was interested in plenty else besides: literature and philosophy were stimulating and, who knows, the law might draw him too when he got to know it.

In any case no decision had to be made yet. The next step was to enrol at Edinburgh University, where he would study mathematics under Philip Kelland, natural philosophy under James Forbes and logic under the famous Sir William Hamilton. James was looking forward to spreading his wings. He celebrated the move in characteristic fashion with a poem: an affectionately ironic tribute to his old school⁷.

If ony here has got an ear,
He’d better tak’ a haud o’ me
Or I’ll begin, wi’ roarin’ din,
To cheer our old Academy.

Dear old Academy,
Queer old Academy,
A merry lot were we, I wot,
When at the old Academy.

There’s some may think me crouse wi’ drink,
And some may think it mad o’ me,
But ither some will gladly come
And cheer our old Academy.

Some set their hopes on Kings and Popes,
But o’ the sons o’ Adam, he
Was first, without the smallest doubt,
That built the first Academy.

Let pedants seek for scraps of Greek,
Their lingo to Macadamize;
Gie me the sense, without pretence,
That comes o’ Scots Academies.

Let scholars all, both grit and small,
Of learning mourn the sad demise;
That’s as they think, but we will drink
Good luck to Scots Academies.