The Man Who Changed Everything

James came to Edinburgh University at 16, a boy who had a penchant for science and mathematics but who would probably nevertheless follow his father’s wish and go in for the law. He left for Cambridge University at 19 as a young man set on a scientific career.

The change of direction was urged on James’ father by Hugh Blackburn and James Forbes as it became more and more clear that the boy’s vocation was, in his own words, for ‘another kind of laws’. John Clerk Maxwell was always slow to make up his mind but in the end made the right decision, as no doubt everyone knew he would. Cambridge was acknowledged to be the best university for anyone likely to make his mark in science and most writers about Maxwell express regret that he did not go there sooner. They may be right but, as we shall see, the 3 years at Edinburgh did much to make him the kind of scientist he was.

Scottish universities strove to open up higher education so that the ‘lad o’ pairts’ from a humble background could take his place alongside the sons of gentlemen. They prided themselves on producing self-confident young men who would be able to tackle any task and hold their own in any company. The courses were broad: future doctors, lawyers, church ministers, teachers and engineers would study Latin, Greek, civil and natural history, mathematics, natural philosophy and mental philosophy. Mental philosophy—we would now call it simply philosophy—was the bedrock. At Edinburgh it carried more prestige than any other subject and had two professorships, one in logic and metaphysics and another in moral philosophy.

Faced with the choice of classes, James was like a hungry child in a cake shop. He decided to start with natural philosophy, mathematics and logic. At first the lectures in natural philosophy and mathematics were too elementary to be interesting but he was captivated at once by Sir William Hamilton’s talks on logic, which soon spilled over to metaphysics and other aspects of philosophy. Hamilton—not to be confused with the Irish mathematician Sir William Rowan Hamilton—was a celebrated philosopher in his own right and an inspirational teacher. James had found someone who did not shirk from answering his awkward questions and he was delighted to find that the answers sometimes came in the form of yet deeper questions. There is little doubt that the profoundly philosophical approach which was to serve Maxwell so well in his work had its roots in Hamilton’s classes.

To understand what this philosophical approach was, and why it was so important, we must take a short historical diversion. David Hume, the great eighteenth century Scottish philosopher, had put the cat among the pigeons with his notion of scepticism: that nothing can be proved, except in mathematics, and that much of what we take to be fact is merely conjecture. This alarmed some of his hard-headed countrymen, who reacted by starting their own ‘Common Sense’ school. They thought it was daft to doubt whether the world exists and wrong to doubt whether God exists. But, these things given, they rejected any belief or method that did not proceed directly from observed fact. The way to make scientific progress, they said, was by simple accretion of experimental results, a narrow interpretation of the principle of induction that the Englishman Francis Bacon had advocated more than a century earlier. Imagination had no place in their system.

In fact, the Common Sense school could hardly have been more wrong; empirical evidence is vital but all innovative scientists are strongly imaginative and make full use of working hypotheses which are often drawn by analogy with other branches of science. Luckily the school’s adherents eventually realised this and came to a view that truly was common sense: analogies and imaginative hypotheses can be wonderful but should be kept in their place; a scientist should remain sceptical about his own pet fancies even when they have led to progress. Many scientists cease to be creative when they fail this test and become slaves to their own creations. Maxwell never did.

Hamilton was very much his own man and expounded his own, sometimes contentious, views. He derided all attempts to ‘prove’ that God exists, holding that knowledge and logic, while essential tools for investigating the universe, were powerless to find its cause. James went along with this but had no doubt that Hamilton was wrong when he belittled mathematics. On safer ground, Hamilton agreed on most points with the Common Sense school but also respected the ideas of Immanuel Kant, Hume’s German contemporary. He stressed Kant’s proposition that all knowledge is relative: we know nothing about things except by their relationship to other things. This struck a powerful chord. It was not long before James was bringing such thoughts to bear on his scientific work. In an exercise for Hamilton on the properties of matter, James wrote:

Now the only thing which can be directly perceived by the senses is Force, to which may be reduced light, heat, electricity, sound and all the other things which can be perceived by the senses.

Twenty years on, when James was checking a draft of Thomson and Tait’s Treatise on Natural Philosophy, he had to correct them on this very point. They had defined mass incorrectly and had to be told ‘matter is never perceived by the senses’. Lacking Maxwell’s philosophical faculty, they had simply not turned their thoughts in the right direction. This little example gives us an idea of how Maxwell was able to explore regions of scientific thought that his contemporaries could not reach.

Maxwell’s greatest work shows two unique characteristics which stem from his philosophical insight. The first is the way he could return to a subject, often after a gap of several years, and take it to new heights using an entirely fresh approach. He did this twice with electromagnetism. The second is even more remarkable. His electromagnetic theory embodied the notion that things we can measure directly, like mechanical force, are merely the outward manifestations of deeper processes, involving entities like electric field strength, which are beyond our powers of visualisation. This presages the view that twentieth century scientists came to. As Banesh Hoffmann puts it in The Strange Story of the Quantum: ‘There is simply no way at all of picturing the fundamental atomic processes of nature in terms of space, time and causality’.

James was not just a thinker. He wanted to make experiments and was fortunate to have inspirational encouragement from James Forbes ¹. The two developed a rare rapport; James used to stay long after hours and was allowed to use the professor’s laboratory to carry out all manner of investigations. Recognising the boy’s talent and potential, Forbes simply let him follow his fancy. This was exactly the way James learnt best; he became expert in using the standard apparatus and in improvising his own when needed. The experience was so exhilarating that James later always tried to give his own research students similar freedom. Even when Director of the Cavendish Laboratory he never told people what research to do unless they asked him. ‘I never try to dissuade a man from trying an experiment’, he said to a friend, ‘if he does not find what he wants he may find out something else’².

Forbes also helped to form the lucid literary style which characterised Maxwell’s scientific writing. James had submitted a sloppily drafted paper to the Royal Society of Edinburgh and Forbes’ mathematical colleague Philip Kelland was asked to referee it. Knowing that James needed to learn the lesson, Forbes undertook to deliver the critical comments himself. He pulled no punches: ‘ ... It is perfectly evident that it must be useless to publish a paper for the use of scientific readers generally, the steps of which cannot, in many places, be followed by so expert an algebraist as Prof. Kelland...’. The sharp reproof was an act of kindness and James knew it. He went on to develop a style of scientific writing that was all his own. Scholars find it as distinctive as others find the sound of Louis Armstrong’s trumpet or the brushwork of Vincent van Gogh. The tone is authoritative but fresh and informal; the equations spring naturally from the arguments. Maxwell never managed to eliminate entirely his propensity to make algebraic slips and some found their way into his papers. Also, the concepts are in places so subtle and original that scholars still argue about exactly what Maxwell meant. Nevertheless, he left a superb body of published work, from which many of the standard texts used by today’s physics and engineering students are derived.

Forbes was an all-round natural philosopher with a wide range of interests but his special passion was earth science, in which he was an energetic pioneer³. He invented the seismometer, measured the temperature of the earth at different depths, and was one of the first people to make a serious study of glaciers. For him, as for James, science was to be found everywhere. Sometimes, at weekends, he became a kind of scientific scoutmaster, taking the students on field trips, where boisterous joshing went along with serious endeavour. On one outing Forbes was uncharacteristically careless with his calibration: probably on purpose, to test the mettle of his young charges. James reports in a letter to Lewis Campbell:

On Saturday, the natural philosophers ran up Arthur’s Seat with the barometer. The Professor set it up at the top and let us pant at it till it ran down with drops. He did not set it straight, and made the hill grow fifty feet: but we got it down again.

Everything Forbes said or did on scientific topics was meat and drink to James, who was fascinated by the entire physical world. He already had keen observation and a flair for practical work; under Forbes’ influence these talents acquired discipline and professional poise. The inspiration that young James drew from Forbes is plainly seen in a book review he wrote many years later for the journal Nature:

If a child has any latent talent for the study of nature, a visit to a real man of science at work 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 conditions of the operation.⁴

When his mentor died in 1868, James told a friend, ‘I loved James Forbes’.

Not surprisingly, Forbes and Hamilton greatly outshone their fellow professors. Philip Kelland gave a useful mathematics course but James was not at all impressed by Professor Wilson’s lectures in moral philosophy which, to his mind, served only to demonstrate that woolly thinking leads to wrong conclusions⁵. He enjoyed chemistry but thought it odd that lectures from Professor Gregory were given separately from practical chemistry sessions under Mr Kemp, particularly as ‘Kemp the Practical’ was apt to describe procedures taught by Gregory as ‘useless and detrimental processes, invented by chemists who want something to do’. This experience helped to form Maxwell’s conviction that practical work is not only essential to a proper scientific education but should be part and parcel of the lecture course, not tacked on as an afterthought.

The formal courses supplied only a small part of the knowledge James acquired during his 3 years at Edinburgh University. The rest came from reading and from making his own experiments. Much of this was done at Glenlair during the long vacation—in those days Scottish Universities closed from late April to early November so that students could go home to help with the farming. Among the many books he borrowed from the university library were Newton’s Opticks and works by some of the great French mathematicians: Fourier’s Théorie analytique de la chaleur, Monge’s Géometrie descriptive, Cauchy’s Calcul differentiel and Poisson’s Traité de mécanique. He was so smitten by Fourier’s book that he bought his own copy for 25 shillings, a considerable sum in 1849. In philosophy his reading included Thomas Hobbes’ Leviathan and Adam Smith’s Theory of Moral Sentiments. As well as all this there was some Latin and Greek, to keep his hand in, and novels and poetry for fun.

At Glenlair James spent a lot of time in an improvised laboratory-cum-workshop above the washhouse. Here he got together all the paraphernalia which the family called ‘Jamesie’s dirt’. He described the scene in a letter to Lewis Campbell:

I have an old door set on two barrels, and two chairs, of which one is safe, and a skylight above, which will slide up and down.

On the door (or table) there is a lot of bowls, jugs, plates, jam pigs^b, 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^c, and a countless variety of little beetles, spiders and woodlice, which fall into the different liquids and poison themselves.

Sir Donald Bradman, greatest of all batsmen, used to say that he developed his superb eye and timing by spending hours as a boy hitting a golf ball against a wall with a cricket stump. James was doing something similar with his rough-and-ready experimenting.

He made crude electromagnetic devices. To make more batteries he electro-plated old jam jars with copper. He did chemical experiments and entertained the local children by letting them spit on a mixture of two white powders to turn it green.

But his chief fascination was with polarised light—light in which the wave vibrations are neatly lined up rather than being higgledy-piggledy⁶. He was enthralled by the beautiful coloured patterns that polarised light revealed in unannealed glass—glass which has been cooled quickly from red heat so that internal strains are ‘frozen’ into its structure, as the outer parts cool faster than the inner. The interest was not only aesthetic; he wanted to investigate the patterns of strain, or distortion, which gave rise to the colours. To get suitable glass he cut bits of ordinary window glass into geometrical shapes, heated them until they were red-hot and then cooled them rapidly.

At first he had no ready-made device for making polarised light and had to improvise. He knew that when ordinary light meets a glass surface at a certain angle, the part of the beam that is reflected is polarised. So he made a polariser using a large match box and two pieces of glass set with sealing wax at the correct angle. Another method was to pass light through a stack of ‘polarising plates’, thin slices of a crystalline material. To get suitable plates he spent hours patiently sawing and polishing strips of brittle saltpetre.

The coloured patterns turned out to be even more striking than expected. By ingenious jury-rigging he built a camera lucida, which made a virtual image of the coloured patterns appear on a piece of paper, so that he could copy them in watercolour. He sent some of the paintings to William Nicol, the famous optician whose workshop he had visited with his uncle John and Lewis Campbell 2 years before. Nicol was so impressed that he gave James a pair of his beautiful Iceland spar polarising prisms. James prized them all his life. For the task in hand they gave him a much easier and more reliable supply of polarised light.

There was more to do. Looking at pretty patterns in glass was all very well, but James saw it as a first step. Could the same method be used more generally to show up the patterns of strain in solid bodies of different shapes when put under different kinds of mechanical stress—something of great interest to engineers? To test the idea James needed a transparent material that he could easily make into different shapes and then distort by stretching, squashing or twisting. How about jelly? It would not be amenable to stretching or squashing but it would be perfect for twisting, and all he needed was gelatine from the kitchen. He made a clear jelly in the shape of a thick ring, using a paper cylinder as the outer part of the mould and a cork as the inner. When it had set, he held the paper steady and applied torsional stress to the jelly by twisting the cork. Then he shone polarised light through the stressed cylinder of jelly and the strain patterns showed up beautifully. More jellies followed, twisted in different ways. This was the birth of the photoelastic method, which has been a boon to engineers—to try out the design of a component or structure they simply make a scale model from a transparent material, such as epoxy resin, and use polarised light to show the strain patterns under various loads.

These DIY adventures did much more than improve James’ experimental skill; they helped to give him the deep feeling for nature’s materials and processes that later pervaded all his theoretical work and was at least as important a part of that work as his mathematical ability.

There were also, of course, James’ ‘props’—mathematical investigations that took his fancy. Two of these were published while he was at Edinburgh University. Both were read to the Royal Society of Edinburgh by Philip Kelland because James was still considered too young to do so himself. The first followed naturally from his ovals paper of 3 years earlier. It was about the geometrical properties of the type of curve traced out by a point on one curve when it is rolled on another. An everyday example is the curve followed by a point on the outside of a bicycle wheel rolling on a flat road—an inverted U shape called a cycloid. One of the simpler results in James’ paper is:

If the curve A when rolled on a straight line produces a curve C, and if the curve A when rolled upon itself produces the curve B, then the curve B when rolled upon the curve C will produce a straight line.

Intriguing stuff for geometers but not likely to have much practical application.

James’ second paper was of a different order. It was an astonishing achievement for a 19 year-old working almost entirely on his own. The mathematics went hand-in-glove with his experiments using polarised light and dealt with the elasticity of solid bodies—the way they distort when put under stress. He set out for the first time the general mathematical theory of photoelasticity based on strain functions, and derived the particular functions for cylinders, spheres and beams of various sections. James verified some of these results by his own experiments and illustrated the paper with carefully hand-coloured drawings of the strain patterns shown up by polarised light. He had worked hard on this paper but through inexperience sent in a draft which was tortuous to read because he had not taken enough trouble with the wording. At this point he received the strong rebuke from Forbes which has already been reported. James saw the fault at once and put the paper right. If his passage to scientific manhood can be marked down to a single episode, this was it.

Despite all this solitary activity, it was by no means a hermit’s life for James at Glenlair. He delighted in the companionship of his father, who was in some ways more like an elder brother. He helped in the fields and passed time with the local lads. On hot days he tried to persuade them to join him swimming in the peat-brown pool where two rivers joined but they were afraid of the eels. He played with the estate children and organised them to fetch the water each morning. He joined in the ‘Happy Valley’ social life. But with so many thoughts and schemes whirring in his mind he longed for the chance to toss ideas around with friends. He wrote long letters to Lewis Campbell, describing his researches and his thoughts on philosophical issues and imploring him to visit.

For the first year at Edinburgh University he had enjoyed the company of his close friends from school. Then Lewis Campbell left for Oxford, and P. G. Tait and another friend, Allan Stewart, for Cambridge. He began to feel he was paddling in a backwater while they were striking out for exciting new shores. Perhaps he should, after all, prepare for a career at the Scottish Bar. He resolved to do some serious reading, but events then took a happy turn and he wrote jauntily to Campbell:

I have notions of reading the whole of Corpus Juris and Pandects in no time at all; but these are getting somewhat 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.

John Clerk Maxwell had, at length, agreed that James should go to Cambridge. This was not the end of the matter, as there was also the choice of college. Forbes strongly recommended his alma mater, Trinity. P. G. Tait was already at St Peter’s, known as Peterhouse, which was small and select, and Lewis Campbell’s younger brother Robert was bound for Caius, which was highly regarded but so full that all freshmen had to lodge out. The decision went in favour of Peterhouse.

So James left for Cambridge at the age of 19. He had already acquired a vast store of knowledge on all manner of subjects, having read far more than most educated people read in a lifetime. He was an experienced experimenter and had published three mathematical papers. Yet he had not worked under any pressure; there was immense intellectual power in reserve.

His ways were still odd. He had kept his Galloway accent. In strange company he was deeply reserved but when at ease with friends he would be the hub of the group, delighting them with genial banter and a flow of thought-provoking ideas on any topic. He dressed tidily but with no notion of smartness, still less fashion. He was indifferent to any kind of luxury, preferring to travel third class on the railway because he liked a hard seat. Lewis Campbell’s mother summed him up in her diary:

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.

It was arranged that James would take rooms in Peterhouse, Cambridge, on 18 October 1850.