Professor Maxwell's Duplicitous Demon

by Brian Clegg

  Glenlair wasn’t a grand aristocratic country house – it was effectively a large farmhouse,¶ though Maxwell would extend it considerably in the 1860s. It was big enough to entertain and to have space for Maxwell’s scientific ventures when he was older, but on a scale where it still felt homely. Glenlair would remain an important focal point for Maxwell throughout his life.||

  Despite the suggestion that he was rendered hesitant by the bad treatment of his tutor, Maxwell seems not to have been a sensitive child. And it’s just as well, given his reception when he was sent to the Edinburgh Academy for the first time at the age of ten. Schoolchildren have never been slow to pick on those who are different, and Maxwell offered them rich opportunities for mockery, especially as the first-year class was full and so he was plunged straight in with older, better-established boys.

  It wasn’t just his accent, marking him out as provincial, that made the young Maxwell a target for mockery. He arrived at the school dressed in a combination of tweed jacket, frilly-collared shirt and brass-buckled shoes that were guaranteed to make him look like a mongrel throwback from fashion history. Maxwell reported that he returned home on the first day with his tunic reduced to rags, though he appeared to find this more amusing than frightening.

  The Academy was a relatively new school, which had been open for just eighteen years when Maxwell first attended. It was set up to compete with the classical education provided by English public schools. As such, it had a focus on giving its pupils independence and hard discipline alongside a rigid curriculum that focused intensely on the classics with perhaps a spot of maths; there was very little science. As the father of the founder of the Scouting movement Robert Baden-Powell commented in 1832: ‘Scientific knowledge is rapidly spreading among all classes except the higher, and the consequence must be, that that class will not long remain the higher.’

  Having such a limited curriculum seemed to be a mark of pride in the public schools. John Sleath, High Master of the prestigious St Paul’s School in London during the early part of the nineteenth century, wrote to his parents: ‘At St Paul’s School we teach nothing but the classics, nothing but Latin and Greek. If you want your boy to learn anything else you must have him taught at home, and for that purpose we give him three half-holidays a week.’

  This was a period when public schools were hardly centres of excellence. For example, the pupils of Rugby School took their masters prisoner at sword-point and were overcome after the reading of the Riot Act resulted in an armed rescue. With very little parental supervision, many schools, even the big names, provided a shoddy education in return for their fees. At Eton, to keep the costs of teaching staff down, boys could be taught in groups that were nearly 200 strong. While conditions were not so extreme at Edinburgh, in Maxwell’s early years, classes could have 60 or more pupils.

  However, reforms were underway in the school system, with more opportunity to have a ‘modern’ side as an alternative to the classics, and Edinburgh Academy was arguably more up-to-date in its approach than many of its older English equivalents. Even so, not used to the pressures of school life, having always had the time to think at his own pace, Maxwell came across as slow to learn. A combination of this and his rural accent earned him the nickname Dafty, which stuck even when it became clear that he was extremely academically gifted. Inevitably, though, so far away from his familiar home and the estate, it took Maxwell a while to bed in. A classmate called him ‘A locomotive under full steam, but with the wheels not gripping the track’.**

  Maxwell was not exactly a loner at school, but simply seemed to carry on as he had before, doing his own thing – if others wanted to join him, that was fine, but he seemed in no hurry to conform. Thankfully, his aunts quickly provided him with more conventional clothing when it was realised that his dress appeared more than a little eccentric. Maxwell certainly seemed comfortable when at home at Isabella’s house, 31 Heriot Row, a handsome four-storey grey stone townhouse with a small park out the front. He had a chance to explore both the house’s excellent library and what the natural world of Edinburgh had on offer for him to observe. Though the school took boarders, it always had day boys as well, including Maxwell.

  With time, Maxwell’s limited social contact at school grew. A like-minded student who did not consider it embarrassing to be academic, Lewis Campbell moved to live near Heriot Row, and soon the two boys spent their journeys to and from school together, developing a strong bond that would last a lifetime. They had now reached an age when the school added mathematics to its limited classical curriculum – something omitted in the first two years – and Maxwell not only found that he excelled at the subject, but that he and Campbell shared a love of maths (and a certain amount of rivalry in their ability to solve mathematical problems).

  Once this barrier was broken through, it seemed easier to gain friends who had an interest in science and nature, notably Peter Tait. Another lifelong friend, Tait would himself go on to become one of Scotland’s leading physics professors, in his early career even managing to beat Maxwell to take an academic post. At school, Maxwell came second to Tait in mathematics in 1846 (at the time his best subjects were scripture, biography and English verses) but pulled ahead in 1847. When secure in his little group with Tait and Campbell, Maxwell loved the opportunity to puzzle through mathematical and physical challenges, something that inspired him at the age of fourteen to come up with his first academic paper – though strangely his investigations owed as much to the arts as the sciences.

  The young mathematician

  Maxwell’s father regularly took him to meetings of both the Royal Society of Edinburgh and the Royal Scottish Society of Arts (RSSA). It was here that Maxwell became familiar with the work of the local artist David Ramsay Hay. In Hay’s philosophy, Maxwell found a point of view that was similar to his own – Hay both delighted in the beauty of nature and wanted to apply scientific measurements to it. Maxwell would later spend much effort on the nature of colour and colour vision – Hay was interested in a mathematical representation of the beauty of colour. But, equally, Hay was fascinated by the mathematics of shape and it was here that Maxwell’s paper seems to have drawn its inspiration. Hay would later give a paper at the RSSA on ‘Description of a machine for drawing a perfect egg-oval’. Maxwell’s youthful paper was on the subject of curves such as ovals that can be drawn using a pencil, a piece of string and pins.

  Maxwell’s experimental apparatus resembled a primitive version of the popular 1960s toy Spirograph. By placing pins through a sheet of paper into a piece of card and looping a length of string around the pins, it’s possible with some care to draw simple geometric shapes. With a single pin, you get a circle. Two pins produce the dual foci of an egg-like ellipse. This much was standard school fare, but Maxwell took the investigation significantly further. He looked at what would happen with the string tied to one or more pins and the pencil, allowing for different numbers of loops around each of the two pins, and worked out an equation that linked the number of loops, the distance between the pins and the length of the string.

  Maxwell shared his work with his father, who showed it to his friend James Forbes, Professor of Natural Philosophy†† at Edinburgh University. Fascinated by this precocious piece of work, Forbes brought in a mathematician from the university, Philip Kelland, who checked through the literature for precedents.‡‡ Although some similar work had been done by the French scientist and philosopher René Descartes, Kelland discovered that not only was Maxwell’s approach simpler and easier to understand than Descartes’, it was more general than the results that Descartes had published.

  Given the originality of young Maxwell’s work, Forbes was not going to let the effort go by rewarded with nothing more than a pat on the head. He managed to present Maxwell’s paper, now grandly titled ‘Observations on Circumscribed Figures Having a Plurality of Foci, and Radii of Various Proportions’, at the Royal Society of Edinburgh in April 1846. The fourteen-year-old Maxwell could not presen
t the paper himself as he was both too young to do so and not a member, but he had regularly attended Royal Society meetings with his father and was present to hear his work read. The paper was well received and cemented Maxwell’s growing feeling that his future lay in science and mathematics. It is too long (and, frankly, too boring) to reproduce here, but here is the opening sentence to get a feel for the young Maxwell’s precocious (and somewhat long-winded) output:

  Some time ago while considering the analogy of the Circle and the Ellipsis – and the common method of drawing the latter figure by means of a cord of any given length – fixed by the ends of the foci – which rests on the principle, that the sum of the two lines drawn from the foci to any point in the circumference is a constant quantity, it occurred to me that the Sum of the Radii being constant was the essential condition in all circumscribed figures, and that the foci may be of any number and the radii of various proportions.

  Maxwell must have been delighted to see as august a body as the Royal Society of Edinburgh begin the description of his work with: ‘Mr Clerk Maxwell ingeniously suggests the extension of the common theory of the foci of the conic sections to curves of a higher degree of complication in the following manner:—.’ Although Maxwell continued with his general education, he began to read voraciously from the books and papers of the scientific greats, developing a particular affection for the down-to-earth approach of the self-taught English scientist Michael Faraday, who had become a leading light of the Royal Institution in London by the time Maxwell was at school.

  Churchman and country squire

  We tend these days to make a clear distinction between scientific study and religious beliefs, but Maxwell came from the last generation in the British tradition where there was no feeling of conflict between the two. Like many of the scientific greats before him (including Faraday and, in his own strange way, Newton), Maxwell had a deeply held religious faith. On his breaks from Edinburgh, back home in Glenlair, the family and their servants would join together each day in prayer, and the entire household made the five-mile trek each Sunday to attend the Presbyterian Church of Scotland’s Parton Kirk – where his mother was buried, in a grave inside the ruins of the Old Kirk that would eventually also hold his father, Maxwell himself and Maxwell’s widow. While he was in Edinburgh, his Aunt Jane made sure this observance was kept up, taking him to attend both Episcopal and Presbyterian churches, cementing a religious faith that remained strong throughout Maxwell’s life.

  Regular breaks at Glenlair would remain an essential for Maxwell, whether he was a student or professor. It was a total break from the bustle of the city or the rigours of an academic institution. In his obituary for Maxwell, his friend Peter Tait would comment of his schooldays:

  [H]e spent his occasional holidays in reading old ballads, drawing curious diagrams, and making rude§§ mechanical models. His absorption in such pursuits, totally unintelligible to his schoolfellows (who were then quite innocent of mathematics), of course procured him a not very complimentary nickname …

  Wherever he worked as an adult – he would later be based in Aberdeen, London and Cambridge – Maxwell’s summers would be spent on the Glenlair estate. When at home, in almost all respects, Maxwell would be a typical country gentleman of the period – except for his unusual enthusiasm for and delight in nature. Where most of his contemporaries enjoyed nothing better than a mass slaughter in the shooting season, Maxwell never took part in hunting and shooting.

  Even though he continued to live at 31 Heriot Row with Aunt Isabella, the influence of Maxwell’s family was about to wane, as he transferred from the Academy to Edinburgh University at the age of sixteen. It might seem after his clear demonstration of mathematical originality that he would have already set his sights on a mathematical or scientific career, but this was a period when professional scientists like Michael Faraday and Faraday’s former boss Sir Humphry Davy were in the minority. The word ‘scientist’ was only coined in 1834 when Maxwell was three, and took a while to settle in. Some alternatives of the period were ‘scientician’ and ‘scientman’. Maxwell is often considered one of the first truly modern scientists.

  It was not that landed gentry did not partake in science. It was just that someone of Maxwell’s status was far more likely to perform their scientific work as an amusement, a hobby to pass the time – so Maxwell’s original intention had been to follow his father in entering the law. However, Edinburgh University was still using the traditional broad approach of the ancient university curricula, so had both mathematical and natural philosophy (science) content in its degree course. It’s notable from a letter that Maxwell wrote to Lewis Campbell in November 1847 that the maths and science were the parts that dominated his interest:

  As you say, sir, I have no idle time. I look over notes and such like until 9.35, then I go to Coll., and I always go one way and cross streets at the same places; then at 10 comes Kelland [mathematics lecturer, Philip Kelland]. He is telling us about arithmetic, and how the common rules are the best. At 11 there is Forbes [Maxwell’s father’s friend, the physics professor], who has now finished introduction and properties of bodies, and is beginning Mechanics in earnest. Then at 12, if it is fine, I perambulate the Meadows; if not, I go to the Library and do references. At 1 I go to Logic [with Sir William Hamilton].

  The only passing mention of the classics in his letter is to say, ‘I intend to read a few Greek and Latin [textbooks] beside’. Classics was a compulsory part of the majority of university courses. There is no mention at all of the law – this would be picked up after his university degree.

  Perhaps most importantly, Maxwell had access to the university’s limited laboratory equipment (likely to be in an outhouse, as there was no purpose-built lab at Edinburgh in 1847) when he had the time, encouraged by family friend Professor James Forbes. It was here, and in a workroom at Glenlair during the long summer vacation, as much as in the formal training he received at the university in logic and natural philosophy, that Maxwell’s unstructured, youthful scientific curiosity was forged into a first-class scientific mind.

  The university life

  At the time, some of the personal oddities that had got Maxwell mocked at school still remained part of his nature. His early biographers note: ‘When he entered the University of Edinburgh, James Clerk Maxwell still occasioned some concern to the more conventional among his friends by the originality and simplicity of his ways. His replies in ordinary conversation were indirect and enigmatical, often uttered with hesitation and in a monotonous key.’ While he grew out of this (apart, apparently, from when ‘ironically assumed’), his relative frugality, preferring the third-class railway carriage to the first, and a tendency to lose himself in thought while at the dinner table would remain with him for life.

  The experimental side of the course at Edinburgh was limited and sometimes verged on the amateurish. Maxwell noted in a letter to his friend Lewis Campbell:

  On Saturday, the natural philosophers ran up Arthur’s Seat with the barometer. The Professor [presumably Forbes] 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.

  The barometer in question was likely to be an inverted tube of mercury, measuring atmospheric pressure which was then used to calculate the height above sea level of the famous rocky outcrop above Edinburgh.

  In the same letter, Maxwell makes a first mention of a devil that would be a companion for much of his life – though not the titular demon of this book. He wrote:

  Then a game of the Devil, of whom there is a duality and a quaternity of sticks, so that I can play either conjunctly or severally. I can jump over him and bring him round without leaving go of the sticks, I can also keep him up behind me.

  This refers to the game known as ‘the devil on two sticks’, now more commonly called diabolo, where a double cone, joined point to point, is kept in the air using a string between two rods.


  For much of his career, Maxwell would supplement his academic work with experiments in a series of home laboratories that would eventually have been better equipped than a university. It was not until he was involved in setting up the prestigious Cavendish Laboratory in Cambridge (see Chapter 8) that he would have significant access to a professional, university-based workshop. During his time at Edinburgh University, he got together a small lab at Glenlair in a room over the wash-house. In the summer of 1848 (when Maxwell was seventeen), he wrote to Lewis Campbell:

  I have regularly set up shop now above the wash-house at the gate, in a garret. 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 [sic] a lot of bowls, jugs, plates, jam pigs,¶¶ 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,††† and a countless variety of little beetles, spiders, and wood lice, which fall into the different liquids and poison themselves … I am making copper seals with the device of a beetle. First, I thought a beetle was a good conductor, so I embedded one in wax (not at all cruel, because I slew him in boiling water in which he never kicked), leaving his back out, but he would not do.

  Although Maxwell was busy with his experiments that summer, it didn’t stop him from writing highly mathematical papers. He had continued to do this since his first success at the Royal Society of Edinburgh aged fourteen, though often the documents were just handwritten for the consumption of his friends. However, in 1848 he wrote a paper stretching to 22 long pages called ‘On the Theory of Rolling Curves’, published the following year in the Transactions of the Royal Society of Edinburgh. This combines geometry with some sophisticated algebra and calculus, describing how one curve, rolling along another curve (which is ‘fixed to the paper’) would produce a third curve.