Professor Maxwell's Duplicitous Demon

by Brian Clegg

  We’ve already met the second law of thermodynamics when I introduced myself, but let’s take a step back to discover where the whole business came from. As we have seen, the prevalent theory on the nature of heat at the start of the nineteenth century was caloric theory. This considered heat to be a fluid called caloric. One of the essential properties of caloric was that it repelled itself. This meant that if you had a hot object and a cold one in contact, there would be more caloric in the hot than the cold. This meant more repulsion in the hot thing’s caloric, so the caloric from there would naturally move into the cold object until a balance was achieved. The hot object would get cooler and the cold object hotter. (It’s that second law again.)

  This theory had proved surprisingly effective, bearing in mind it was wrong. As well as supporting the second law, it predicted that a gas should try to expand as it got hotter, as there was more caloric to fit into it. In 1824 the French scientist and engineer Sadi Carnot developed the first concepts in thermodynamics, explaining the limits on the efficiency of steam engines, entirely based on caloric theory. The man who took Carnot’s ideas and brought them into a more modern viewpoint of thermodynamics was JCM’s frequent correspondent and friend, William Thomson, later Lord Kelvin.

  Thomson’s work in formulating thermodynamics was aided by input from an unlikely source – the brewer James Joule (who, in a neat symmetry, had been tutored by Dalton). It was Joule who helped kill off caloric theory by showing that heat was not a special fluid in its own right, but simply a manifestation of energy, which could be reliably and consistently converted to and from mechanical energy. We also need to throw in the contribution of the German physicist Rudolf Clausius who worked in parallel with Thomson (and Maxwell) on thermodynamics.

  The outcome of these collective geniuses at work was to develop several laws of thermodynamics. The two biggies were the first law – the conservation of energy – stating that energy can neither be made nor destroyed, but is just transferred from one form to another (these forms, most importantly, including heat); and my demonic law, the second law. This started in the days of caloric – the idea of the fluid naturally moving from hot to cold – but would become formalised in terms of both heat flow and entropy.

  Bearing in mind the identification of heat as energy, it became important to understand how that energy manifested in matter. One common and well-understood form of energy was kinetic energy, the energy of movement. And, in gases at least, if matter could be considered to be made up of actual atoms and molecules, then the movement of those tiny particles could well provide the energy that was described as heat. The faster the particles moved, the hotter the gas.‡ It was for this reason that JCM would take atoms on board.

  However, we’re getting ahead of ourselves. The youthful James Clerk Maxwell is about to take up his post as Professor of Natural Philosophy at Marischal College. We’re off to the granite city.

  Notes

  1 – Tait’s observation that Thomson was ‘dead against atoms’ was in a letter to Thomas Andrews written on 18 December 1861, noted in Crosbie Smith and Norton Wise, Energy and Empire: A Biographical Study of Lord Kelvin (Cambridge: Cambridge University Press, 1989), p. 354.

  * His teacher, Leucippus, may also have been involved, but there is little evidence of his existence and it’s possible Democritus simply invented Leucippus as a kind of ‘fake news’ support for his theory – if so, he was my kind of guy.

  † Or for us demons to torment souls in hell.

  ‡ In reality it’s a little more complex than this, as energy can also be tucked away in the vibrations of molecules that aren’t moving freely and in the energy levels of electrons around atoms, but this is a good starting point.

  Chapter 3

  The young professor

  Marischal College is not a name that you will find on the British university scene any longer, but when the fresh-faced 24-year-old Maxwell was appointed Regent and Professor of Natural Philosophy in April 1856, starting work in August, it was a well-known constituent of the Scottish academic establishment. Though the vast, dour grey granite main building still stands on Broad Street at the heart of Aberdeen, it is now used by the city council. However, in Maxwell’s day, the college was a respected institution with a solid history stretching back to 1593. Like all ancient colleges at the time, the education it provided was broader than a modern university curriculum, though most students would have been on a path towards a career in law, the church, medicine or education.

  A city divided

  When Maxwell arrived at his new workplace, there was already talk in the air about the college’s demise. Scotland had, at the time, five universities, and two of them were in the small city of Aberdeen, then with a population of only around 35,000 people.* Marischal shared the city with the hundred-years older King’s College – this was a pre-Reformation foundation and its Catholic roots were not considered ideal for educating ministers of the Protestant kirk. In reality, ‘shared the city’ was not strictly true: the city itself was split in two, as if it had taken sides between the two establishments.

  The ‘old’ and ‘new’ towns were pretty much independent, with a mile’s gap in between them. Aberdeen old town was a relic, an island in a rural landscape consisting of King’s College itself, the old cathedral and accommodation for those who worked there. Marischal was located in the bigger and thriving new town. This had been rebuilt pretty much from scratch at the start of the nineteenth century, centred on the sweeping Union Street, a 70-foot-wide boulevard to emphasise the solid worth of the granite city – so indeed it was very much a new town in Maxwell’s day.

  Though relatively small, Aberdeen had strong commercial roots, exporting a considerable amount of its trademark granite alongside textiles from the port, which also featured shipbuilders’ yards. The newest addition in 1850, and something that opened up the city’s trade even more, was the railway link, running down through Edinburgh to London, making Aberdeen far more attractive and accessible to a relatively cosmopolitan visitor like Maxwell.

  By the time he was appointed, the religious divisions that had resulted in the setting up of the two separate universities were waning. Two years later, in 1858, Cambridge would finally drop the requirement for undergraduates to be members of the Church of England or its affiliates such as the Scottish Episcopal Church. Similarly, a Royal Commission had been set up as early as 1837 to look into the need for two separate universities in Aberdeen.

  King’s College was against a merger, but it was generally felt that the separate existence of King’s and Marischal colleges was not beneficial to the education system in Scotland. Maxwell appears to have been aware of the situation, but not unduly worried. His immediate concern was finding somewhere to live in a city that he had probably never visited before. He took up lodgings with a Mrs Byers a few minutes’ walk away from the college, his rooms reached via a quaint spiral staircase that took him above a law firm, J.D. Milne Advocates, at 129 Union Street, a location now featuring a string of familiar high street names from McDonald’s to mobile phone shops.

  Never a great enthusiast for college politics, Maxwell kept his head down and concentrated on his work as the in-fighting between the two universities continued. In fact, he noted in a letter to his aunt:

  I have been keeping up friendly relations with the King’s College men, and they seem to be very friendly too. I have not received any rebukes yet from our men for so doing, but I find that families of some of our professors have no dealings, and never had, with those of the King’s people.

  In keeping with the scale of the city, the entire university that was Marischal was not much larger than an Oxbridge college, with twenty staff (fourteen professors and six lecturers) and 250 students enrolled when Maxwell arrived. It was an enviable position that involved a very short academic year, running only from November to April – so that the students were available back home on the farm or for seasonal work – leaving the staff with plenty of time to pursue th
eir own research. For Maxwell this would mean the opportunity to spend half of his year at Glenlair, both working on natural philosophy and devoting his attention to the maintenance of the estate.

  Although Maxwell was used to working in relative isolation when he was at Glenlair, it must have come as something of a shock to move from the vibrant atmosphere of Cambridge and the intellectual cut-and-thrust of the Apostles meetings to the academic backwater that Marischal represented. He had no doubt hoped to find the opportunity for the same mix of highbrow thought and enjoyable banter among his fellow academics, but the rest of the staff at Marischal proved to be much older than he was. It might not have been unheard of to make such young appointments in the universities of the day, but it certainly wasn’t a Marischal tradition. The next closest in age of the other staff members was a 40-year-old, while the average age across Marischal’s fellows and staff was 55.

  This is not to say that Maxwell was made to feel unwelcome in his new post – quite the reverse. He was often invited out to dine with other staff members and seems to have been readily accepted into the fold – but it was inevitably a very different kind of environment from Cambridge. A letter Maxwell wrote to his school friend Lewis Campbell made it clear how things had changed: ‘No jokes of any kind are understood here. I have not made one for 2 months and if I feel one coming on I shall bite my tongue.’

  His lectures were terrible

  There seems something of a dichotomy in regard to Maxwell’s abilities as a professor in those early years. Like a number of other greats – Newton and Einstein, for example – he had some limitations as a lecturer. This was mentioned by friends such as Peter Tait, who would eventually remark in his obituary of Maxwell:

  [T]he rapidity of his thinking, which he could not control, was such as to destroy, except for the very highest class of students, the value of his lectures. His books and his written addresses (always gone over twice in MS.) are models of clear and precise exposition; but his extempore lectures exhibited, in a manner most aggravating to the listener, the extraordinary fertility of his imagination.†

  One of Maxwell’s best students at Aberdeen, a David Gill,‡ said that ‘his lectures were terrible’. It seems from Gill’s lecture notes that Maxwell prepared very clear, well-structured lectures, but had a tendency to diverge into anecdotes and analogies that left his students adrift – not helped by his lifelong tendency to make arithmetic errors. It was easy enough to correct these in his papers, but the slips he made during lectures made them something of an intellectual minefield.

  It’s worth considering, though, that most of the attendees at Maxwell’s lectures in Aberdeen would have been very different from the students on a modern-day physics course. These were not scientific specialists – physics was just one of many topics covered on their four-year curriculum, which included everything from Greek and Latin to philosophy and logic. These students were probably of a reasonable calibre, as Marischal College was unusual for Scottish universities of the time in having an entrance exam and in only charging a relatively low fee of £5, with plenty of bursaries. This meant that around half of the students were from working families, who had won places on their merits.

  Only in the third year would the natural sciences dominate for around 50 students. In his inaugural lecture, Maxwell emphasised that his course would require a shift of mindset:

  The work which lies before us this session is the study of Natural Philosophy. We are to be engaged during several months in the investigation of the laws which regulate the motion of matter. When we next assemble in this room we are to banish from our minds every idea except those which necessarily arise from the relations of Space, Time and Force. This day is the last on which we shall have time or liberty to deliberate on the arguments for or against this exclusive course of study, for, as soon as we engage on it, the doctrines of the science itself will claim our constant and undivided attention. I would therefore ask you seriously to consider whether you are prepared to devote yourself during this session to the study of the Physical Sciences, or whether you feel reluctant to leave behind you the humanizing pursuits of Philology and Ethics for a science of brute matter where the language is that of mathematics and the only law is the right of the strongest that might makes right.

  It may have been that Maxwell’s emphasis on mathematics (even allowing for an element of typical tongue-in-cheek phrasing), which he put more weight on than most of his contemporaries, was the reason his lecturing failed to endear him to many of his students. It’s also worth stressing that Maxwell was limited by the standard approach to teaching science at the time, which would not have included any laboratory work. Given his lifelong dedication to experimenting, despite being primarily what we would now think of as a theoretical physicist, it’s no surprise that he brought up the importance of experiment in that inaugural lecture:

  I ought now to tell you what my own opinion is with respect to the necessary truth of physical laws – whether I think them true only so far as experiment can be brought forward to prove them or whether I believe them to be true independent of experiment. On the answer which I give to this question will depend the whole method of treating the foundations of our science.

  I have no reason to believe that the human intellect is able to weave a system of physics out of its own resources without experimental labour. Whenever the attempt has been made it has resulted in an unnatural and self-contradictory mass of rubbish.§ In fact unless we have something before us to theorize upon we immediately lose ourselves in that misty region from which I have just warned you.

  The lack of practical opportunities for students in Aberdeen did not mean that Maxwell was limited to ‘chalk and talk’ in his lectures. Demonstrations were already well established both in public venues such as the Royal Institution in London and as part of physics teaching in universities. Maxwell would discover that Marischal’s stock cupboard was well equipped with demonstration equipment, even if it was not always of the most up-to-date nature.

  Despite any limitations in his presentation skills, Maxwell was a highly appreciated professor. He might not have yet developed the skills to put a lecture across well, but he was very hands-on and was ready to discuss scientific topics with anyone interested. The same David Gill who had called him a terrible lecturer also commented that Maxwell’s teaching influenced the whole of his life. Students found that it was worth suffering his lectures if they then put in the effort to ask for more information. Maxwell also put on a voluntary advanced class for the fourth-year students – not part of the formal university teaching programme – which brought in the likes of Newton’s laws, electricity and magnetism, topics that were considered too technical for most students. At the time, there was no honours degree available at Aberdeen, but Maxwell had instituted the intellectual equivalent for the physics course.

  Lord of the rings

  While in position at Marischal College, Maxwell demonstrated the breadth of his ability to think around a difficult problem by putting a considerable amount of effort into a challenge set by St John’s College, Cambridge for its Adams Prize. This was a somewhat bizarre competition (still running) set up in honour of John Couch Adams, who had the misfortune to have produced a considerable amount of early data that suggested the existence of the planet Neptune, only to have his observations ignored, leaving the French co-discoverer of the planet, Le Verrier, to take the laurels.

  The Adams Prize could, in principle, be set on any mathematical, astronomical or natural philosophy problem, but in the early years it was dominated by astronomical topics, not entirely surprisingly given that those in charge of the prize topic, George Airy and James Challis, were both astronomers. The challenges tended to involve so much work that the competition was not exactly over-subscribed. Maxwell entered to take on a topic set in 1855 that required hand-in of entries at the end of 1856 with results announced in 1857. This was the fourth time the prize challenge had been set – of the first three years, two had a single
entrant, one had no entrants at all.

  The topic for 1855 was the rings of Saturn, which, as we have seen, Maxwell had already started to work on during the summer vacation before heading off to Aberdeen. Ever since Galileo had seen something strange about the planet’s appearance through his crude telescope and had drawn it as if it had jug-eared handles, assuming that what he saw was three stars that were lodged against each other, the rings had been a mystery. Apparently unique in the solar system (we now know that other gas giant planets have rings, though none is as dramatic as Saturn’s), this structure seemed to defy nature.

  The challenge was set out as follows:

  The problem may be treated on the supposition that the system of Rings is exactly, or very approximately, concentric with Saturn, and symmetrically disposed about the plane of his equator, and different hypotheses may be made respecting the physical constitution of the Rings. It may be supposed (1) that they are rigid; (2) that they are fluid or part aeriform; (3) that they consist of masses of matter not mutually coherent. The question will be considered to be answered by ascertaining, on these hypotheses severally, whether the conditions of mechanical stability are satisfied by the mutual attractions and motions of the Planet and the Rings.