by Brian Clegg
Maxwell was intrigued by Clausius’ idea, but disliked the assumptions his rival had made. To make things simple, Clausius decided that it was acceptable to assume that all the molecules move at the same speed for a particular temperature. This certainly makes the mathematics easier to handle – but at the cost of losing the central statistical element of the theory and becoming totally unrealistic.
Temperature is not dependent on the speed (and hence kinetic energy) of an individual molecule, but on the average speed of the whole collection. Let’s think specifically of that kitchen with its freshly brewed coffee pot. Some molecules in the air would have come into contact with the hot stove or with a windowsill heated by the Sun and as a result would be moving particularly quickly. Others would have given up energy as a result of contact with cooler matter and would have slowed down. There would be a whole distribution of different speeds and energies making up that average. Understanding the different probabilities involved was essential to developing a numerical analysis.
Statistics to the rescue
By bringing the statistics front and centre, Maxwell transformed the approach to the behaviour of gases. His was the first generation who could sensibly do so. Probability theory was only starting to be introduced in universities when Maxwell was an undergraduate. What had been a technique limited to considering games of chance|||| and insurance premiums was increasingly seen as a tool that could be valuable in the physical sciences. For example, Maxwell’s father’s friend at Edinburgh, Professor James Forbes, had attempted to use probability theory to assess the likelihood that two stars, apparently very close to each other when seen through a telescope, were part of the same binary system, rather than simply happening to appear from the Earth to be situated in roughly the same direction.
Another eminent physicist of the day who became Maxwell’s friend at Cambridge, George Stokes, the Lucasian Professor of Mathematics (a position held in their time by both Newton and Stephen Hawking), was responsible for some of the experimental data that Maxwell used in developing his ‘dynamical’ theory of gases. Maxwell notes:
From Prof. Stokes’s experiments on friction in air, it appears that the distance travelled by a particle between consecutive collisions is about 1/447,000 of an inch, the mean velocity being about 1505 feet per second; and therefore each particle makes 8,077,200,000 collisions per second.
We now refer to the ‘Maxwell distribution’ of speeds of molecules in gases, and his mathematical solution to provide the distribution of molecular speeds given a particular temperature is still used today. This was only the start of Maxwell’s pair of papers on the subject, to be published in 1860, which covered everything from the basics of pressure and thermal conductivity to viscosity and the way a gas diffused through different materials, seen from the molecular viewpoint.
His results on viscosity produced a particularly surprising outcome. Viscosity is a measure of the amount of drag a fluid presents to a body moving through it.*** The higher the viscosity, the more a gas (or liquid) resists movement. It had been assumed that the viscosity of a gas would increase with the gas’s pressure. Just as the gas pushes more on its container as pressure goes up, it seemed reasonable that it would push more on anything that tried to pass through it, slowing it down more.
But Maxwell’s theory suggested that viscosity should be independent of pressure. Admittedly there will be more molecules in the way at higher pressure – so you could imagine it’s the difference between wading through a full ball pool and one with just a few balls in it – but these molecules providing resistance to motion are also themselves moving. Maxwell’s calculations showed that the molecules’ ability to get out of the way of their fellows would counter exactly the extra quantity present in any particular volume. It would take a few years, but Maxwell would later demonstrate this experimentally.
Maxwell had made his first great contribution to physics – and one that at the time was given significantly more weight by many than his masterpiece on electromagnetic theory. Certainly, it was a topic that became something of a trademark for Maxwell. When a few years later he had attended a lecture at the Royal Institution in London and got wedged in a crowd trying to leave the lecture theatre, Michael Faraday was prompted to remark: ‘Ho, Maxwell, cannot you get out? If any man can find his way through a crowd, it should be you.’ This was a clear reference to Maxwell’s expertise on the paths of molecules.
The result of his analysis was not perfect. Maxwell had made a range of assumptions and at least one technical error, which would be pointed out by Clausius. And, as would remain the case throughout his career, his workings suffered from regular arithmetical slips. The German physicist Gustav Kirchhoff later commented: ‘He is a genius, but one has to check his calculations before one can accept them.’ However, it seemed that Maxwell had reached as far as he wanted to go with molecules for the moment. He would return to kinetic theory, but not for several years.
A new family
The work that Maxwell was doing was unlikely to have gone unnoticed by the principal of Marischal College, the Reverend Daniel Dewar.††† Dewar was an interesting character who had risen from poverty. His father had been a blind fiddle player and Dewar spent his youth acting as his father’s guide, porter and cash collector as they toured Scotland searching out the next gig. For whatever reason, Dewar was spotted by a rich benefactor as a youth with potential, paying for him to attend a private school.
Dewar went on to become a minister of the Church of Scotland. After he was appointed minister of the Greyfriars church in Aberdeen, associated with King’s College, he came to the notice of the university and was elected Professor of Moral Philosophy there. Unfortunately, his rising fame as a preacher making him something close to a celebrity did not sit well with the college’s idea of the decorum required of its professors. When Dewar would not resign from his ministry he was dismissed. He moved to Glasgow, where he took over the curiously named Tron church.‡‡‡
It was from this position that in 1832 Dewar was elected the principal of Marischal College. His was an external, Crown appointment and Dewar’s humble origins and unseemly drive to succeed apparently did not go down well with the staff of the college, where it was noted snobbishly that he got the post with ‘the unanimous disapproval of the College’. Yet, with time, Dewar’s work ethic came to be appreciated, especially when he obtained funding for significant enhancement of the infrastructure, including construction of the impressive new granite main building.
Maxwell was a regular visitor to the principal’s lodgings, a modest detached house (considering Dewar’s role) at 13 Victoria Street West in Aberdeen. Although it is entirely possible that with such a small staff, Dewar would frequently expect to see Maxwell at his lodgings, it has been suggested that their first contact may have been over a book, Gaelic Astronomy, by a teacher called D.M. Connell, the book itself written in Gaelic. Dewar had an interest in the language and had contributed to a Gaelic/English dictionary, so it may well have been a discussion of this 1856 work that first brought Maxwell to Victoria Street West.
At that time, Maxwell was 25, Dewar 71 and his wife Susan 60. Soon, the visits came to involve something more than a narrow discussion. Maxwell enjoyed covering a wide range of topics from theology and philosophy to literature and history with Dewar, a freedom of thought he had missed when moving from Cambridge to join the less socially minded Aberdeen fellows. And it was in the Victoria Street house that Maxwell met the Dewars’ daughter Katherine Mary, one of seven children (though three had died and only one other, Katherine’s younger brother Donald, lived at home).
Seven years older than Maxwell, Katherine was intrigued by his work and began to help with his colour experiments, making detailed observations as well as assisting with the practical side when Maxwell was caught up with theory. Maxwell became sufficiently close to the Dewars that he was asked to join them in September 1857 when the family took their annual break at a relative’s home near Dunoon on Scotl
and’s west coast. This holiday seems to have cemented the relationship: the following February, Maxwell proposed to Katherine.
He wrote to his aunt, Miss Cay:
Dear Aunt, this comes to tell you that I am going to have a wife. I am not going to write out a catalogue of qualities, as I am not fit; but I can tell you that we are quite necessary to one another, and understand each other better than most couples I have seen. Don’t be afraid; she is not mathematical; but there are other things besides that, and she certainly won’t stop the mathematics.
The couple were married on 2 June 1858. Maxwell’s lifelong correspondent and friend since school days Lewis Campbell was the best man (a reciprocal arrangement, as Maxwell had performed the same role for Campbell just a few weeks earlier down in Brighton). As well as supporting Maxwell’s experiments in the sciences, Katherine also shared a wider range of interests with him, from literature and theology to walking and horse riding (though neither enjoyed any ‘country sports’ that involved killing animals). Though it appears Katherine was significantly less high-spirited than Maxwell, they were, without doubt, a well-matched couple, which would help greatly for the months of the year they would spend together in the relative isolation of Glenlair.
Accommodating the British Ass
During the first year of the Maxwells’ marriage, it’s likely that Maxwell had one thing foremost in his mind as far as work was concerned – the British Association for the Advancement of Science meeting. This organisation, usually contracted to BA, though Maxwell habitually referred to it as the British Ass, which is still going strong as the abbreviated British Science Association, had been started in 1831 as a way of improving the public understanding of science. Unlike the exclusive Royal Society, or the laboratory-centred Royal Institution, the BA was for the everyman and was specifically intended to have neither a building nor funds, but rather to provide pop-up events around the country to spread the scientific word.
After its founding, the BA put on a series of annual events, each of which lasted several days – effectively its annual meeting provided what would now be called a science festival. These gatherings attracted big crowds. Maxwell had been attending them regularly since the 1850 Edinburgh meeting, though he probably missed Dublin in 1857. The venue for a meeting was settled only a year in advance – and at the 1858 Leeds event (a meeting Maxwell had to miss due to his wedding), it was agreed that the 1859 meeting would be held in Aberdeen.
This no doubt thrilled Maxwell, but the only problem with the idea was that Aberdeen had no venue suitable for the large-scale lectures and discussions that were central to a BA meeting. Although the universities both had lecture theatres, and the more central Marischal College’s main lecture theatre would be used for smaller side-events, they had nothing with the capacity required for the jamboree that the main BA meeting had become.
There had been talk for some time about building a music hall in Aberdeen, and the BA meeting provided a focus for making it happen. With Maxwell among its shareholders, the Music Hall Company set to work on the rapid construction of a spacious venue in Union Street. Almost inevitably constructed of granite, the imposing 50-foot-high internal space was capable of seating 2,400 and is still a major feature of the Aberdeen cityscape today.§§§ The meeting, opened by Prince Albert, was a huge success.
Getting the Prince Consort along was a major feather in the organisers’ caps. The location probably helped. Aberdeen might have been remote indeed from London, but it was handily located just 50 miles from one of Albert’s pet projects, the Balmoral estate, where he had recently built a new castle, soon to be a favourite hideaway of Queen Victoria. In total, Maxwell gave three talks in the main venue – on his theory of gases, on colour theory, and on Saturn’s rings.
Maxwell and the Prince were not the only attractions at a gathering that would see over 2,500 tickets sold. There were events ranging from a talk on the geology of northern Scotland to exhibitions of scientific instruments. One of the huge successes of the Royal Institution in London had been the public demonstrations – the flashier the better – and the BA event would not have disappointed with its displays of electrical discharges. It even seemed to get ahead of its time by demonstrating ‘wireless telegraphy’ before it had been invented – but although this term would later be applied to radio, the 1859 Aberdeen demonstration involved sending messages across the River Dee using the electrical conductivity of the water. Yet for all the 361 papers presented, there can be little doubt that by far the most significant for the history of science was Maxwell’s first public outing of his ‘Dynamical Theory of Gases’ including his distribution for molecular velocities.
The exposure that Maxwell received at the BA meeting in Aberdeen made a wider section of the British scientific establishment aware of his capabilities, and it was well-timed, as his career was about to be put in jeopardy. His position as Regius Professor was one that traditionally would have been a post for life, had he desired it. Other young professors with similar positions – Thomson at Glasgow and Tait soon after at Edinburgh – would never move on in their careers. But Maxwell was soon to lose the only position he would ever hold in the Scottish academic system.
Leaving Aberdeen
During Maxwell and Katherine’s engagement in 1858, the Universities (Scotland) Act was published, making it definite that Marischal College and King’s College would be merged to form a single University of Aberdeen. The year after their wedding, it had become clear that Maxwell would be unable to stay in post. There was only to be a single chair of Natural Philosophy at the new united university, and this went to Maxwell’s better-established rival from King’s College, David Thomson (no relation to William).
All-in-all, after the successes of the previous two years, culminating in the British Association for the Advancement of Science meeting, 1860 began on a disastrous note for Maxwell. Not only did he lose his position because of the merger of the Aberdonian universities, he failed in his attempt to succeed James Forbes as Professor of Natural Philosophy at Edinburgh, a role that must have seemed ideal for Maxwell.
Here he was beaten by his old school friend Peter Tait (a fact that was hard to resent, though, as Maxwell had pipped Tait to the post to take the Marischal College position). This may seem an odd decision, given their relative publications; Tait had certainly not achieved anywhere near as much scientifically as Maxwell. It seems likely that the appointment was made because Tait was recognised as a significantly better lecturer, and the panel electing the professor, including William Gladstone,¶¶¶ had limited scientific qualifications. An article by David Forfar and Chris Pritchard, comparing the work of Maxwell and Tait, comments:
The evidence of Maxwell’s superiority in research was, of course, already available to those with their eyes open. His investigation of the conditions required for the stability of Saturn’s rings oozed originality. Yet, Thomson, Forbes, Stokes and Hopkins [English mathematician William Hopkins] merely resubmitted the testimonials in support of Maxwell which they had proffered to the authorities at Marischal College four years earlier and Faraday, as was his wont, declined to provide a reference at all. Only Airy drew attention to the fertility of Maxwell’s theoretical astrophysics. As a body then his referees appear to have lapsed in shameful indolence or, more likely, failed to grasp the significance of Maxwell’s work.
To make the year worse, Maxwell contracted smallpox, becoming dangerously ill over the summer. But once he had recovered, things finally began to look up. As well as publishing on the kinetic theory of gases, it was 1860 when his work on colour theory won him the Royal Society’s Rumford Medal. He made another significant set of talks at the 1860 British Association for the Advancement of Science meeting, this year in Oxford, though his appearance was overshadowed by the now infamous debate over evolution between Bishop Samuel ‘Soapy Sam’ Wilberforce and Thomas ‘Darwin’s bulldog’ Huxley. Most significantly, two months after being turned down for Edinburgh, Maxwell finally gained a new posi
tion: the chair in Natural Philosophy (specifically dealing with physics and astronomy) at King’s College London.
Newly married, Maxwell was about to move from the quiet and relatively rural Aberdeen to the largest, most dynamic city in Europe.
Notes
1 – Information on the Royal Commission from Universities of Kings College and Marischal College, Aberdeen. First Report of the Commissioners, 1838 (1837–38), cited: http://gdl.cdlr.strath.ac.uk/haynin/haynin0509.htm
2 – Maxwell’s letter to his aunt, Miss Cay, from 129 Union Street, Aberdeen, dated 27 February 1857, is quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 263.
3 – Maxwell’s letter to Lewis Campbell complaining of the lack of jokes at Marischal is quoted in J.J. Thomson’s section of James Clerk Maxwell: A Commemorative Volume 1831–1931 (Cambridge: Cambridge University Press, 1931), p. 13.
4 Peter Tait’s explanation for Maxwell’s poor lecturing is from Peter Tait, ‘James Clerk Maxwell: Obituary’, Proceedings of the Royal Society of Edinburgh, Vol. 10 (1878–80), 331–9.
5 – David Gill’s opinion that Maxwell’s lectures were terrible is taken from George Forbes, David Gill: Man and Astronomer (London: John Murray, 1916), p. 14.
6 – Maxwell’s emphasis on mathematics and stress on the importance of experiment from his inaugural lecture at Marischal comes from Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), pp. 419–31.
7 – The wording of the Adams Prize topic is taken from Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 505.
