Professor Maxwell's Duplicitous Demon

by Brian Clegg

  By the time he got to his Mathematical Society paper, though, he had decided to go with his proposal to satisfy the mathematicians:

  I propose, but with great diffidence, to call this vector the Curl of the original vector function. It represents the direction and magnitude of the subject matter carried by the vector. I have sought for a word that shall neither, like Rotation, Whirl, or Twirl, connotate motion, nor, like Twist, indicate a helical or screw structure which is not of the nature of a vector at all.

  The life academic

  It might seem that everything was going swimmingly at Glenlair. Maxwell wrote the first of his definitive books, undertook experiments, and developed theory. His family life was everything he had hoped for with the exception of having children. And he had said on leaving London that he would never return to academia. Yet perhaps he also felt that there was something missing from his life. He could discuss his work with Katherine and could exchange ideas with other scientists in letters, but it wasn’t the same as having lively discussion with other experts in the field. Maxwell seems to have missed the opportunity for broader intellectual exchange.

  The first opportunity that tempted him to think of getting back into the academic world was when the post of Principal at Scotland’s oldest university, St Andrews,|||| came up in late 1868. Maxwell wavered on whether to apply. In a letter to William Thomson at the end of October he wrote:

  One great objection is the East Wind, which I believe is severe in those parts. Another is that my proper line is in working not in governing, still less in reigning and letting others govern.

  Four days later it seemed as if Maxwell had made up his mind. He wrote to Lewis Campbell:

  I have given considerable thought to the subject of the candidature, and have come to the decision not to stand. The warm interest which you and other professors*** have taken in the matter has gratified me very much … but I feel that my proper path does not lie in that direction.

  Yet after another four days, Maxwell had clearly reversed his decision and began writing to contacts to try to win support for this political appointment, particularly any he felt could influence the Home Secretary, the magnificently named Gathorne Gathorne-Hardy. By 9 November he was writing to Thomson:

  When I last wrote, I had not been at St Andrews. I went last week and have gone in for the Principalship. If you can certify me having been industrious &c since 1856, or if you can tell me what scientific men are conservative††† or still better if you can use any influence yourself in my favour pray do so. 6 Professors out of 9 [at St Andrews] have memorialized the Ld Adv. & Home Sec. for me together with Principal Tulloch the V. Chancellor. Of the other 3, one Prof Shairp is a candidate and one, Prof. Bell does not approve of memorials at all and is neutral.

  Despite the apparent support of the resident professors, it was not to be. Although the post was rumoured to be due to go to a ‘man of science’, it may have been that Maxwell’s lack of administrative experience counted against him with the political decision-makers. But this did not mean that Maxwell would remain at Glenlair for the rest of his working life. When, a few years later in 1871, he was approached with the offer of a new post that would truly wrench physics away from the medieval concept of natural philosophy and bring it to the forefront at a great university, Maxwell, pushed out of his stay-at-home frame of mind by the opportunity at St Andrews, decided it was time for a fresh challenge.

  Notes

  1 – Maxwell’s fondness for entertaining children is described in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 40.

  2 – Norbert Wiener’s reference to Maxwell as the father of modern automatic control is noted in Rodolphe Sepulchre, Governors and Feedback Control, available at: www.clerkmaxwellfoundation.org/Governors.pdf

  3 – Maxwell’s letter to Peter Tait, written from Glenlair on 7 November 1870, on the naming of the mathematical term that would be called ‘curl’, is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), pp. 568–9.

  4 – Maxwell’s introduction of the mathematical term ‘curl’ is from James Clerk Maxwell, ‘Remarks on the Mathematical Classification of Physical Quantities’, Proceedings of the London Mathematical Society, s1–3 (1871), pp. 224–33.

  5 – Maxwell’s letter to Thomson from Glenlair dated 30 October 1868, citing the east wind as a reason not to apply for a post at St Andrews, is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), pp. 457–9.

  6 – Maxwell’s letter to Campbell from Glenlair dated 3 November 1868, saying he would not stand, is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), p. 460.

  7 – Maxwell’s letter to Thomson from Glenlair dated 9 November 1868 saying he would stand is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), p. 463.

  * And, yes, once again, Maxwell’s scientific discoveries are fundamental to our ability to be able to do this.

  † We’re not sure why. Perhaps his usual mount was lame.

  ‡ Physicists love billiard balls as models – no doubt a sign of misspent youths.

  § Real billiard balls are not like this – they are not perfectly rigid, so they deform as they come into contact, giving a short period of acceleration in an impact that isn’t instantaneous, and they lose energy to heat and sound, but physics models often involve simplification to make the mathematics manageable.

  ¶ Stirring the tea changes things again, reducing the relaxation time for the distribution of temperature but introducing a new disturbance in the form of a vortex. Who would have thought a cup of tea involved so much physics?

  || Foucault is probably best known for his pendulum, which changes its direction of swing with the Earth’s rotation (and gave Umberto Eco a good title for a book).

  ** The speed of light has now been fixed at 299,792.458 kilometres per second, as the metre is defined as 1/299,792,458th of the distance light travels in a second.

  †† A single weight would do the job, but would be unstable – having a pair enables them to balance each other out.

  ‡‡ The integral, one of the main vehicles of calculus, here gives the area under the curve of a graph of the changing speed of the governor – in this case reflecting the displacement of the governor, rather than the measured speed. This enables the governor to bring the speed to the required value however large the variation, whereas with a moderator, speed will still increase, but less so than if the moderator was not there.

  §§ ‘Cybernetics’ and ‘governor’ are both from the same Greek root, meaning a steersman, but governor was distorted in passing through a Latin version of the word.

  ¶¶ Arthur Cayley, an English mathematician, at the time the Sadlerian Professor of Pure Mathematics at Cambridge.

  |||| To be precise, the position was Principal of the United College of St Salvador and St Leonard in the University of St Andrews.

  *** Campbell was, at the time, Professor of Greek at St Andrews.

  ††† Gathorne-Hardy was a member of the Conservative government, which was probably why Maxwell said this, though Maxwell was also by nature conservative with a small c.

  Chapter 8

  Cambridge beckons

  The approach that would signal the beginning of the last great phase of Maxwell’s scientific life came from the University of Cambridge. Although Cambridge had proved a mathematical inspiration and remained in many ways an academic spiritual home to Maxwell, it was not at the time the most advanced British establishment in terms of the sciences. However, the chancellor of the university was determined to change this.

  The Cavendish connection

  Unusually for the nominally top per
son in a university (even today), the Cambridge chancellor had scientific leanings. Like Maxwell, he had been an outstanding mathematician of his year, becoming Second Wrangler and winning the prestigious Smith’s Prize. What’s more, the chancellor was the grand-nephew of Henry Cavendish, another Cambridge graduate, who had been one of the leading scientists at the end of the eighteenth century. Henry Cavendish had played a significant part in the establishment of the Royal Institution and had undertaken the first experiment to provide a reasonable measurement of the density of the Earth, making it possible to calculate for the first time Newton’s gravitational constant, G.

  The current Cambridge chancellor was also a Cavendish – William Cavendish, the Duke of Devonshire – an extremely rich man, who, as a politician, had served on the Royal Commission on Scientific Education, set up among concerns that the country was falling behind its competitors in scientific prowess. Cavendish was prepared to donate a large sum to the university on the understanding that it built a physics laboratory and endowed a chair of experimental physics.

  In the quaint terminology of the time, the Chair of Experimental Physics was founded by a Grace of the Senate on 9 February 1871 stating that ‘the principal duty of the professor is to teach and illustrate the laws of Heat, Electricity and Magnetism; to apply himself to the advancement of the knowledge of such subjects; and to promote their study in the university’. This meant that the university was on the hunt for a dynamic, world-class physicist, with the dual role of becoming the first Cavendish Professor and supervising the construction of a leading-edge laboratory. The first people to be approached were Maxwell’s old friend, William Thomson, and the German physicist Hermann von Helmholtz, who like Maxwell did significant work on electromagnetism and thermodynamics.

  However, Thomson did not want to leave Edinburgh and was concerned at the limited support available in Cambridge from instrument makers, an essential if the laboratory was to be successful. Helmholtz, at the time based in Heidelberg, was just in the process of negotiating a post in Berlin, the mathematical capital of Europe. As a result, Maxwell received a letter in mid-February 1871 from Edward Blore at Trinity College:

  My Dear Maxwell

  Our Professorship of Experimental Physics is now founded & though the Salary is not magnificent (£500 a year) yet there is a general wish in the university that this branch of Science should be supported in a way creditable to the University. The Duke of Devonshire has undertaken the expense of the building & Apparatus, & it remains for us that we should appoint the Professor. Many residents of influence are desirous that you should occupy the post hoping that in your hands this University would hold a leading place in this department. It has, I believe, been ascertained that Sir W. Thomson would not accept the Professorship. I mention this in case you should wish to avoid the possibility of coming into the field against him.

  Maxwell knew he was not the first choice. He replied immediately to Blore, saying:

  Though I feel much interested in the proposed chair of Experimental Physics I had no intention of applying for it when I got your letter, and I have none now unless I come to see that I can do some good by it.

  He went on to ask details of the job – the duties, who made the appointment, how long he would be expected to serve, how many terms a year and so forth. The details were sent to Maxwell three days later by George Stokes, the Lucasian Professor at Cambridge, and within a week Maxwell had decided to stand.

  Maxwell was elected to the post on 8 March 1871. Or, more accurately, he was appointed. The professorship was in principle in the hands of the Senate of the university. Strictly speaking, this comprises all holders of an MA or higher degree from the university, plus significant officers such as the Vice Chancellor, but in practice it would have been just those resident at the time. Of around 300 members, only thirteen voted – not entirely surprisingly, as they were only offered a single choice. The decision was clearly made behind the scenes, based on approaches to key figures.

  Cambridge was lucky to end up with Maxwell, as neither of his rivals had his practical experience of running an estate alongside his excellence in physics, which would surely have helped when it came to managing the construction project – though as Maxwell pointed out in his letter to Blore, Thomson had practical experience of running a university laboratory, which he did not. In March 1871, Maxwell took a tour of the few existing physics laboratories in the UK, picking up the best practice to pull together in designing the new facility.

  A different professor

  It’s interesting to think for a moment about why James Clerk Maxwell was offered this particular position, how he saw his role, and how his ideas might have been shaped by his experiences in London. At first sight, this master theoretician might not seem the ideal candidate to become professor of experimental physics, but we need to remember that Maxwell had proved a more than capable experimenter, and one who was prepared to go the extra mile and set up laboratories in his home both in London and at Glenlair when nothing was available otherwise. He had also remained in close contact with Cambridge since leaving King’s College London, helping to reform the Mathematics Tripos examination system in 1866 and 1867.

  The mix of talents that he could bring to Cambridge is reflected in a letter to Maxwell from John Strutt (Lord Rayleigh) who would go on to replace Maxwell as Cavendish Professor on his death. Among other things, Rayleigh discovered the element argon and explained why the sky is blue. Rayleigh wrote:

  When I came here [Cambridge] last Friday I found every one talking about the new professorship, and hoping that you would come … There is no one here in the least fit for the post. What is wanted by most who know anything about it is not so much a lecturer as a mathematician who has actual experience in experimenting, and who might direct the energies of the younger Fellows and bachelors into a proper channel.

  In his inaugural lecture at Cambridge in 1871, Maxwell remarked that the new laboratory would be worthy of the university if ‘by the free and full discussion of the relative value of different scientific procedures, we succeed in forming a school of scientific criticism, and in assisting the development of the doctrine of method’. For Maxwell neither the Ancient Greek approach of armchair philosophising which had dominated universities until Newton’s day, nor the pure mechanical experimental approach that had driven the industrial revolution was the way forward.

  In his vision of the future of physics, Maxwell saw a close, symbiotic partnership between experiment and the development of theory – neither should operate in isolation. Arguably, a major factor in developing this viewpoint (leaving aside how closely it reflected the interaction of experiment and theory in his own working life) was the downside of the engineering-dominated approach at King’s. Although Maxwell had nothing against practical, applied science, he saw clearly that it was necessary to move away from industry-driven goals and to be able to address the fundamentals.

  It was also clear to Maxwell that something needed to be done about the Cambridge syllabuses. As we have seen, he was involved a few years before his appointment in the redesign of the Mathematics Tripos, helping to expand it beyond its old topics to take in more modern aspects of physics, such as electricity, magnetism and heat – and he would write a major textbook, the Treatise on Electricity and Magnetism, to support this. Now he had the chance to make sure that the broadest modern physics curriculum was covered with the introduction of experimental physics to Natural Sciences – though he was still constrained also to include elements of physics in the Mathematics Tripos.

  Along with other supporters of laboratories in universities, his approach was in the vanguard of transforming experimental physics from simple observation to making measurements to support or dispose of theories. In his opening lecture, Maxwell first pointed out the limitation of making more and more accurate measurements with no extension of theory.

  The characteristic of modern experiments – that they consist principally of measurements – is so prominent th
at the opinion seems to have got abroad that, in a few years, all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry these measurements to another place of decimals.*

  If this is really the state of things to which we are approaching, our Laboratory may perhaps become celebrated as a place of conscientious labour and consummate skill; but it will be out of place in the University, and ought rather to be classed with the other great workshops of our country, where equal ability is directed to more useful ends.

  Then, however, Maxwell went on to show his faith in there being far more to come: ‘But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continuously be poured.’ He pointed out that even when progress has largely been about polishing the decimal points, science ‘is preparing the materials for the subjugation of new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers’.

  He realised that no university was better positioned to do this than Cambridge – an institution that has gone from strength to strength since Maxwell’s appointment, so that it is now one of the world’s leading universities for physics. This is likely to be part of the answer to a second question about the appointment, which is why Maxwell would have accepted, having voluntarily given up his position in London. It seems unlikely that the attraction of Glenlair would ever have palled for him. But the opportunity in Cambridge to set in motion something that could be transformative for the physics he loved was simply too great. And, just in case it didn’t work out too well, he put himself forward on the understanding that he would not have to stay in post for longer than a year.