by Brian Clegg
Maxwell followed up his initial manuscript with a paper presented to the Royal Society of Edinburgh, where he brought out further his idea that colour blindness was typically caused by one of the three colour systems in the eye being defective. If so, he felt it should be possible to make combinations of colour on the colour top which identified what sensitivities were missing in people’s colour perception.
He also spent some time trying to match a range of colours using different combinations on his top. By now Maxwell had settled firmly on red, green and blue as the definitive primary colours of light. Producing a good range of browns seems to have given him the most problems. In a letter to William Thomson, who had expressed doubts about achieving this colour at all by mixing light primaries, Maxwell noted: ‘I have been thinking about what you say about Brown. I have matched ground coffee tolerably though the surface is bad chocolate cakes & improvised browns with black, red & a little blue & green.’
Maxwell would never know the practical importance of his work, but his colour triangle gave an essential understanding that allowed us eventually to produce the colour screens we now use on everything from TVs to computers and phones. Each coloured pixel on the screen is made up of separate red, green and blue elements, and their relative proportions are used to produce the whole range of millions of colours typically on display … all based on Maxwell’s ground-breaking approach. As was the case in many such developments, there was parallel work going on – as we have seen, German physicist Hermann von Helmholtz came to similar conclusions on the way that colours in light added, but pigments subtracted.
Once Maxwell had clearly demonstrated the colour model we now use, it might be expected that others would quickly fall into place and accept it. But the red, yellow, blue model was so strong, and so firmly supported by the artistic fraternity, that it took years of repetition and demonstration for Maxwell to get broad agreement. As late as 1870, a good fifteen years later, he wrote to a former Trinity College friend, Cecil Monro:
Mr W. Benson, architect, 147 Albany Street, Regents Park, N. W., told me that you had been writing to Nature, and that yours [supporting Maxwell] was the only rational statement in a multitudinous correspondence on colours … No other architect in the Architect’s Society believes him. This is interesting to me, as showing the chromatic condition of architects.
Quantifying Faraday’s fields
Light and colour vision were not, however, Maxwell’s only, or even his primary interest. Ever since his childhood experiments at Glenlair he had been intrigued by the magical-seeming ability of magnets to influence other pieces of metal from afar, and at university he had become an ever more enthusiastic devotee of Michael Faraday, following with interest Faraday’s many experiments with electricity and magnetism. Faraday’s idea of magnetic and electrical fields with their lines of force would fascinate Maxwell.
The field approach was generally regarded as an interesting model for electricity and magnetism – a useful way to think about them – but not one that would ever be susceptible to mathematical study. (Faraday was mocked by some of his contemporaries for his lack of mathematical expertise.) To work mathematically with electromagnetism, a similar approach to that applied to gravity was used. This involved an ‘inverse square law’ – forces acting remotely which decreased with the square of the distance away from point sources.
Maxwell was sure that Faraday’s ideas were sound and looked for a way to provide a mathematical basis for those mystical-sounding lines of force that were central to Faraday’s understanding. As we have seen, Maxwell seems to have been driven by his relatively unusual academic background. Cambridge was very strong on mathematics, but tended to apply it to the sciences with which maths had always been strongly linked, such as astronomy. Edinburgh, by contrast, gave Maxwell the grounding in electromagnetism, but would not have encouraged taking a mathematical approach to it. Maxwell was able to bring the two approaches together.
The idea of a field is something like a three-dimensional version of a contour map. Any point on the map has a particular value for the height of the land at that location, and the contours on the map are the equivalents of lines of force, joining points of equal height. The equivalent in electromagnetism would be joining points with equal strengths of electrical or magnetic fields. But the complexity of moving to a field model was greater than the need to move from a two-dimensional map to a three-dimensional field. The values at each point on a map are just numbers reflecting the altitude – mathematicians refer to such number-only values as scalars. But each point in an electrical or magnetic field represents both a size and a direction – they are called vectors.
In the 1850s, the mathematics needed to handle vectors was yet to be fully developed, but Maxwell was aware of the basics and of some of the requirements to analyse a field mathematically. He asked for help from fellow Scot William Thomson, who had already done some work on electricity using vectors, basing it on his better-developed study of the flow of heat. Thomson had discovered that, by some strange natural coincidence, the equations describing the strength and direction of the ‘electrostatic’ force between electrical charges were the same as those that dealt with the rate of flow and direction of flow of heat.
Maxwell took Thomson’s guidance on the mathematics of vectors, but went his own way on applying it. He thought of electricity as behaving like a fluid that was flowing through a porous substance, while magnetism seemed like vortices within the fluid. The lines of flow of his fluid corresponded to Faraday’s lines of force, and the speed of the flow provided the ‘flux density’ which was a measure of the strength of the electrical or magnetic field. The difference in porousness of the materials that the imaginary fluid flowed through corresponded to the way that different substances reacted to electrical and magnetic fields.
It ought to be stressed, however, that Maxwell did not think that electricity actually was such a penetrating fluid. There was a clear lesson from the study of heat to be learned here. For about 100 years, most of the work on heat assumed that there was a real, invisible fluid called caloric, which flowed from a hot object to a colder one that it was in contact with. The caloric theory had had some success in explaining how heat behaved, but ultimately it proved ineffective, and a better explanation that considered heat to be the kinetic energy of atoms and molecules in a substance took over.
Maxwell’s fluid was never intended to be the electromagnetic equivalent of caloric. His fluid was purely imaginary and the flow of his fluid was not electricity itself, but rather was an analogy for the strength of the electrical and magnetic fields. And it worked surprisingly well. One of the results that Maxwell got pretty much for free out of this model was that by using a non-compressible fluid to represent the field, it meant that there was always the same amount of fluid in the same volume, which produced an interesting mathematical result.
If there was always the same amount of fluid in the same volume, the flow of fluid would drop off with the square of the distance from the source. If the same amount of fluid travelled through a wider and wider space, then its rate of flow depended on the surface area of a cross-section of that space. Think, for instance, of a liquid moving out through a funnel in the reverse direction from usual, going from the narrow end to the wider one. If the fluid can’t compress or stretch and has to fill all the space available, then it will have to be going a lot slower at the wide end of the funnel than at the entrance. The speed it moves at will depend on the size of the opening.
Similarly, if we think of liquid emerging from a point and heading out in all directions, then the surface area of the ‘opening’ is just the surface area of a sphere – 4 π r2, where r is the radius of the sphere – so the surface area the fluid has to fill increases with the square of the distance from the centre. We see the fluid moving slower – which in Maxwell’s analogy means the strength of the field dropping off – reducing in speed with the inverse square of the distance from the source. This was exactly what happ
ened in experiments on the electromagnetic field.
As noted above, Maxwell always saw his approach as an analogy – a model of reality that did not have any direct resemblance to what was actually happening, but which produced useful results. He commented in his paper describing his ideas, named On Faraday’s Lines of Force:
I do not think that [the fluid analogy] contains even the shadow of a true physical theory; in fact, its chief merit as a temporary instrument of research is that it does not, even in appearance, account for anything.
Not only did Maxwell’s fluid model fit with Faraday’s force fields while predicting the inverse square law of the traditional ‘action at a distance’ mathematics, it was better than the action at a distance approach when dealing with the boundaries between materials. Though Maxwell could not see how to take the step into modelling changing electrical and magnetic fields that would be necessary to deal with many of the phenomena that had enabled Faraday to come up with the electrical generator and motor, this was impressive stuff for someone who had only just graduated and was in his early twenties. As well as presenting his ideas to the Cambridge Philosophical Society, Maxwell also sent his paper On Faraday’s Lines of Force to his hero, Michael Faraday, in London.
Faraday was by now in his sixties, but was still working at the Royal Institution and replied to Maxwell:
I received your paper, and thank you very much for it. I do not venture to thank you for what you have said about ‘Lines of Force’, because I know you have done it for the interests of philosophical truth; but you must suppose it is work grateful to me, and gives me much encouragement to think on. I was at first almost frightened when I saw such mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well.
For the benefit of working men
Faraday, as we have seen, had not had the benefit of a university education. The closest he came to formal training before beginning work at the Royal Institution was to attend the City Philosophical Society, a group set up with the specific intention of helping those from humble backgrounds to better themselves. Although Maxwell had a more privileged upbringing, he was aware from his contacts back at Glenlair of the limited opportunity for working men to improve their education, and also how Faraday had benefited from the ‘Phil Soc’. And, being Maxwell, he could not stand back and assume someone else would sort the problem out.
At Cambridge, Maxwell was one of the founders of the Working Men’s‡‡ College, which provided evening classes for self-improvement. Not only did he give some of the lectures himself, he toured local businesses, asking them to allow their men to leave their jobs early on lecture nights. In a letter to his father, written in March 1856, he noted:
We are also agitating in favour of early closing of shops. We have got the whole of the ironmongers, and all the shoemakers but one. The booksellers have done it some time. The Pitt Press keeps late hours, and is to be petitioned to shut up.
This enthusiasm for outreach and the betterment of those from humble beginnings would continue through future posts where Maxwell would regularly get involved with local working men’s educational organisations, such as the mechanics’ institutes often found in industrial towns and cities.
Maxwell soon became comfortable in his new position as a graduate student, though he still cherished his summers in Scotland, whether at Glenlair or spending time with relatives. In 1854, this resulted in his first recorded encounter with love. Maxwell spent a week with the Cays, his mother’s family, in the Lake District. Among his mother’s brother’s children on the trip was Maxwell’s cousin Lizzie – fourteen to his 23. There seems little doubt that Maxwell fell in love. Lizzie’s age was less of a concern then than it would be now at a time when girls often married at sixteen after a lengthy courtship. However, the family seems to have been set against the match.
There was awareness of the risks of marrying such a close relation as a first cousin, even though it was relatively common among the upper classes, notably in the royal family where it occurred frequently. The Clerks and the Maxwells had over the century or so since their first intermarriage frequently wed cousins. But, for whatever reason, it was not to be. If Maxwell and Lizzie exchanged any letters they have not survived – the story of their brief passion has only been related via Lizzie’s daughter, who at the time was aged 90.
Another personal event of that year was Maxwell becoming a Justice of the Peace – a magistrate. It’s not clear how frequently (if at all) Maxwell carried out the role, which was often nominally taken by the lord of the manor, but it shows an awareness of his personal responsibilities as a member of the establishment that would come through strongly when he later inherited the Glenlair estate.
One interesting ‘might have been’ turned up at the start of 1855. His friend Cecil Monro wrote to Maxwell saying, ‘NEWTON MUST BE TRANSLATED, and you are the one to do it’. This was a reference to Isaac Newton’s masterpiece, the lengthy (and sometimes near-impenetrable) work Philosophiae Naturalis Principia Mathematica, usually just known as the Principia. This three-volume book contains both Newton’s laws of motion and his work on gravitation, and was originally published in Latin. It had been translated into English in 1729 by Andrew Motte, but by the 1850s that version was seeming too archaic to be used as a serious scientific document.
It wasn’t entirely surprising that there was demand for an English version of the most important work by the man generally regarded at the time as the greatest English scientist, if not the world’s. Monro drolly pointed out that Maxwell’s Latin was good enough ‘for practical purposes … [though] it is very true that you don’t seem ever to have displayed such acquaintance in your college examinations’. Monro may have known that a significant reason why Maxwell was yet to be elected a Fellow of Trinity College was because it was considered that he needed to attend more to the classics.
Maxwell replied at his most whimsical:
Dear Monro
It is a fearful thing to answer when a man tackles you with arguments. I wont argufy at all, leastways not with them as tries to argufix me. I wd be most happy to give any assistance in my power to the translator of Newton, short of taking on the work of his hands. For that I am not prepared. I am prepared to refuse resist & rebel. I wd as soon think of translating Butlers Analogy§§ for the Mathematical Journal.
It was not to be.
This letter and a number of others from Maxwell were written from 18 India Street in Edinburgh, two doors down from the Clerk Maxwells’ old house. Their own place, 14 India Street, had been rented out once Glenlair was completed, and the Maxwells never lived there again, but when Maxwell had gone to Cambridge, his Aunt Isabella moved from her house in Heriot Row to India Street, and it was number 18 that Maxwell used as a pied-à-terre in Edinburgh.
A new destination
It’s quite possible that Maxwell, getting well established in Cambridge, would have taken his ideas on electricity and magnetism further at this stage of his career. But in February 1856, his old professor James Forbes wrote to him about an opening at Marischal College in Aberdeen. The university was looking for a Professor of Natural Philosophy, which Forbes thought was a position that would ideally suit Maxwell.
As Forbes put it:
I have no idea whether the situation would be any object to you; but I thought I would mention it, as I think it would be a pity were it not filled by a Scotchman, and you are the person who occurs to me as best fitted for it.
There is no evidence that Maxwell had ever been to Aberdeen before, a good 120 miles from Edinburgh and altogether less sophisticated than the capital. And there was no doubt that the country boy had had many of his rough edges rubbed off at Edinburgh and Cambridge, perhaps giving him some expectation of lively intellectual surroundings. But gaining a professorship would be an impressive position to kickstart his career.
Forbes was also at pains to point out that he had no influence over this appointment, as it was in the hands o
f the Crown, though it’s not clear if this suggests that otherwise he would have attempted to bias things in Maxwell’s favour. Maxwell noted in a letter to his father a couple of days after receiving the notification from Forbes:
I think the sooner I get into regular work the better, and that the best way of getting into such work is to profess one’s readiness by applying for it. The appointment lies with the Crown – that is, the Lord Advocate¶¶ and the Home Secretary. I suppose the correct thing to do is to send certificates of merit, signed by swells, to one or other of these officers.
The idea that Maxwell should become a professor at the age of 24, having only graduated with a BA less than two years earlier, would seem outrageous now. However, modern academic positions have a much stronger hierarchy and career progression than was the case at the time. In practice, Maxwell had everything that was needed for the post, since he had been made a Fellow of Trinity in October 1855, which gave him his academic CV. His friends William Thomson and Peter Tait had both been awarded professorships at younger ages – Thomson became Glasgow’s Professor of Natural Philosophy at the tender age of 22, while Tait became the Professor of Mathematics in Belfast at 23.||||
With his application sent off, and a flurry of requests for support sent to the great and the good, which this kind of royal appointment required, Maxwell returned to Glenlair for the Easter vacation. His father had been suffering for some time from a lung infection, which got progressively worse over the following days. John Clerk Maxwell died on 3 April, leaving Maxwell with a major new responsibility as head of the Glenlair estate.