by Brian Clegg
I hope it is not in fashion at Cambridge, and at any rate that you do not meddle with it. If it does anything, it is more likely to be harm than good; and if harm ensues, the evil might be irreparable, so let me hear that you have dismissed it.
‘Electro-biology’ sounds like an early attempt at understanding the electrical aspect of the brain and nervous system, but was in reality an alternative term for animal magnetism. Both labels were attempts to give mesmerism (also known as hypnotism) a more scientific-sounding context. Electro-biology was particularly favoured as a term among stage hypnotists. Table-turning would have been considered even worse by Maxwell’s devout father. It was a form of séance where the table was lifted and moved as the participants sat around it, supposedly powered by spirit intervention, but more likely to be due to the practitioner’s use of his or her feet or hands.
It’s quite possible that Maxwell was put off further exploration by the fate of Michael Faraday, who experimented with table-turning and showed that the movement of the table was due to the pressure of participants’ fingers on it, quite possibly unconsciously making it move as they hoped. Faraday was then deluged with letters asking if he could explain various other phenomena as if, Maxwell noted, ‘Faraday had made a proclamation of Omniscience. Such is the fate of men who make real experiments in the popular occult sciences … Our anti-scientific men here triumph over Faraday.’ It’s likely Maxwell did not want to suffer a similar fate.
It was around this time that Lewis Campbell wrote a pen sketch of Maxwell that is interesting to set against the rather stern-looking portraits of the day. Campbell describes Maxwell as follows:
His dark brown eye seems to have deepened, some parts of the iris being almost black … His hair and incipient beard were raven black, with a crisp strength in each particular hair, that gave him more the look of a Nazarite than of a nineteenth century youth. His dress was plain and neat, only remarkable for the absence of anything adventitious (starch, loose collar, studs, etc.), and an ‘aesthetic’ taste might have perceived in its sober hues the effect of his marvellous eye for harmony of colour.
Cats and rhymes
One thing that didn’t change for Maxwell while at Cambridge was his enthusiasm for animals. Many Cambridge colleges banned the keeping of dogs (and still do – the dog belonging to the current Master of Selwyn College is officially designated the college cat), which Maxwell would have found a wrench, but he made up for it by making friends with the cats that were employed to keep mice down in college. Being Maxwell, this led to an experiment which gained him a questionable reputation at the time, as he explained looking back in a letter to his wife Katherine written in 1870 when he was visiting Trinity College as an examiner for mathematics:
There is a tradition in Trinity that when I was here I discovered a method of throwing a cat so as not to light on its feet, and that I used to throw cats out of windows. I had to explain that the proper object of the research was to find how quick the cat would turn round, and that the proper method was to let the cat drop on a table or bed from about two inches, and that even then the cat lights on her feet.
Maxwell also kept up a habit of writing verse while at Cambridge. This would be a pastime he indulged in throughout his life, covering the whole gamut from translations of classical poetry, through serious odes, love poems to his wife when later married, and ventures into comic verse. Sometimes his work would touch on very specific aspects of his work and experience, such as his Cambridge piece ‘Lines written under the conviction that it is not wise to read Mathematics in November after one’s fire is out’. The opening verses of another poem from his youthful Cambridge days, entitled ‘A Vision (of a Wrangler, of a University, of Pedantry and of Philosophy)’ illustrates Maxwell in full comic mode:
Deep St Mary’s bell had sounded,
And the twelve notes gently rounded
Endless chimneys that surrounded
My abode in Trinity.
(Letter G, Old Court, South Attics)
I shut up my mathematics,
That confounded hydrostatics –
Sink it in the deepest sea.
In the grate the flickering embers
Served to show how dull November’s
Fogs had stamped my torpid members,
Like a plucked and skinny goose.
And as I prepared for bed, I
Asked myself with voice unsteady,
If of all the stuff I read, I
Ever made the slightest use.
The Wranglers
At the time, all Cambridge students were required to take a series of mathematics papers in their finals. The basic exams, which could be passed by learning the fundamentals of the course, were relatively straightforward. But honours students took papers providing them with an extended set of problems over four days. The questions were deliberately obscure, requiring a different kind of thinking and taxing the students’ reasoning skills to the limit. The scale of this undertaking can be seen from the details of the 1854 Tripos,¶ where honours students took sixteen papers, comprising 44.5 hours of examination, working through 211 questions, while the best of the best went on to spend three more days on the 63 additional questions of the Smith’s Prize papers.
Those who completed the whole of this gruelling mathematical challenge and came through with first-class honours were given the title ‘Wrangler’, their position in the listing as hard-fought as the ‘Head of the River’ in the rowing races. Achieving top position as ‘Senior Wrangler’ was widely regarded as the ultimate academic achievement in Britain and was feted far beyond Cambridge.
Maxwell achieved the position of Second Wrangler,|| and in the separate, even harder mathematical exams for the Smith’s Prize was declared joint winner with Senior Wrangler Edward Routh, who would go on to be influential in the mathematics of moving bodies and would develop the beginnings of what became control systems theory.
It’s arguable that Maxwell’s mix of an Edinburgh and Cambridge education provided the perfect combination to break out of the approach to physics that was deeply embedded in academia at the time. Had he stayed in the Scottish system he would have been absorbed into a tradition that combined experiment with natural philosophy – but Cambridge gave him the extra abilities to take a more detailed mathematical approach, and the capacity to work with the rigour needed to move on to the next stage of the development of physics. Maxwell developed a working method that was a hybrid of the two traditions.
Maxwell’s success in the mathematics exams and the Smith’s Prize was exactly what he needed to ensure a continued place at the university, winning him the position of bachelor-scholar at Trinity with the near certainty of a fellowship to follow soon in the future. Now he had more time for his own projects. Continuing his fascination with light from his investigations of polarisations and the stress experiments, Maxwell found a new interest in the way that human beings perceive different colours.
Colour vision
At the time, doctors could do little more than peer at an open eye and hope to see into it, but Maxwell constructed one of the first ophthalmoscopes, in effect a microscope for examining the inner workings of the eye. With it, he subjected human and particularly dogs’ eyes to lengthy study, and was able to reveal the network of blood vessels on the inner surface. He wrote to his aunt, Miss Cay, in Edinburgh in the spring of 1854:
I have made an instrument for seeing into the eye through the pupil. The difficulty is to throw the light in at that small hole and look at it at the same time; but that difficulty is overcome, and I can see a large part of the back of the eye quite distinctly with the image of the candle on it. People find no inconvenience in being examined, and I have got dogs to sit quite still and keep their eyes steady. Dogs’ eyes are very beautiful behind, a copper-coloured ground, with glorious bright patches and networks of blue, yellow and green, with blood-vessels great and small.
This work with his ophthalmoscope appealed to his continued interest in the detail of
natural phenomena, but it gave no obvious clues as to the mechanism within the eye that enables us to distinguish between colours.
In working this out, Maxwell had two lines of enquiry. The better-established understanding at the time came from artists, who for centuries had been mixing different pigments to produce a palette of colours. The painters considered that red, yellow and blue were the ‘primary’ colours, able to produce any of the other colours when mixed together. The versatile English doctor and physicist Thomas Young had suggested that the eye worked in a similar fashion to the artist’s palette, but in reverse. Different areas of the retina, Young believed, were sensitive to red, yellow and blue – or to be more precise, he suggested that each ‘sensitive filament’ of the optic nerve was split into three portions, one dealing with each of the primary colours, hence being able to construct the colour range that we see.
Maxwell was also aware of a strand of more physics-related experiments on light and colour from the natural sciences, which stretched back to Isaac Newton. It was while Newton was himself at Trinity College that he had performed his famous experiments. Piercing the blinds of his room, he had let a narrow beam of sunlight through and split it into the rainbow colours using a prism that he bought at a local fair.**
It was Newton who dreamed up red, orange, yellow, green, blue, indigo and violet as the colours of the rainbow. In reality, seven appears a strange number to have selected. There are far more colours if you examine a rainbow under the microscope, but to the naked eye there only appear to be six broad bands, merging Newton’s three variants of blue into two. It’s thought Newton went for the number seven so there would be the same number of rainbow colours as musical notes, an appeal to the harmony of nature. The ability of a prism to produce a rainbow was well known – that’s why they were on sale at the fair as toys – but the prevailing theory at the time for why this happened was that the incoming white light was being coloured by impurities in the glass.
Newton’s genius was to separate off individual colours from a prism’s output and send them through a second prism. No individual colour was changed by passing through a second piece of glass – suggesting that the prism did not add the colour, but merely separated out the colours that were already present in the white light of the Sun. Newton confirmed this by focusing the rainbow colours with a lens and producing white light again. If these colours were all in white light, but when that light fell on, say, a red apple we see only red, it seemed reasonable that the apple was absorbing many of the colours in the spectrum while reflecting only the red.
Some colours that we can see, though, simply aren’t present in a rainbow spectrum of light. Think of brown or magenta (cerise in fashion terms), for example. Such oddities could only be produced by mixing other colours – but how this was to be done caused confusion. Over time, Newton’s successors started using a wheel or ‘top’ with different colours on, which was spun so that the colours seemed to combine in the eye. Professor Forbes at Edinburgh had repeatedly attempted to produce white through a combination of variants of red, yellow and blue on a wheel – but had failed. Similarly, Forbes had used one of the artist’s most familiar combinations – mixing yellow and blue to make green – and discovered that, bizarrely, his spinning wheel appeared to produce not green at all, but a dirty shade of pink.
The true primaries
It was Maxwell, now what we’d call a graduate student, who followed up the idea of German physicist Hermann von Helmholtz, building on Newton’s observations, that there were two different processes involved: that colours in light added together to produce new shades, while colours in a pigment were subtractive (i.e. they took away some of the colours of light) and had to be treated separately. As Newton had suspected, when we see an object as a certain colour – a red postbox, for example – what our eyes actually detect is the light that is re-emitted by the box. If white light, with all the colours in it, is falling on the box and we see red, then the pigments in the paint have absorbed the other colours. And when we mix pigments, such as yellow and blue, the resultant colour we see (green in this case) is what’s left when the rest of the colours in the light have been absorbed by those two pigments.
This meant that the artist’s primary colours weren’t really primaries at all, but were the leftovers when the primaries were absorbed, the diametric opposites of primaries,†† which modern scientists would probably have called anti-primaries. Through a combination of experiment and logic, Maxwell realised that the true primaries of light (as opposed to pigments) were in reality red, green and blue or violet – when he made up a colour disc with these colours and spun it, he saw white. In making this change he was going against his old Edinburgh professor Forbes who stuck (with many of his contemporaries) to the earlier idea of red, yellow and blue as the primary colours of light, despite the failure of their experiments.
This wasn’t enough for Maxwell, though. He built his own totally new version of the colour top, using three paper discs, one for each primary colour, so he could spin different combinations of red, green and blue to study the resultant perceived colours. These discs were provided by the Edinburgh printer and artist David Hay, who had inspired Maxwell’s teenage paper on drawing curves, and whose colour printing was considered to be among the best in Great Britain. The term ‘top’ suggests a self-supporting spinning device, but in reality, his mechanism consisted of a flat metal disc to support the paper sheets, pivoted on a handle, so it was shaped something like a round skillet with a spinning pan.
In an early manuscript on the subject from February 1855, Maxwell described the device as a ‘teetotum’ (an alternative word for a top). He tells us:
It may be spun by means of the fingers but if more speed is required it ought to be spun by means of a thread wound round the part of the axis immediately below the disc. This is best done by slipping the knot on the thread behind the little brass pin under the disc and after winding it up placing the axis vertical & so that the two grooves in it rest in the two hooks belonging to the brass handle. When the string is pulled, the hooks keep the axis vertical and thus the teetotum may be spun steadily on the smallest table or tea tray.
Maxwell aged 24 with one of his colour wheels in 1855.
Getty Images
It is entirely possible that the idea of constructing his colour top had its inspiration in an entertainment from Maxwell’s youth. One of his favourite toys as a child was the phenakistoscope, more mundanely known as the magic disc. This spun a disc with a series of illustrations drawn around its edge. The disc was viewed from the rear through a series of slots in the disc, reflecting the images in a mirror to produce the effect of a very short moving picture. Maxwell drew the pictures for many of his own mini-movies to spin on the magic disc, with subjects covering everything from the cow jumping over the Moon to a dog catching a rat. The merger of the still images in the brain to produce a combined effect could well have suggested a similar approach in the top.
Maxwell’s colour top also had room for a fourth colour which was in a continuous circle around the centre of the disc. This meant that he could adjust the amounts of each primary to match the colour represented in that circle. He went on to produce a mathematical formula relating the percentages of the primaries to the resultant hue.
From his formula, Maxwell was able to produce a ‘colour triangle’ which started with the three primaries in the corners of an equilateral triangle and mixed the amounts of the colours according to the distance to the corners (see Figure 1). An important outcome of this work was the realisation that what we perceive as the colour in a beam of light is not the same thing as the absolute colour of the light used. While monochromatic light of a particular wavelength will be seen as, say, orange, the brain also combines the input from the different colour-determining sensors in the eye, known as cones, to enable the colour to be produced from a mix of the primary colours.
Similarly, Maxwell was able to use his triangle to understand the detail of how pigm
ents appear to have particular colours. For example, if you shine white light onto a pigment that strongly absorbs the middle of the spectrum, around green, the result will be that red and blue wavelengths are mostly re-emitted, producing magenta – which is effectively anti-green. And the old artist’s favourite of mixing yellow and blue to produce green works because cyan pigment mostly absorbs red, while yellow pigment mostly absorbs blues, leaving only green to be re-emitted.
FIG. 1. Each corner of the colour triangle corresponds to a single primary colour. The colour at the point marked ‘?’ mixes r of red, b of blue and g of green – the central W point has equal amounts of each colour, producing white.
A peculiar inability
Maxwell notes that some individuals have a ‘peculiar inability’ to distinguish certain colours – his work on the perception of colour went hand in hand with a deep interest in those who were colour blind, suffering from ‘Daltonism’ as it was often known then, after the Manchester chemist John Dalton, who suffered from the condition and was one of the first to study the phenomenon scientifically. Maxwell also records that the most interesting result is that ‘different eyes in similar circumstances agree to the most minute accuracy [on a colour] while the same eyes in different lights give different results’.
So, he had discovered, our perception of colour is strongly affected by lighting etc. but is remarkably consistent between individuals who have normal colour vision. But Maxwell, with a good scientist’s caution, was not willing to expand his observations too far from the small sample he originally had access to. He noted: ‘These results however can be completely verified only by a large number of observations.’ For the rest of his working life, he would invite visitors to try out a range of colour mixing devices he invented to widen his sample, and would ask friends both to take the test and to bring forward anyone they knew who didn’t see colour the same way as the majority.