This non-technical review of Maxwell's contributions to the quantitative theory of colour was presented at a symposium in Aberdeen to celebrate the 150th anniversary of his appointment as professor of natural philosophy at Marischal College. Maxwell maintained his interest in the science of light and colour from his childhood to the last decade of his life. He lavished the same care and imagination on these studies as he did on his epochal contributions to electromagnetism and statistical physics.
James Clerk Maxwell's contributions to electromagnetism, the kinetic theory of gases, thermodynamics and statistical mechanics are rightly recognized as among the greatest contributions to science, providing the essential link between Newtonian physics and the revolutions in physics that were to take place in the early decades of the twentieth century. At the same time, he had a deep interest in many other topics. In particular, his interest in the science of colour remained with him throughout his life, from early childhood to his last decade. In this paper, Maxwell's achievements in the science of colour are set in their historical context. The story will begin with the history of light and colour from Snell to Young. Then, Maxwell's early interest in colour phenomena will be discussed, leading to his development of the quantitative theory of colour vision.
2. From Snell to Young
In 1621, Willebrord van Snel van Royen discovered the law of refraction when a light ray crosses the interface between two media. In modern notation, the well-known form of what is known as Snell's law is written(2.1)where n1 and n2 are the refractive indices of the two media and θ1 and θ2 are the angles of incidence and refraction. This is the law which is at the heart of optics, lenses, microscopes and telescopes. One of the first applications of Snell's law was made by René Descartes to account for the formation of rainbows. He studied the internal reflection of light within spherical raindrops and showed that there is a minimum angle of deflection of the light rays amounting to 42° for a single reflection within the raindrop. If there are two internal reflections, the minimum angle is 51°. This theory predicted correctly the observed angles of single and double rainbows with respect to a line from the Sun through the observer's head to the centre of the rainbow. A sketch of the origin of single and double rainbows appeared in Descartes' Les Météores of 1637 (figure 1). There was, however, no understanding of the origin of the colours in the rainbow. This was to be elucidated by Isaac Newton.
In 1665–1666, Newton was aged 22 and in these years he discovered the binomial theorem, the integral and differential calculuses, the theory of colour in optics and unified celestial mechanics and the theory of gravity. These were staggering achievements. In the field of optics and colour, the key experiment of these years was Newton's ‘experimentum crucis’. He passed sunlight though a high quality prism and observed that white light was split up into the colours of the spectrum. He then passed this spectrum through a hole that allowed only one of the colours to be selected. On passing this single colour through a second prism, he found that the light was not split up into any further colours. In Newton's words, ‘Light itself is a heterogeneous mixture of differently refrangible rays’ (Turnbull et al. 1959–1977).
This result gave rise to one of Newton's many disputes with other scientists. The French experimenters could not reproduce the result of the experimentum crucis, but found instead that the separate colours could be split up into further colours. It turned out that Newton had found the correct answer owing to his use of higher quality prisms than those available to the French scientists, but it was many years before Newton's view prevailed (Shaffer 1989).
Since different colours are refracted through different angles, white light is not focused at a single point by a lens, the phenomenon known as chromatic aberration. To get round his problem, Newton invented the all-reflecting, or Newtonian, telescope (figure 2a). He built the telescope himself, including the grinding of the mirrors. The resulting telescope had superior imaging qualities when compared with the Galilean refracting telescope, as he demonstrated in his paper published in the Phil. Trans. R. Soc. in 1672.
Newton divided the spectrum into seven colours, the famous VIBGYOR sequence of violet, indigo, blue, green, yellow, orange and red (figure 2b). In his choice of seven colours, he was influenced by the ideas of harmonic proportion, which had been set out in Kepler's great treatise The harmony of the world of 1618 and which had influenced all aspects of the arts and sciences in the seventeenth and eighteenth centuries. The treatise contained the discovery of Kepler's third law of planetary motion, which was crucial in Newton's discovery of the law of gravity, and so there is no doubt that Newton knew the treatise well. There are seven different notes in the just harmonic scale, their frequencies all being in the ratios of small whole numbers, and so Newton divided the spectrum into seven colours. Newton's seven colour theory was elaborated by Voltaire in his Élémens de la Philosophie de Neuton of 1738.
The next notable figure in the story is Thomas Young, whose brilliant researches of 1801 not only put the wave theory of light on a firm physical foundation but also resulted in the theory of three-colour vision. His most famous experiment was the double-slit experiment in which he found that, when sunlight is passed through a single narrow slit and then through a pair of similar slits, a characteristic pattern of bright and dark bands is observed on a screen. He interpreted the appearance of this pattern of light rays in terms of the constructive and destructive interference of light waves. This was conclusive evidence in favour of the wave theory of light.
In the same paper, he also discussed how the eye would perceive lights of different wavelengths or colours. In his picture, the light receptors in the retina of the eye act as resonators which are excited by the incoming light waves. He realized, however, that there was a problem with this picture. In his words:
As it is almost impossible to conceive each sensitive point of the retina to contain an infinite number of particles, each capable of vibrating in perfect unison with every possible undulation, it becomes necessary to suppose the number limited: for instance to the three principal colours, red, yellow and blue … and that each of the particles is capable of being put into motion more or less forcibly by undulations differing less or more from perfect unison. … each sensitive filament of the nerve may consist of three portions, one for each principal colour.
There are several interesting points about Young's proposal. First, he took the three principal colours to be red, yellow and blue. Second, there was no distinction between the mixing of lights and the mixing of pigments. Third, the theory was qualitative rather than quantitative.
3. The young Maxwell
James Clerk Maxwell came from a distinguished Scottish family. Although born in Edinburgh, he spent most of his childhood at the family estate at Glenlair in the Dumfries and Galloway region. By great good fortune, James's cousin, Jemima Wedderburn, who was 8 years his senior, was a brilliant artist who painted scenes from family life almost every day. Her watercolours, a number of which can be viewed on the James Clerk Maxwell Foundation's website (http://www.clerkmaxwellfoundation.org), are a wonderful record of life at Glenlair and Edinburgh. Among my favourites are the paintings of James and Jemima ‘tubbing’, meaning using washing tubs as coracles in a nearby duck pond. James had an insatiable curiosity about everything. According to the biography by Campbell & Garnett (1882), from his earliest years, he would continually ask, ‘Show me how it doos’, or ‘What's the go o'that?’ If he did not receive a satisfactory answer to the latter question, he would ask, ‘But what's the particular go o'that?’
At home, James's father, John Maxwell, James and Jemima were fascinated by the new range of optical toys which became available during the 1830s. These relied upon the phenomenon of the persistence of vision by which the eye and brain preserve the image for approximately 1/20th of a second. As in a cinematographic film, the appearance of movement is obtained by viewing the images faster than the eye can track individual frames.
The thaumatrope was invented in 1825 by the London physician John Paris, who made the toy popular. Two images are printed on either side of a circular card which was then rotated rapidly about a diameter by twisted strings attached at opposite ends of this diameter. Owing to the persistence of vision, the images on either side of the disc are observed to be superimposed.
In 1832, Belgian physicist Joseph Plateau and his sons introduced the phenakistoscope, meaning ‘spindle viewer’. About a dozen images were drawn on the disc which was then rotated about its axis and the images viewed in a mirror by looking through radial slits cut in the disc. The viewer sees the images very rapidly one after the other, producing the effect of a moving image.
The phenakistoscope was soon overtaken by the zoetrope which was invented in 1834 by William Horner. Now, the images were painted on a strip which was pasted to the inside of a rotating cylinder. The images were viewed through the slits in the rotating drum. Zoetropes became popular, a 1905 supplement of the New York Sunday American and Journal newspaper including a cardboard cut-out entitled ‘Make Your Own Zoetrope’ (this can be downloaded from the web-site http://brightbytes.com/collection/zoetrope.pdf).
James and Jemima delighted in these scientific toys. As expressed by Campbell & Garnett:
This was a source of endless amusement to the two cousins, the younger generally contriving, and in part executing, the elder giving life and spirit to the creatures represented. The cow jumping over the waxing and waning moon, the dog pursuing the rat in and out of his hole, the circus horse, on which the man is jumping through the hoop, have the firmness and truth of touch, the fullness of life, familiar to the many admirers of [Jemima Wedderburn]—the tadpole that wriggles from the egg and changes gradually into a swimming frog; the cog-wheels moved by the pendulum, and acting with the precision of clockwork.
James was not yet 10 when they invented many of their own designs. James remained fond of the zoetrope and in 1861 improved its performance by inserting concave lenses instead of slits on the drum so that the virtual image appeared on axis while it rotated (figure 3). The resulting image was much improved and a wider field of view observable. He set this invention as a problem in the Cambridge 1869 tripos examinations.
James attended Edinburgh Academy from 1841 to 1847 and lived at the house of his aunt Isabella Wedderburn. He was regarded as somewhat eccentric by his schoolmates. As his biographers wrote, ‘Some eccentricity of behaviour earned him the name Dafty’ (Campbell & Garnett 1882). But he took this all in good part and his originality was soon recognized by his school friends. This was also the period of his first scientific papers. In 1846, his paper On the description of oval curves was read to the Royal Society of Edinburgh by Prof. James David Forbes.1
After high school, Maxwell proceeded to Edinburgh University where among the books he borrowed from the library were Newton's Optics and Poisson's Mechanics. During his years at Edinburgh University, he published papers On the theory of rolling curves (1849) and The equilibrium of elastic solids (1850) in the Transactions of the Royal Society of Edinburgh.
In 1847, Maxwell was taken by his uncle John Cay to visit the optical laboratory of William Nicol, the distinguished optician and inventor of the Nicol prism. Maxwell later recalled that:
I was taken to see [William Nicol], and so, with the help of ‘Brewster's Optics’ and a glazier's diamond, I worked at polarisation of light, cutting crystals, tempering glass, etc.
In 1848, he undertook a series of experiments on the chromatic effects of polarized light in doubly refracting materials, crystals and mechanically strained glasses. He remarked on the ‘gorgeous entanglements of colours’ in strained glasses.
Maxwell went up to Trinity College, Cambridge, in 1850 and was to remain there until his appointment to the Chair of Natural Philosophy at Marischal College, Aberdeen in 1856. In his letter of recommendation, Forbes wrote to William Whewell, Master of Trinity College:
Pray do not suppose that … I am not aware of his exceeding uncouthness, as well Mathematical as in other respects … I thought the Society and Drill of Cambridge the only chance of taming him and much advised his going.In his obituary of Maxwell, his great friend Peter Guthrie Tate wrote:
… he brought to Cambridge in the autumn of 1850, a mass of knowledge which was really immense for so young a man, but in a state of disorder appalling to his methodical private tutor.
4. Maxwell's quantitative theory of colour mixing
In 1855, Maxwell was awarded a fellowship at Trinity College. Among his many interests, he studied the composition of light by means of his colour top, which was central to his first major assault upon the quantitative theory of colour (figure 4).
The three coloured paper discs could be clamped to the wooden disc of the top in such a way as to allow different amounts of the primary colours to be mixed when the top was spun (figure 5a). A smaller central disc contained the colour sample which was to be matched by adding together different amount of the primary colours. To eliminate the effect of the different brightnesses of the central disc and the outer colours, different amounts of black could be added to the central disc. Maxwell demonstrated that all colours could be synthesized by different combinations of the three primary lights, red, green and blue. He also distinguished clearly between the results of mixing lights of different colours and mixing pigments. For example, he confirmed Helmholtz's discovery that mixing blue and yellow light does not produce green, but rather ‘a pinkish tint’.
By 1855, Maxwell had adopted the three-colour receptor theory of Young with primary lights red, green and blue, and determined experimentally colour equations which quantified how much of each primary colour was necessary to create any particular colour. All colours could then be represented on a colour triangle in which the distance from the corners indicated how much of each primary colour has to be mixed (figure 5b). Note that these colour diagrams are projections onto a two-dimensional plane of three-dimensional colour space. He carried out his colour matching experiments with many independent observers and found little variation between them. These experiments also suggested an explanation for colour blindness if one of the three sets of receptors in the eye was not present. Figure 5c shows a modern version of Maxwell's colour triangle.
5. Maxwell at Marischal College, Aberdeen
Maxwell accepted the post of professor of natural philosophy at Marischal College, Aberdeen in 1856 to be closer to his family and the estate at Glenlair. His father died in 1856 and in 1859 he married Katherine Mary Dewar, daughter of the principal of Marischal College. He was made redundant when Marischal and King's colleges combined in 1860.
Maxwell's 5 years at Aberdeen were among the most innovative and important periods of his life. In 1857, he won the prestigious Adams Prize for his work on The motion of Saturn's rings. This was also the period of his papers on The dynamical top (1857) and The theory of colours (1857, 1859–1860). He was also developing his ideas on electromagnetism which were to reach their culmination over the succeeding 5 years with the formulation of what we now call Maxwell's equations.
Maxwell was not fully satisfied with the results of his experiments with the colour top and so devised a series of ‘light boxes’ which enabled different amounts of the three primary lights to be mixed more precisely. The perfected light box, constructed by the firm of Smith and Ramage of Aberdeen, was portable and so could be used as a tool to study the colour sensitivities of many subjects (figure 6).
To understand how the light box worked, let us first use it backwards (figure 7a). If white light is shone through the eyepiece at A, on passing through the prisms and mirror, the normal spectrum of colours is produced at B. At B, there are three adjustable slits which allow different amounts of blue, green and red light to be transmitted.
If we now shine white light onto the slits at B, only the blue, green and red colours are combined at A (figure 7b). The amount of each colour could be precisely measured from the width of the slits at B. In addition, a comparison white light beam could be viewed at A. To obtain an intense enough light source, bright sunlight was shone onto white paper to provide a white light source.
Maxwell used the light box to study many different aspects of colour vision for large samples of subjects. The experiments gave precise information about the composition of different colours and provided the forerunners of the modern chromaticity, or Commission Internationale d'Éclairage (CIE), diagrams which define how different colours can be synthesized from chosen primary colours. These convey information about the different variables of colour vision, namely, the spectral colour and the degree of saturation. An example of such a diagram is shown in figure 5d.
Maxwell was awarded the Rumford Medal of the Royal Society of London in 1860 for his researches in colour vision. He continued using light boxes after he moved to King's College London in 1860. He designed and had built an 8 ft light box which was housed in a large garret which ran the whole length of his house at 8 Palace Gardens Terrace, Kensington in London. Campbell & Garnett noted that:
When experimenting at the window with the colour-box …, he excited the wonder of his neighbours, who thought him mad to spend so many hours in staring into a coffin.
Also in 1861, Maxwell took the first coloured photograph. A small piece of tartan ribbon was photographed by a professional photographer on three plates through red, green and blue-violet filters. Three positive plates were produced and these were projected through the same filters onto a screen. When these images were combined, a reasonably fully coloured image was produced. This additive three-colour separation technique is employed nowadays in colour astrophotography.
6. Maxwell's legacy
Maxwell's studies provided the basis for the present understanding of the processes of colour vision and also for the quantitative measurement of colour which underpins a huge variety of modern manufacturing and service industries. The light sensors in the retina are the rods and cones. The rods are very sensitive and can register the arrival of individual photons of light but have no colour discrimination. The cones are less sensitive but are sensitive to light centred on red, green and blue wavelengths. The sensitivity curves shown in figure 8 illustrate versions on normal three-colour vision for different species and different forms of colour blindness.
What we actually perceive is determined by a large number of other factors and this takes us into the realm of physiology and psychology (e.g. Lamb & Bourrieau 1995). But the important lesson from Maxwell's colour mixing experiments is that it is only when monochromatic light is used that there is a unique relationship between colour and wavelength. Any particular colour can be produced in a number of different ways provided the same total signals are applied to the three different cone types.
Maxwell understood that pigments are in a sense the opposite of lights. They absorb some wavelengths and reflect others. For example, suppose we shine white light onto a pigment which absorbs strongly in the central region of the optical spectrum. The light we see reflected consists of the red and blue ends of the spectrum, resulting in the colour magenta. This understanding of the difference between mixing lights and pigments also solved the ‘green problem’. Blue and yellow pigments absorb the ends of the spectrum and so, when they are mixed, the residual reflected light is centred about green wavelengths.
What we actually perceive is determined by many other factors—is the surface smooth or rough, is it highly reflective or polarizing, and so on? Furthermore, the blue cones are rather sparsely distributed on the retina. This can fool the eye if the object is observed with low angular resolution.
Maxwell continued his studies of colour and optical phenomena during his subsequent career at Kings' College London, at his home at Glenlair and at the Cavendish Laboratory, Cambridge. From ca 1860 onwards was the period of his development of his deep insights into electromagnetism, the unification of light and electromagnetism, thermodynamics and statistical mechanics, for which he is rightly best remembered. It was characteristic of him, however, that he brought to the quantitative study of colour the same imagination and experimental skill which he displayed in all his other researches. It is remarkable that he was able to maintain his interests over such a vast range of the physical sciences and that he continued to make fundamental contributions to all of them throughout his career.