It is generally considered that Maxwell's greatest contribution to science was his theory of electromagnetic radiation, and that his second greatest contribution was his kinetic theory, especially his theory of the distribution of molecular speeds. These were indeed great achievements, and one cannot quarrel with this assessment. He also made important contributions in several other theoretical and experimental fields, notably: (1) colour theory and colour perception, (2) the theory of Saturn's rings, (3) thermodynamics, and (4) the theory of governors (servomechanisms).
Maxwell's major contributions were in theoretical science, and it is easy to forget that he was a highly competent experimentalist, and was very enthusiastic about carrying out experiments to test his theories. He was skillful in the design of scientific instruments, and particularly noteworthy was his apparatus for measuring the viscosity of gases. After he became director of the Cavendish laboratories at Cambridge he devoted much time and effort to the design of equipment for lecture demonstrations and for use in the undergraduate laboratories.
Maxwell wrote about one hundred papers for publication, and four books, namely Theory of Heat (1870), Treatise on Electricity and Magnetism (1873), Matter and Motion (1877), and Elementary Treatise on Electricity (published posthumously in 1881). All of these books appeared in further editions. With T.H. Huxley he was joint scientific editor of the ninth edition of the Encyclopaedia Britannica, to which he contributed many articles. This was a particularly famous edition, in that it included authoritative and detailed articles on many scientific topics, with full mathematical treatments. During the last few years of his life Maxwell devoted much time to editing the unpublished electrical researches of the eccentric genius Henry Cavendish (1731-1810). The resulting book, Un-published Electrical Researches of the Hon. Henry Cavendish, which appeared in the year of Maxwell's death (1879), is recognized as a classic in the history of science, and shows that Maxwell had a masterly grasp of the history and philosophy of science. It had the effect of greatly enhancing Cavendish's reputation, disclosing many advances that he had made but had not published. The book is enriched by valuable comments by Maxwell, in which Cavendish's work is related to later work.
Unlike some scientists, who work on various topics in sequence, with little overlap between different fields,
Maxwell tended to work on a number of topics simultaneously. He worked on colour vision from 1849, when he was a student at Edinburgh, until 1871, when he went to Cambridge as Cavendish Professor. His work on electromagnetic theory began shortly after his graduation from Cambridge in 1854 and continued until his death in 1879. There was often an interval of several years between his papers on the same subject. Twelve years elapsed between his two most important papers on kinetic theory (in 1867 and 1879), and six years between his first and second papers on electromagnetism (in 1855 and 1861). In the rest of this article the topics will therefore be grouped by subject and not dealt with chronologically. Colour theory, kinetic theory and other topics will be discussed in the present Part 2, while Part 3 will be largely devoted to electromagnetic theory.
Maxwell's work on colour theory and colour vision was less original than much of his other work, since to a great extent it involved extending the work of others. At the same time it has to be recognized that Maxwell was one of the great pioneers of the theory of colour, and of colour physiology, being the first to put the subject on a quantitative basis.
Isaac Newton (1642-1727) had concluded that white light was composed of seven basic colours, but artists were aware of the fact that any desired hue can be obtained by combining three primary colours. Important scientific work based on the idea of three primary colours was carried out earlier in the 191h century by Thomas Young (1773-1829), who obtained evidence for the wave theory of light rather than the corpuscular theory favoured by Newton. Young also postulated that the eye contains three colour receptors, corresponding to red, yellow, and blue, and that the eye recognises colours by the superposition of images from these receptors.
Maxwell took up the subject where Young had left off. He began his studies of colour in 1849, at the age of 18, while an undergraduate at the University of Edinburgh; Professor Forbes, who did much work on colour, encouraged him to work in his laboratories. In 1855, while Professor at Marischal College, Aberdeen, he presented to the Royal Society of Edinburgh a paper entitled "Experiments on colour, as perceived by the eye, with remarks on colour-blindness". He demonstrated to the audience what had become his favourite instrument in this field, a specially designed colour top, having a flat surface to which he could attach coloured sectors of various sizes; this device was an improvement over the device that Young had used for mixing colours. Maxwell's article, largely experimental, is a model of thoroughness, and marks the beginning of the science of quantitative colorimetry. Maxwell showed that red, green and blue make a better set of primary colours than red, yellow and blue. He distinguished clearly, for the first time, between hue (spectral colour, defined by its wavelength), tint (degree of saturation of colour), and shade (intensity of illumination). His wife helped him by acting as one of the observers he used in his experiments. Some of his observers suffered from colour-blindness, and his results convinced him of the essential correctness of Young's three-receptor theory.
His procedure was to obtain matches between various mixtures of colours, and to relate the compound colours to the primary ones by means of equations. He constructed colour diagrams consisting of equilateral triangles, with the primary colours at the angular points. Any colour produced from a mixture of only two primaries was represented by a point on the side of the triangle. If three primary colours were involved the point was within the diagram.
In 1858, while still at Aberdeen, Maxwell abandoned the colour top and arranged for the construction of a colour box, with which he could combine colours; he later constructed other colour boxes based on the same principle. His wife and several others continued to assist him in making observations with these devices. In 1860 he presented to the Royal Society a major paper, "On the theory of compound colours, and the relations of the colours of the spectrum", which was later published in the Philosophical Transactions. In it he established which colours had to be added or subtracted to produce any compound colour.
During the next ten years, at King's College, London, and at Glenlair, Maxwell pursued his interest in colour. He published a number of further papers, but they were more in the nature of reviews of his earlier work.
The claim is often made that Maxwell was the first to take a colour photograph, in 1861. This is not true, since Sir John Herschel (1792-1871) and Edmond Becquerel (1820-1891) took coloured photographs of spectra in 1842 and 1843 respectively; examples of their work are still in existence. Maxwell may perhaps have been the first person to produce a coloured image of an object, which is more challenging than photographing a spectrum. He did not really take a coloured photograph at all; he produced three black and white positive transparencies, and by projecting them simultaneously on a screen, using red, green and blue light, he created a fairly good image of a "bow made of ribbon, striped with various colours". The ribbon, which had red, green and blue stripes, was tied into a rosette. It no longer exists, and is sometimes referred to as a tartan, but it does not appear to correspond to any known tartan. These investigations were begun soon after Maxwell took up his appointment at King's College, London, and the technical work was carried out by Thomas Sutton, a lecturer on photography at King's, who prepared the written account of the experiments.
The demonstration was of particular importance in connection with Maxwell's colour theory. Three black and white photographs were taken, through red, green and blue filters. The red filter was a solution of ferrous thiocyanide, the green filter a solution of cupric chloride, and the blue filter a solution of ammoniacal cuprous sulphate. The negatives were made on wet collodion containing silver iodide, and from them glass positives were prepared. The first public demonstration of the image formed by projecting the three negatives with the coloured lights was in May, 1861, at the Royal Institution, and one of the interested spectators was Michael Faraday.
It emerged much later that there was a curious anomaly about the demonstration. The photographic emulsions available at the time were sensitive only to the blue end of the spectrum; they were only slightly sensitive to green, and not at all to red. How then was it possible for Maxwell and Sutton to produce an image that did show the greens and reds? The answer was provided in 1961, just one hundred years after the demonstration, by Ralph M. Evans of the Eastman Kodak Company. The greens show up only faintly, and can be explained by the slight sensitivity of the emulsions to green. The reds, however, should not have shown up at all, and yet they did. By reproducing the experiment under the original conditions, and using copies of the original transparent positives, which are still at the Cavendish Laboratory, Evans was able to show that the red dye used in the ribbon also reflected a good deal of ultraviolet light, to which the emulsion was sensitive. As a result, the red stripes on the ribbon produced a good image not because they were red but because of the ultraviolet light they reflected.
Maxwell's three-colour system provided the basis for modern colour photography, but it took about 90 years for this to become commercially feasible. In 1935 Eastman Kodak introduced its Kodachrome materials, involving three layers containing organic dyes of the three primary colours. Not until 1942 was it possible to obtain coloured prints, and only in the 1950's was the technique commercially available.
Maxwell's work on the rings of the planet Saturn is of particular interest since it led to his later more important work on the kinetic theory of gases. In 1855 Cambridge University announced that the subject assigned for its 1857 Adams Prize was a theoretical study of Saturn's rings, with special reference to two possibilities: that the rings were solids, and that they were fluid. The Adams Prizes had been instituted in 1848 for an essay on a specified topic in celestial mechanics; the examiners for the prize expected the essays to be based on substantial pieces of original research, worthy of publication in a scientific journal. The prize could be awarded annually, but no essay had ever been submitted until Maxwell, shortly after his arrival in Aberdeen, met the 16 December 1856 deadline for the 1857 award. His essay, which won the Prize, was the only one submitted.
At the time, astronomers had observed three concentric rings about Saturn, all in the same plane. It was known that at least some regions of the rings must be quite thin, since in some areas the planet can be plainly seen. Maxwell began his work at Cambridge and continued it after taking up his appointment at Marischal College, Aberdeen. He carried out a careful theoretical treatment, and concluded that the rings could not be solid or liquid, since the mechanical forces acting upon rings of such immense size would break them up. He suggested that instead the rings are composed of a vast number of individual solid particles rotating in separate concentric orbits at different speeds. His final article on the subject, "On the stability of the motion of Saturn's rings", published in the Proceedings of the Royal Society of Edinburgh in 1859, ran to 90 pages and is a monumental, meticulous and lucid analysis of the problem.
Later studies, including observations from Voyageur spacecraft, have confirmed Maxwell's conclusions. The particulate nature of the rings is confirmed by observations of stars seen right through portions of the rings. Spectroscopic studies have shown that the particles are composed of impure ice, or at least are ice-covered. Radar observations making use of the Doppler effect have confirmed the range of speeds predicted by Maxwell. It appears that the particles have diameters ranging from a few centimetres to a hundred metres.
The kind of mathematics used in Maxwell's treatment of Saturn's rings was directly applicable to the kinetic theory of gases (Chem 13 News, May 1994, pp. 8-10). Early in 1859, when he was still at Aberdeen, he noticed in the Philosophical Magazine a translation of an important paper by the German physicist Rudolph Clausius (1822-1888). In it Clausius derived the fundamental relationship between the pressure-volume product for a gas, and the number of molecules, their mass, and their mean speed. Clausius also discussed the mean free path, and the ratio of the specific heats of a gas in terms of the translational and rotational motions.
Maxwell developed this work in several directions. At the 1859 meeting in Aberdeen of the British Association for the Advancement of Science he presented a theory of the viscosity of gases on the basis of kinetic theory. He concluded that gas viscosities are independent of pressure, and that they increase approximately with the square root of the absolute temperature. At the same meeting he also announced his famous theory of the distribution of molecular speeds. This work was published in the Philosophical Magazine in 1860. In that year Maxwell left Aberdeen and took up his appointment at King's College, London. In the attic of his house in Kensington, with the help of his wife, he carried out experimental measurements of gas viscosities, in order to confirm the conclusions he had drawn about the effects of pressure and temperature. Many of the experiments on temperature dependence of viscosity were made between 510 F and (10.60 C) and 740 F (23.30 C), and it appears that these temperatures were brought about by simply changing the temperature of the attic room; this was arranged by Mrs. Maxwell, who organized the appropriate stoking of the fire. Some work was also done at 1850 F (850 C), and this temperature was achieved by a suitably directed current of steam. The results of this investigation were communicated to the Royal Society in Maxwell's Bakerian Lecture entitled "On the viscosity and internal friction of air and other gases"; the paper was published in the Philosophical Transactions in 1866.
In 1862 Clausius pointed out certain errors in Maxwell's 1860 paper, and Maxwell agreed that the criticisms were valid. Clausius propounded a treatment himself, but this also had unsatisfactory features. Maxwell had to grapple with the problem for some years before finding something with which he was satisfied. In 1867, in the Philosophical Transactions he published a much improved version of his kinetic theory, including a better derivation of his distribution law. Maxwell's work on the distribution of speeds was extended in 1868 by Ludwig Boltzmann (1844-1906) in terms of the distribution of energy, and the whole field of statistical mechanics was based on these treatments.
Later in 1867 Maxwell made another important contribution. In a letter to his friend Peter Guthrie Tait (1831-1901) he proposed a statistical interpretation of the second law of thermodynamics. Maxwell showed how a natural process such as the flow of heat from a higher to a lower temperature could in principle be reversed if one postulated a "finite being" which could control the passage of molecules from one place to another. This imaginary being was later called "Maxwell's demon" (Chem 13 News, February 1992, pages 8-10). The idea of the demon was expounded in his book Theory of Heat, the first edition of which appeared in 1870.
Although he made important contributions to kinetic theory, especially by his distribution law, Maxwell was never convinced of its validity. His doubts were due to certain anomalies, such as the apparent failures of the principle of equipartition of energy, and these could not be resolved until the advent of the quantum theory, over twenty years after his death.
Maxwell had an interest in thermodynamics throughout his career, but wrote no major paper on the subject. He played an important role in the communication and clarification of the obscurely -expressed ideas of the American physicist Josiah Willard Gibbs (1839-1903), particularly through his book Theory of Heat. This book, which eventually ran to 11 editions, gave a particularly clear account of thermodynamics. It included some fundamental equations which have come to be known as the "Maxwell relations".
In 1873, in the course of determining the atomic weight of thallium, an element he had discovered spectroscopically a few years earlier, the English chemist William Crookes (1832-1919) was led to construct what became called a radiometer. This is an eye-catching device that window-shoppers often notice at the stores of opticians and jewellers. A radiometer consists of an evacuated bulb inside which four vanes are mounted on spokes (see Figure 1(a)). Each vane is silvered on one side and blackened on the other. The vanes spin around in the direction that suggests that there is a greater force on the blackened sides than on the silvered sides.
The device at once attracted attention, not only from scientists but from the general public. Queen Victoria was amused, and in 1876 invited some scientists to come to Buckingham Palace to explain it to her. One of them was Maxwell, then Cavendish Professor at Cambridge, and his letter to his uncle describing the visit is worth quoting as it provides a good example of his boyish humour:
"... I was sent for to London, to be ready to explain to the Queen why Otto van Guericke [of 'Madeburgh hemispheres' fame] devoted himself to the discovery of nothing, and to show her the two hemispheres in which he kept it, and the picture of the 16 horses who could not separate the hemispheres, and how after 200 years W. Crookes had come much nearer to nothing and had sealed it up in a glass globe for public inspection. Her majesty however let us off very easily and did not make much ado about nothing, as she has much heavy work cut out for her all the rest of the day..."
One is reminded of a remark that King Charles II had made about two centuries earlier:
"These gentleman spend their days debating nothing." His majesty was complaining of the fact that Robert Boyle, Robert Hooke and others were spending much time working with the vacuum pump that Hooke had invented, and seemed to be wasting their time on nothing. Queen Victoria has no such concerns; she was fascinated by scientific "toys" such as the radiometer and the kaleidoscope, which Sir David Brewster (1781-1868) had invented in 1816.
When Crookes first announced his radiometer most scientists accepted his explanation that the effect was due to the pressure of light. Maxwell refereed Crookes's paper, and accepted that explanation, although he commented that his own theory of electromagnetic radiation predicted alight pressure much smaller than seemed to be involved in the radiometer; Maxwell was always willing to admit that he might be wrong. Ideas about light pressure were much discussed at the time, and the fact that the tails of comets always point away from the sun had been explained as due to the light pressure. There is a story that during a discussion of comets in Maxwell's house the word 'tail' was used so often that Maxwell's terrier began running around in circles chasing his tail.
However, it soon became evident that light pressure could not explain the spinning of the radiometer. For one thing, the light ought to produce a greater force on the silver side, which reflects it, than on the blackened side, which absorbs more of it. In fact the vanes move in the opposite direction.
Another explanation therefore had to be sought. Unquestionably the blackened side will become warmer than the silvered side, because of absorption of light, and the gas near the blackened side will be warmer than that near the silvered side. This led to the second explanation of the movement: because the molecules striking the blackened side are on the average moving faster than those striking the silvered side there will be a greater force on the blackened side. This is a very plausible explanation, and indeed is the one originally accepted by Maxwell; it is still often given at the present day. Maxwell's detailed study of the problem, however, showed to his surprise that the explanation is incorrect.
Maxwell's analysis showed that when a solid is present in a gas in which there is a variation of the temperature, a steady state is soon reached in which there is a steady flow of heat. As far of the surfaces of the vanes are concerned, therefore, there is no net force.
The qualitative solution to the problem was provided by Osborne Reynolds (1842-1912), professor of engineering at Owens College, Manchester, and still remembered for the 'Reynolds number', a dimensionless number related to the motion of a body in a fluid. Early in 1879 Reynolds submitted a paper to the Royal Society in which he considered what he called "thermal transpiration", and also discussed the theory of the radiometer. By thermal transpiration Reynolds meant the flow of gas through porous plates caused by a temperature difference on the two sides of the plates (see Figure 1 (b)). If the gas is initially at the same pressure on the two sides, there is a flow of gas from the colder to the hotter side, resulting in a higher pressure on the hotter side. The explanation is in terms of oblique reflections on the surfaces (see Figure l(c)). A gas molecule moving in the direction AP will on average move faster than one moving in the direction BP, and because surfaces are never completely smooth there will be a net force from right to left on the solid. If, as in a transpiration experiment, the solid cannot move, the gas will instead move from left to right, i.e., from the cooler to the warmer gas.
To explain the radiometer, therefore, one must focus attention not on the faces of the vanes, but on their edges. As seen from Figure 1 (c), the net movement of the vane is away from the warmer gas and towards the cooler gas. The behaviour is just as if there were a greater force on the blackened side of the vane (which as Maxwell showed is not the case), but the explanation must be in terms of what happens not at the sides of the vanes but at their edges.
Maxwell refereed Reynold's paper, and so became aware of Reynold's suggestion. Maxwell at once made a detailed mathematical analysis of the problem, and submitted his paper, "On stresses in ratified gases arising from inequalities of temperature", for publication in the Philosophical Transactions; it appeared in 1879, shortly before his death. The paper gave due credit to Reynold's suggestion that the effect is at the edges of the vanes, but criticized Reynold's mathematical treatment. Reynold's paper had not yet appeared (it was published in 1881), and Reynolds was incensed by the fact that Maxwell's paper had not only appeared first, but had criticized his unpublished work! Reynolds wanted his protest to be published by the Royal Society, but after Maxwell's death this was thought to be inappropriate.
Maxwell's 1879 paper, and the later paper of Reynolds, were important pioneering contributions to the theory of rarefied gases, a field that was to be greatly extended in the present century.
Maxwell's work on governors was inspired by the fact that in carrying out work on electrical units for the British Association (see Pan 3 of this series), Maxwell and his colleagues had used a speed governor to ensure the uniform rotation of a resistance coil. It somewhat resembled the governors used by James Watt on his steam engines; weights attached to a shaft were displaced by centrifugal force and activated a control valve. In 1868 Maxwell published a mathematical treatment of the subject, and his paper, "On governors" in the Proceedings of the Royal Society, is regarded as founding the field of control theory, or cybernetics. The latter word, derived from the Greek word for steersman, was first used by the mathematician Norbert Wiener (1894-1964), who in 1948 published an important book with that title. Today the subject has been broadened to include control and communication in living systems and in computers.
For more on Maxwell's work on photoimaging in colour see Ralph M. Evans, "Maxwell's Color Photography", Scientific American, 205, 117-128 (November, 1961). This article includes a coloured facsimile image of the ribbon. Maxwell's work on kinetic theory, including the investigation of the radiometer, is covered in detail in S:G. Brush, The Kind of Motion that we call Heat, North-Holland Publishing Co., Amsterdam, 1976. This book also deals with the work on thermodynamics, as does Elizabeth Garber, "James Clerk Maxwell and thermodynamics", American Journal of Physics, 37, 146-155 (1969). Maxwell demon references are to be found in Chem 13 News, February 1992, p. 10.