James Clerk Maxwell (1831 - 1879)

It is generally thought that Maxwell's greatest contribution to science is his theory of electromagnetic radiation, and that his second is his kinetic theory, especially his derivation of the speed distribution of gas molecules. But Maxwell also made important contributions in several other areas, including: color theory, thermodynamics, and the theory of the dynamics of Saturn's rings.

Unlike some scientists, who work on different topics in sequence with little overlap between them, Maxwell tended to work on topics simultaneously. He worked on color 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 this article the topics are therefore be grouped by subject and not chronologically.

Color Theory and Color Perception (1849-1870)

Isaac Newton (1642-1727) had concluded that white light was composed of seven basic colors, but artists were aware that any desired hue can be obtained by combining three primary colors (red, green, blue). Important scientific work based on the idea of three primary colors had been carried out earlier in the 19th century by Thomas Young (1773-1829), who obtained evidence that light was a wave rather than a corpuscule, as favored by Newton. Young also postulated that the eye contains three types of color receptors, sensitive to red, yellow, and blue light, and that the eye recognises colors by the superposition of images from these receptors.

Maxwell took up the subject where Young had left off. He began his studies of color in 1849, at the age of 18, while an undergraduate at the University of Edinburgh. In 1855, while Professor at Marischal College, Aberdeen, he presented to the Royal Society of Edinburgh a paper entitled "Experiments on color, as perceived by the eye, with remarks on color-blindness". He demonstrated to the audience his favorite color-experiment device: a specially designed color top which had a flat surface to which he could attach colored sectors of various sizes. 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 colors than red, yellow and blue. He distinguished clearly, for the first time, between hue (spectral color, defined by its wavelength), tint (degree of saturation of color), and shade (intensity of illumination).

His procedure was to obtain matches between various mixtures of colors, and to relate the compound colors to the primary ones by means of equations. He constructed color diagrams consisting of equilateral triangles, with the primary colors at the angular points. Any color produced from a mixture of only two primaries was represented by a point on the side of the triangle. If three primary colors were involved the point was within the diagram.

In 1858, while still at Aberdeen, Maxwell abandoned the color top and arranged for the construction of a color box with which he could combine colors. He later constructed other color boxes based on the same principle. His wife and several others assisted him in making observations with these devices. In 1860 he presented a major paper to the Royal Society, "On the theory of compound colors, and the relations of the colors of the spectrum", which was later published in the Philosophical Transactions. In it he established which colors had to be added or subtracted to produce any compound color.

During the next ten years, at King's College, London, and at Glenlair, Maxwell pursued his interest in color. He published a number of further papers, but they were more in the nature of reviews of his earlier work.

Photoimaging in Color (1861)

The claim is often made that Maxwell was the first to take a color photograph, in 1861. This is not true, since Sir John Herschel (1792-1871) and Edmond Becquerel (1820-1891) took colored photographs of spectra in 1842 and 1843 respectively; examples of their work are still in existence. Maxwell may have been the first person to produce a colored image of an object, which is more challenging than photographing a spectrum. But he did not really take a colored 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 colors". The ribbon, which had red, green and blue stripes, had been tied into a rosette. 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 color 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 colored 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 green and red? The answer was provided in 1961, 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-color system provided the basis for modern color photography, but it took about 90 years for it to become commercially feasible. In 1935 Eastman Kodak introduced its Kodachrome materials, involving three layers containing organic dyes of the three primary colors. Colored prints were not available until 1942, and not commercially available until the 1950's.

Saturn's Rings (1855-1857)

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 for its 1857 Adams Prize would be the theoretical study of Saturn's rings, with special reference to two possibilities: that the rings were solids, or that they were fluid. 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 through them. 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 Voyager spacecraft, have confirmed Maxwell's conclusions. The particulate nature of the rings is confirmed by observations of stars seen 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.

Kinetic Theory of Gases (1859-1878).

The kind of mathematics used in Maxwell's treatment of Saturn's rings was directly applicable to the kinetic theory of gases. 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.

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 based on 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. That same year, Maxwell left Aberdeen and accepted an 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 these experiments were made between 51 °F (10.6 °C) and 74 °F (23.3 °C), and it appears that these temperatures were obtained simply by changing the temperature of the attic! This was arranged by Mrs. Maxwell, who organized the appropriate stoking of the fire. Some work was also done at 185 °F (85 °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 put forward a treatment himself, but it also had unsatisfactory features. Maxwell had to grapple with the problem for some years before he was satisfied. In 1867 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 among the particles. The whole field of statistical mechanics was based on these treatments.

Although he made important contributions to kinetic theory, especially 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.

Thermodynamics

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".

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