# Maxwell, James Clerk (1831–1879)

# MAXWELL, JAMES CLERK

*(1831–1879)*

James Clerk Maxwell, the British physicist, came from a well-known Scottish family, the Clerks; his father adopted the name Maxwell on inheriting an estate originally belonging to that family. Maxwell was educated at Edinburgh University and the University of Cambridge, becoming a fellow of Trinity College in 1855. In 1856 he won the Adams Prize at Cambridge for an essay in which he demonstrated that the rings of Saturn would be unstable if they were continuously solid or fluid and that they must be composed of discrete and separated parts. Maxwell was professor of natural philosophy at Marischal College in Aberdeen from 1856 to 1860 and professor of natural philosophy and astronomy at King's College in London from 1860 to 1865. His first paper on electromagnetism appeared in 1856; his electromagnetic field theory with the derivation of the velocity of light was first published in 1861–1862 and in more rigorous form in 1865; and he began work on the kinetic theory of gases in 1860. From 1865 to 1871 Maxwell remained at his country estate in Scotland where he worked on his *Treatise on Electricity and Magnetism,* which summarized the subject and his contributions thereto. In 1871 he became the first occupant of the Cavendish chair of experimental physics at Cambridge, supervised the construction of the Cavendish Laboratory, and later guided the first research done there. During this period he edited the works of Henry Cavendish. During his lifetime Maxwell also did research on color vision, mechanics, and other topics, and although his fame rests on his theoretical achievements, his experimental work was noteworthy.

## The Electromagnetic Field

Maxwell's greatest contribution to fundamental physics was his concept of the electromagnetic field, a concept that underwent much modification both in the course of his own researches and at the hands of his successors. In modern terms, a field—such as the electric field—is a condition in the space surrounding charged bodies that determines the force that a unit electric charge would experience if it were placed at any point. In field theory all actions are regarded as transmitted from point to point by the contiguous modification of the field between the points, and the field is regarded as the seat of energy. Contemporary physics is dominated by the field-theoretic viewpoint, whether or not it is reinterpreted in terms of quantum theory.

Maxwell aimed at embodying in mathematical notation the ideas of Michael Faraday and, in particular, Faraday's fruitful concept of lines of force. In this Maxwell was inspired by the work of William Thomson (later Lord Kelvin), who had demonstrated the mathematical analogy between the problems of heat flow and of the distribution of static electricity. Maxwell developed similar analogies in his first paper on the subject, "On Faraday's Lines of Force" (1855–1856), drawing separate analogies for different aspects of electromagnetism: between electrical and fluid currents, and between electric or magnetic lines of force and fluid currents. While suggestive, such an endeavor was of course not a unified theory. "I do not think," he wrote, "that we have any right at present to understand the action of electricity, and I hold that the chief merit of a temporary theory is, that it shall guide experiment, without impeding the progress of the true theory when it appears." The beginning of the paper is of interest as a statement of method; Maxwell points out the pitfalls of commitment to a mathematical formula, in which case "we entirely lose sight of the phenomena to be explained," or to a physical hypothesis, the irrelevant parts of which are liable to carry one beyond the truth. He advocates instead the use of physical analogy, "that partial similarity between the laws of one science and those of another which makes each of them illustrate the other."

In his "On Physical Lines of Force" (1861–1862), Maxwell's electromagnetic field theory appears for the first time, presented as a deduction from a detailed model of the ether. Magnetic lines of force are represented as molecular (microscopic) vortices in this ether, the matter of the ether whirling around in planes normal to the direction of the lines of force, so that the latter is the direction of the axes of the vortices. Maxwell found that in this fashion he could represent the properties of lines of force needed for magnetostatics, that is, that the lines should tend to contract along their length and repel each other laterally. But how can neighboring vortices spin in the same sense, since their neighboring boundaries move in opposite directions, and how are these motions initiated and communicated through the ether? Maxwell assumed a layer of tiny idle wheels between each pair of vortex cells in the ethereal substance. These wheels can rotate freely, so that a uniform magnetic field is represented by the vortex cells all spinning at the same rate and in the same sense, and the interspersed wheels rotating in place in the opposite sense. The idle wheels can also move from place to place in a conductor, but they are constrained to rolling contact without slipping with the neighboring vortices. The translatory motion of the wheels is identified with the electric current and used to explain the manner in which a magnetic field is created by an electric current (Hans Christian Ørsted's discovery); it also is used to account for electromagnetic induction. Furthermore, in a dielectric, including the vacuum, the wheels are not free to move in translation, but can only be displaced slightly against the elastic forces of the material of the cells. This action of displacement is the displacement current that forms the new term Maxwell added to previous results, while transforming all of them into his theoretical language. Maxwell then proceeded to calculate the velocity of propagation of transverse waves in his elastic ether. The speed of these waves was proportional to the ratio between the electromagnetic and electrostatic units of charge.

The factor of proportionality between the speed of the waves and the ratio of the units depended in this calculation on the specific model chosen for the ether; the argument showing the two terms to be equal cannot be regarded as very satisfactory. In "A Dynamical Model of the Electromagnetic Field" (1865), the electromagnetic field equations are presented directly without recourse to the ether model, and the relation between velocity of waves and ratio of electrical units is derived directly from the equations. Since, according to Wilhelm Weber and Friedrich Kohlrausch (1857), the ratio between the units was 3.11 × 10^{8} meters/sec., whereas, according to Armand Fizeau, the speed of light was 3.15 × 10^{8} meters/sec., Maxwell drew the important conclusion that light consisted of waves in the electromagnetic ether. This finally gained general acceptance when Heinrich Hertz generated electromagnetic waves by electrical means and showed that they had all the properties of light except that they were of much lower frequency, a result of the conditions of generation.

In his later papers Maxwell no longer relied on specific models of the ether. In the *Treatise* he wrote:

The attempt which I then [in "On Physical Lines of Force"] made to imagine a working model of this mechanism must be taken for no more than it really is, a demonstration that mechanism may be imagined capable of producing a connexion mechanically equivalent to the actual connexion of the parts of the electromagnetic field. The problem of determining the mechanism required to establish a given species of connexion between the motions of the parts of a system always admits of an infinite number of solutions.

Nevertheless, he still regarded the underlying phenomena as motions and stresses in the mechanical ether, maintaining that the energy of magnetism "exists in the form of some kind of motion of the matter in every portion of space," apparently of a vortical character. Maxwell's views differ from those of the twentieth century in the following ways: The electromagnetic field was not regarded as a separate dynamic entity from matter, that is, a material ether; ordinary matter was treated macroscopically, phenomenologically, rather than from the atomic point of view; and the role of charge in the theory was ambiguous. Late in the nineteenth century H. A. Lorentz combined Maxwell's field theory with Continental conceptions of atomicity of charge to establish the classical theory of the dualism of matter and field.

## Kinetic Theory of Gases

Also of fundamental importance was Maxwell's work on the kinetic theory of gases. In deriving the experimental gas laws, previous investigators had made the simplified assumption that all the gas molecules moved with the same speed. In "Illustrations of the Dynamical Theory of Gases" (1860), Maxwell first derived the equilibrium distribution of the velocities of the molecules: the components of the velocity along a given direction are distributed according to Carl Friedrich Gauss's error law. This paper also contained the startling result, later demonstrated experimentally, that the viscosity (internal friction) of a gas should be independent of its density. Maxwell wrote two other pathfinding papers on the kinetic theory; their main subject was the derivation of the transport coefficients of a gas (coefficients of diffusion, viscosity, and thermal conductivity) and, in the last of them, the discussion of radiometric phenomena.

Maxwell's work on the kinetic theory may be regarded as constituting the first important introduction of statistical reasoning into physics and the first steps in the development of statistical mechanics, later continued by Ludwig Boltzmann and Josiah Gibbs. In statistical mechanics the use of statistics is not a manifestation of any indeterminism in the purported fundamental laws of nature, as it is in quantum physics; rather it is the reflection of our ignorance of the exact motions of the enormous number of molecules in any macroscopic system. The very immensity of this number (there are about 6 × 10^{23} hydrogen atoms in one gram of hydrogen) and the minuteness of the individual molecules give assurance that in ordinary experiments the measurable properties will be statistical in character and thus will be exactly the properties singled out by a statistical theory.

Maxwell's demon, a hypothetical being that apparently could reverse the tendency of isolated systems toward increase of disorder or entropy and so would violate the second law of thermodynamics, appears in his *Theory of Heat* (London, 1872, pp. 308–309). The thermal equilibration of neighboring vessels containing gas, representing a state of maximum disorder, could be destroyed by a being capable of seeing the individual molecules of the gas who acts so as to let only the faster molecules in one container pass through a small hole into the other, and the slower ones in the latter to pass in the reverse sense. Since the temperature is determined by the mean energy of motion of the molecules, this process would result in the gas in one vessel becoming warmer than that in the other, without any interference from outside the system. The demon has been exorcised by L. Brillouin and others (see Brillouin's *Science and Information Theory,* New York, 1956, Ch. 13). To obtain the information about an approaching molecule that the demon needs in order to decide whether or not to open the hole, the demon must absorb at least one quantum of light, the energy of which is reasonably greater than the mean energy of the quanta of thermal radiation that are always present. The absorption of this quantum demonstrably leads to a greater increase in entropy in the total system (including the demon) than the decrease obtained by properly manipulating the hole.

** See also ** Boltzmann, Ludwig; Energy; Ether; Faraday, Michael; Gibbs, Josiah; Matter; Motion; Philosophy of Physics; Quantum Mechanics.

## Bibliography

The *Scientific Papers of James Clerk Maxwell,* including his semipopular lectures but not the *Treatise* and other books, appear in two volumes edited by W. D. Niven (Cambridge, U.K.: Cambridge University Press, 1890). See in particular his Bradford address, "Molecules," Vol. II, pp. 361–377, in which he expresses most lucidly his religious and metaphysical position. The *Treatise on Electricity and Magnetism,* 3rd ed., edited by J. J. Thomas, was published in 1892 at Oxford. The standard biography is Lewis Campbell and William Garnett, *The Life of James Clerk Maxwell* (London: Macmillan, 1882).

*Arthur E. Woodruff (1967)*

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