Maxwell, James Clerk (1831-1879)

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James Clerk Maxwell is the one theoretical physicist between Isaac Newton and Albert Einstein of a stature comparable to theirs. Maxwell's contributions to science ranged over many areas, of which the two greatest were his creation of the electromagnetic theory of light, and his work on molecular physics, gas theory, and statistical mechanics. He entered the scientific scene in the early 1850s, immediately after the principle of conservation of energy had been established. Its impact is seen everywhere in his work.

A descendant of a distinguished Scottish family, the Clerks of Penicuik, and, by an illegitimate line, of the ninth Lord Maxwell, he was born in Edinburgh but lived much of his life at his estate in Galloway in southwest Scotland, where he inherited 2,000 acres of rich farmland. From the ages of ten to nineteen he was educated in Edinburgh, entering the University of Edinburgh in 1847. At nineteen he went on to Cambridge University to take the rigorously severe mathematical tripos, from which he graduated in 1854 second in order of merit. He became Fellow of Trinity College in the following year and then, in 1856, at twenty-five, was appointed professor of natural philosophy at Marischal College, Aberdeen. In 1858 he married Katherine Mary Dewar, daughter of the principal. Though lacking any prior scientific training, she became an enthusiast in experimental research and worked closely with Maxwell on several experiments, first in color vision and then in physics. They had no children.

In 1860 Maxwell became a professor at King's College, London, where he served for five years. He retired from professorial life in 1866, at the age of thirty-five, to spend six years writing his famous Treatise on Electricity and Magnetism (1873). During the same time he also produced his small but important Theory of Heat (1871). In 1871 he was appointed Cavendish Professor of Experimental Physics at Cambridge and was responsible for designing and setting up the Cavendish Laboratory. Maxwell died of abdominal cancer in 1879 at age forty-eight.

When Maxwell began studying electricity and magnetism in 1854, the field was in a state of confusion. The laws of electric and magnetic force had been established by Charles Augustin de Coulomb in the 1780s, and impressive mathematical structures had been built on them. However, the triumph was unsettled by Hans Christian Oersted's discovery in 1820 of electromagnetism—a peculiar twisting action exerted by an electric current on a magnet. This departure from Newtonian attractions and repulsions met two contrasting reactions. André Marie Ampère sought to reinterpret Oersted's force as a disguised form of attraction. Michael Faraday treated it as primary and related it geometrically to properties of lines of magnetic and electric force.

It is wrong to see Maxwell's achievement as one of merely translating Faraday's ideas into precise mathematical language. Though he once described Faraday as "the nucleus of everything electric since 1830," two other men, William Thomson (Lord Kelvin) and Wilhelm Weber, were equally influential.From Faraday Maxwell gained a way of thinking; from Thomson, the first mathematizations of Faraday's ideas and several groundbreaking connections to the concept of energy; from Weber, the remarkable insight that the ratio of the two kinds of force, electrostatic and electromagnetic, somehow involves a velocity.

Between 1855 and 1868 Maxwell devoted great effort (five substantial papers) to clearing up the confusions in electromagnetism. The outcome was the dramatic discovery that light is an electromagnetic phenomenon, and the prediction—twenty-seven years before they were detected by Heinrich Hertz—of radio waves. Crucial was Maxwell's devising in 1861 of a speculative "ether" transmitting Faraday's lines of magnetic force. To his astonishment he found that this ether would transmit waves. Using some measurements by Weber and Friedrich Kohlrausch, Maxwell then calculated their velocity and found, to his even greater astonishment, that it was just equal to the velocity of light. Thus the great discovery was made and thus began the great intellectual metamorphosis, shaped by Maxwell and Einstein, in which the velocity of light was transformed from an isolated quantity into a universal fundamental constant influencing every part of physics.

The essence of Maxwell's later development of his theory was in the electromagnetic equations and the idea that electric and magnetic energies, instead of being located on charged bodies, are disseminated through space. That he could so quickly discard his ether model was closely related to the new doctrines of energy. Rather than attempt to explain light or electromagnetism in terms of a mechanism, Maxwell demonstrated that one set of unexplained equations describes both. Philosophically, the theory became a theory of relations. In this line of thought, Maxwell was strongly influenced by his mentor at Edinburgh, Sir William Hamilton, who held that all human knowledge is of relations rather than absolutes.

Maxwell's Treatise on Electricity and Magnetism (1873) covered every branch of the science and was a source of ideas and discoveries for fifty years to come.

In 1859 Maxwell, who had just completed a famous essay on the structure of the rings of Saturn, chanced to read a paper by Rudolph Clausius on gas theory. Maxwell had proved that the rings had to be composed of large numbers of independent bodies constantly colliding with each other. Clausius, expanding on earlier work by James Prescott Joule and August Karl Krönig, proposed that in a gas the rapidly moving molecules are constantly colliding. His interest at once aroused, Maxwell in a few months had written the first of several papers that created the modern kinetic theory of gases.

Maxwell's and Clausius's innovations were of two kinds, mathematical and physical. Mathematically, the key to dealing with large numbers of molecules was statistics, used not as a means of processing scientific data but as a fundamental explanatory idea. Clausius recognized that molecules must travel a certain average distance between collisions—the mean free path—but restrictively assumed that they all have the same speed. Maxwell transformed the discussion by introducing his velocity distribution function, giving the proportion of molecules traveling with a particular speed. Armed with this mathematical weapon, he could attack many previously intractable physical phenomena. He obtained theoretical formulas for viscosity, diffusion, and heat conduction in gases that then could be compared with experimental data. One startling consequence was that the viscosity of a gas should be independent of its pressure. When this was confirmed in independent experiments by Oskar Emil Meyer and by Maxwell and his wife, it added tremendous credibility to the theory.

The work on gas theory had many extensions. In 1865 Johann Josef Loschmidt used estimates of the mean free path to make the first generally accepted estimate of atomic diameters. In later papers Maxwell, Ludwig Boltzmann, and Josiah Willard Gibbs extended the mathematics beyond gas theory to a new generalized science of statistical mechanics. When joined to quantum mechanics, this became the foundation of much of modern theoretical condensed matter physics.

Through his famous "demon" Maxwell addressed one mystery of energy physics: the relation between the first law of thermodynamics, which states that energy as a whole is conserved, and the second law, which states that mechanical energy will be gradually dissipated. Maxwell was the first person to realize and forcefully argue that the second law is a statistical rather than a dynamical truth. Following this clue, Boltzmann in 1872 found the exact formal expression relating entropy to probability. Their work, togetherwith earlier reflections by Kelvin, framed a discussion of irreversibility in physics, embracing even the nature of time, that has continued to this day.

Ampère, André-Marie; Clausius, Rudolf Julius Emmanuel; Electricity; Electricity, History Of; Faraday, Michael; Gibbs, Josiah Willard; Magnetism and Magnets; Molecular Energy; Oersted, Hans Christian; Thomson, William.

Brush, S. G. (1976). The Kind of Motion We Call Heat, Vols. 1-2. Amsterdam: North-Holland.

Buchwald, J. T. (1985). From Maxwell to Microphysics. Chicago: University of Chicago Press.

Campbell, L., and Garnett, W. (1882). The Life of James Clerk Maxwell. London: Macmillan.

Everitt, C. W. F. (1975). James Clerk Maxwell, Physicist and Natural Philosopher. New York: Scribner.

Harman, P. (1998). The Natural Philosophy of James Clerk Maxwell. Cambridge, Eng.: Cambridge University Press.

Siegel, D. M. (1991). Innovation in Maxwell's Electromagnetic Theory. Cambridge, Eng.: Cambridge University Press.

Whittaker, E. T. (1954). History of the Theories of Aether and Electricity, Vols. 1-2. New York: Philosophical Library.

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