Maxwell, James Clerk

I

Introduction

Maxwell, James Clerk (1831-1879), British physicist, whose theory of the electromagnetic field and electromagnetic theory of light, and introduction of a statistical function in the theory of gases, revolutionized physics. These ideas led to the relativity and quantum theories of the 20th century.

Maxwell was born in Edinburgh. He wrote his first paper, on oval curves, while still at school. He entered Edinburgh University in 1847, where he wrote two substantial papers: on the geometry of curves rolling on one another, and on the properties of elastic solids. He became interested in colour theory, and in the 1850s, on the basis of experiments with tinted papers and spectral colours, he established the modern theory of colour vision. He followed Thomas Young in using red, green, and blue primaries to form colour combinations. In May 1861 he projected the first trichromatic colour photograph.

Maxwell entered Peterhouse College, Cambridge University, in October 1850, but moved to Trinity College after one term. He became the pupil of the famous mathematics coach William Hopkins, graduating second wrangler (that is, taking second place) in 1854. Elected a fellow of Trinity in 1855, he was appointed Professor of Natural Philosophy at Marischal College, Aberdeen, in 1856. He lost his post when the two Aberdeen colleges were joined to form the University of Aberdeen in 1860, and moved to King’s College, London, to become Professor of Natural Philosophy and Astronomy, a post he resigned in 1865.

II

Electromagnetism and Light

Rejecting explanations (modelled on the theory of gravitation) in terms of forces acting at a distance, Michael Faraday had interpreted electricity and magnetism in terms the electromagnetic “field”, defined by imaginary lines of force. William Thomson (Lord Kelvin) had shown that these ideas could be expressed in mathematical terms.

Initially guided by Thomson, Maxwell developed Faraday’s work. He first illustrated the geometry of lines of force by the physical analogy of streamlines in a fluid (see Fluid Mechanics). Seeking a theory of the field grounded on the mechanics of an ether, a medium for transmission, he found its basis in Thomson’s 1856 proposal that the Faraday effect—the rotation of polarized light in a magnetic field—could be explained by the rotation of vortices in an ether. In his paper “On Physical Lines of Force” (1861-1862) Maxwell set out an ether model of rotating vortices (representing magnetism) separated by “idle wheel” particles (whose motion represents the flow of an electric current).

The modification of the ether model to encompass electrostatics unexpectedly led to his electromagnetic theory of light. He showed that a disturbance in the electric or magnetic field should lead to a disturbance travelling as a wave through space. He demonstrated the close agreement between the velocity of these waves and the measured velocity of light. He developed the established theory that light was propagated by an ether by asserting that this ether was electromagnetic, and he thus unified optics and electromagnetism.

Maxwell had from the first emphasized that his “idle wheel” ether model was conjectural, and in 1864 he discarded this model as a temporary scaffolding for his theory. He achieved a more general presentation of his electromagnetic theory of light in terms of the transmission of energy through the ether. He retained mechanical foundations by grounding the general equations of the electromagnetic field (the forerunners of what are now known as the four “Maxwell equations”, as reformulated in the 1880s by Oliver Heaviside and Heinrich Hertz) on general equations of dynamics. He expounded this theory in his Treatise on Electricity and Magnetism (1873).

The production of electromagnetic waves by Hertz in 1887 led to the acceptance of Maxwell’s theory of the electromagnetic field. In the 20th century it came to be detached from its formulation in terms of ether.

III

The Kinetic Theory of Gases

The subject of the University of Cambridge’s Adams Prize for 1857 was a study of the motions of Saturn‘s rings, whose structure and stability were in doubt at the time. On winning the prize and revising his essay for publication in 1859, Maxwell concluded that the ring system of Saturn consists of concentric rings of particles.

Alerted to problems of particle motions, Maxwell became interested in a paper by Rudolf Clausius on the kinetic theory of gases—the theory that explains the behaviour of gases in terms of the motions of their molecules, or constituent particles. Clausius had used a probabilistic argument to calculate the motions of the gas molecules, and Maxwell advanced on his procedure by introducing a statistical function (identical in form to the distribution formula in the theory of errors) for the distribution of velocities among the gas molecules. He established results for gaseous diffusion, viscosity, and thermal conductivity.

He turned to an experimental investigation of the viscosity of gases at different temperatures and pressures, observing the decay in the torsional oscillation of discs. He found that gas viscosity was a linear function of the absolute temperature. In his paper “On the Dynamical Theory of Gases” (1867), he suggested that gas molecules should be considered as centres of a force of repulsion that falls off in strength as the fifth power of the separation, a result in agreement with this experimental finding. He also presented a new derivation of the law of distribution of velocities.

Maxwell perceived that the kinetic theory of gases bore on wider problems in the theory of heat, and he expounded the implications of his theory in his “demon” paradox (a term coined by Thomson). According to the second law of thermodynamics, heat flows from hot to cold bodies unless work is done to force it to flow the other way. But Maxwell’s theory that the velocities of gas molecules are widely distributed suggests that individual faster-moving molecules could move from a cold to a hot body transferring heat as they did so. It would require the action of the demon to manipulate molecules in sufficient numbers to produce an observable flow of heat from the cold body to the hotter one, and thus violate the second law of thermodynamics. This law therefore applies only to large groups of molecules; it is a statistical law.

Maxwell’s ideas on gases and thermodynamics were developed by Ludwig Boltzmann in the 1870s, and became the accepted basis for these areas of physics.

IV

The Cavendish Laboratory

Appointed to the new professorship of experimental physics at Cambridge University in 1871, Maxwell designed the Cavendish Laboratory. It opened in April 1874 and Maxwell, as its first director, instituted a programme of precision measurements in electricity. One of his last accomplishments was to edit Henry Cavendish’s Electrical Researches (1879).