Oliver Heaviside

English mathematician, physicist, and electrical engineer

• Born: May 18, 1850
• Birthplace: London, England
• Died: February 3, 1925
• Place of death: Torquay, Devon, England

Heaviside invented the distortionless transmission line for telegraph and telephone cables. He also invented operational calculus and vector calculus, using the latter to simplify James Clerk Maxwell’s electromagnetic field equations to their modern form.

Primary fields: Communications; electronics and electrical engineering; mathematics; physics

Primary inventions: Distortionless transmission lines; operational calculus

Early Life

Oliver Heaviside (HEHV-ee-sid) was born on May 18, 1850, in London, England. His father was Thomas Heaviside, a watercolorist and engraver, and his mother was Rachel Elizabeth West, whose brother-in-law was Sir Charles Wheatstone, coinventor of the telegraph in the 1830’s. Oliver was born in the slums of London and suffered from scarlet fever as a child, which left him partially deaf and unable to relate easily with other children. Although he was a good student, he left school at age sixteen to study at home, concentrating for two years on telegraphy, electromagnetism, and the study of German and Danish.

At the age of eighteen, with assistance from his famous uncle, Heaviside began his first and only paid job as a telegraph operator with the Great Northern Telegraph Company, beginning in Denmark in 1868. Three years later, he was transferred by the company back to England at its office dealing with overseas traffic in Newcastle upon Tyne, where he became a chief operator. During his six years of employment, he published two papers on electric circuits and telegraphy (in 1872 and 1873), which interested the Scottish physicistJames Clerk Maxwell enough to mention them in the second edition of his Treatise on Electricity and Magnetism (1873).

Heaviside became so fascinated with Maxwell’s treatise that he gave up his job in 1874 at the age of twenty-four and returned to his parents’ home in London to devote himself full-time to studying it and learning the requisite advanced mathematics. During this time, he grew increasingly deaf and reclusive, remaining single all of his life. After several years, he had mastered Maxwell’s electromagnetic theory and its associated mathematics before setting it aside to develop his own ideas, including the invention of new forms of mathematics to recast Maxwell’s equations in their modern vector form.

Life’s Work

Oliver Heaviside began his research in 1880 on the skin effect in telegraph transmission lines that increased the resistance near the center of the lines with increasing frequency and concentrated the current flow near the surface, or “skin,” of the conductors. In 1880, he patented the coaxial cable as a way to transmit high-frequency signals more efficiently. He was able to apply Maxwell’s equations to the skin-effect problem and solved them for conductors of any shape, showing how the current was distributed and how resistance increased with frequency because of eddy currents induced by the changing magnetism caused by rapidly alternating current. He published this work in 1885 in a paper on “Electromagnetic Induction and its Propagation” in The Electrician.

In the course of his electrical research, Heaviside began to adapt complex numbers to the theory of electric circuits. In this work, he introduced the Heaviside step function to aid in mathematical modeling of circuits. He also independently formulated vector analysis along lines similar to the work of Josiah Willard Gibbs in the United States, and he invented an operational form of calculus for solving linear differential equations by transforming them into algebraic equations. His mathematical work led to controversy because he did not apply rigorous methods to the derivation of his results, viewing them as pragmatic and experimental. Nevertheless, this work became the basis for much of electrical engineering in the twentieth century and provided the key to his success in reformulating Maxwell’s equations in a simpler form and obtaining solutions from them.

In 1884, Heaviside applied his new ideas of vector analysis to electromagnetic theory. Maxwell’s original equations linking electric and magnetic fields were extremely cumbersome, requiring twenty equations in twenty variables representing the sources and spatial components of the fields. With the use of vector notation and the vector calculus operators he had invented, Heaviside reduced Maxwell’s equations to just four elegant vector equations in two variables, emphasizing the basic symmetries between electric and magnetic fields. Two of these equations derive from Gauss’s law and describe the source and structure of electric and magnetic fields. The other two equations generalize Ampere’s current law and Faraday’s voltage law to show how changing electric fields produce magnetic fields and changing magnetic fields produce electric fields. For several years, these vector forms of Maxwell’s equations were called the Heaviside-Hertz equations because Heinrich Hertz was the first to apply them in his discovery of radio waves.

In 1885, Heaviside applied Maxwell’s equations to electrical transmission lines to obtain the modern form of the telegrapher’s equations. He applied these equations to the trans-Atlantic submarine telegraph cable, which suffered from distortion problems. In 1887, he recommended that induction coils be added to telephone and telegraph lines to correct this distortion. Unfortunately, his ideas were ignored for political reasons but were eventually adopted by the American Telephone and Telegraph Company (AT&T) based on a patent given to Michael Pupin in 1904. When AT&T later offered to purchase Heaviside’s rights, he refused the money for lack of full recognition even though he had very little income. In 1891, he was elected as a fellow of the Royal Society.

In the 1890’s, Heaviside became interested in the problem of the age of Earth, which had been calculated to be about 100 million years by Lord Kelvin some thirty years earlier by assuming uniform thermal conductivity in the cooling of the planet. This notion proved to be a great challenge to Charles Darwin, whose theory of evolution required several billion years. In 1894, Heaviside used his operational calculus to repeat Kelvin’s calculation, but making the assumption of a change in thermal conductivity near the surface of Earth corresponding to its crust. This calculation led to a much older age of Earth, which could be on the order of billions of years depending on a range of values for the heat constants.

At the age of forty-seven, after his parents had died, Heaviside began living by himself for the first time in his life. Friends arranged for him to receive a civil list pension of 120 pounds per year as a government-recognized authority. In 1897, he left London and moved to a house in Newton Abbott a few miles from Paignton, Devon, in the southwest corner of England, with an elderly lady as a servant. One of his last scientific contributions was an explanation for Guglielmo Marconi’s success in transmitting radio waves across the Atlantic Ocean over the curvature of Earth. In 1902, Heaviside proposed the existence of a charged layer in the upper atmosphere, now known as the Kennelly-Heaviside layer of the ionosphere, which transmits radio waves by reflection between it and Earth’s surface. In 1908, he moved to Torquay in Devon, where he lived his last years as a virtual hermit.

Impact

The main impact of Heaviside’s work came from the mathematical techniques he invented and their applications in electromagnetic theory. He used these techniques to simplify Maxwell’s electromagnetic equations and applied them to a wide range of transmission-line problems. His independent invention of vector analysis, including the divergence and curl operators of vector calculus, made it possible to reduce the twenty equations of Maxwell’s electromagnetic field theory to their modern form of just four compact and symmetric equations. It was this form of Maxwell’s equations that led Heinrich Hertz to his 1887 discovery of radio waves. Heaviside’s invention of operational calculus, similar to the method of Laplace transforms that largely replaced it after 1937, led him to many important solutions of Maxwell’s equations. These mathematical techniques have had wide applications in many areas of engineering and physics since their invention.

Heaviside’s work is especially important for his innovations in electrical engineering, including the complex-number analysis of electric circuits and the invention of the telegrapher’s equation. He introduced much of the modern terminology of alternating-current circuit analysis, including such terms as conductance, permeability, inductance, impedance, admittance, reactance, and reluctance. His derivation of the telegrapher’s equation to analyze transmission lines led him to recommend adding induction coils, which made it possible to have distortion-free transmission over long-distance cables for a wide range of frequencies as required in modern telephone communications. One of his final contributions was the publication of his three-volume Electromagnetic Theory (1950), summarizing and extending much of his life’s work.

Bibliography

Heaviside, Oliver. Electrical Papers. New York: American Mathematical Society, 2003. This compilation of Heaviside’s papers reveals the work of a scientific genius and the breadth and depth of his mathematical methods applied to electrical science.

Hunt, Bruce J. The Maxwellians. Ithaca, N.Y.: Cornell University Press, 1991. Places Heaviside’s work in the context of a group of scientists who developed the ideas of Maxwell into their present form, including Heinrich Hertz, Oliver Lodge, and George F. Fitzgerald.

Lee, George. Oliver Heaviside and the Mathematical Theory of Communications. London: Longmans, Green, 1947. This thirty-two-page monograph prepared for the British Council describes the works of Heaviside.

Nahin, Paul J. Oliver Heaviside: Sage in Solitude—The Life, Work, and Times of an Electrical Genius of the Victorian Age. Baltimore: The Johns Hopkins University Press, 2002. This definitive biography includes many photos, sketches, and descriptions of Heaviside’s mathematical work.

Searle, George F. C. Oliver Heaviside, the Man. St. Albans, England: C.A.M., 1987. This reprint of a 1950 centenary volume is edited by one of the last living friends of Heaviside, who also knew Hertz and Maxwell.

Yavetz, Ido. From Obscurity to Enigma: The Work of Oliver Heaviside, 1872-1889. Boston: Birkhäuser Verlag, 1995. Provides fascinating insights into how Heaviside combined mathematics with his genius for electrical science.