---
title: "Oliver Heaviside"
chunk: 4/4
source: "https://en.wikipedia.org/wiki/Oliver_Heaviside"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:06:27.222356+00:00"
instance: "kb-cron"
---

== Innovations and discoveries ==
Heaviside did much to develop and advocate vector methods and vector calculus. Maxwell's formulation of electromagnetism consisted of 20 equations in 20 variables. Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (
  
    
      
        
          
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            E
          
        
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            J
          
        
         
        
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    {\displaystyle {\textbf {B}},{\textbf {E}},{\textbf {J}}~{\text{and}}~\rho }
  
), the form by which they have been known ever since (see Maxwell's equations). Less well known is that Heaviside's equations and Maxwell's are not exactly the same, and in fact it is easier to modify the former to make them compatible with quantum physics. The possibility of gravitational waves was also discussed by Heaviside using the analogy between the inverse-square law in gravitation and electricity. With quaternion multiplication, the square of a vector is a negative quantity, much to Heaviside's displeasure. As he advocated abolishing this negativity, he has been credited by C. J. Joly with developing hyperbolic quaternions, though in fact that mathematical structure was largely the work of Alexander Macfarlane.
He invented the Heaviside step function, using it to calculate the current when an electric circuit is switched on. He was the first to use the unit impulse function now usually known as the Dirac delta function. He invented his operational calculus method for solving linear differential equations. This resembles the currently used Laplace transform method based on the "Bromwich integral" named after Bromwich who devised a rigorous mathematical justification for Heaviside's operator method using contour integration. Heaviside was familiar with the Laplace transform method but considered his own method more direct.
Heaviside developed the transmission line theory (also known as the "telegrapher's equations"), which increased the transmission rate over transatlantic cables by a factor of ten. It originally took ten minutes to transmit each character, and this immediately improved to one character per minute. Closely related to this was his discovery that telephone transmission could be greatly improved by placing electrical inductance in series with the cable. Heaviside also independently discovered the Poynting vector.
Heaviside advanced the idea that the Earth's uppermost atmosphere contained an ionised layer known as the ionosphere; in this regard, he predicted the existence of what later was dubbed the Kennelly–Heaviside layer. In 1947, Edward Appleton received the Nobel Prize in Physics for proving that this layer really existed.

=== Electromagnetic terms ===
Heaviside coined the following terms of art in electromagnetic theory:

admittance (reciprocal of impedance) (December 1887);
elastance (reciprocal of permittance, reciprocal of capacitance) (1886);
conductance (real part of admittance, reciprocal of resistance) (September 1885);
electret for the electric analogue of a permanent magnet, or, in other words, any substance that exhibits a quasi-permanent electric polarization (e.g. ferroelectric);
impedance (July 1886);
inductance (February 1886);
permeability (September 1885);
permittance (now called capacitance) and permittivity (June 1887);
reluctance (May 1888);
Heaviside is sometimes incorrectly credited with coining susceptance (the imaginary part of admittance) and reactance (the imaginary part of impedance). The former was coined by Charles Proteus Steinmetz (1894). The latter was coined by Édouard Hospitalier (1893).

== Publications ==

1885, 1886, and 1887, "Electromagnetic induction and its propagation", The Electrician.
1888/89, "Electromagnetic waves, the propagation of potential, and the electromagnetic effects of a moving charge", The Electrician.
1889, "On the Electromagnetic Effects due to the Motion of Electrification through a Dielectric", Phil.Mag.S.5 27: 324.
1892 "On the Forces, Stresses, and Fluxes of Energy in the Electromagnetic Field" Phil.Trans.Royal Soc. A 183:423–80.
1892 "On Operators in Physical Mathematics" Part I. Proc. Roy. Soc. 1892 Jan 1. vol.52 pp. 504–529
1892 Heaviside, Oliver (1892). Electrical Papers. Vol. 1. Macmillan Co, London and New York. ISBN 9780828402354.
1893 "On Operators in Physical Mathematics" Part II Proc. Roy. Soc. 1893 Jan 1. vol.54 pp. 105–143
1893 "A gravitational and electromagnetic analogy," The Electrician, vol.31, pp. 281–282 (part I), p. 359 (part II)
1893 reproduced in, Electromagnetic Theory vol I, Chapter 4 Appendix B pp. 455-466
1893 Heaviside, Oliver (1893). Electromagnetic Theory. Vol. 1. The Electrician Printing and Publishing Co, London. ISBN 978-0-8284-0235-4.
1894 Heaviside, Oliver (1894). Electrical Papers. Vol. 2. Macmillan Co, London and New York.
1899 Heaviside, Oliver (1899). Electromagnetic Theory. Vol. 2. The Electrician Printing and Publishing Co, London.
1912 Heaviside, Oliver (1912). Electromagnetic Theory. Vol. 3. The Electrician Printing and Publishing Co, London.
1925. Electrical Papers. 2 vols Boston 1925 (Copley)
1950 Electromagnetic theory: The complete & unabridged edition. (Spon) reprinted 1950 (Dover)
1970 Heaviside, Oliver (1970). Electrical Papers. Chelsea Publishing Company, Incorporated. ISBN 978-0-8284-0235-4.
1971 "Electromagnetic theory; Including an account of Heaviside's unpublished notes for a fourth volume" Chelsea, ISBN 0-8284-0237-X
2001 Heaviside, Oliver (1 December 2001). Electrical Papers. American Mathematical Society. ISBN 978-0-8218-2840-3.

== See also ==

1850 in science
Electric displacement field
Biot–Savart law
Bridge circuit § Heaviside bridge

== References ==

== Further reading ==

== External links ==

=== Archival collections ===
Oliver Heaviside selected papers [microform], 1874-1922, Niels Bohr Library & Archives