Oliver Heaviside
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Oliver Heaviside ( ; 18 May 1850 – 3 February 1925) was an English
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
who invented a new technique for solving differential equations (equivalent to the
Laplace transform In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a f ...
), independently developed
vector calculus Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a ...
, and rewrote
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science.


Early life

Heaviside was born in
Camden Town Camden Town () is an area in the London Borough of Camden, around north-northwest of Charing Cross. Historically in Middlesex, it is identified in the London Plan as one of 34 major centres in Greater London. Laid out as a residential distri ...
, London, at 55 Kings Street (now Plender Street), the youngest of three children of Thomas, a draughtsman and wood engraver, and Rachel Elizabeth (née West). He was a short and red-headed child, and suffered from
scarlet fever Scarlet fever, also known as scarlatina, is an infectious disease caused by ''Streptococcus pyogenes'', a Group A streptococcus (GAS). It most commonly affects children between five and 15 years of age. The signs and symptoms include a sore ...
when young, which left him with a hearing impairment. A small legacy enabled the family to move to a better part of Camden when he was thirteen and he was sent to Camden House Grammar School. He was a good student, placing fifth out of five hundred pupils in 1865, but his parents could not keep him at school after he was 16, so he continued studying for a year by himself and had no further formal education.Bruce J. Hunt (1991) The Maxwellians,
Cornell University Press The Cornell University Press is the university press of Cornell University, an Ivy League university in Ithaca, New York. It is currently housed in Sage House, the former residence of Henry William Sage. It was first established in 1869, maki ...
Heaviside's uncle by marriage was Sir
Charles Wheatstone Sir Charles Wheatstone (; 6 February 1802 – 19 October 1875) was an English physicist and inventor best known for his contributions to the development of the Wheatstone bridge, originally invented by Samuel Hunter Christie, which is used to m ...
(1802–1875), an internationally celebrated expert in telegraphy and electromagnetism, and the original co-inventor of the first commercially successful telegraph in the mid-1830s. Wheatstone took a strong interest in his nephew's education and in 1867 sent him north to work with his older brother Arthur Wheatstone, who was managing one of Charles' telegraph companies in
Newcastle-upon-Tyne Newcastle upon Tyne, or simply Newcastle ( , Received Pronunciation, RP: ), is a City status in the United Kingdom, cathedral city and metropolitan borough in Tyne and Wear, England. It is England's northernmost metropolitan borough, located o ...
. Two years later he took a job as a telegraph operator with the Danish Great Northern Telegraph Company laying a cable from Newcastle to
Denmark Denmark is a Nordic countries, Nordic country in Northern Europe. It is the metropole and most populous constituent of the Kingdom of Denmark,, . also known as the Danish Realm, a constitutionally unitary state that includes the Autonomous a ...
using British contractors. He soon became an electrician. Heaviside continued to study while working, and by the age of 22 he published an article in the prestigious ''
Philosophical Magazine The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Dictionary of National Biography#Oxford Dictionary of ...
'' on 'The Best Arrangement of Wheatstone's Bridge for measuring a Given Resistance with a Given Galvanometer and Battery' which received positive comments from physicists who had unsuccessfully tried to solve this algebraic problem, including
Sir William Thomson William Thomson, 1st Baron Kelvin (26 June 182417 December 1907), was a British mathematician, Mathematical physics, mathematical physicist and engineer. Born in Belfast, he was the Professor of Natural Philosophy (Glasgow), professor of Natur ...
, to whom he gave a copy of the paper, and
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...
. When he published an article on the duplex method of using a telegraph cable, he poked fun at R. S. Culley, the engineer in chief of the Post Office telegraph system, who had been dismissing duplex as impractical. Later in 1873 his application to join the Society of Telegraph Engineers was turned down with the comment that "they didn't want telegraph clerks". This riled Heaviside, who asked Thomson to sponsor him, and along with support of the society's president he was admitted "despite the P.O. snobs". In 1873, Heaviside had encountered Maxwell's newly published, and later famous, two-volume '' Treatise on Electricity and Magnetism''. In his old age Heaviside recalled: Undertaking research from home, he helped develop
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
theory (also known as the "'' telegrapher's equations''"). Heaviside showed mathematically that uniformly distributed
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
in a telegraph line would diminish both
attenuation In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a Transmission medium, medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and ...
and
distortion In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
, and that, if the inductance were great enough and the insulation resistance not too high, the circuit would be distortionless in that
currents Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (hy ...
of all
frequencies Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
would have equal speeds of propagation. Heaviside's equations helped further the implementation of the telegraph.


Middle years

From 1882 to 1902, except for three years, Heaviside contributed regular articles to the trade paper '' The Electrician'', which wished to improve its standing, for which he was paid £40 per year. This was hardly enough to live on, but his demands were very small and he was doing what he most wanted to. Between 1883 and 1887 he averaged 2–3 articles per month and these articles later formed the bulk of his ''Electromagnetic Theory'' and ''Electrical Papers''. In 1880, Heaviside researched the
skin effect In electromagnetism, skin effect is the tendency of an alternating current, alternating electric current (AC) to become distributed within a Conductor (material), conductor such that the current density is largest near the surface of the conduc ...
in telegraph transmission lines. That same year he patented, in England, the
coaxial cable Coaxial cable, or coax (pronounced ), is a type of electrical cable consisting of an inner Electrical conductor, conductor surrounded by a concentric conducting Electromagnetic shielding, shield, with the two separated by a dielectric (Insulat ...
. In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as
quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...
s) to its modern
vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...
terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
. The four re-formulated Maxwell's equations describe the nature of electric charges (both static and moving), magnetic fields, and the relationship between the two, namely electromagnetic fields. Between 1880 and 1887, Heaviside developed the
operational calculus Operational calculus, also known as operational analysis, is a technique by which problems in Mathematical Analysis, analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomia ...
using p for the
differential operator In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and retur ...
, (which Boole had previously denoted by D'), giving a method of solving differential equations by direct solution as
algebraic equation In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0, where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x^5-3x+1=0 is an algebraic equati ...
s. This later caused a great deal of controversy, owing to its lack of
rigour Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mat ...
. He famously said, "Mathematics is an experimental science, and definitions do not come first, but later on. They make themselves, when the nature of the subject has developed itself." On another occasion he asked, "Shall I refuse my dinner because I do not fully understand the process of digestion?" In 1887, Heaviside worked with his brother Arthur on a paper entitled "The Bridge System of Telephony". However the paper was blocked by Arthur's superior, William Henry Preece of the
Post Office A post office is a public facility and a retailer that provides mail services, such as accepting letter (message), letters and parcel (package), parcels, providing post office boxes, and selling postage stamps, packaging, and stationery. Post o ...
, because part of the proposal was that loading coils (
inductor An inductor, also called a coil, choke, or reactor, is a Passivity (engineering), passive two-terminal electronic component, electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typic ...
s) should be added to telephone and telegraph lines to increase their self-induction and correct the distortion which they suffered. Preece had recently declared self-inductance to be the great enemy of clear transmission. Heaviside was also convinced that Preece was behind the sacking of the editor of ''The Electrician'' which brought his long-running series of articles to a halt (until 1891). There was a long history of animosity between Preece and Heaviside. Heaviside considered Preece to be mathematically incompetent, an assessment supported by the biographer Paul J. Nahin: "Preece was a powerful government official, enormously ambitious, and in some remarkable ways, an utter blockhead." Preece's motivations in suppressing Heaviside's work were more to do with protecting Preece's own reputation and avoiding having to admit error than any perceived faults in Heaviside's work. The importance of Heaviside's work remained undiscovered for some time after publication in ''The Electrician''. In 1897,
AT&T AT&T Inc., an abbreviation for its predecessor's former name, the American Telephone and Telegraph Company, is an American multinational telecommunications holding company headquartered at Whitacre Tower in Downtown Dallas, Texas. It is the w ...
employed one of its own scientists, George A. Campbell, and an external investigator Michael I. Pupin to find some respect in which Heaviside's work was incomplete or incorrect. Campbell and Pupin extended Heaviside's work, and AT&T filed for patents covering not only their research, but also the technical method of constructing the coils previously invented by Heaviside. AT&T later offered Heaviside money in exchange for his rights; it is possible that the Bell engineers' respect for Heaviside influenced this offer. However, Heaviside refused the offer, declining to accept any money unless the company were to give him full recognition. Heaviside was chronically poor, making his refusal of the offer even more striking. In 1959, Norbert Wiener published his fiction ''The Tempter'' and accused AT&T (named ''Williams Controls Company'') and Michael I. Pupin (named ''Diego Dominguez'') of having usurped Heaviside's inventions. But this setback had the effect of turning Heaviside's attention towards electromagnetic radiation, and in two papers of 1888 and 1889, he calculated the deformations of electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser medium. This included a prediction of what is now known as
Cherenkov radiation Cherenkov radiation () is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefro ...
, and inspired his friend George FitzGerald to suggest what now is known as the Lorentz–FitzGerald contraction. In 1889, Heaviside first published a correct derivation of the magnetic force on a moving charged particle, which is the magnetic component of what is now called the
Lorentz force In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...
. In the late 1880s and early 1890s, Heaviside worked on the
concept A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, ...
of
electromagnetic mass Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles. It was first derived by J. J. Thomson in 1881 and was ...
. Heaviside treated this as material
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
, capable of producing the same effects. Wilhelm Wien later verified Heaviside's expression (for low velocities). In 1891 the British
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
recognized Heaviside's contributions to the mathematical description of electromagnetic phenomena by naming him a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
, and the following year devoting more than fifty pages of the ''Philosophical Transactions'' of the Society to his vector methods and electromagnetic theory. In 1905 Heaviside was given an honorary doctorate by the
University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...
.


Later years and views

In 1896, FitzGerald and John Perry obtained a civil list pension of £120 per year for Heaviside, who was now living in Devon, and persuaded him to accept it, after he had rejected other charitable offers from the Royal Society. In 1902, Heaviside proposed the existence of what is now known as the
Kennelly–Heaviside layer The Heaviside layer, sometimes called the Kennelly–Heaviside layer, named after Arthur E. Kennelly and Oliver Heaviside, is a layer of ionised gas occurring roughly between above the ground — one of several layers in the Earth's ion ...
of the
ionosphere The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays ...
. Heaviside's proposal included means by which radio signals are transmitted around the Earth's curvature. The existence of the ionosphere was confirmed in 1923. The predictions by Heaviside, combined with Planck's radiation theory, probably discouraged further attempts to detect radio waves from the
Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
and other
astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists within the observable universe. In astronomy, the terms ''object'' and ''body'' are of ...
s. For whatever reason, there seem to have been no attempts for 30 years, until Jansky's development of
radio astronomy Radio astronomy is a subfield of astronomy that studies Astronomical object, celestial objects using radio waves. It started in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation coming from the Milky Way. Subsequent observat ...
in 1932. Heaviside was an opponent of Albert Einstein's
theory of relativity The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical ph ...
.Eves, Howard. (1988). ''Return to Mathematical Circles: A Fifth Collection of Mathematical Stories and Anecdotes''. PWS-Kent Publishing Company. p. 27. Mathematician Howard Eves has commented that Heaviside "was the only first-rate physicist at the time to impugn Einstein, and his invectives against relativity theory often bordered on the absurd". In later years his behavior became quite eccentric. According to associate B.A. Behrend, he became a recluse who was so averse to meeting people that he delivered the manuscripts of his ''
Electrician An electrician is a tradesman, tradesperson specializing in electrical wiring of buildings, transmission lines, stationary machines, and related equipment. Electricians may be employed in the installation of new electrical components or the ...
'' papers to a grocery store, where the editors picked them up. Though he had been an active cyclist in his youth, his health seriously declined in his sixth decade. During this time Heaviside would sign letters with the initials "''W.O.R.M.''" after his name. Heaviside also reportedly started painting his fingernails pink and had granite blocks moved into his house for furniture. In 1922, he became the first recipient of the
Faraday Medal The Faraday Medal is a top international medal awarded by the UK Institution of Engineering and Technology (IET) (previously called the Institution of Electrical Engineers (IEE)). As one of the world's most prestigious awards in engineering, it ...
, which was established that year. On Heaviside's religious views, he was a Unitarian, but not religious. He was even said to have made fun of people who put their faith in a supreme being. Heaviside died on 3 February 1925, at
Torquay Torquay ( ) is a seaside town in Devon, England, part of the unitary authority area of Torbay. It lies south of the county town of Exeter and east-north-east of Plymouth, on the north of Tor Bay, adjoining the neighbouring town of Paignt ...
in
Devon Devon ( ; historically also known as Devonshire , ) is a ceremonial county in South West England. It is bordered by the Bristol Channel to the north, Somerset and Dorset to the east, the English Channel to the south, and Cornwall to the west ...
after falling from a ladder, and is buried near the eastern corner of
Paignton Paignton ( ) is a seaside town on the coast of Tor Bay in Devon, England. Together with Torquay and Brixham it forms the unitary authority, borough of Torbay which was created in 1968. The Torbay area is a holiday destination known as the Engli ...
cemetery. He is buried with his father, Thomas Heaviside (1813–1896), and his mother, Rachel Elizabeth Heaviside. The gravestone was cleaned thanks to an anonymous donor sometime in 2005. He was always held in high regard by most electrical engineers, particularly after his correction to
Kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...
's transmission line analysis was vindicated, but most of his wider recognition was gained posthumously.


Heaviside Memorial Project

In July 2014, academics at
Newcastle University Newcastle University (legally the University of Newcastle upon Tyne) is a public research university based in Newcastle upon Tyne, England. It has overseas campuses in Singapore and Malaysia. The university is a red brick university and a mem ...
, UK and the Newcastle Electromagnetics Interest Group founded the Heaviside Memorial Project in a bid to fully restore the monument through public subscription. The restored memorial was ceremonially unveiled on 30 August 2014 by Alan Heather, a distant relative of Heaviside. The unveiling was attended by the Mayor of Torbay, the Member of Parliament (MP) for Torbay, an ex-curator of the Science Museum (representing the
Institution of Engineering and Technology The Institution of Engineering and Technology (IET) is a multidisciplinary professional engineering institution. The IET was formed in 2006 from two separate institutions: the Institution of Electrical Engineers (IEE), dating back to 1871,Engin ...
), the Chairman of the Torbay Civic Society, and delegates from Newcastle University.


The Institution of Engineering and Technology

A collection of Heaviside's papers is held at the
Institution of Engineering and Technology The Institution of Engineering and Technology (IET) is a multidisciplinary professional engineering institution. The IET was formed in 2006 from two separate institutions: the Institution of Electrical Engineers (IEE), dating back to 1871,Engin ...
(IET) Archive Centre. The collection consists of notebooks containing mathematical equations and calculations, annotated pamphlets mainly relating to telegraphy, manuscript notes, drafts of papers, correspondence, drafts of articles for ‘Electromagnetic Theory’. An audio tribute from 1950 to Oliver Heaviside by Oliver E Buckley, President of Bell Telephone Labs, has been digitised and accessible on the IET Archives biography of Oliver Heaviside. In 1908 Oliver Heaviside was made an Honorary Member of the
Institution of Electrical Engineers The Institution of Electrical Engineers (IEE) was a British professional organisation of electronics, electrical, manufacturing, and information technology professionals, especially electrical engineers. It began in 1871 as the Society of Tel ...
(IEE). His entry reads as: “1908 Oliver Heaviside FRS” in the IEE Roll of Honorary Members and Faraday Medallists 1871-1921 In 1922, he became the first recipient of the
Faraday Medal The Faraday Medal is a top international medal awarded by the UK Institution of Engineering and Technology (IET) (previously called the Institution of Electrical Engineers (IEE)). As one of the world's most prestigious awards in engineering, it ...
, which was established that year. Later on, in 1950 the Institution of Electrical Engineers Council established the Heaviside Premium Award “The Committee have considered the establishment of some form of permanent memorial to Oliver Heaviside and as a result recommend that a Heaviside Premium to the value of £10 be awarded each year for the best mathematical paper accepted.”


Innovations and discoveries

Heaviside did much to develop and advocate
vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...
methods and
vector calculus Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a ...
. Maxwell's formulation of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
consisted of 20 equations in 20 variables. Heaviside employed the
curl cURL (pronounced like "curl", ) is a free and open source computer program for transferring data to and from Internet servers. It can download a URL from a web server over HTTP, and supports a variety of other network protocols, URI scheme ...
and
divergence In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal neighborhood of each point. (In 2D this "volume" refers to ...
operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (\textbf, \textbf, \textbf ~\text ~\rho), the form by which they have been known ever since (see
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
). 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 Gravitational waves are oscillations of the gravitational field that travel through space at the speed of light; they are generated by the relative motion of gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by H ...
was also discussed by Heaviside using the analogy between the inverse-square law in gravitation and electricity. With
quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...
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 Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician. Life Macfarlane was born in Blairgowrie, Scotland, to Daniel MacFarlane (Shoemaker, Blairgowrie) and Ann Small. He s ...
. He invented the
Heaviside step function The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Differen ...
, using it to calculate the current when an
electric circuit An electrical network is an interconnection of electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e. ...
is switched on. He was the first to use the unit impulse function now usually known as the
Dirac delta function In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line ...
. He invented his
operational calculus Operational calculus, also known as operational analysis, is a technique by which problems in Mathematical Analysis, analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomia ...
method for solving
linear differential equation In mathematics, a linear differential equation is a differential equation that is linear equation, linear in the unknown function and its derivatives, so it can be written in the form a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) wher ...
s. This resembles the currently used
Laplace transform In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a f ...
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 In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
theory (also known as the " telegrapher's equations"), which had the effect of increasing 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 In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the wat ...
. Heaviside advanced the idea that the Earth's uppermost atmosphere contained an ionized layer known as the
ionosphere The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays ...
; in this regard, he predicted the existence of what later was dubbed the
Kennelly–Heaviside layer The Heaviside layer, sometimes called the Kennelly–Heaviside layer, named after Arthur E. Kennelly and Oliver Heaviside, is a layer of ionised gas occurring roughly between above the ground — one of several layers in the Earth's ion ...
. In 1947 Edward Victor 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 In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interact ...
: *
admittance In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the multiplicative inverse, reciprocal of Electrical impedance, impedance, analogous to how Electrical resistanc ...
''(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 In physics and materials science, ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoel ...
); * impedance (July 1886); *
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
(February 1886); * permeability (September 1885); * permittance (now called capacitance) and
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
(June 1887); *
reluctance Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the ...
(May 1888); Heaviside is sometimes incorrectly credited with coining ''
susceptance In electrical engineering, susceptance () is the imaginary part of admittance (), where the real part is conductance (). The reciprocal of admittance is impedance (), where the imaginary part is reactance () and the real part is resistance ( ...
'' (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 M. Hospitalier (1893).Steinmetz, Charles Proteus; Bedell, Frederick
"Reactance"
''Transactions of the American Institute of Electrical Engineers'', vol. 11, pp. 768–776, 1894,
cied to, Blondel, A., "A propos de la reactance", ''L'Industrie Electrique'', 10 May 1893.
This is confirmed by Heaviside himself
"The term 'reactance' was lately proposed in France, and seems to me to be a practical word."
br />Heaviside, ''Electromagnetic Theory'', vol. 1, p. 439, 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 * 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
pp. 455-466
* 1893 * 1894 * 1899 * 1912 * 1925. ''Electrical Papers''. 2 vols Boston 1925 (Copley) * 1950 ''Electromagnetic theory: The complete & unabridged edition''. (Spon) reprinted 1950 (Dover) * 1970 * 1971 "Electromagnetic theory; Including an account of Heaviside's unpublished notes for a fourth volume" Chelsea, * 2001


See also

* 1850 in science *
Electric displacement field In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, com ...
*
Biot–Savart law In physics, specifically electromagnetism, the Biot–Savart law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the ...
*


References


Further reading

* '' Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences'', Theme Issue
"Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory"
vol. 37, iss. 2134, 13 December 2018. * * * * Calvert, James B. (2002

from
University of Denver The University of Denver (DU) is a private research university in Denver, Colorado, United States. Founded in 1864, it has an enrollment of approximately 5,700 undergraduate students and 7,200 graduate students. It is classified among "R1: D ...
. * * * Jeffreys, Harold (1927) ''Operational Methods in Mathematical Physics'', Cambridge University Press, 2nd edition 1931 * * Laithwaite, E. R., "''Oliver Heaviside – establishment shaker''". Electrical Review, 12 November 1982. * * Lŭtzen J: ''Heaviside's Operational Calculus and the attempts to rigorize it'', Arch. Hist. Exact Sci. 21 (1980) 161–200 * *
Mende, F.F., "What is Not Taken into Account and they Did Not Notice Ampere, Faraday, Maxwell, Heaviside and Hertz", ''AASCIT Journal of Physics'', Vol.1, No.1, (March 2015), pp.28–52.
* *
Rocci, Alessio (2020), "Back to the Roots of Vector and Tensor Calculus: Heaviside versus Gibbs", ''Archive for History of Exact Sciences''.
* Whittaker E T (1929): ''Oliver Heaviside'', Bull. Calcutta Math Soc vol.20 1928–29 199–220 *


External links

* * The Dibner Library Portrait Collection, "
Oliver Heaviside
'". * * * * Gustafson, Grant, "
Heaviside's Methods
'". math.Utah.edu. (
PDF Portable document format (PDF), standardized as ISO 32000, is a file format developed by Adobe Inc., Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, computer hardware, ...
) * Heather, Alan
Oliver Heaviside
Torbay Amateur Radio Society. * Katz, Eugenii, . Hebrew University of Jerusalem. * * McGinty, Phil, "

'". Devon Life, Torbay Library Services. * Naughton, Russell, "

1850 – 1925''". Adventures in CyberSound. * * "Ron D." (2007
Heaviside's Operator Calculus
* Eric W. Weisstein,

. ''Eric Weisstein's World of Scientific Biography.'' Wolfram Media, Inc.


Archival collections


Oliver Heaviside selected papers [microform
1874-1922, Niels Bohr Library & Archives">icroform">Oliver Heaviside selected papers [microform
1874-1922, Niels Bohr Library & Archives
{{DEFAULTSORT:Heaviside, Oliver 1850 births 1925 deaths 19th-century British physicists 20th-century British physicists 19th-century English mathematicians 20th-century English mathematicians Burials in Devon English electrical engineers English physicists English Unitarians Fellows of the Royal Society Independent scientists People associated with electricity People from Camden Town Relativity critics