Oliver Heaviside
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Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English
self-taught Autodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teachers and professors) or institutions (such as schools). Generally, autodidacts are individu ...
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, structure, space, models, and change. History On ...
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 caus ...
who invented a new technique for solving
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s (equivalent to the
Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integra ...
), independently developed
vector calculus Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...
, 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, and electric circuits. ...
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 The telegrapher's equations (or just telegraph equations) are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver ...
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.


Biography


Early life

Heaviside was born in
Camden Town Camden Town (), often shortened to Camden, is a district of northwest London, England, north of Charing Cross. Historically in Middlesex, it is the administrative centre of the London Borough of Camden, and identified in the London Plan as o ...
, 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). The infection is a type of Group A streptococcal infection (Group A strep). It most commonly affects childr ...
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 students 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 ''The Maxwellians'' is a book by Bruce J. Hunt, published in 1991 by Cornell University Press; a paperback edition appeared in 1994, and the book was reissued in 2005. It chronicles the development of electromagnetic theory in the years after the ...
,
Cornell University Press The Cornell University Press is the university press of Cornell University; currently housed in Sage House, the former residence of Henry William Sage. It was first established in 1869, making it the first university publishing enterprise in t ...
Heaviside's uncle by marriage was Sir
Charles Wheatstone Sir Charles Wheatstone FRS FRSE DCL LLD (6 February 1802 – 19 October 1875), was an English scientist and inventor of many scientific breakthroughs of the Victorian era, including the English concertina, the stereoscope (a device for di ...
(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. Two years later he took a job as a telegraph operator with the Danish
Great Northern Telegraph Company GN Store Nord A/S is a Danish manufacturer of hearing aids (GN ReSound/GN Hearing) and headsets ( Jabra (GN Audio)). GN Store Nord A/S is listed on NASDAQ OMX Copenhagen (ISIN code DK0010272632). History The Great Northern Telegraph Company ...
laying a cable from Newcastle to
Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Danish Realm, Kingdom of Denmark ...
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)" Oxford Dictionary of National Biography, Oxford Univer ...
'' on 'The Best Arrangement of
Wheatstone's Bridge A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The primary benefit of the circuit is its ability to provi ...
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 physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...
, 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 mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
. 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 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 Te ...
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 transmi ...
theory (also known as the "''
telegrapher's equations The telegrapher's equations (or just telegraph equations) are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver ...
''"). Heaviside showed mathematically that uniformly distributed inductance in a telegraph line would diminish both
attenuation In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variabl ...
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 signa ...
, and that, if the inductance were great enough and the
insulation Insulation may refer to: Thermal * Thermal insulation, use of materials to reduce rates of heat transfer ** List of insulation materials ** Building insulation, thermal insulation added to buildings for comfort and energy efficiency *** Insulated ...
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 (stre ...
of all frequencies 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, he contributed regular articles to the trade paper ''
The Electrician ''The Electrician'', published in London from 1861–1863 and 1878–1952, was the one of the earliest and foremost electrical engineering periodicals and scientific journals. It was published in two series: The original ''Electrician'' was publi ...
'', 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 these 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 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 conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ( insulating material); many coaxial cables also have a p ...
. 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. Hamilton defined a quatern ...
s) to its modern
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s 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, and electric circuits. ...
. 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 analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. History Th ...
using p for the differential operator, (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 many authors, the term ''algebraic equation'' ...
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 ma ...
. 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 somewhat more defensively, "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 Sir William Henry Preece (15 February 1834 – 6 November 1913) was a Welsh electrical engineer and inventor. Preece relied on experiments and physical reasoning in his life's work. Upon his retirement from the Post Office in 1899, Preece was m ...
of the
Post Office A post office is a public facility and a retailer that provides mail services, such as accepting letters and parcels, providing post office boxes, and selling postage stamps, packaging, and stationery. Post offices may offer additional serv ...
, because part of the proposal was that loading coils (
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
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 Paul J. Nahin (born November 26, 1940 in Orange County, California) is an American electrical engineer and author who has written 20 books on topics in physics and mathematics, including biographies of Oliver Heaviside, George Boole, and Claude Sh ...
: "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'', and so its rights lay in the public domain. In 1897,
AT&T AT&T Inc. is an American multinational telecommunications holding company headquartered at Whitacre Tower in Downtown Dallas, Texas. It is the world's largest telecommunications company by revenue and the third largest provider of mobile te ...
employed one of its own scientists, George A. Campbell, and an external investigator
Michael I. Pupin Mihajlo Idvorski Pupin ( sr-Cyrl, Михајло Идворски Пупин, ; 4 October 1858Although Pupin's birth year is sometimes given as 1854 (and Serbia and Montenegro issued a postage stamp in 2004 to commemorate the 150th anniversary o ...
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. 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, and inspired his friend George FitzGerald to suggest what now is known as the
Lorentz–FitzGerald contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGeral ...
. 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 the late 1880s and early 1890s, Heaviside worked on the
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by ...
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 for ...
. Heaviside treated this as material
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
, capable of producing the same effects.
Wilhelm Wien Wilhelm Carl Werner Otto Fritz Franz Wien (; 13 January 1864 – 30 August 1928) was a German physicist who, in 1893, used theories about heat and electromagnetism to deduce Wien's displacement law, which calculates the emission of a blackbody ...
later verified Heaviside's expression (for low
velocities Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
). 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 judges 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, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
.


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 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 an ...
. 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 center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
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 in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
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 celestial objects at radio frequencies. The first detection of radio waves from an astronomical object was in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation comin ...
in 1932. Heaviside was an opponent of Albert Einstein's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
.Eves, Howard. (1988). ''Return to Mathematical Circles: A Fifth Collection of Mathematical Stories and Anecdotes''. PWS-Kent Publishing Company. p. 27. Mathematician
Howard Eves Howard Whitley Eves (10 January 1911, New Jersey – 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics. Eves received his B.S. from the University of Virginia, an M.A. from Harvard Universi ...
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 Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-center, in geometry * Eccentricity (graph theory) of a v ...
. 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 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 maintenance ...
'' 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)). It is part of the IET Achievement Medals collection of awards. ...
, 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 Paig ...
in
Devon Devon ( , historically known as Devonshire , ) is a ceremonial and non-metropolitan county in South West England. The most populous settlement in Devon is the city of Plymouth, followed by Devon's county town, the city of Exeter. Devon is ...
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 borough of Torbay which was created in 1998. The Torbay area is a holiday destination known as the English Riviera. Paignt ...
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 primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
'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, 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 A member of parliament (MP) is the representative in parliament of the people who live in their electoral district. In many countries with bicameral parliaments, this term refers only to members of the lower house since upper house members of ...
(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, and ...
), the Chairman of the Torbay Civic Society, and delegates from Newcastle University.


The Heaviside Collection 1872–1923

A collection of Heaviside's notebooks, papers, correspondence, notes and annotated pamphlets on telegraphy 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, and ...
(IET) Archive Centre.


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 *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
methods and
vector calculus Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...
.
Maxwell's Maxwell's, last known as Maxwell's Tavern, was a bar/restaurant and music club in Hoboken, New Jersey. Over several decades the venue attracted a wide variety of acts looking for a change from the New York City concert spaces across the river. Ma ...
formulation of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
consisted of 20 equations in 20 variables. Heaviside employed the curl and
divergence In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of t ...
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, and electric circuits. ...
). 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 waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
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. Hamilton defined a quatern ...
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 quaternion In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form :q = a + bi + cj + dk, \quad a,b,c,d \in \mathbb \! where the squares of i, j, and k are +1 and distinct eleme ...
s, 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, Blairgowire) 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 (1850–1925), the value of which is zero for negative arguments and one for positive argum ...
, using it to calculate the
current 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 (stre ...
when an
electric circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, ...
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 Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. History Th ...
method for solving
linear differential equation In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b ...
s. This resembles the currently used
Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integra ...
method based on the "
Bromwich integral In mathematics, the inverse Laplace transform of a function ''F''(''s'') is the piecewise-continuous and exponentially-restricted real function ''f''(''t'') which has the property: :\mathcal\(s) = \mathcal\(s) = F(s), where \mathcal denotes the L ...
" 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 transmi ...
theory (also known as the "
telegrapher's equations The telegrapher's equations (or just telegraph equations) are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver ...
"), 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 Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of th ...
in series with the cable. Heaviside also independently discovered the Poynting vector. 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 an ...
; in this regard, he predicted the existence of what later was dubbed the Kennelly–Heaviside layer. 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. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
: *
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 reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittan ...
''(reciprocal of impedance)'' (December 1887); *
elastance Electrical elastance is the reciprocal of capacitance. The SI unit of elastance is the inverse farad (F−1). The concept is not widely used by electrical and electronic engineers. The value of capacitors is invariably specified in units of c ...
''(reciprocal of permittance, reciprocal of capacitance)'' (1886); * conductance ''(real part of admittance, reciprocal of resistance)'' (September 1885); *
electret An electret (formed as a portmanteau of ''electr-'' from "electricity" and ''-et'' from "magnet") is a dielectric material that has a quasi-permanent electric charge or dipole polarization (electrostatics), polarisation. An electret generates int ...
for the electric analogue of a permanent magnet, or, in other words, any substance that exhibits a quasi-permanent electric polarization (e.g.
ferroelectric 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 piezoelectric and pyroelectric, with the ad ...
); * impedance (July 1886); * inductance (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 ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
(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 geo ...
(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 Charles Proteus Steinmetz (born Karl August Rudolph Steinmetz, April 9, 1865 – October 26, 1923) was a German-born American mathematician and electrical engineer and professor at Union College. He fostered the development of alternati ...
(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) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
*
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 ...
* *
Heaviside–Lorentz units Heaviside–Lorentz units (or Lorentz–Heaviside units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that th ...


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 university, private research university in Denver, Colorado. Founded in 1864, it is the oldest independent private university in the Mountain States, Rocky Mountain Region of the United States. It is ...
. * * * 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) * 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. {{DEFAULTSORT:Heaviside, Oliver 1850 births 1925 deaths 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