Oliver Heaviside

Oliver Heaviside FRS[1] (/ˈhɛvisaɪd/; 18 May 1850 – 3 February 1925) was an English self-taught electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques for the solution of differential equations (equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science for years to come.[2]

Oliver Heaviside
Born18 May 1850
Died3 February 1925 (aged 74)
Torquay, Devon, England
Known forHeaviside cover-up method
Kennelly–Heaviside layer
Heaviside step function
Differential operators
Vector analysis
Heaviside condition
Coaxial cable
AwardsFaraday Medal (1922)
Fellow of the Royal Society[1]
Scientific career
FieldsElectrical engineering, mathematics and physics
InstitutionsGreat Northern Telegraph Company


Early life

Heaviside was born in Camden Town, London, at 55 Kings Street[3]:13 (now Plender Street). He was a short and red-headed child, and suffered from scarlet fever 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, placed 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.[4]:51

Heaviside's uncle by marriage was Sir Charles Wheatstone (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[5] and in 1867 sent him north to work with his own, older brother Arthur, who was managing one of Wheatstone's telegraph companies in Newcastle-upon-Tyne.[4]:53

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 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 on 'The Best Arrangement of Wheatstone's Bridge for measuring a Given Resistance with a Given Galvanometer and Battery'[6] which received positive comments from physicists who had unsuccessfully tried to solve this algebraic problem, including Sir William Thomson, to whom he gave a copy of the paper, and James Clerk Maxwell. When he published an article on the duplex method of using a telegraph cable,[7] 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".[4]:60

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:

I remember my first look at the great treatise of Maxwell's when I was a young man… I saw that it was great, greater and greatest, with prodigious possibilities in its power… I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly… It will be understood that I preach the gospel according to my interpretation of Maxwell.[8]

Undertaking research from home, he helped develop transmission line theory (also known as the "telegrapher's equations"). Heaviside showed mathematically that uniformly distributed inductance in a telegraph line would diminish both attenuation and distortion, and that, if the inductance were great enough and the insulation resistance not too high, the circuit would be distortionless while currents of all frequencies would have equal speeds of propagation.[9] 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, 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.[4]:71

In 1880, Heaviside researched the skin effect in telegraph transmission lines. That same year he patented, in England, the coaxial cable. In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector 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. 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 using p for the differential operator, (which Boole[10] had previously denoted by D), giving a method of solving differential equations by direct solution as algebraic equations. This later caused a great deal of controversy, owing to its lack of rigour. 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."[11] On another occasion he asked somewhat more defensively, "Shall I refuse my dinner because I do not fully understand the process of digestion?"[12]

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, because part of the proposal was that loading coils (inductors) 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).[13] 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.[3]: xi–xvii, 162–183

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 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.[14]

But this setback had the effect of turning Heaviside's attention towards electromagnetic radiation,[15] 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.

In 1889, Heaviside first published a correct derivation of the magnetic force on a moving charged particle,[16] which is now called the Lorentz force.

In the late 1880s and early 1890s, Heaviside worked on the concept of electromagnetic mass. Heaviside treated this as material mass, capable of producing the same effects. Wilhelm Wien later verified Heaviside's expression (for low velocities).

In 1891 the British Royal Society recognized Heaviside's contributions to the mathematical description of electromagnetic phenomena by naming him a Fellow of the Royal Society, 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.

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.[15]

In 1902, Heaviside proposed the existence of what is now known as the Kennelly–Heaviside layer of the ionosphere. 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 and other astronomical objects. For whatever reason, there seem to have been no attempts for 30 years, until Jansky's development of radio astronomy in 1932.

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 papers to a grocery store, where the editors picked them up.[17] 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.[3]: xx In 1922, he became the first recipient of the Faraday Medal, which was established that year.

On Heaviside's religious views, he was a Unitarian, but not a religious one. He was even said to have made fun of people who put their faith in a supreme being.[18]

Comparison of before and after the monument restoration
Comparison of before and after the restoration project.

Heaviside died on 3 February 1925, at Torquay in Devon after falling from a ladder,[19] and is buried near the eastern corner of Paignton 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.[20] Most of his 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[21] in a bid to fully restore the monument through public subscription.[22][23] 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 MP for Torbay, an ex-curator of the Science Museum (representing the Institution of Engineering and Technology), the Chairman of the Torbay Civic Society, and delegates from Newcastle University.[24]

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 (IET) Archive Centre.[25]

Innovations and discoveries

Heaviside did much to develop and advocate vector methods and the vector calculus.[26] 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 (B, E, J, and ρ), 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.[27] The possibility of gravitational waves was also discussed by Heaviside using the analogy between the inverse-square law in gravitation and electricity [28]

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.[29] 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.[30] Heaviside was familiar with the Laplace transform method but considered his own method more direct.[31][32]

Heaviside developed the transmission line 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.[33] Heaviside also independently discovered the Poynting vector.[3]:116–118

Heaviside advanced the idea that the Earth's uppermost atmosphere contained an ionized layer known as the ionosphere; 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:


  • 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 01. vol.52 pp. 504–529
  • 1892 Heaviside, Oliver (1892). Electrical Papers. Volume 1. Macmillan Co, London and New York.
  • 1893 "On Operators in Physical Mathematics" Part II Proc. Roy. Soc. 1893 Jan 01. vol.54 pp. 105–143
  • 1893 "A gravitational and electromagnetic analogy," The Electrician.
  • 1893 Heaviside, Oliver (1893). Electromagnetic Theory. Volume 1. The Electrician Printing and Publishing Co, London.
  • 1894 Heaviside, Oliver (1894). Electrical Papers. Volume 2. Macmillan Co, London and New York.
  • 1899 Heaviside, Oliver (1899). Electromagnetic Theory. Volume 2. The Electrician Printing and Publishing Co, London.
  • 1912 Heaviside, Oliver (1912). Electromagnetic Theory. Volume 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. ISBN 978-0-8218-2840-3.

See also


  1. ^ a b Anon (1926). "Obituary Notices of Fellows Deceased: Rudolph Messel, Frederick Thomas Trouton, John Venn, John Young Buchanan, Oliver Heaviside, Andrew Gray". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 110 (756): i–v. Bibcode:1926RSPSA.110D...1.. doi:10.1098/rspa.1926.0036.
  2. ^ Hunt, B. J. (2012). "Oliver Heaviside: A first-rate oddity". Physics Today. 65 (11): 48–54. Bibcode:2012PhT....65k..48H. doi:10.1063/PT.3.1788.
  3. ^ a b c d Nahin, Paul J. (9 October 2002). Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age. JHU Press. ISBN 978-0-8018-6909-9.
  4. ^ a b c d Bruce J. Hunt (1991) The Maxwellians, Cornell University Press ISBN 978-0-8014-8234-2
  5. ^ Sarkar, T. K.; Mailloux, Robert; Oliner, Arthur A.; Salazar-Palma, M.; Sengupta, Dipak L. (2006). History of Wireless. John Wiley & Sons. p. 230. ISBN 978-0-471-78301-5.
  6. ^ Heaviside 1892, pp. 3-8.
  7. ^ Heaviside 1892, pp. 18-34.
  8. ^ Sarkar, T. K.; Mailloux, Robert; Oliner, Arthur A.; Salazar-Palma, M.; Sengupta, Dipak L. (30 January 2006). History of Wireless. John Wiley & Sons. p. 232. ISBN 978-0-471-78301-5.
  9. ^  One or more of the preceding sentences incorporates text from a publication now in the public domainKempe, Harry Robert (1911). "Telephone" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. 26 (11th ed.). Cambridge University Press. p. 554.
  10. ^ "A Treatise on Differential Equations", 1859
  11. ^ Heaviside 1893, "On Operators in Physical Mathematics, Part II" (pg121)
  12. ^ Heaviside, "Mathematics and the Age of the Earth" in Electromagnetic Theory vol. 2
  13. ^ Hunt, Bruce J. (2004). "Heaviside, Oliver". Oxford Dictionary of National Biography.
  14. ^ Wiener, Norbert (1993). Invention: The Care and Feeding of Ideas. Cambridge, Massachusetts: MIT Press. pp. 70–75. ISBN 0-262-73111-8.
  15. ^ a b Hunt 2004.
  16. ^ Heaviside, O. (1889). "XXXIX.On the electromagnetic effects due to the motion of electrification through a dielectric". Philosophical Magazine. Series 5. 27 (167): 324. doi:10.1080/14786448908628362.
  17. ^ "Pages with the Editor" (PDF). Popular Radio. New York: Popular Radio, Inc. 7 (6): 6. June 1925. Retrieved 14 August 2014.
  18. ^ Pickover, Clifford A. (1998). "Oliver Heaviside". Strange Brains and Genius: The Secret Lives of Eccentric Scientists and Madmen. Plenum Publishing Company Limited. ISBN 9780306457845. Religion: A Unitarian, but not religious. Poked fun at those who put their faith in a Supreme Being.
  19. ^ "Oliver Heaviside". Journal of the AIEE. 44 (3): 316–317. March 1925. doi:10.1109/JAIEE.1925.6537168. Retrieved 31 October 2017.
  20. ^ Mahon, Basil (2009). Oliver Heaviside: Maverick mastermind of electricity. The Institution of Engineering and Technology. ISBN 9780863419652.
  21. ^ "Heaviside Memorial Project Homepage". Nature. Heaviside Memorial Project. 165 (4208): 991–3. 27 July 2014. Retrieved 31 July 2014.
  22. ^ "Bid to restore Paignton monument to Oliver Heaviside". www.torquayheraldexpress.co.uk. Herald Express. 27 July 2014. Archived from the original on 6 August 2014. Retrieved 29 July 2014.
  23. ^ "The Heaviside Memorial Project". www.newcastle.ac.uk. Newcastle University. 29 July 2014. Archived from the original on 29 July 2014. Retrieved 29 July 2014.
  24. ^ "Restored Heaviside memorial unveiled on Saturday". www.torquayheraldexpress.co.uk. Herald Express. 1 September 2014. Archived from the original on 3 September 2014. Retrieved 1 September 2014.
  25. ^ Savoy Hill House 7-10, Savoy Hill, London WC2R 0BU Email: archives@theiet.org
  26. ^ See especially Electromagnetic Theory, vol.1 chap.3 pp.132-305 where he gave a complete account
  27. ^ Topological Foundations of Electromagnetism, World Scientific Series in Contemporary Chemical Physics, 13 March 2008, Terence W. Barrett.
  28. ^ A gravitational and electromagnetic analogy,Electromagnetic Theory, 1893, 455-466 Appendix B. This was 25 years before Einstein's paper on this subject
  29. ^ Electromagnetic Theory,vol.II, para.271, eqns 54,55
  30. ^ See the paper of Jeffreys quoted in the Bromwich WP article
  31. ^ Electromagnetic Theory vol 3, section starting on p.324. Available online
  32. ^ A rigorous version of Heaviside's operational calculus has been constructed see Mikusinski J: The Operational Calculus, Pergamon Press 1959
  33. ^ Wiener, Norbert (1993). Invention: The Care and 70–75. Cambridge, Massachusetts: MIT Press. ISBN 0-262-73111-8.

Further reading

Sorted by date.

External links


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. The SI unit of admittance is the siemens (symbol S); the older, synonymous unit is mho, and its symbol is ℧ (an upside-down uppercase omega Ω). Oliver Heaviside coined the term admittance in December 1887.

Admittance is defined as


Y is the admittance, measured in siemens
Z is the impedance, measured in ohms

Resistance is a measure of the opposition of a circuit to the flow of a steady current, while impedance takes into account not only the resistance but also dynamic effects (known as reactance). Likewise, admittance is not only a measure of the ease with which a steady current can flow, but also the dynamic effects of the material's susceptance to polarization:



Electrical elastance is the inverse 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 capacitance rather than inverse capacitance. However, it is used in theoretical work in network analysis and has some niche applications at microwave frequencies.

The term elastance was coined by Oliver Heaviside through the analogy of a capacitor as a spring. The term is also used for analogous quantities in some other energy domains. It maps to stiffness in the mechanical domain, and is the inverse of compliance in the fluid flow domain, especially in physiology. It is also the name of the generalised quantity in bond-graph analysis and other schemes analysing systems across multiple domains.


An electret (formed of electr- from "electricity" and -et from "magnet") is a dielectric material that has a quasi-permanent electric charge or dipole polarisation. An electret generates internal and external electric fields, and is the electrostatic equivalent of a permanent magnet. Although Oliver Heaviside coined this term in 1885, materials with electret properties were already known to science and had been studied since the early 1700s. One particular example is the electrophorus, a device consisting of a slab with electret properties and a separate metal plate. The electrophorus was originally invented by Johan Carl Wilcke in Sweden and again by Alessandro Volta in Italy.

Energy current

Energy current is a flow of energy defined by the Poynting vector (E × H), as opposed to normal current (flow of charge). It was originally postulated by Oliver Heaviside. It is also an informal name for Energy flux.

Heaviside (Martian crater)

Heaviside is an impact crater in the Mare Australe quadrangle of Mars, located at 70.7°S latitude and 95.3°W longitude. It is 87.4 km in diameter. It was named after British physicist Oliver Heaviside; the name was approved in 1973 by the International Astronomical Union (IAU) Working Group for Planetary System Nomenclature (WGPSN).

Heaviside condition

The Heaviside condition, named for Oliver Heaviside (1850–1925), is the condition an electrical transmission line must meet in order for there to be no distortion of a transmitted signal. Also known as the distortionless condition, it can be used to improve the performance of a transmission line by adding loading to the cable.

Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a discontinuous function, named after Oliver Heaviside (1850–1925), whose value is zero for negative arguments and one for positive arguments. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.

The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely. Oliver Heaviside, who developed the operational calculus as a tool in the analysis of telegraphic communications, represented the function as 1.

The simplest definition of the Heaviside function is as the derivative of the ramp function:

The Heaviside function can also be defined as the integral of the Dirac delta function: H′ = δ. This is sometimes written as

although this expansion may not hold (or even make sense) for x = 0, depending on which formalism one uses to give meaning to integrals involving δ. In this context, the Heaviside function is the cumulative distribution function of a random variable which is almost surely 0. (See constant random variable.)

In operational calculus, useful answers seldom depend on which value is used for H(0), since H is mostly used as a distribution. However, the choice may have some important consequences in functional analysis and game theory, where more general forms of continuity are considered. Some common choices can be seen below.

Approximations to the Heaviside step function are of use in biochemistry and neuroscience, where logistic approximations of step functions (such as the Hill and the Michaelis menten equations) may be used to approximate binary cellular switches in response to chemical signals.

History of Maxwell's equations

In electromagnetism, one of the fundamental fields of physics, the introduction of Maxwell's equations (mainly in "A Dynamical Theory of the Electromagnetic Field") was one of the most important aggregations of empirical facts in the history of physics. It took place in the nineteenth century, starting from basic experimental observations, and leading to the formulations of numerous mathematical equations, notably by Charles-Augustin de Coulomb, Hans Christian Ørsted, Carl Friedrich Gauss, Jean-Baptiste Biot, Félix Savart, André-Marie Ampère, and Michael Faraday. The apparently disparate laws and phenomena of electricity and magnetism were integrated by James Clerk Maxwell, who published an early form of the equations, which modify Ampère's circuital law by introducing a displacement current term. He showed that these equations imply that light propagates as electromagnetic waves. His laws were reformulated by Oliver Heaviside in the more modern and compact vector calculus formalism he independently developed. Increasingly powerful mathematical descriptions of the electromagnetic field were developed, continuing into the twentieth century, enabling the equations to take on simpler forms by advancing more sophisticated mathematics.

Kennelly–Heaviside layer

The Kennelly–Heaviside layer, named after Arthur E. Kennelly and Oliver Heaviside, also known as the E region or simply the Heaviside layer, is a layer of ionised gas occurring between roughly 90–150 km (56–93 mi) above the ground — one of several layers in the Earth's ionosphere. It reflects medium-frequency radio waves. Because of this reflective layer, radio waves radiated into the sky can return to Earth beyond the horizon. This "skywave" or "skip" propagation technique has been used since the 1920s for radio communication at long distances, up to transcontinental distances.

Propagation is affected by time of day. During the daytime the solar wind presses this layer closer to the Earth, thereby limiting how far it can reflect radio waves. Conversely, on the night (lee) side of the Earth, the solar wind drags the ionosphere further away, thereby greatly increasing the range which radio waves can travel by reflection. The extent of the effect is further influenced by the season, and the amount of sunspot activity.

List of Fellows of the Royal Society elected in 1891

Fellows of the Royal Society elected in 1891.

Loading coil

A loading coil or load coil is an inductor that is inserted into an electronic circuit to increase its inductance. The term originated in the 19th century for inductors used to prevent signal distortion in long-distance telegraph transmission cables. The term is also used for inductors in radio antennas, or between the antenna and its feedline, to make an electrically short antenna resonant at its operating frequency.

The concept of loading coils was discovered by Oliver Heaviside in studying the problem of slow signalling speed of the first transatlantic telegraph cable in the 1860s. He concluded additional inductance was required to prevent amplitude and time delay distortion of the transmitted signal. The mathematical condition for distortion-free transmission is known as the Heaviside condition. Previous telegraph lines were overland or shorter and hence had less delay, and the need for extra inductance was not as great. Submarine communications cables are particularly subject to the problem, but early 20th century installations using balanced pairs were often continuously loaded with iron wire or tape rather than discretely with loading coils, which avoided the sealing problem.

Loading coils are historically also known as Pupin coils after Mihajlo Pupin, especially when used for the Heaviside condition and the process of inserting them is sometimes called pupinization.

Paignton Cemetery

Paignton Cemetery is a burial ground situated within the town of Paignton, Devon, England. Notable people with memorials within the cemetery include the scientist Oliver Heaviside and Victoria Cross recipient William Harry Thomas Sylvester.

Paul J. Nahin

Paul J. Nahin (born November 26, 1940) is an American engineer and author who has written 18 books on topics in physics and mathematics, including biographies of Oliver Heaviside, George Boole, and Claude Shannon, books on mathematical concepts such as Euler's formula and the imaginary unit, and a number of books on the physics and philosophical puzzles of time travel.

Born in California, he graduated from Brea Olinda High School in 1958, and thereafter received a B.S. from Stanford University in 1962, an M.S. from the California Institute of Technology in 1963, and a Ph.D. from the University of California, Irvine in 1972.He thereafter taught at Harvey Mudd College, the University of Virginia, and the Naval Postgraduate School in Monterey, California.As of 2004, Nahin is an emeritus professor of electrical engineering at the University of New Hampshire. He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics and, in 1979, the first Harry Rowe Mimno writing award from the IEEE Areospace and Electronic Systems Society.

Permeability (electromagnetism)

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself, otherwise known as distributed inductance in Transmission Line Theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter µ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.

In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons per ampere squared (N·A−2). The permeability constant µ0, also known as the magnetic constant or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum. Until May 20, 2019, the magnetic constant had the exact (defined) value µ0 = 4π × 10−7 H/m ≈ 12.57 × 10−7 H/m.

On May 20, 2019 a revision to the SI system has gone into effect, making the vacuum permeability no longer a constant but rather a value that needs to be determined experimentally; 4π × 1.000 000 000 82 (20) 10−7 H·m−1 is a recently measured value in the new system. It will be proportional to the dimensionless fine-structure constant with no other dependencies.A closely related property of materials is magnetic susceptibility, which is a dimensionless proportionality factor that indicates the degree of magnetization of a material in response to an applied magnetic field.

Post Office Research Station

The Post Office Research Station was first established as a separate section of the General Post Office in 1909.In 1921, the Research Station moved to Dollis Hill, north west London, initially in ex-army huts.The main permanent buildings at Dollis Hill were opened in 1933 by Prime Minister Ramsay MacDonald.In 1968 it was announced that the station would be relocated to a new centre to be built at Martlesham Heath in Suffolk. This was formally opened on 21 November 1975 by Queen Elizabeth and is today known as Adastral Park.

The old Dollis Hill site was released for housing, with the main building converted into a block of luxury flats and an access road named Flowers Close, in honour of Tommy Flowers. Much of the rest of the site contains affordable housing administered by Network Housing.

Paddock, a World War II concrete two-level underground bunker, was built in secret in 1939 as an alternative Cabinet War Room underneath a corner of the Dollis Hill site. Its surface building was demolished after the war.


In electrical engineering, susceptance (B) is the imaginary part of admittance, where the real part is conductance. The inverse of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI units, susceptance is measured in siemens. Oliver Heaviside first defined this property in June 1887.

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 publication of A Treatise on Electricity and Magnetism by James Clerk Maxwell. The book draws heavily on the correspondence and notebooks as well as the published writings of George Francis FitzGerald, Oliver Lodge, Oliver Heaviside, Heinrich Hertz, and Joseph Larmor.

The book has nine chapters; their titles and section headings are:

FitzGerald and Maxwell's Theory

FitzGerald and the Dublin School, Maxwell’s Theory, Reflection and Refraction, FitzGerald’s Accomplishment.

FitzGerald, Lodge, and Electromagnetic Waves

Oliver Lodge, Maxwell and Electromagnetic Waves, Lodge and "Electromagnetic Light", FitzGerald and "The Impossibility . . .", The Undetected Waves.

Heaviside the Telegrapher

Oliver Heaviside, Cable Empire, At Newcastle, Cables and Field Theory, Heaviside on Propagation, Turning to Maxwell.

Ether Models and the Vortex Sponge

Models, Wheels and Bands, Charging Displacement, "We Find Ourselves in a Factory", The Vortex Sponge, "Mathematical Machinery".

"Maxwell Redressed"

Energy Paths, Model Research, "When Energy Goes from Place to Place . . .", Heaviside’s Equations.

Waves on Wires

"Beams of Dark Light", Loading and the Distortionless Circuit, Suppression, Campaigning for Recognition, Lightning.

Bath, 1888

Hertz’s Waves, Reception, "The Murder of Ψ", Practice vs Theory.

The Maxwellian Heyday

Strengthening the Links, The Origins of the FitzGerald Contraction, What Is Maxwell’s Theory?

The Advent of the Electron

Joseph Larmor and the Rotational Ether, Inventing Electrons, "Larmor’s Force," Assimilating Electrons, Conclusion.



From Maxwell's Equations to "Maxwell's Equations".

Abbreviations, Bibliography (10 pages), Index (6 pages).

Weber (unit)

In physics, the weber (symbol: Wb) is the SI derived unit of magnetic flux. A flux density of one Wb/m2 (one weber per square metre) is one tesla.

The weber is named after the German physicist Wilhelm Eduard Weber (1804–1891).

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