Editing Oliver Heaviside (section)

==Innovations and discoveries==
{{electromagnetism|Scientists}}
Heaviside did much to develop and advocate [[Vector (geometric)|vector]] methods and [[vector calculus]].<ref>See especially '''Electromagnetic Theory''', 1893 "The Elements of Vectorial Algebra and Analysis," vol.1 chap.3 pp.132–305 where he gave a complete account of the modern system</ref> [[James Clerk Maxwell|Maxwell's]] formulation of [[electromagnetism]] consisted of 20 equations in 20 variables. Heaviside employed the [[curl (mathematics)|curl]] and [[divergence]] operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (<math>\textbf{B}, \textbf{E}, \textbf{J} ~\text{and} ~\rho</math>), 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.<ref>''Topological Foundations of Electromagnetism'', World Scientific Series in Contemporary Chemical Physics, 13 March 2008, Terence W. Barrett.</ref> The possibility of [[gravitational waves]] was also discussed by Heaviside using the analogy between the inverse-square law in gravitation and electricity.<ref>A gravitational and electromagnetic analogy,''Electromagnetic Theory'', 1893, 455–466 Appendix B. This was 25 years before Einstein's paper on this subject</ref> With [[quaternion]] multiplication, the square of a vector is a negative quantity, much to Heaviside's displeasure. As he advocated abolishing this negativity, he has been credited by [[C. J. Joly]]<ref>{{cite book |last=Hamilton |title=Elements of Quaternions |year=1899 |page=[https://archive.org/details/elementsquatern01hamigoog/page/n200 163] |publisher=Longmans, Green, and co. |isbn=9780828402194 |url=https://archive.org/details/elementsquatern01hamigoog|edition=2nd |editor-first=C.J. |editor-last=Joly}}</ref> with developing [[hyperbolic quaternion]]s, though in fact that mathematical structure was largely the work of [[Alexander Macfarlane]].

He invented the [[Heaviside step function]], using it to calculate the [[Electric current|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]].<ref>'''Electromagnetic Theory''', vol.II, para.271, eqns 54,55</ref> He invented his [[operational calculus]] method for solving [[linear differential equation]]s. This resembles the currently used [[Laplace transform]] method based on the "[[Inverse Laplace transform|Bromwich integral]]" named after [[Thomas John I'Anson Bromwich|Bromwich]] who devised a rigorous mathematical justification for Heaviside's operator method using contour integration.<ref>See the paper of Jeffreys quoted in the Bromwich WP article</ref> Heaviside was familiar with the Laplace transform method but considered his own method more direct.<ref>'''Electromagnetic Theory''' vol 3, section starting on p.324. Available online</ref><ref>A rigorous version of Heaviside's operational calculus has been constructed see Mikusinski J: '''The Operational Calculus''', Pergamon Press 1959</ref>

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.<ref>{{cite book| last=Wiener |first=Norbert | title = Invention: The Care and 70–75| location = Cambridge, Massachusetts|url=https://books.google.com/books?id=G3Q2qOtOeLYC| year = 1993| publisher = MIT Press| isbn = 0-262-73111-8}}</ref> Heaviside also independently discovered the [[Poynting vector]].<ref name =Nahin/>{{rp|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 [[neologism|coined]] the following terms of art in [[electromagnetic theory]]:
* [[admittance]] ''(reciprocal of impedance)'' (December 1887);
* [[elastance]] ''(reciprocal of permittance, reciprocal of capacitance)'' (1886);
* [[Electrical conductance|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]]);
* [[Electrical impedance|impedance]] (July 1886);
* [[inductance]] (February 1886);
* [[Permeability (electromagnetism)|permeability]] (September 1885);
* [[permittance]] (now called capacitance) and [[permittivity]] (June 1887);
* [[reluctance]] (May 1888);<ref>Ronald R. Kline, ''Steinmetz: Engineer and Socialist'', p. 337, Johns Hopkins University Press, 1992 {{ISBN|0801842980}}.</ref>
Heaviside is sometimes incorrectly credited with coining ''[[susceptance]]'' (the imaginary part of admittance) and [[electrical reactance|''reactance'']] (the imaginary part of impedance). The former was coined by [[Charles Proteus Steinmetz]] (1894).<ref>Kline, p. 88</ref> The latter was coined by M. Hospitalier (1893).<ref>Steinmetz, Charles Proteus; Bedell, Frederick, [https://babel.hathitrust.org/cgi/pt?id=iau.31858046100776&view=1up&seq=830 "Reactance"], ''Transactions of the American Institute of Electrical Engineers'', vol. 11, pp. 768–776, 1894,<br />cied to, Blondel, A., "A propos de la reactance", ''L'Industrie Electrique'', 10 May 1893.<br />This is confirmed by Heaviside himself, [https://archive.org/details/electromagnetict0001heav/page/439/mode/1up "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.</ref>