Editing Oliver Heaviside (section)

==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''.<ref name=Hunt91/>{{rp|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 [[quaternion]]s) to its modern [[Vector (geometric)|vector]] terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four [[differential equation]]s 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 <math>p</math> for the [[differential operator]], (which Boole had previously denoted by <math>D</math>''<ref>"A Treatise on Differential Equations", 1859</ref>''), giving a method of solving differential equations by direct solution as [[algebraic equation]]s. 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."<ref>{{Cite journal |doi = 10.1098/rspl.1893.0059|title = VIII. On operations in physical mathematics. Part II|journal = Proceedings of the Royal Society of London|volume = 54|issue = 326–330|pages = 105–143|year = 1894|s2cid = 121790063}}</ref> On another occasion he asked, "Shall I refuse my dinner because I do not fully understand the process of digestion?"<ref>Heaviside, "Mathematics and the Age of the Earth" in ''Electromagnetic Theory'' vol. 2</ref>

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 [[General Post Office|Post Office]], because part of the proposal was that [[loading coil]]s ([[inductor]]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).<ref>{{cite ODNB|chapter=Heaviside, Oliver|title=Oxford Dictionary of National Biography|first=Bruce J.|last=Hunt|year=2004|doi=10.1093/ref:odnb/33796|chapter-url=http://www.oxforddnb.com/view/article/33796|chapter-url-access=subscription}}</ref> 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.<ref name=Nahin/>{{rp| xi–xvii, 162–183}}

The importance of Heaviside's work remained undiscovered for some time after publication in ''The Electrician''. In 1897, [[AT&T Corp.|AT&T]] employed one of its own scientists, [[George Ashley Campbell|George A. Campbell]], and an external investigator [[Mihajlo Idvorski Pupin|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.<ref>{{cite book| author = Wiener, Norbert | title = Invention: The Care and Feeding of Ideas| year = 1993| publisher = MIT Press| isbn = 0-262-73111-8| pages = [https://archive.org/details/inventioncarefee0000wien/page/70 70]–75| location = Cambridge, Massachusetts|url=https://archive.org/details/inventioncarefee0000wien | url-access = registration | author-link = Wiener, Norbert}}</ref><ref>{{cite book |author=Wiener, Norbert |title=The Tempter |publisher=Random House |year=1959 |location=New York}}</ref><ref>{{cite book |author=Montagnini, Leone |title=Harmonies of Disorder – Norbert Wiener: A Mathematician-Philosopher of Our Time|publisher=Springer|location=Cham (Switzerland)|year=2017|isbn=978-3-31984455-8|pages=249–252}}</ref>

But this setback had the effect of turning Heaviside's attention towards electromagnetic radiation,{{sfn|Hunt|2004}} 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 Francis FitzGerald|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,<ref>{{Cite journal | doi = 10.1080/14786448908628362| title = XXXIX.On the electromagnetic effects due to the motion of electrification through a dielectric| journal = Philosophical Magazine |series=Series 5| volume = 27| issue = 167| pages = 324–339| year = 1889| last1 = Heaviside | first1 = O. | url = https://zenodo.org/record/1431195}}</ref> 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]] of [[electromagnetic mass]]. Heaviside treated this as material [[mass]], capable of producing the same effects. [[Wilhelm Wien]] later verified Heaviside's expression (for low [[Velocity|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]].