Jacqueline Hochheiser, Corporate Communications
Introduction
Oliver Heaviside was a British, self-taught mathematician, physicist and electrical engineer who, although made great contributions to both mathematics and telegraphy, flew under the radar and is now eclipsed by other more well-known names such as James Clerk Maxwell. Heaviside created the four vector-form equations that we now know today as Maxwell’s equations, and also formulated the Telegrapher’s Equations, which detail how voltages and currents propagate as waves along a long-distance circuit or transmission line often used for telegraphs in the late 1800s to early 1900s.
English Origins
Heaviside was born on May 18th, 1850 and lived at 55 Kings Street in Camden Town, London, UK as the youngest of three children born to Thomas Heaviside and Rachel Elizabeth West. Heaviside’s father was a draughtsman and wood engraver and the family lived a middle-class life. Early on, Heaviside suffered from Scarlett Fever, which left him hard of hearing and hindered his ability to communicate and socialize with fellow children at school. His father was also known to be a drunk, which lead Heaviside to abstain from alcohol for the duration of his life.
He was sent to Camden Grammar School where he placed 5th out of a class of 500 students in 1865. However, despite the fact that he was bright, his parents could not afford to send him to school after he turned 16. With only a basic understanding of algebra and trigonometry, Heaviside left school, but this did little to deter him from becoming a self-made force in the engineering and mathematical fields later in life.
After Heaviside left school, one of his uncles, Sir Charles Wheatstone, took a strong interest in his nephew’s education. Wheatstone was an internationally celebrated expert in telegraphy and electromagnetism, and the original co-inventor of the first commercially successful telegraph in the mid-1830s.
Wheatstone sent Heaviside north to work with his older brother, Arthur Wheatstone who was managing one of Charles’ telegraph companies in Newcastle, England. Two years later, Heaviside took a job as a telegraph operator with the Great Northern Telegraph company while continuing to study on his own. By the age of 22, Heaviside had published his first article in the philosophical Magazine on “The Best Arrangement of Wheatstone’s Bridge for Measuring a Given Resistance with a Given Galvanometer and Battery.”
It was during his independent studies that Heaviside came across James Clerk Maxwell’s equations for the first time in 1873. He was greatly influenced by Maxwell’s famous two-volume Treatise on Electricity and Magnetism. Although he didn’t fully understand the equations at the time, he would use his own expertise to streamline the equations to make them more comprehensible. He would also later use these same, streamlined equations to help him formulate his Telegrapher’s Equations.
Maxwell’s Equations & Transmission Line Theory
As previously stated, the four equations that we use today called Maxwell’s Equations, were actually written by Heaviside in vector form, which was converted from Maxwell’s original equations in quaternations. While there were over 20 original equations, Heaviside’s streamlined four have been most commonly used even today in modern textbooks.
Quaternations are an extension of complex numbers developed by Sir William Hamilton, and according to Heaviside, the mathematical representation of quaternations was hard to read and lengthy. He paired it down to the well-known vector form which uses simplified language using algebra and variables to display the equations.
His next great achievement was in 1884, while exploring how energy moves through the electromagnetic field. While Maxwell had given formulas based on the electric and magnetic fields E and H for how energy is distributed in the field, he never explained how it got from one place to another. Using the four equations, Heaviside was able to show mathematically that uniformly distributed inductance in a telegraph line would diminish both attenuation and distortion. Therefore, if inductance were great enough and the insulation resistance not too high, the circuit would be without distortion and currents of all frequencies would have equal speeds of propagation. This revelation was especially useful in long-distance transmission, which directly correlated to the advancement of telegraphy at the time.
This was how the Telegrapher’s Equations came about. Heaviside surmised that the equations treat voltage and current as continuous waves traveling down a line and combines line resistance (R), inductance (L), capacitance (C), and conductance (G) into paired differential equations. This also gave way to the Heaviside Condition, which states that a transmission line is completely free of distortion is R/L = G/C. It proved that signals pass without blurring or dispersion when this exact balance is met.
Later Life
In Heaviside’s later years, he became increasingly reclusive and eccentric. In order to avoid contact with people, he went to such extremes as to leave his scientific papers at a local grocery store for the editors of the Electrician magazine to then pick up in his absence. In 1922, however, Heaviside became the first recipient of the Faraday Medal, which was established that same year. He eventually died in Torquay, UK on February 3rd, 1925 at the age of 74. He is buried at Paignton Cemetery with his father, Thomas, and his mother, Rachel.
References
- https://www.oliver-heaviside.com/oliver-heaviside/
- https://ia601802.us.archive.org/24/items/communications_fermat/Belrose-MUL-2014-Vol2-Mar_Apr-005.pdf
- https://en.wikipedia.org/wiki/Oliver_Heaviside
- https://royalsocietypublishing.org/rsta/article/376/2134/20170457/115691/On-Heaviside-s-contributions-to-transmission-line
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