Fig. 1 Maxwelton Chapel, Dumfries & Galloway, Scotland

Almost exactly 10 years ago I made a ‘pilgrimage’ to visit the grave of James Clerk Maxwell at Parton Kirk in Dumfries and Galloway in the south-west of Scotland, [1]. I went with a friend who lived near Dumfries, and we rode together on our vintage motorcycles on a beautiful summer’s day. My friend assured me (based on his local knowledge) that Maxwell’s regular place of worship was actually Maxwelton Chapel a few miles away [2], so we rode there and parked our bikes at the gate, Fig. 1.

The reason for writing about this in *Engineer’s Diary* is that it makes me think about the development of electromagnetic theory from our modern perspective. Much of the modern world is a result of the application of electromagnetic theory over the last 200 years or so since the ground-breaking discoveries of Faraday, Oersted, Ampère, Gauss and many other pioneers (1820-1835). These discoveries were formulated in an integrated system of equations by James Clerk Maxwell, more or less in the heyday of *Natural Philosophy* (classical physics). This period anticipated the era of ‘modern’ physics characterized by the discovery of radiation (predicted theoretically by Maxwell) and sub-atomic particles. The applications, the research, and the analytical and experimental tools are all developing today at a spectacular rate that could not possibly have been foreseen even quite recently.

This is illustrated by the fact that I’m writing this on a desktop computer that can produce engineering electromagnetic calculations at the most sophisticated level including 3D and time-stepping nonlinear problems with an enormous database of material properties; while on my smartphone I can watch videos in professional animated graphics explaining the significance and interpretation of Maxwell’s equations. Wow!

Although Maxwell was well connected in many spheres of engineering, it is a deep question as to whether the many technological revolutions of the last two centuries could possibly have been foreseen by Maxwell’s generation. For example, Maxwell corresponded with William Thomson (Lord Kelvin) from the time of Thomson’s work on the transatlantic telegraph cable, but signal transmission was predominantly by Morse Code until well after Maxwell’s death. Maxwell would have been able to travel by rail between London, Cambridge, Edinburgh, and even quite close to his family home in the rural fastness of south-west Scotland; but the railways of that time were powered by steam, and local transport was horse-drawn. The golden era of the development of electric traction did not begin until a few years after Maxwell’s death. Modern physics likewise came later with the works of Hertz, the Curies, J.J. Thomson, Einstein and many others, while some of the ‘old school’ such as Kelvin regarded some of it with reserve. But because of his mathematical and theoretical vision, it is tantalizing to wonder how Maxwell’s contribution to physics would have grown even further had he lived another 30 years beyond his premature death in 1879.

Further reflections along these lines can be found in [3], in which Profs. Lowther and Freeman assert that the community of electric machine designers made little use of Maxwell’s equations *per se* until the advent of the digital computer in the 1960s and the development of numerical methods such as the finite-difference and finite-element methods. They refer to the widespread use of the magnetic equivalent circuit throughout the industry, and they offer an interesting and very plausible argument that this method can be traced back to article 499 in Maxwell’s *Treatise* [4]. Personally I feel that their article [3] is a little harsh, because it pays only limited attention to the work of Carter (the effective air-gap coefficient), Field (eddy currents), Wieseman (field plotting), Hague (direct solution of Laplace’s equation), and the formulation of inductances and forces between excited conductors, all of which (and much more) can be traced back to the *Treatise* and to Maxwell’s generous references to contemporary workers such as Weber and others including Thomson (Kelvin). All of those works were developed before 1930.

Lowther and Freeman make specific reference to the Maxwell stress tensor which is an integral part of numerical analysis for calculating force and torque, especially in the ‘total simulation’ approach that is so widely used today. But I think they understate the fact that the preferred ‘industrial’ or ‘practical’ methods and formulas, crude as they may seem in comparison, were in many cases inspired by the genius of engineers who *had to get results* with slide-rules, test data, and equivalent circuits because the direct solution of Maxwell’s equations was not practical in their environment for most of the 150 years in question.

The photo in Fig. 1 prompts a few (admittedly lightweight) thoughts along these lines. Both motorcycles were made in the 1950s, and we can ask if they have *any* accessories whose operation can be described by Maxwell’s equations? Sparking plugs, for a start! One of them has a traditional magneto, developed at the time of the First World War — an impulse-generating electrical machine that relies directly on Faraday’s law and the theory of the transformer and the sudden interruption of currents in inductive circuits. The other one has an electronic *magneto*, developed in the 1970s and 1980s, based on a permanent-magnet generator. Both machines have DC generators with brushes and commutators. Both of them have a wiring system that includes lights (incandescent tungsten-filament lamps or nowadays LEDs) and horns. The horn itself is a kind of electromagnetic actuator — rather interesting in that it does no more than to produce an unpleasant noise. Even with machines built half-a-century or a century ago, electromagnetic interference was an important issue in relation to telephone, telegraph, and radio transmissions, necessitating the suppression of EMI from the sparking plug and the DC generator commutator, and in some cases with vibrating-contact voltage regulators. So even in 1950 we can find a technologically sophisticated product (for its time) that is rich in examples of product design and associated effects to which — *in hindsight* — Maxwell’s equations directly apply.

Take a moment. Put your computer into ‘sleep’ mode. Close your eyes. Imagine yourself walking along a sunny country lane far from any city or railway (and still further from any airport), and try a mental exercise to imagine yourself as James Clerk Maxwell — not at the University of Cambridge or Aberdeen or Edinburgh or King’s College London or anywhere else, but in the remote countryside of Dumfriesshire — and set yourself a mental task, for example, to formulate in words any one of Maxwell’s equations, or all of them if you feel particularly energetic. If you’re in the office and your boss taps you on the shoulder and asks, ‘Why are you asleep?’ simply reply that you are formulating Maxwell’s equations and contemplating their application to the company’s products and all their electromagnetic side-effects, before returning to your day-job of trying to solve them. You are not wasting time and you are certainly not asleep.

While we were standing by the church gate, with a magnificent array of rhododendrons in flower nearby, an old Land-Rover arrived. It belonged to the caretaker of the church and its grounds, who was naturally curious about our presence there. After exchanging a few cordial words explaining the reason for our visit, we walked up to the church and he very kindly unlocked it and took us in for a brief tour. Afterwards we stood chatting by the bikes, and took a few photographs. On the caretaker’s jersey was an emblem for his garden services company, *A. J. Maxwell*. Have a look on the internet for images of James Clerk Maxwell, and read about the kindliness and friendliness and affability of that ancient family [5], and it is hard not to think about the connectedness of people and ideas over many generations. That the church and grounds are tended and cherished today is a quiet reflection on the reverence we have not only for Maxwell but for all our great thinkers.

References :

[1] https://en.wikipedia.org/wiki/Parton,_Dumfries_and_Galloway[2] This is not verified. The chapel was built in 1868, only ten years before Maxwell’s death at the age of 48. His most famous work,

*A Treatise on Electricity and Magnetism*, was published in 1873.

[3] Lowther D.A. and Freeman E.M.,

*The application of the research work of James Clerk Maxwell in electromagnetics to industrial frequency problems*, Philosophical Transactions of the Royal Society (doi:10.1098/rsta.2007.2188); one contribution of 20 to a Theme Issue ‘James Clerk Maxwell 150 years on’.

[4] Maxwell J.C.,

*A Treatise on Electricity and Magnetism*, [1873] Dover Publications N.Y., 1954 (unabridged republication of the Third Edition published by Clarendon Press, 1894).

[5] Mahon B,

*The Man Who Changed Everything, The Life of James Clerk Maxwell*, Wiley, 2003.