Jun 132017

Today is the birthday (1831) of James Clerk Maxwell FRS FRSE, a Scottish mathematical physicist whose most notable achievement was to formulate the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism, and light as manifestations of the same phenomenon. Maxwell’s equations for electromagnetism have been called the “second great unification in physics” after the first one realized by Isaac Newton. When most people think of the masterminds of physics they think of Einstein and Newton, but rarely conjure up Maxwell. Yet his accomplishment was of the same magnitude as theirs. Furthermore, his work led directly to the technological accomplishments of the late 19th and 20th centuries including the generation of electricity, leading in turn to electric lighting, the alternator in the internal combustion engine, digital computing, and on and on . . . Unification of forces is a BIG DEAL, not just theoretically, but in practical terms.

With the publication of “A Dynamical Theory of the Electromagnetic Field” in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. Maxwell proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. The unification of light and electrical phenomena led to the prediction of the existence of radio waves, which, of course led to the development of radio and television.

I’ll try not to make your eyes glaze over with Maxwell’s equations, but I would like to venture some attempt at the magnitude of his work. First, a little biographical stuff. His genius was immediately obvious to all he encountered rivalled only by his insatiable curiosity. Maxwell was born at 14 India Street, Edinburgh, to John Clerk Maxwell of Middlebie, an advocate, and Frances Cay. His father was a man of comfortable means of the Clerk family of Penicuik, holders of the baronetcy of Clerk of Penicuik. His father’s brother was the 6th Baronet. Maxwell’s parents met and married when they were well into their 30s, and his mother was nearly 40 when he was born. They had had one earlier child, a daughter named Elizabeth, who died in infancy.

When Maxwell was young his family moved to Glenlair House, which his parents had built on the 1,500 acres (610 ha) Middlebie estate. All indications are that Maxwell had an unquenchable curiosity from an early age. By the age of three, everything that moved, shone, or made a noise drew the question: “what’s the go o’ that?” In a passage added to a letter from his father to his sister-in-law Jane Cay in 1834, his mother described this innate sense of inquisitiveness:

He is a very happy man, and has improved much since the weather got moderate; he has great work with doors, locks, keys, etc., and “show me how it doos” is never out of his mouth. He also investigates the hidden course of streams and bell-wires, the way the water gets from the pond through the wall….

Maxwell was taught by his mother, as was the norm in Victorian Scotland until the age of 8 when she died of cancer. He was then taught briefly by a 16-year-old tutor hired by his father. Little is known about the young man except that he treated Maxwell harshly, chiding him for being slow and wayward. Consequently his father dismissed him and sent his son to prestigious Edinburgh Academy. The 10-year-old Maxwell with rural mannerisms and Galloway accent did not fit in well and the other students called him “Daftie,” which biographers usually say he tolerated without complaint. But a classmate wrote that one time when he was being teased by a group of boys he turned on them with a look of demonic ferocity, and after that they left him in peace.

Maxwell was brilliant at geometry at an early age. He rediscovered the regular polyhedra, for example, before he received any formal instruction. His academic prowess remained unnoticed until, at the age of 13, he won the school’s mathematical medal and first prize for both English and poetry. Maxwell’s interests ranged far beyond the school syllabus and he did not pay particular attention to examination performance. He wrote his first scientific paper at the age of 14. In it he described a mechanical means of drawing mathematical curves with a piece of twine, and the properties of ellipses, Cartesian ovals, and related curves with more than two foci. His work “Oval Curves” was presented to the Royal Society of Edinburgh by James Forbes, a professor of natural philosophy at Edinburgh University, but Maxwell was deemed too young to present the work himself. The work was not entirely original, since René Descartes had also examined the properties of such multifocal ellipses in the 17th century, but he had simplified their construction.

Maxwell left the Academy in 1847 at age 16 and began attending classes at the University of Edinburgh. He had the opportunity to attend the University of Cambridge, but decided, after his first term, to complete the full course of his undergraduate studies at Edinburgh. He did not find his classes at Edinburgh University very demanding, and was therefore able to immerse himself in private study during free time at the university and particularly when back home at Glenlair where he experimented with improvised chemical, electric, and magnetic apparatus, but his chief concerns regarded the properties of polarized light. He constructed shaped blocks of gelatine, subjected them to various stresses, and with a pair of polarizing prisms, given to him by William Nicol, viewed the colored fringes that had developed within the jelly. Through this practice he discovered photoelasticity, which is a means of determining the stress distribution within physical structures, which eventually he used to analyze the load bearing properties of metal bridge structures.

At age 18, Maxwell contributed two papers for the Transactions of the Royal Society of Edinburgh. One of these, “On the Equilibrium of Elastic Solids”, laid the foundation for an important discovery later in his life, which was the temporary double refraction produced in viscous liquids by shear stress. His other paper was “Rolling Curves” and, just as with the paper “Oval Curves” that he had written at the Edinburgh Academy, he was again considered too young to stand at the rostrum to present it himself. The paper was delivered to the Royal Society by his tutor Kelland instead.

In October 1850, already an accomplished mathematician, Maxwell left Scotland for the University of Cambridge. He initially attended Peterhouse, but before the end of his first term transferred to Trinity, where he believed it would be easier to obtain a fellowship. In November 1851, Maxwell studied under William Hopkins, whose success in nurturing mathematical genius had earned him the nickname of “senior wrangler-maker” (“senior wrangler” is the top undergraduate in mathematics in final examinations). In 1854, Maxwell graduated from Trinity with a degree in mathematics. He scored second highest in finals, coming behind Edward Routh and earning the title of second wrangler. He was later declared equal with Routh in the more exacting ordeal of the Smith’s Prize examination. Immediately after earning his degree, Maxwell read his paper “On the Transformation of Surfaces by Bending” to the Cambridge Philosophical Society. This is one of the few purely mathematical papers he had written, demonstrating Maxwell’s growing stature as a mathematician. He decided to remain at Trinity after graduating and applied for a fellowship, which was a process that he expected to take a couple of years.

Maxwell was made a fellow of Trinity on 10 October 1855, sooner than was the norm, and was asked to prepare lectures on hydrostatics and optics and to set examination papers. The following February he was urged by a colleague to apply for the newly vacant Chair of Natural Philosophy at Marischal College in Aberdeen. His father assisted him in the task of preparing the necessary references, but died on 2 April at Glenlair before either knew the result of Maxwell’s candidacy. Maxwell accepted the professorship at Aberdeen, leaving Cambridge in November 1856. From there he went from success to success in Edinburgh, Cambridge, and London.  Let’s turn now to his achievements.

Maxwell is best remembered for his equations which unified light, electricity, and magnetism into a single phenomenon with varied dimensions. Let me pause and take stock of that idea in the most general terms. The ultimate goal of mathematical physics is to SIMPLIFY the way we look at the world by reducing complex observations to simple rules.  Newton was a towering giant in this respect. He showed that force and motion could be reduced to some basic equations, whether you’re talking about firing a cannon, piloting a ship, or falling from a tall building. F = ma (force equals mass times acceleration) has stood the test of time. As physics has evolved since Newton, more and more forces have been unified into a grand theory.  Electro-magnetic forces, and forces within the atom have already been unified, and it looks as though gravity is within reach with the recent discovery of gravitational waves. Then we will have the “theory of everything” which is a slightly grandiose way of saying that all forces in the universe will be subsumed under one umbrella. Maxwell was a monumentally important figure along that path – every bit as important as Newton and Einstein.

Maxwell had studied and commented on electricity and magnetism as early as 1855 when his paper “On Faraday’s lines of force” was read to the Cambridge Philosophical Society. The paper presented a simplified model of Faraday’s work and how electricity and magnetism are related. He reduced all of the current knowledge into a linked set of differential equations with 20 equations in 20 variables. This work was later published as “On Physical Lines of Force” in March 1861. Maxwell’s equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. They underpin all electric, optical and radio technologies, including power generation, electric motors, wireless communication, cameras, televisions, computers etc. Maxwell’s equations describe how electric and magnetic fields are generated by charges, currents, and changes of each other. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to gamma-rays and everything in between: red, orange, yellow, microwaves, X-rays, intra-red, etc. That’s a lot of stuff.

Within his lifetime other physicists showed that his 20 equations could be boiled down to 4 (see lead photo) which is conventionally how they are perceived nowadays.

Following Newton, Maxwell was  interested in the physics of color but also color perception. From 1855 to 1872, he published at intervals a series of investigations concerning the perception of color, color-blindness, and color theory, and was awarded the Rumford Medal for “On the Theory of Colour Vision.”

Maxwell was also interested in applying his theory of color perception color photography stemming directly from his psychological work on color perception. He argued that if a sum of any three lights could reproduce any perceivable color, then color photographs could be produced with a set of three colored filters. In the course of his 1855 paper, Maxwell proposed that, if three black-and-white photographs of a scene were taken through red, green and blue filters and transparent prints of the images were projected on to a screen using three projectors equipped with similar filters, when superimposed on the screen the result would be perceived by the human eye as a complete reproduction of all the colors in the scene. During an 1861 Royal Institution lecture on color theory, Maxwell presented the world’s first demonstration of color photography by this principle of three-color analysis and synthesis. Thomas Sutton, inventor of the single-lens reflex camera, took the picture. He photographed a tartan ribbon three times, through red, green, and blue filters, also making a fourth photograph through a yellow filter, which, according to Maxwell’s account, was not used in the demonstration. Because Sutton’s photographic plates were insensitive to red and barely sensitive to green, the results of this pioneering experiment were far from perfect.

Maxwell also investigated the kinetic theory of gases. Originating with Daniel Bernoulli, this theory was advanced by the successive work of John Herapath, John James Waterston, James Joule, and particularly Rudolf Clausius, to such an extent as to put its general accuracy beyond a doubt; but it received enormous development from Maxwell, who in this field appeared as an experimenter (on the laws of gaseous friction) as well as a mathematician. Between 1859 and 1866, he developed the theory of the distributions of velocities in particles of a gas, work later generalized by Ludwig Boltzmann. The formula, called the Maxwell–Boltzmann distribution, gives the fraction of gas molecules moving at a specified velocity at any given temperature. In the kinetic theory, temperatures and heat involve only molecular movement. This approach generalized the previously established laws of thermodynamics and explained existing observations and experiments in a better way than had been achieved previously.

Maxwell’s work on thermodynamics led him to devise the thought experiment that came to be known as Maxwell’s demon, where the second law of thermodynamics (law of entropy) is violated by an imaginary being capable of sorting particles by energy. This thought experiment, as has been demonstrated multiple times, is fatally flawed. Observing the particles and opening the door require more energy than is gained by the sorting of the particles.

Maxwell published a paper “On governors” in the Proceedings of Royal Society, vol. 16 (1867–1868). This paper is considered a central paper in the early days of control theory. In this context “governors” refers to the centrifugal governor used to regulate steam engines. A lithograph of Maxwell’s governor hung in the Woodward Governor factory on Slough Trading Estate where I got my first job as an inventory clerk in the stock room as a teenager.

Maxwell’s insatiable curiosity led him to inquire into all manner of subjects including the density of the earth and the composition of water. He was also able to prove that the rings of Saturn were composed of solid particles.

Maxwell died in Cambridge of abdominal cancer on 5 November 1879 at the age of 48. His mother had died at the same age of the same type of cancer. The minister who regularly visited him in his last weeks – he was an ardent Presbyterian – was astonished at his lucidity and the immense power and scope of his memory, and commented,

His illness drew out the whole heart and soul and spirit of the man: his firm and undoubting faith in the Incarnation and all its results; in the full sufficiency of the Atonement; in the work of the Holy Spirit. He had gauged and fathomed all the schemes and systems of philosophy, and had found them utterly empty and unsatisfying — “unworkable” was his own word about them — and he turned with simple faith to the Gospel of the Saviour.

As death approached Maxwell told a Cambridge colleague

I have been thinking how very gently I have always been dealt with. I have never had a violent shove all my life. The only desire which I can have is like David to serve my own generation by the will of God, and then fall asleep.

Maxwell is buried at Parton Kirk beside his parents, near Castle Douglas in Galloway close to where he grew up.

Here’s a Scottish variation on a theme from Galloway.  It’s called Scotch Broth but is not the traditional mutton and barley soup. It’s a chicken, barley, and vegetable soup served with oatmeal dumplings.  The old, traditional recipe calls for boiling the dumpling in a cloth in the soup for an hour, but more modern cooks make small dumplings and cook them directly in the soup.  The original recipe calls for an old boiling hen, but you can use a young chicken. I usually do.

Galloway Scotch Broth with Oatmeal Dumplings



1 3-4 lb chicken (or boiling fowl)
4 oz (115g) barley
8 oz (225g) split peas
1 oz (30g) whole peas
2 leeks, chopped
3 carrots, chopped
1 turnip, chopped
4 brussels sprouts
2 small blades kale, chopped
fresh parsley
chicken stock (optional)


2 oz (60g) beef dripping (or lard)
1 onion, finely chopped
½ lb (250g) fine oatmeal.
salt and pepper.


Put 7 pints (3.6 L) of water (or chicken stock if you prefer) in a large stock pot.  Bring to the boil, then add salt to taste and all the soup ingredients. Simmer gently for about 2 hours (more if using a fowl). Make sure the barley is cooked through.

Meanwhile prepare the dumplings. Make a stiff dough by placing the dumpling ingredients in a bowl, mixing them, then adding cold water a little at a time until it all comes together but is not wet. Roll out dumplings about 1” in diameter and set aside.

Remove the chicken from the soup. Add the dumplings and continue to cook for about 30 minutes. Strip as much chicken meat from the bones as you wish, and add it back to the soup for a few minutes to heat through before serving. Reserve the rest of the chicken meat for other uses.

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