The Life and Science of James Clerk Maxwell
The Life and Science of James Clerk Maxwell

(1831-1879) Physicist and Mathematician

“The theory of relativity would have never been possible without the mathematical equations first described by James Maxwell."
-Albert Einstein

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James Clerk Maxwell may not be a household name when it comes to scientists, but his contributions to the field ranks him with some of the great scientists of all time.He is mainly known for his ground breaking work in electromagnetics, spurring a field that has given rise to many of the great accomplishments of the twentieth century.His equations, which relate the effects of electricity and magnetism to one another, are key in the development of modern relativity theory and the development electrical components and electronic systems.Like many great scientists, Maxwell was ahead of his time and his equations were not completely understood by his peers, but as science and mathematics progressed the beauty and genius behind his equations was fully revealed.

On June 13, 1831, James Clerk Maxwell was born in Edinburgh, Scotland.With the exception of an older sister that died at a young age, he was an only child.His father, John, was a lawyer who was in his forties by the time James was born.John was considered to be an intelligent, but somewhat eccentric man.When James was young, his mother, Frances Cay, died after a prolonged illness (believed now to be cancer).After his mother’s passing, James was raised by his father and his aunt, Jane Cay and lived on his family’s estate, Glenair in Edinburgh. (Tolstoy 1981 10-12)

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Even at an early age, James showed a fascination with the world around him and an amazing memory.At the age of two, he had already begun to investigate mirrors and their effect on sunlight.At the age of eight, James could recite the 119th Psalm. One of James's favorite mischievous things to do as a child was to row a washtub in the family duck pond. The humorous 1841 drawing on the left is by a cousin of James and shows him rowing out of the reach of one of his tutors, who is trying to catch him with a rake (Campbell 1882 13-20).

Despite the active presence of his father and kind nurturing of his aunt, James’s childhood wasn't always happy.Like mainly children in the Victorian era, James’s tutors often used physical violence such as hitting him in the head with a ruler and pulling his ears until the bled to discipline him. It took some time before his father and aunt became aware of the problem, but once they did James's father decided to enroll his son in Edinburgh Academy.When James began to attend school there, his classmates tormented him relentlessly.He was often picked on because of his stuttering problems and was given the nickname “Dafty” for his eccentric personality (Tolstoy 1981 19-23).

As James became older, he began to take a more involved interest in science and mathematics.He was especially interested in geometry and published his first work on ellipses at the age of fourteen.At about that time, he began to regularly attend meetings of the Royal Society in Edinburgh with his father. When James was sixteen, he graduated from Edinburgh Academy and enrolled at University of Edinburgh in the fall of 1847.He studied there for three years and did some interesting work, expanding on geometrical theories and papers he had begun earlier while at Edinburgh Academy.He also published some works that expanded upon some of the mathematical principals developed by G. G. Stokes, including The Equilibrium of Elastic Solids, which was published in 1850 (Tolstoy 1981 38-49).

After three years at the University of Edinburgh, Maxwell enrolled at Cambridge University, considered to be the top university academically, especially in math, at the time.While at Cambridge, Maxwell worked at such a pace that he fell ill with “brain fever” and was bedridden, unable to even sit up in bed.He recovered about a month later with “a new perception of the Love of God” (Campbell 1882 92-94).

Even though Maxwell is best known for his works in electromagnetism, he also did research in other areas while at Cambridge.One of the main areas of research for many Scottish scientists at the time was in the area of color and color wheels.Specifically, Maxwell was interested in the classification of colors and colorblindness.His research in the field of colorblindness help verify Thomas Young’s theory that color blindness is caused by one of three “absent sensations” in the retina.Maxwell also came up with his own color classification system, which for anyone who looks at the controls on a TV or computer monitor will look familiar.He denoted colors in terms of four variables, its hue, intensity, brightness, and tint (Harman 1998 37-48).

Maxwell also did some work in astronomy while at Cambridge and published On the Stability of the Motion of Saturn’s Rings in 1870.In this work, Maxwell examines the motion of the rings of Saturn through mathematical analysis using potential theory, Taylor’s theorem, and Fourier analysis.The paper is the first work to correctly state the rings of Saturn must be made up of particles.Maxwell accomplishes this by proving mathematically that a solid ring could not rotate around Saturn permanently and the rotation would break up the ring.The model developed by Maxwell instead shows a ring of particles that is stable in its rotation (Harman 1998 48-57).

After graduating from Cambridge, Maxwell taught at Aberdeen University. He was remembered as a pretty odd professor at the college, he would often fall asleep and then suddenly awaken during class. He was also not very good at teaching down to most of the students who couldn't keep up with his lectures. While at Aberdeen, Maxwell married the daughter of the head of the college, Katherine Mary Dewar. His wife was supportive of his scientific endeavors and often helped him in his laboratories when necessary (Tricker 1966 96).

In addition to his scientific writing, James Maxwell also wrote some rather unique poetry. What made his poetry so interesting is that they described scientific processes and mathematical equations (in rhyme no less!). Below is a stanza from A Problem in Dynamics (1857) and is a humorous reflection of Maxwell's somewhat eccentric, science-driven personality (Campbell 1882 329).

An inextensible heavy chain
Lies in a smooth horizontal plane,
An impulsive force is applied at A,
Required the initial motion of K.
Let ds be the infinitesimal link,
Of which for the present we've only to think;
Let T be the tension and T + dT
The same for the end that is nearest to B.
Let a be put, by a common convention,
For the angle at M 'twixt OX and the tension...

Maxwell’s most famous work however, is his Treatise on Electricity and Magnetism.This work contains all of the basic equations still used in electromagnetic studies.In the simplest of terms, the work develops the idea that magnetic field produce electric current and electric current produces magnetic fields and describes the mathematical relationship between the two. Previously, electric and magnetic fields had been thought to be separate, but Maxwell showed that there is not only a relationship between the two, but also theorized that white light (the nature of which had been quite puzzling to scientists at the time) is made up of electromagnetic waves. He made this deduction after observing that electromagnetic waves traveled at the speed of light (Harman 1998 162-174).

Just as Calculus was developed in part by Newton to describe the Physics he developed, many of Maxwell’s works made significant contributions to the field of mathematics.The equation he developed to relate the magnetic field produced by an electric current, which is a vector with components containing the derivative of the function with respect to each direction, is known as the delta operator (or del).Maxwell’s work also made some important contributions to field mathematics which in addition to being used for Physics, is also used mathematically in areas such as meteorology (Tricker 1966 108-121).

Perhaps the most significant use of Maxwell’s equations that affects us today is the implementation of his equations in electronics and electric circuits.From computers, to televisions, to microwaves, and many more are all made up of components built upon his equations.The two basic components that are made possible by these equations are the inductor and the capacitor.The inductor uses the equation relating a changing current to a magnetic field to resist changes in current.The capacitor uses Maxwell’s work on dielectric materials to resist a change in voltage.

The one name that James Maxwell is often associated with is Michael Faraday, Maxwell's predecessor in the study of electromagnetics. Although they worked in the same field, they didn't have many similarities beyond that. Faraday was a generation older than Maxwell. In fact, Faraday's initial discovery of magnetic induction came at almost exactly the same time as Maxwell's birth. But the differences didn't stop there, Maxwell grew in a privileged family and attended the best schools, Faraday grew up poor and didn't have the educational background of Maxwell. Maxwell emphasized mathematical analysis in his research, Faraday relied on lab experiments and observation. Throughout their respective careers, Faraday and Maxwell remained cordial on a personal level, but had some heated exchanges about various theories in their field. A letter Maxwell wrote to Faraday asking for a letter of recommendation is polite and personal, but when writing about scientific theories, Maxwell is all business. He begins one letter to Faraday with "Dear Sir- If a sphere were set in rotation about any diameter, it would continue to revolve about that diameter forever." (Campbell 1882 337)

The differences in Maxwell and Faraday's scientific process represented an emerging change in Physics during the nineteenth century. As the science being studied became more complex, an increasing need for mathematics for scientists appeared. Complex, changing magnetic fields cannot be described simply using diagrams and words; high level mathematics is needed. This is perhaps the area where Maxwell stands out among scientists of the time, he was one of the first to attempt to describe phenomena such as the relationship between electric current and magnetic fields. These contributions were extremely important because they allowed scientists to take the step from observing some neat things you can do in the lab to the development of methods that can be used to predict these occurrences with such accuracy that they can be adapted to create all of the great electric devices that we often take for granted today.

Late in life, Maxwell retreated back to his estate at Glenair, a place for which he had great fondness. His health declined throughout most of the 1870's until he died on November 5th, 1879 (Tricker 1966 99). Even at the end of his life, Maxwell remained sharp mentally. In his final days, he remained upbeat and calm, even though he was probably in great pain (Campbell 1886 197-204). It was only nine years after his death the Heinrich Hertz proved electromagnetic waves can travel through space, exactly as Maxwell had predicted mathematically years earlier (Tolstoy 1981 127).

In the end, Maxwell’s equations are still regarded as one of the greatest mathematical accomplishments in the history of science.Only a handful of scientists can claim to have had nearly as much an impact on the development of science and technology as he has.Even though he is not exactly a household name like Einstein or Newton, most certainly consider him one of the greatest scientists of the nineteenth century, if not all time.

Links to On-Line Resources

There isn't as much information about James Maxwell available on line and some other scientists, and most of the resources available on-line only provide brief descriptions of Maxwell's life and achievements. While they do provide a good introduction, they usually are not much more than the equivalent of a short encyclopedia article describing basic facts and accomplishments. Maxwell's family estate, Glenair, has its own web page and has some interesting pictures of what the estate looks like today (sadly it has deteriorated quite a bit since Maxwell's time). There is one resource on-line that is very valuable and that is a free copy (in PDF format) of a transcription of the rare 1882 book The Life of James Maxwell, which provides a very detailed look at Maxwell's life and scientific works.

The Life of James Maxwell is available at: http://www.sonnetusa.com/maxbio/index.htm
The Glenair homepage: http://www.soft.net.uk/glenlair/

Some more web pages on James Maxwell:

- University of St. Andrews: http://www-groups.dcs.standrews.ac.uk/~history/
Mathematicians/Maxwell.html

- Web4Study Biography: http://www.web4study.com/biographies/scientists/MaxwellJames.htm

- University of South Dakota: http://www.usd.edu/phys/courses/phys300/gallery/clark/maxwell.html - The James Clerk Maxwell Foundation: http://www.rpi.edu/~rosss2/maxwell1.html

- University of Zagreb: http://www.phy.hr/~dpaar/fizicari/xmaxwell.html

- Encyclopaedia Britannica: http://www.britannica.com/eb/article?eu=114888

Bibliography

Campbell, Lewis and William Garnett. The Life of James Clerk Maxwell. London: Macmillian and Co. 1882.

Fishbane, Paul, Stephen Gasiorowicz, and Stephen Thornton.Physics for Scientists and Engineers: Second Edition.
Upper River Saddle, New Jersey: Prentice Hall.1996.

Harman, Peter M.The Natural Philosophy of James Clerk Maxwell.Cambridge:Cambridge University Press, 1998.

Maxwell, James Clerk.A Treatise on Electricity and Magnetism.Two volumes, 1873.

Tolstoy, Ivan.James Clerk Maxwell: A Biography.Chicago:University of Chicago Press, 1981.

Tricker, R.A.R.The Contributions of Faraday & Maxwell to Electrical Science. London: Pergamon, 1966.