James Clerk Maxwell

James Clerk Maxwell
James Clerk Maxwell
Born	13 June 1831 Edinburgh, Scotland, United Kingdom
Died	5 November 1879 Cambridge, England
Nationality	Scottish
Alma mater	University of Edinburgh, University of Cambridge
Known for	Maxwell's Equations The Maxwell Distribution Maxwell's Demon
Awards	Rumford Medal Adams Prize
Scientific career
Fields	Mathematics, Science
Doctoral advisor	William Hopkins

James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. His most significant achievement was aggregating a set of equations in electricity, magnetism and inductance — Maxwell's equations — including an important modification of Ampère's circuital law. It was the most unified model of electromagnetism yet. It is famous for introducing to the physics community a detailed model of light as an electromagnetic phenomenon, building upon the earlier hypothesis advanced by Michael Faraday.

He also developed the Maxwell distribution, a statistical means to describe aspects of the kinetic theory of gases. These two discoveries helped usher in the era of modern physics, laying the foundation for future work in such fields as special relativity and quantum mechanics. He is also known for creating the first true colour photograph in 1861.

Maxwell demonstrated that electric and magnetic fields travel through space, in the form of waves, and at the constant speed of light. Finally, in 1861 Maxwell wrote a four-part publication in the Philosophical Magazine called On Physical Lines of Force where he first proposed that light was in fact undulations in the same medium that is the cause of electric and magnetic phenomena.

Maxwell is considered by many physicists to be the scientist of the nineteenth century most influential on twentieth century physics. His contributions to the science are considered by many to be of the same magnitude as those of Isaac Newton and Albert Einstein. In 1931, on the centennial of Maxwell's birthday, Einstein himself described Maxwell's work as the "most profound and the most fruitful that physics has experienced since the time of Newton."

Biography

Early life and education

James Clerk Maxwell was born on 13 June 1831 at 14 India Street, Edinburgh, to John Clerk Maxwell, an advocate, and Frances Maxwell (née Cay). Maxwell's father was a man of comfortable means, related to the Clerk family of Penicuik, Midlothian, holders of the baronetcy of Clerk of Penicuik; his brother being the 6th Baronet. He had been born John Clerk, adding the surname Maxwell to his own after he inherited a country estate in Middlebie, Kirkcudbrightshire from connections to the Maxwell family, themselves members of the peerage. Maxwell's parents did not meet and marry until they were well into thirties, unusual for the times, and Frances Maxwell was nearly 40 when James was born. They had had one earlier child, a daughter, Elizabeth, who had died in infancy. They named their only surviving child James, a name that had sufficed not only for his grandfather, but by many of his ancestors.

The family moved when Maxwell was young to "Glenlair", a house his parents had built on the 1500-acre (6.1 km²) Middlebie estate. All indications suggest that Maxwell had maintained 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 letter to his sister-in-law Jane Cay in 1834, his father 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...

Recognizing the potential of the young boy, his mother Frances took responsibility for James' early education, which in Victorian era was largely the job of the woman of the house. She was however taken ill with abdominal cancer, and after an unsuccessful operation, died in December 1839 when Maxwell was only eight. James' education was then overseen by John Maxwell and his sister-in-law Jane, both of whom played pivotal roles in the life of Maxwell. His formal schooling began unsuccessfully under the guidance of a sixteen-year old hired tutor. Little is known about the young man John Maxwell hired to instruct his son, except that he treated the younger boy harshly, chiding him for being slow and wayward. John Maxwell dismissed the tutor in November 1841, and after considerable thought, sent James to the prestigious Edinburgh Academy. He lodged during term times at the house of his aunt Isabella; while there his passion for drawing was encouraged by his older cousin Jemima, herself a talented artist.

Edinburgh Academy, where Maxwell was schooled

The ten-year old Maxwell, raised in isolation on his father's countryside estate, did not fit in well at school. The first year had been full, obliging him to join the second year with classmates a year his senior. His mannerisms and Galloway accent struck the other boys as rustic, and arriving on his first day at school wearing home-made shoes and tunic earned him the unkind nickname of "Daftie". Maxwell, however, never seemed to have resented the epithet, bearing it without complaint for many years. Any social isolation at the Academy however ended when he met Lewis Campbell and Peter Guthrie Tait, two boys of a similar age, and themselves to become notable scholars. They would remain lifetime friends.

Maxwell was fascinated by geometry at an early age, rediscovering the regular polyhedra before any formal instruction. Much of his talent went unnoticed however, and, despite winning the school's scripture biography prize in his second year, his academic work remained unremarkable, until, at the age of 13, he won the school's mathematical medal, and first prizes for English and poetry.

For his first scientific work, at the age of only 14, Maxwell wrote a paper describing a mechanical means of drawing mathematical curves with a piece of twine, and the properties of ellipses and curves with more than two foci. His work, Oval Curves, was presented to the Royal Society of Edinburgh by James Forbes, professor of natural philosophy at Edinburgh University, Maxwell deemed too young for the task. The work was not entirely original, Descartes having examined the properties of such multifocal curves in the seventeenth century, though Maxwell had simplified their construction.

Middle years

A young Maxwell at Trinity College, Cambridge. He is holding the colour wheel which he invented.

Maxwell left the Academy in 1847 at the age of 16 and began attending classes at the University of Edinburgh. Having the opportunity to attend Cambridge after his first term, Maxwell decided instead to complete the full three terms of his undergraduate studies at Edinburgh. The main reason for this was that Cambridge was too far from home, and would present him with the opportunity to see his father only twice a year. Another reason was Maxwell's concern for his future. He wanted to become a scientist, but jobs in science were rare at this time, and it would have been much more difficult to obtain a lecturing post at a university as prestigious as Cambridge.

Maxwell did not find his classes at Edinburgh especially demanding, and was able to immerse himself in private study during free time at the university, and particularly when back home at Glenlair. There he would experiment with improvised chemical and electromagnetic apparatus, but his chief preoccupation was the properties of polarised light. He constructed shaped blocks of gelatine, subjecting them to various stresses, and with a pair of polarising prisms gifted him by the famous scientist William Nichol, would view the coloured fringes developed within the jelly. Maxwell had discovered photoelasticity, a means of determining the stress distribution within physical structures.

Edinburgh University academic staff included some highly regarded names, and Maxwell's first year tutors included Sir William Hamilton, who lectured on logic and metaphysics, Philip Kelland on mathematics, and James Forbes on natural philosophy.

In his eighteenth year Maxwell contributed two papers for the Transactions of the Royal Society of Edinburgh—one of which, On the Equilibrium of Elastic Solids, laid the foundation for an important discovery of his later life: the temporary double refraction produced in viscous liquids by shear stress. The other was titled Rolling Curves; as with his schoolboy paper Oval Curves, Maxwell was considered too young to stand at the rostrum and present it himself, and it was delivered to the Royal Society by his tutor Kelland.

In October 1850, already an accomplished mathematician, Maxwell left Scotland for Cambridge University. He initially attended Peterhouse, but before the end of his first term transferred to Trinity College, where he believed it would be easier to obtain a fellowship. At Trinity, he was elected to the secret society known as the Cambridge Apostles. In November 1851, Maxwell studied under William Hopkins, whose success in nurturing mathematical genius had earned him the nickname of "senior wrangler-maker". A considerable part of Maxwell's translation of his electromagnetism equations was accomplished during Maxwell's career as an undergraduate in Trinity.

In 1854, Maxwell graduated from Trinity with a degree in mathematics. He scored second-highest in the final examination behind Edward Routh, thereby earning himself the title of Second Wrangler, but was declared equal with the Senior Wrangler Routh in the more exacting ordeal of the Smith's Prize examination. Immediately after taking his degree, Maxwell read to the Cambridge Philosophical Society a novel memoir, On the Transformation of Surfaces by Bending. This is one of the few purely mathematical papers he published, and it exhibited at once the full genius of its author. About the same time, his elaborate memoir, On Faraday's Lines of Force appeared, in which he gave the first indication of some of the electrical investigations which culminated in the greatest work of his life.

Maxwell married Katherine Mary Dewar at the age of 27. They remained devotedly in love with each other for the duration of their shared lives, but would have no children.

Later years

In 1865, Maxwell moved to Glenlair, which he had inherited from his father. In 1865, he resigned his Chair of Physics and Astronomy at King's College, London. There was a rumour that he might resign because of pressure from King's College. However, his years in Glenlair (1865-1871), before he went to Cambridge University, ended up quite productively.

James and Katherine Maxwell, 1869.

Maxwell also made contributions to the area of optics and color vision, being credited with the discovery that colour photographs could be formed using red, green, and blue filters. He had the photographer Thomas Sutton photograph a tartan ribbon three times, each time with a different colour filter over the lens. The three images were developed and then projected onto a screen with three different projectors, each equipped with the same colour filter used to take its image. When brought into focus, the three images formed a full colour image. The three photographic plates now reside in a small museum at 14 India Street, Edinburgh, the house where Maxwell was born.

Maxwell's work on colour blindness won him the Rumford Medal by the Royal Society of London. He wrote an admirable textbook of the Theory of Heat (1871), and an excellent elementary treatise on Matter and Motion (1876). Maxwell was also the first to make explicit use of dimensional analysis, also in 1871.

In 1871, he was the first Cavendish Professor of Physics at Cambridge. Maxwell was put in charge of the development of the Cavendish Laboratory. He supervised every step of the progress of the building and of the purchase of the very valuable collection of apparatus paid for by its generous founder, the 7th Duke of Devonshire (chancellor of the university, and one of its most distinguished alumni). One of Maxwell's last great contributions to science was the editing (with copious original notes) of the electrical researches of Henry Cavendish, from which it appeared that Cavendish researched such questions as the mean density of the earth and the composition of water, among other things.

The extended biography The Life of James Clerk Maxwell, by his former schoolfellow and lifelong friend Professor Lewis Campbell, was published in 1882 and his collected works, including the series of articles on the properties of matter, such as Atom, Attraction, Capillary Action, Diffusion, Ether, etc., were issued in two volumes by the Cambridge University Press in 1890.

He died in Cambridge of abdominal cancer at the age of 48. He had been a devout Christian his entire life. Maxwell is buried at Parton Kirk, near Castle Douglas in Galloway, Scotland.

Personality

From the start of his childhood, religion touched all aspects of Maxwell's life. Both his father and mother were devout churchgoers (Presbyterian and Episcopalian) and instilled a strong faith in their son. All information available suggests that neither in his adolescence, nor in his later years, did Maxwell ever reject the fundamental principles of his Christian faith. Ivan Tolstoy, author of one of Maxwell's biographies, remarked at the frequency with which scientists writing short biographies on Maxwell often omit the subject of his religion.

As a great lover of British poetry, Maxwell memorized poems and wrote his own. The best known is Rigid Body Sings closely based on Comin' Through the Rye by Robert Burns, which he apparently used to sing while accompanying himself on a guitar. It has the immortal opening lines[1]:

Gin a body meet a body

Flyin' through the air.

Gin a body hit a body,

Will it fly? And where?

A collection of his poems was published by his friend Lewis Campbell in 1882.

Physics

Colour analysis

The first permanent colour photograph, taken by James Clerk Maxwell in 1861.

From 1855 to 1872, he published at intervals a series of valuable investigations connected with the Perception of Colour and Colour-Blindness, for the earlier of which he received the Rumford medal from the Royal Society in 1860. The instruments which he devised for these investigations were simple and convenient in use. For example, Maxwell's discs were used to compare a variable mixture of three primary colours with a sample colour by observing the spinning "colour top." In 1856, Maxwell was appointed to the chair of Natural Philosophy in Marischal College, Aberdeen, which he held until the fusion of Aberdeen's two colleges in 1860.

In 1859, he won the Adams Prize in Cambridge for an original essay, On the Stability of Saturn's Rings, in which he concluded the rings could not be completely solid or fluid. Maxwell demonstrated stability could ensue only if the rings consisted of numerous small solid particles, which he called "brickbats". He also mathematically disproved the nebular hypothesis (which stated that the solar system formed through the progressive condensation of a purely gaseous nebula), forcing the theory to account for additional portions of small solid particles.

In 1860 he became a professor at King's College London. In 1861, Maxwell was elected to the Royal Society. He researched elastic solids and pure geometry during this time.

Kinetic theory

Main article: Maxwell-Boltzmann distribution

One of Maxwell's greatest investigations was on the kinetic theory of gases. Originating with Daniel Bernoulli, this theory was advanced by the successive labours 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.

In 1866, he formulated statistically, independently of Ludwig Boltzmann, the Maxwell-Boltzmann kinetic theory of gases. His formula, called the Maxwell 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.

Electromagnetism

Main article: Maxwell's Equations

A postcard from Maxwell to Peter Tait.

The greatest work of Maxwell's life was devoted to electricity. Maxwell's most important contribution was the extension and mathematical formulation of earlier work on electricity and magnetism by Michael Faraday, André-Marie Ampère, and others into a linked set of differential equations (originally, 20 equations in 20 variables, later re-expressed in quaternion- and vector-based notations). These equations, which are now collectively known as Maxwell's equations (or occasionally, "Maxwell's Wonderful Equations"), were first presented to the Royal Society in 1864, and together describe the behaviour and relation between electric and magnetic fields, as well as their interactions with matter.

Maxwell showed that the equations predict the existence of waves of oscillating electric and magnetic fields that travel through empty space at a speed that could be predicted from simple electrical experiments; using the data available at the time, Maxwell obtained a velocity of 310,740,000 m/s. In his 1864 paper A Dynamical Theory of the Electromagnetic Field, Maxwell wrote,

The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.

Maxwell was proven correct, and his quantitative connection between light and electromagnetism is considered one of the great triumphs of 19th century physics.

At that time, Maxwell believed that the propagation of light required a medium for the waves, dubbed the luminiferous aether. Over time, the existence of such a medium, permeating all space and yet apparently undetectable by mechanical means, proved more and more difficult to reconcile with experiments such as the Michelson-Morley experiment. Moreover, it seemed to require an absolute frame of reference in which the equations were valid, with the distasteful result that the equations changed form for a moving observer. These difficulties inspired Albert Einstein to formulate the theory of special relativity, and in the process Einstein dispensed with the requirement of a luminiferous aether.

Mathematics

Control theory

Maxwell published a famous paper "On governors" in the Proceedings of Royal Society, vol. 16 (1867-1868). This paper is quite frequently considered a classical paper of the early days of control theory. Here governors refer to the governor (device) or the centrifugal governor used in steam engines.

Legacy

Maxwell was ranked 24th on Michael H. Hart's list of the most influential figures in history and 89th on the BBC poll of the 100 Greatest Britons. His name is honoured in a number of ways:

• The maxwell (Mw), a compound derived CGS unit measuring magnetic flux.
• Maxwell Montes, a mountain range on Venus, one of only three features on the planet that are not given female names.
• The James Clerk Maxwell Telescope, the largest submillimetre-wavelength astronomical telescope in the world, with a diameter of 15 metres.
• The 1977 James Clerk Maxwell building of the University of Edinburgh, housing the schools of mathematics, physics, computer science and meteorology.
• The James Clerk Maxwell building at the Waterloo campus of King's College London, in commemoration of him being Professor of Natural Philosophy at King's from 1860 to 1865. The university also has a chair in Physics named after him, and a society for undergraduate physicists.
• The £4 million James Clerk Maxwell Centre of the Edinburgh Academy was opened in 2006 to mark his 175th anniversary.
• James Clerk Maxwell Road in Cambridge, which runs beside the Cavendish Laboratory.
• The University of Salford's main building was named after him.
• Maxwell bridge, a bridge circuit involving resistors, a capacitor and an inductor

Publications

• On the Description of Oval Curves, and those having a plurality of Foci. Proceedings of the Royal Society of Edinburgh, Vol. ii. 1846.
• Illustrations of the Dynamical Theory of Gases. 1860.
• On Physical Lines of Force. 1861.
• A Dynamical Theory of the Electromagnetic Field. 1865.
• On Governors. Proceedings of the Royal Society, Vol. 16 (1867-1868) pp. 270-283.
• Theory of Heat. 1871.
• On the Focal Lines of a Refracted Pencil. Proceedings of the London Mathematical Society s1-4(1):337-343, 1871.
• A Treatise on Electricity and Magnetism. Clarendon Press, Oxford. 1873.
• Molecules. Nature, September, 1873.
• On Hamilton's Characteristic Function for a Narrow Beam of Light. Proceedings of the London Mathematical Society s1-6(1):182-190, 1874.
• Matter and Motion, 1876.
• On the Results of Bernoulli's Theory of Gases as Applied to their Internal Friction, their Diffusion, and their Conductivity for Heat.
• "Ether", Encyclopaedia Britannica, Ninth Edition (1875-89).

References

• Campbell, Lewis (1882). The Life of James Clerk Maxwell (PDF). Edinburgh: MacMillan. OCLC 2472869. Retrieved 2008-02-20. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

• Glazebrook, R. T. (1896). James Clerk Maxwell and Modern Physics. MacMillan. ISBN 978-1-40672-200-0.

• Harman, Peter. M. (2004). Oxford Dictionary of National Biography, volume 37. Oxford University Press. ISBN 019861411X.

• Harman, Peter M. (1998). The Natural Philosophy of James Clerk Maxwell. Cambridge University Press. ISBN 052100585X. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)

• Mahon, Basil (2003). The Man Who Changed Everything – the Life of James Clerk Maxwell. Hoboken, NJ: Wiley. ISBN 0470861711.

• Porter, Roy (2000). Hutchinson Dictionary of Scientific Biography. Hodder Arnold H&S. ISBN 978-1859863046.

• Timoshenko, Stephen (1983). History of Strength of Materials. Courier Dover Publications. ISBN 0486611876.

• Tolstoy, Ivan (1982). James Clerk Maxwell: A Biography. University of Chicago Press. ISBN 0-226-80787-8.

External links

• Works by James Clerk Maxwell at Project Gutenberg
• O'Connor, John J.; Robertson, Edmund F., "James Clerk Maxwell", MacTutor History of Mathematics Archive, University of St Andrews
• Genealogy and Coat of Arms of James Clerk Maxwell (1831-1879) - Numericana
• Campbell, Lewis, "The Life of James Clerk Maxwell". 1882. [Digital Preservation]
• Maxwell's Legacy, James C. Rautio (2005)
• The James Clerk Maxwell Foundation Including a virtual tour of the museum.
• Maxwell Year 2006 Events planned to mark 175th anniversary of Clerk Maxwell's birth.
• James Clerk Maxwell Centre, Edinburgh Academy Opened in Maxwell's 175th anniversary year.