# James Clerk Maxwell

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James Clerk Maxwell | |
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Born | June 13, 1831 Edinburgh |

Died | November 5, 1879 Cambridge |

**James Clerk Maxwell** (June 13, 1831–November 5, 1879) was a Scottish mathematical physicist, born in Edinburgh. Maxwell developed a set of equations expressing the basic laws of electricity and magnetism as well as the Maxwell distribution in the kinetic theory of gases. He was the last representative of a younger branch of the well-known Scottish family of Clerk of Penicuik.

Maxwell had perhaps the finest mathematical mind of any theoretical physicist of his time. Maxwell is widely regarded as the nineteenth century scientist who had the greatest influence on twentieth century physics, making contributions to the fundamental models of nature. In 1931, on the centennial anniversary of Maxwell's birthday, Einstein described Maxwell's work as the "*most profound and the most fruitful that physics has experienced since the time of Newton.*"

Algebraic mathematics with elements of geometry are a feature of much of Maxwell's work. Maxwell demonstrated that electric and magnetic forces are two complementary aspects of electromagnetism. He showed that electric and magnetic fields travel through space, in the form of waves, at a constant velocity of 3.0 × 10^{8} m/s. He also proposed that light was a form of electromagnetic radiation.

The scientific compound derived CGS unit measuring magnetic flux (commonly abbreviated as *f*), the maxwell (Mx), is named in his honour. A mountain range on Venus, Maxwell Montes, is named after him, as is the James Clerk Maxwell Telescope, the largest sub-mm astronomical telescope in the world, with a diameter of 15 metres.

## Contents |

## Biography

### Early years

Maxwell was born at 14 India Street, Edinburgh, Scotland. He was the only child of Edinburgh lawyer John Clerk. Maxwell's early education was provided by his Christian mother and included studying the Bible. Most of his early childhood was spent at the family estate Glenlair near Dumfries. Maxwell's mother died when he was just eight years old. Maxwell then went to Edinburgh Academy in his youth. His school nickname was "Dafty", earned when he arrived for his first day of school wearing home-made shoes. In 1845, at the age of 14, Maxwell wrote a paper describing mechanical means of drawing mathematical curves with a piece of string.

### Middle years

In 1847, Maxwell attended Edinburgh University studying natural philosophy, moral philosophy, and mental philosophy. At Edinburgh, he studied under Sir William Hamilton, 9th Baronet. In his eighteenth year, while still a student in Edinburgh, he contributed two papers to the *Transactions of the Royal Society of Edinburgh* — one of which, *On the Equilibrium of Elastic Solids*, laid the foundation of one of the most singular discoveries of his later life, the temporary double refraction produced in viscous liquids by shear stress. In 1850, Maxwell left for Cambridge University and initially attended Peterhouse, but eventually left for Trinity College where he believed it was easier to obtain a fellowship. At Trinity, he was elected to a secret society known as the Cambridge Apostles. In November 1851, Maxwell studied under the tutor William Hopkins (nicknamed the "wrangler maker"). A considerable part of the translation of his electromagnetism equations was accomplished during Maxwell's career as an undergraduate in Trinity.

In 1854, Maxwell graduated with a degree as second wrangler in mathematics from Trinity (scoring second-highest in the mathematics exam) and was declared equal with the senior wrangler of his year in the higher ordeal of the Smith's prize examination. For more than half of his relatively short life he held a prominent position in the foremost rank of scientists, usually as a college professor. Immediately after taking his degree, he 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 to experts 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.

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 1856, Maxwell was appointed to the chair of Natural Philosophy in Marischal College, Aberdeen, which he held until the fusion of the two colleges there 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. He also mathematically disproved the nebular hypothesis (which stated that 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 was a professor at King's College in London. In 1861, Maxwell was elected to the Royal Society. He researched elastic solids and pure geometry during this time.

#### Kinetic theory

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 1865, Maxwell moved to the estate he inherited from his father in Glenlair, Kirkcudbrightshire, Scotland. In 1868 he resigned his Chair of Physics and Astronomy at King's College, London.

In 1866, he statistically formulated, 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 previous laws of thermodynamics, explaining the observations and experiments in a better way. Maxwell's work on thermodynamics led him to devise the thought experiment that came to be known as Maxwell's demon.

#### Electromagnetism

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 of both the electric and magnetic fields, as well as their interactions with matter.

Furthermore, Maxwell showed that the equations predict 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. Maxwell (1865) wrote:

*This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.*

Maxwell proved 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 Einstein to formulate the theory of special relativity, and in the process Einstein abandoned the requirement of a luminiferous aether.

### Later years and afterwards

Maxwell also made contributions to the area of optics and colour 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 resulting image's colours were somewhat unnatural, because the filters passed invisible wavelengths of light, but the principle was sound. 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 allowed him to win 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).

In 1871, he was the first Cavendish Professor of Physics at Cambridge. Maxwell supervised the development of the Cavendish Laboratory. He superintended every step of the progress of the building and of the purchase of the very valuable collection of apparatus with which it was equipped at the expense of 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.

Maxwell had married Katherine Mary Dewar when he was 27 years of age, but had fathered no children. He died in Cambridge of abdominal cancer at the age of 48. He had been a devout Christian his entire life.

Maxwell had unified the work of previous electromagnetic and optical experiments at last, reducing their experimental results and observations into a series of mathematical equations. These equations (as well as the Maxwell distribution) have proved to be extremely useful in physics ever since. They hold true in all cases and therefore yielded several new laws of electromagnetism and optics, most importantly electromagnetic radiation. The equations are fundamental to radio and television, and can be used for studying X-rays, gamma rays, infrared rays, and other forms of radiation.

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.

## Quotations

- "Aye, I suppose I could stay up that late." — Maxwell, on being told on his arrival at Cambridge University that there would be a compulsory 6 a.m. church service.
- "... I have the capacity of being more wicked than any example that man could set me, and ... if I escape, it is only by God's grace helping me to get rid of myself, partially in science, more completely in society, —but not perfectly except by committing myself to God ..." — Maxwell, circa 1853.
- "The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field" — Albert Einstein
- "He achieved greatness unequalled." — Max Planck
- "Maxwell's importance in the history of scientific thought is comparable to Einstein's (whom he inspired) and to Newton's (whose influence he curtailed)" — Ivan Tolstoy (Biographer)
- "From a long view of the history of mankind - seen from, say, ten thousand years from now - there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade." — Richard Feynman
- "Maxwell's equations have had a greater impact on human history than any ten presidents." — Carl Sagan

## Publications

- Maxwell, James Clerk, "
*On the Description of Oval Curves, and those having a plurality of Foci*". Procedure of the Royal Society of Edinburgh, Vol. ii. 1846. - Maxwell, James Clerk, "
*Illustrations of the Dynamical Theory of Gases*". 1860. - Maxwell, James Clerk, "
*On Physical Lines of Force*". 1861. - Maxwell, James Clerk, "
*A Dynamical Theory of the Electromagnetic Field*". 1865. - Maxwell, James Clerk, "
*Theory of Heat*". 1871. - Maxwell, James Clerk, "
*A Treatise on Electricity and Magnetism*". Clarendon Press, Oxford. 1873. - Maxwell, James Clerk, "
*Molecules*". Nature, September, 1873. - Maxwell, James Clerk, "
*On the Results of Bernoulli's Theory of Gases as Applied to their Internal Friction, their Diffusion, and their Conductivity for Heat*".

## Honours

Maxwell was ranked #24 on Michael H. Hart's list of the most influential figures in history and #91 on the BBC poll of the 100 Greatest Britons.

## See also

**Main**: Maxwell's demon | Maxwell's equations | Maxwell's theorem (a theorem in probability theory) | Maxwell-Boltzmann distribution | Scottish Enlightenment | Maxwell**Physics**: Scientific method | Wave-particle duality | Crookes radiometer**Electromagnetism**: Maxwell | Classical electromagnetism | Light | Photoelectric effect | Magnetic field | Radiation pressure | Electrons**Radio waves**: History of radio | Microwaves | Radar

**People**: Peter Guthrie Tait | Oliver Heaviside | Albert Einstein | Hans Christian Ørsted | Heinrich Rudolf Hertz | Michael Faraday | Willard Gibbs | Joseph Stefan | Joseph John Thomson | Hendrik Lorentz | James Fitzjames Stephen | George Gabriel Stokes | Lewis Campbell | Fleeming Jenkin**Schools**: Trinity College, Cambridge | Edinburgh University | Edinburgh Academy | University of Cambridge**Other**: Analytical Society | Encyclopædia Britannica | Pi, the movie | Solar nebula | Venus | Photography | Color photography**Lists**: List of Scots | List of physics topics | History of physics | List of physicists | Timeline of materials technology | Timeline of electromagnetism and classical optics | Timeline of processes | Timeline of solar system astronomy | Intellectual history of time | The 100 | 100 Greatest Britons | List of Christian scientists**Commemoration**: The James Clerk Maxwell Telescope is named after him, as are several streets in the United Kingdom.

## Links, resources, and references

- Works by James Clerk Maxwell at Project Gutenberg
- Campbell, Lewis, "
*The Life of James Clerk Maxwell*". 1882. [Digital Preservation] - Maxwell, James Clerk, "
*A Treatise on Electricity & Magnetism*". Dover Publications, New York. 1873. ISBN 0-486-60636-8 (Vol. 1) ISBN 0-486-60637-6 (Vol. 2) - Jack, Peter Michael, "
*Maxwell-equations: A Brief Note*". Physical space as a quaternion structure - I. - Glenlair Today
- Wolfram Research's Maxwell
- MacTutor's Maxwell
- Victorian Web's Maxwell
- Maxwell and the Christian Proposition
- 1911
*Britannica Maxwell* - The James Clerk Maxwell Foundation Including a virtual tour of the museum.