James Clerk Maxwell

# James Clerk Maxwell

Overview
James Clerk Maxwell of Glenlair
Glenlair
Glenlair House, near the village of Corsock in the Scottish Council area of Dumfries and Galloway, was the home of the physicist James Clerk Maxwell . The original structure was designed for Maxwell's father by Walter Newall; Maxwell himself oversaw the construction of an extension in the late...

(13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

, magnetism
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...

and optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

into a consistent theory. Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon, namely the electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

.
Discussion
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Quotations

Colour as perceived by us is a function of three independent variables at least three are I think sufficient, but time will show if I thrive.

Maxwell, in a letter to William Thomson, The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862 (1990), p. 245.

In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data.

Letter to Lewis Campbell (9 November 1851) in Ch. 6 : Undergraduate Life At Cambridge October 1850 to January 1854 — ÆT. 19-22, p.159
Encyclopedia
James Clerk Maxwell of Glenlair
Glenlair
Glenlair House, near the village of Corsock in the Scottish Council area of Dumfries and Galloway, was the home of the physicist James Clerk Maxwell . The original structure was designed for Maxwell's father by Walter Newall; Maxwell himself oversaw the construction of an extension in the late...

(13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

, magnetism
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...

and optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

into a consistent theory. Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon, namely the electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

. Subsequently, all other classic laws or equations of these disciplines became simplified cases of Maxwell's equations. Maxwell's achievements concerning electromagnetism have been called the "second great unification in physics", after the first one realised by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

.

Maxwell demonstrated that electric and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s travel through space in the form of waves
WAVES
The WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...

, and at the constant speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. In 1865 Maxwell published A Dynamical Theory of the Electromagnetic Field
A Dynamical Theory of the Electromagnetic Field
"A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared...

. It was with this that he first proposed that light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

was in fact undulations in the same medium that is the cause of electric and magnetic phenomena. His work in producing a unified model of electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

is one of the greatest advances in physics.

Maxwell also helped develop the Maxwell–Boltzmann distribution, which is a statistical means of describing aspects of the kinetic theory of gases
Kinetic theory
The kinetic theory of gases describes a gas as a large number of small particles , all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container...

. These two discoveries helped usher in the era of modern physics, laying the foundation for such fields as special relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

.

Maxwell is also known for presenting the first durable colour photograph
Color photography
Color photography is photography that uses media capable of representing colors, which are traditionally produced chemically during the photographic processing phase...

in 1861 and for his foundational work on the rigidity
Structural rigidity
In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.-Definitions:...

of rod-and-joint frameworks like those in many bridges.

Maxwell is considered by many physicists to be the 19th-century scientist who had the greatest influence on 20th-century physics. His contributions to the science are considered by many to be of the same magnitude as those of Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

and Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

. In the millennium poll—a survey of the 100 most prominent physicists—Maxwell was voted the third greatest physicist of all time, behind only Newton and Einstein. 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." Einstein kept a photograph of Maxwell on his study wall, alongside pictures of Michael Faraday
Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....

and Newton.

### Early life, 1831–39

James Clerk Maxwell was born 13 June 1831 at 14 India Street, Edinburgh
Edinburgh
Edinburgh is the capital city of Scotland, the second largest city in Scotland, and the eighth most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a rural area...

, to John Clerk
John Clerk-Maxwell of Middlebie
John Clerk of Middlebie was a Scottish advocate. He bought the Glenlair estate in the parish of Parton, Kirkcudbrightshire, and built its estate house....

An advocate is a term for a professional lawyer used in several different legal systems. These include Scotland, South Africa, India, Scandinavian jurisdictions, Israel, and the British Crown dependencies of Jersey, Guernsey and the Isle of Man...

, and Frances Cay. Maxwell's father was a man of comfortable means, of the Clerk family of Penicuik
Penicuik
Penicuik is a burgh and civil parish in Midlothian, Scotland, lying on the west bank of the River North Esk. The town was developed as a planned village in 1770 by Sir James Clerk of Penicuik. It became a burgh in 1867. The town was well known for its paper mills, the last of which closed in 2005....

, Midlothian, holders of the baronetcy of Clerk of Penicuik
Clerk Baronets
There has been one creation of baronets with the surname Clerk . It was created in the Baronetage of Nova Scotia by Letters Patent dated 24 March 1679, for John Clerk of Pennycuik , whose father, also John Clerk of Penicuik, had returned from Paris in 1647 with a considerable fortune and purchased...

; his brother being the 6th Baronet
Sir George Clerk, 6th Baronet
Sir George Clerk of Pennycuik, 6th Baronet PC, DL , was a British Tory politician.-Background:Clerk was the son of James Clerk, third son of Sir George Clerk-Maxwell, 4th Baronet, by his wife Janet Irving, daughter of George Irving, of Newton.-Political career:Clerk sat as Member of Parliament for...

. James was the first cousin of notable 19th century artist Jemima Blackburn
Jemima Blackburn
Jemima Wedderburn Blackburn was a Scottish painter whose work gives us an evocative picture of rural life in 19th-century Scotland. One of the most popular illustrators in Victorian Britain, she illustrated 27 books. Her greatest ornithological achievement was the second edition of her Birds from...

.

He had been born John Clerk, adding the surname Maxwell to his own after he inherited a country estate in Middlebie
Middlebie
Middlebie is a hamlet and parish in Dumfries & Galloway, south-west Scotland. It is approximately east of Ecclefechan, and north-east of Annan, on the banks of the Middlebie Burn....

, Kirkcudbrightshire
Kirkcudbrightshire
The Stewartry of Kirkcudbright or Kirkcudbrightshire was a county of south-western Scotland. It was also known as East Galloway, forming the larger Galloway region with Wigtownshire....

from connections to the Maxwell family, themselves members of the peerage
Peerage
The Peerage is a legal system of largely hereditary titles in the United Kingdom, which constitute the ranks of British nobility and is part of the British honours system...

.

Maxwell's parents did not meet and marry until they were well into their thirties, which was unusual for the time; moreover, his mother was nearly 40 years old when James was born. They had had one earlier child, a daughter, Elizabeth, who died in infancy. They named their only surviving child James, a name that had sufficed not only for his grandfather, but also many of his other ancestors.

When Maxwell was young his family moved to Glenlair
Glenlair
Glenlair House, near the village of Corsock in the Scottish Council area of Dumfries and Galloway, was the home of the physicist James Clerk Maxwell . The original structure was designed for Maxwell's father by Walter Newall; Maxwell himself oversaw the construction of an extension in the late...

House, which his parents had built on the 1500 acre (6.1 km2) Middlebie estate
Estate (house)
An estate comprises the houses and outbuildings and supporting farmland and woods that surround the gardens and grounds of a very large property, such as a country house or mansion. It is the modern term for a manor, but lacks the latter's now abolished jurisdictional authority...

. 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 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..."

### Education, 1839–47

Recognising the potential of the young boy, his mother Frances took responsibility for James' early education, which in the 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
The Edinburgh Academy is an independent school which was opened in 1824. The original building, in Henderson Row on the northern fringe of the New Town of Edinburgh, Scotland, is now part of the Senior School...

. He lodged during term times at the house of his aunt Isabella. During this time his passion for drawing was encouraged by his older cousin Jemima
Jemima Blackburn
Jemima Wedderburn Blackburn was a Scottish painter whose work gives us an evocative picture of rural life in 19th-century Scotland. One of the most popular illustrators in Victorian Britain, she illustrated 27 books. Her greatest ornithological achievement was the second edition of her Birds from...

, who was herself a talented artist.

The ten-year-old Maxwell, having been 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
Galloway
Galloway is an area in southwestern Scotland. It usually refers to the former counties of Wigtownshire and Kirkcudbrightshire...

accent struck the other boys as rustic, and his having arrived on his first day of school wearing a pair of homemade shoes and a tunic, earned him the unkind nickname of "Daftie". Maxwell, however, never seemed to have resented the epithet, bearing it without complaint for many years. Social isolation at the Academy ended when he met Lewis Campbell and Peter Guthrie Tait
Peter Guthrie Tait
Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...

, two boys of a similar age who were to become notable scholars later in life. They would remain lifetime friends.

Maxwell was fascinated by geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

at an early age, rediscovering the regular polyhedron
Regular polyhedron
A regular polyhedron is a polyhedron whose faces are congruent regular polygons which are assembled in the same way around each vertex. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive - i.e. it is transitive on its flags...

before any formal instruction. Much of his talent however, went overlooked, and despite winning the school's scripture biography prize in his second year his academic work remained unnoticed until, at the age of 13, he won the school's mathematical medal and first prize for both English and poetry.

Maxwell 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 ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

s, Cartesian oval
Cartesian oval
In geometry, a Cartesian oval, named after René Descartes, is determined as follows. Let and be fixed points in the plane, and let and denote the Euclidean distances from these points to a third variable point . Let and be arbitrary real numbers. Then the Cartesian oval is the locus of...

s, and related curves with more than two foci
Focus (geometry)
In geometry, the foci are a pair of special points with reference to which any of a variety of curves is constructed. For example, foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola...

. His work, Oval Curves, was presented to the Royal Society of Edinburgh
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity, operating on a wholly independent and non-party-political basis and providing public benefit throughout Scotland...

by James Forbes
James David Forbes
James David Forbes was a Scottish physicist and glaciologist who worked extensively on the conduction of heat and seismology. Forbes was a resident of Edinburgh for most of his life, educated at the University and a professor there from 1833 until he became principal of the United College of St...

, who was a professor of natural philosophy at Edinburgh University. Maxwell was deemed too young for the work presented. The work was not entirely original, since Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

had also examined the properties of such multifocal curves in the seventeenth century, but Maxwell had simplified their construction.

### Edinburgh University, 1847–50

Maxwell left the Academy in 1847 at the age of 16 and began attending classes at the University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...

. Having had the opportunity to attend the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

after his first term Maxwell instead decided to complete the full course of his undergraduate studies at Edinburgh. The academic staff of Edinburgh University included some highly regarded names, and Maxwell's first year tutors included Sir William Hamilton
Sir William Hamilton, 9th Baronet
Sir William Hamilton, 9th Baronet was a Scottish metaphysician.-Early life:He was born in Glasgow. He was from an academic family, including Robert Hamilton, the economist...

, who lectured him on logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

and metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

, Philip Kelland
Philip Kelland
Philip Kelland PRSE FRS was an English mathematician. He was known mainly for his great influence on the development of education in Scotland.-Early life:Kelland was born in 1808 in Dunster, Somerset, England...

on mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, and James Forbes
James David Forbes
James David Forbes was a Scottish physicist and glaciologist who worked extensively on the conduction of heat and seismology. Forbes was a resident of Edinburgh for most of his life, educated at the University and a professor there from 1833 until he became principal of the United College of St...

on natural philosophy
Natural philosophy
Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...

.
Maxwell, however, 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. There he would experiment with improvised chemical, electric, and magnetic apparatuses, but his chief concerns regarded the properties of polarized light. He constructed shaped blocks of gelatine, subjected them to various stresses
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

, and with a pair of polarizing prisms
Nicol prism
A Nicol prism is a type of polarizer, an optical device used to produce a polarized beam of light from an unpolarized beam. See polarized light. It was the first type of polarizing prism to be invented, in 1828 by William Nicol of Edinburgh...

given to him by the famous scientist William Nicol he would view the coloured fringes which had developed within the jelly. Through this practice Maxwell discovered photoelasticity
Photoelasticity
Photoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress...

, which is a means of determining the stress distribution within physical structures.

Maxwell contributed two papers for the Transactions of the Royal Society of Edinburgh at the age of 18. 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
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s by shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

. His other paper was titled Rolling curves, and just as with the paper Oval Curves that he had written at the Edinburgh Academy, Maxwell was again considered too young to stand at the rostrum and present it himself. The paper was delivered to the Royal Society by his tutor Kelland instead.

### Cambridge University, 1850–56

In October 1850, already an accomplished mathematician, Maxwell left Scotland for Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

. He initially attended Peterhouse
Peterhouse, Cambridge
Peterhouse is a constituent college of the University of Cambridge, England. It is the oldest college of the University, having been founded in 1284 by Hugo de Balsham, Bishop of Ely...

, but before the end of his first term transferred to Trinity College
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...

, where he believed it would be easier to obtain a fellowship. At Trinity, he was elected to the elite secret society known as the Cambridge Apostles
Cambridge Apostles
The Cambridge Apostles, also known as the Cambridge Conversazione Society, is an intellectual secret society at the University of Cambridge founded in 1820 by George Tomlinson, a Cambridge student who went on to become the first Bishop of Gibraltar....

. In November 1851, Maxwell studied under William Hopkins
William Hopkins
William Hopkins FRS was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the senior-wrangler maker....

, whose success in nurturing mathematical genius had earned him the nickname of "senior wrangler-maker". A considerable part of Maxwell's translation of his equations regarding electromagnetism was accomplished during his time at Trinity.

In 1854, Maxwell graduated from Trinity with a degree in mathematics. He scored second highest in the final examination, coming behind Edward Routh
Edward Routh
Edward John Routh FRS , was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century...

, and thereby earning himself the title of Second Wrangler. He was later declared equal with Routh, however, in the more exacting ordeal of the Smith's Prize
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in theoretical Physics, mathematics and applied mathematics at the University of Cambridge, Cambridge, England.- History :...

examination. Immediately after earning his degree, Maxwell read a novel paper to the Cambridge Philosophical Society entitled On the transformation of surfaces by bending. This is one of the few purely mathematical papers he had written, and it demonstrated Maxwell's growing stature as a mathematician. Maxwell decided to remain at Trinity after graduating and applied for a fellowship, which was a process that he could expect to take a couple of years. Buoyed by his success as a research student, he would be free, aside from some tutoring and examining duties, to pursue scientific interests at his own leisure.

The nature and perception of colour was one such interest, and had begun at Edinburgh University while he was a student of Forbes. Maxwell took the coloured spinning tops
Top
A top is a toy that can be spun on an axis, balancing on a point. This motion is produced in the most simple forms of top by twirling the stem using the fingers. More sophisticated tops are spun by by holding the axis firmly while pulling a string or twisting a stick or pushing an auger as shown...

invented by Forbes, and was able to demonstrate that white light would result from a mixture of red, green and blue light. His paper, Experiments on colour, laid out the principles of colour combination, and was presented to the Royal Society of Edinburgh in March 1855. Fortunately for Maxwell this time it would be he himself who delivered his lecture.

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
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, and to set examination papers. However, the following February he was urged by Forbes to apply for the newly vacant Chair of Natural Philosophy at Marischal College
Marischal College
Marischal College is a building and former university in the centre of the city of Aberdeen in north-east Scotland. The building is owned by the University of Aberdeen and used for ceremonial events...

, Aberdeen. His father assisted him in the task of preparing the necessary references, but he would die on 2 April, at Glenlair before either knew the result of Maxwell's candidacy. Maxwell nevertheless accepted the professorship at Aberdeen, leaving Cambridge in November 1856.

### Aberdeen University, 1856–60

The 25-year-old Maxwell was a decade and a half younger than any other professor at Marischal, but engaged himself with his new responsibilities as head of department, devising the syllabus and preparing lectures. He committed himself to lecturing 15 hours a week, including a weekly pro bono
Pro bono
Pro bono publico is a Latin phrase generally used to describe professional work undertaken voluntarily and without payment or at a reduced fee as a public service. It is common in the legal profession and is increasingly seen in marketing, technology, and strategy consulting firms...

lecture to the local working men's college. He lived in Aberdeen during the six months of the academic year, and spent the summers at Glenlair, which he had inherited from his father.

His mind was focused on a problem that had eluded scientists for two hundred years: the nature of Saturn's rings
Rings of Saturn
The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...

. It was unknown how they could remain stable without breaking up, drifting away or crashing into Saturn. The problem took on a particular resonance at this time as St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....

The Adams Prize is awarded each year by the Faculty of Mathematics at the University of Cambridge and St John's College to a young, UK based mathematician for first-class international research in the Mathematical Sciences....

. Maxwell devoted two years to studying the problem, proving that a regular solid ring could not be stable, and a fluid ring would be forced by wave action to break up into blobs. Since neither was observed, Maxwell concluded that the rings must comprise numerous small particles he called "brick-bats", each independently orbiting Saturn. Maxwell was awarded the £130 Adams Prize in 1859 for his essay On the stability of Saturn's rings; he was the only entrant to have made enough headway to submit an entry. His work was so detailed and convincing that when George Biddell Airy
George Biddell Airy
Sir George Biddell Airy PRS KCB was an English mathematician and astronomer, Astronomer Royal from 1835 to 1881...

read it he commented "It is one of the most remarkable applications of mathematics to physics that I have ever seen." It was considered the final word on the issue until direct observations by the Voyager
Voyager program
The Voyager program is a U.S program that launched two unmanned space missions, scientific probes Voyager 1 and Voyager 2. They were launched in 1977 to take advantage of a favorable planetary alignment of the late 1970s...

flybys of the 1980s confirmed Maxwell's prediction. Maxwell would also go on to disprove mathematically the nebular hypothesis (which stated that the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

formed through the progressive condensation
Condensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

of a purely gaseous nebula), forcing the theory to account for additional portions of small solid particles.

In 1857 Maxwell befriended the Reverend Daniel Dewar, who was the Principal of Marischal, and through him met Dewar's daughter, Katherine Mary Dewar. They were engaged in February 1858 and married in Aberdeen on 2 June 1859. Seven years Maxwell's senior, comparatively little is known of Katherine although it is known that she helped in his lab and worked on experiments in viscosity. Maxwell's biographer and friend Campbell adopted an uncharacteristic reticence on the subject of Katherine, though describing their married life as "one of unexampled devotion".

In 1860, Marischal College merged with the neighbouring King's College
King's College, Aberdeen
King's College in Old Aberdeen, Scotland is a formerly independent university founded in 1495 and an integral part of the University of Aberdeen...

to form the University of Aberdeen
University of Aberdeen
The University of Aberdeen, an ancient university founded in 1495, in Aberdeen, Scotland, is a British university. It is the third oldest university in Scotland, and the fifth oldest in the United Kingdom and wider English-speaking world...

. There was no room for two professors of Natural Philosophy, and Maxwell, despite his scientific reputation, found himself laid off. He was unsuccessful in applying for Forbes' recently vacated chair at Edinburgh, the post instead going to Tait. Maxwell was granted the Chair of Natural Philosophy at King's College London
King's College London
King's College London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. King's has a claim to being the third oldest university in England, having been founded by King George IV and the Duke of Wellington in 1829, and...

instead. After recovering from a near-fatal bout of smallpox
Smallpox
Smallpox was an infectious disease unique to humans, caused by either of two virus variants, Variola major and Variola minor. The disease is also known by the Latin names Variola or Variola vera, which is a derivative of the Latin varius, meaning "spotted", or varus, meaning "pimple"...

in the summer of 1860, Maxwell headed south to London with his wife Katherine.

### King's College London, 1860–65

Maxwell's time at King's was probably the most productive of his career. He was awarded the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

's Rumford Medal
Rumford Medal
The Rumford Medal is awarded by the Royal Society every alternating year for "an outstandingly important recent discovery in the field of thermal or optical properties of matter made by a scientist working in Europe". First awarded in 1800, it was created after a 1796 donation of $5000 by the... in 1860 for his work on colour, and was later elected to the Society in 1861. This period of his life would see him display the world's first light-fast colour photograph, further develop his ideas on the viscosity Viscosity Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity... of gases, and propose a system of defining physical quantities—now known as dimensional analysis Dimensional analysis In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per... . Maxwell would often attend lectures at the Royal Institution Royal Institution The Royal Institution of Great Britain is an organization devoted to scientific education and research, based in London.-Overview:... , where he came into regular contact with Michael Faraday Michael Faraday Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry.... . The relationship between the two men could not be described as close, as Faraday was 40 years Maxwell's senior and showed signs of senility. They nevertheless maintained a strong respect for each other's talents. This time is especially known for the advances Maxwell made in the fields of electricity and magnetism. He had examined the nature of both electric and magnetic fields in his two-part paper On physical lines of force, published in 1861, in which he had provided a conceptual model for electromagnetic induction Electromagnetic induction Electromagnetic induction is the production of an electric current across a conductor moving through a magnetic field. It underlies the operation of generators, transformers, induction motors, electric motors, synchronous motors, and solenoids.... , consisting of tiny spinning cells of magnetic flux Magnetic flux Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber... . Two more parts later added to the paper were published in early 1862. In the first of these he discussed the nature of electrostatics Electrostatics Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges.... and displacement current Displacement current In electromagnetism, displacement current is a quantity that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density, and it has an associated magnetic field just as actual currents do. However it is not an electric... . The final part dealt with the rotation of the plane of polarization of light in a magnetic field, a phenomenon discovered by Faraday and now known as the Faraday effect Faraday effect In physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon, that is, an interaction between light and a magnetic field in a medium... . ### Later years In 1865, Maxwell resigned the chair at King's College London and returned to Glenlair with Katherine. He wrote a textbook entitled Theory of Heat (1871), and an elementary treatise, Matter and Motion (1876). Maxwell was also the first to make explicit use of dimensional analysis Dimensional analysis In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per... , in 1871. In 1871, he became the first Cavendish Professor of Physics Cavendish Professor of Physics The Cavendish Professorship is one of the senior Professorships in Physics at Cambridge University. It was founded by grace of 9 February 1871 alongside the famous Cavendish Laboratory which was completed three years later... at Cambridge. Maxwell was put in charge of the development of the Cavendish Laboratory Cavendish Laboratory The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the university's School of Physical Sciences. It was opened in 1874 as a teaching laboratory.... . He supervised every step in 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 William Cavendish, 7th Duke of Devonshire William Cavendish, 7th Duke of Devonshire KG, PC , styled as Lord Cavendish of Keighley between 1831 and 1834 and known as The Earl of Burlington between 1834 and 1858, was a British landowner, benefactor and politician.-Background and education:Cavendish was the son of William Cavendish, eldest... (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 Henry Cavendish Henry Cavendish FRS was a British scientist noted for his discovery of hydrogen or what he called "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper "On Factitious Airs". Antoine Lavoisier later reproduced Cavendish's experiment and... , from which it appeared that Cavendish researched, amongst other things, such questions as the mean Mean In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean.... density Density The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight... of the earth and the composition of water. He 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. Maxwell is buried at Parton Kirk, near Castle Douglas Castle Douglas Castle Douglas , a town in the south of Scotland in Dumfries and Galloway, lies in the eastern part of Galloway known as the Stewartry, between the towns of Dalbeattie and Gatehouse of Fleet.-History:... in Galloway, Scotland. The extended biography The Life of James Clerk Maxwell, by his former schoolfellow and lifelong friend Professor Lewis Campbell, was published in 1882. 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 Cambridge University Press Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world... in 1890. ### Personality As a great lover of Scottish poetry, Maxwell memorised poems and wrote his own. The best known is Rigid Body Sings, closely based on Comin' Through the Rye Comin' Through the Rye "Comin' Thro' the Rye" is a poem written in 1782 by Robert Burns . It is well known as a traditional children's song, with the words put to the melody of the Scottish Minstrel Common' Frae The Town... by Robert Burns Robert Burns Robert Burns was a Scottish poet and a lyricist. He is widely regarded as the national poet of Scotland, and is celebrated worldwide... , which he apparently used to sing while accompanying himself on a guitar. It has the opening lines A collection of his poems was published by his friend Lewis Campbell in 1882. Many appreciations of Maxwell remark upon his remarkable intellectual qualities being matched by social awkwardness. Ivan Tolstoy, author of one of Maxwell's biographies, has noted the frequency with which scientists writing short biographies of Maxwell omit the subject of his Christianity Christianity Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings... . He was an evangelical Presbyterian, and in his later years became an Elder of the Church of Scotland Church of Scotland The Church of Scotland, known informally by its Scots language name, the Kirk, is a Presbyterian church, decisively shaped by the Scottish Reformation.... . Maxwell's religious beliefs and related activities have been the focus of several peer-reviewed and well-referenced papers. Attending both Church of Scotland (his father's denomination) and Episcopalian Scottish Episcopal Church The Scottish Episcopal Church is a Christian church in Scotland, consisting of seven dioceses. Since the 17th century, it has had an identity distinct from the presbyterian Church of Scotland.... (his mother's denomination) services as a child, Maxwell later underwent an evangelical Evangelicalism Evangelicalism is a Protestant Christian movement which began in Great Britain in the 1730s and gained popularity in the United States during the series of Great Awakenings of the 18th and 19th century.Its key commitments are:... conversion in April 1853, which committed him to an anti-positivist position. ### Electromagnetism Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/6 when "On Faraday's lines of force" was read to the Cambridge Philosophical Society Cambridge Philosophical Society The Cambridge Philosophical Society is a scientific society at University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of theology and medicine... . The paper presented a simplified model of Faraday's work, and how the two phenomena were related. He reduced all of the current knowledge into a linked set of differential equation Differential equation A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders... s with 20 equations in 20 variables. This work was later published as "On physical lines of force" in March 1861. Around 1862, while lecturing at King's College, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He considered this to be more than just a coincidence, and commented "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." Working on the problem further, Maxwell showed that the equations predict the existence of waves Electromagnetic wave equation The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum... of oscillating electric and magnetic fields Electromagnetic radiation Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space... 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". His famous equations, in their modern form of four partial differential equations, first appeared in fully developed form in his textbook A Treatise on Electricity and Magnetism A Treatise on Electricity and Magnetism A Treatise on Electricity and Magnetism is a two volume treatise on electromagnetism written by James Clerk Maxwell in 1873.-See also:* On Physical Lines of Force* A Dynamical Theory of the Electromagnetic Field-External links:... in 1873. Most of this work was done by Maxwell at Glenlair during the period between holding his London post and his taking up the Cavendish chair. Maxwell expressed electromagnetism in the algebra of quaternions and made the electromagnetic potential the centerpiece of his theory. In 1881 Oliver Heaviside Oliver Heaviside Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and... replaced Maxwell’s electromagnetic potential field by ‘force fields’ as the centerpiece of electromagnetic theory. Heaviside reduced the complexity of Maxwell’s theory down to four differential equations, known now collectively as Maxwell's Laws or Maxwell's equations Maxwell's equations Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations... . According to Heaviside, the electromagnetic potential field was arbitrary and needed to be "murdered". However, the use of scalar and vector potentials is now standard in the solution of Maxwell's equations. A few years later there was a great debate between Heaviside and Peter Guthrie Tait Peter Guthrie Tait Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical... about the relative merits of vector analysis and quaternions. The result was the realization that there was no need for the greater physical insights provided by quaternions if the theory was purely local, and vector analysis became commonplace. Maxwell was proven correct, and his quantitative connection between light and electromagnetism is considered one of the great accomplishments of 19th century mathematical physics Mathematical physics Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and... . Maxwell also introduced the concept of the electromagnetic field in comparison to force lines that Faraday discovered. By understanding the propagation of electromagnetism as a field emitted by active particles, Maxwell could advance his work on light. 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 Frame of reference A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an... in which the equations were valid, with the distasteful result that the equations changed form for a moving observer. These difficulties inspired Albert Einstein Albert Einstein Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history... to formulate the theory of special relativity Special relativity Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's... , and in the process Einstein dispensed with the requirement of a luminiferous aether. ### Colour analysis Maxwell contributed to the field of optics Optics Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light... and the study of colour vision Color vision Color vision is the capacity of an organism or machine to distinguish objects based on the wavelengths of the light they reflect, emit, or transmit... , creating the foundation for practical colour photography Color photography Color photography is photography that uses media capable of representing colors, which are traditionally produced chemically during the photographic processing phase... . From 1855 to 1872, he published at intervals a series of valuable investigations concerning the perception of colour, colour-blindness and colour theory, for the earlier of which the Royal Society awarded him the Rumford Medal Rumford Medal The Rumford Medal is awarded by the Royal Society every alternating year for "an outstandingly important recent discovery in the field of thermal or optical properties of matter made by a scientist working in Europe". First awarded in 1800, it was created after a 1796 donation of$5000 by the...

. The instruments which he devised for these investigations were simple and convenient to 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 the course of his 1855 paper on the perception of colour, Maxwell proposed that if three black-and-white photographs of a scene were taken through red, green and violet
RGB color model
The RGB color model is an additive color model in which red, green, and blue light is added together in various ways to reproduce a broad array of colors...

filters
Filter (optics)
Optical filters are devices which selectively transmit light of different wavelengths, usually implemented as plane glass or plastic devices in the optical path which are either dyed in the mass or have interference coatings....

, and transparent prints of the images were projected onto 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 colours in the scene.

During an 1861 Royal Institution lecture on colour theory, Maxwell presented the world's first demonstration of colour photography by this principle of three-colour analysis and synthesis, the basis of nearly all subsequent photochemical and electronic methods of colour photography. Thomas Sutton
Thomas Sutton (photographer)
Thomas Sutton was an English photographer, author, and inventor.-Life:Thomas Sutton went to school in Newington Butts and studied architecture for four years before studying at Caius College, Cambridge graduating in 1846 as the twenty-seventh wrangler. He opened a photographic studio in Jersey the...

, inventor of the single-lens reflex camera
Single-lens reflex camera
A single-lens reflex camera is a camera that typically uses a semi-automatic moving mirror system that permits the photographer to see exactly what will be captured by the film or digital imaging system, as opposed to pre-SLR cameras where the view through the viewfinder could be significantly...

, did the actual picture-taking. He photographed a tartan
Tartan
Tartan is a pattern consisting of criss-crossed horizontal and vertical bands in multiple colours. Tartans originated in woven wool, but now they are made in many other materials. Tartan is particularly associated with Scotland. Scottish kilts almost always have tartan patterns...

ribbon three times, through red, green and blue filters. He also made a fourth exposure through a yellow filter, but according to Maxwell's account this was not used in the demonstration. Because Sutton's photographic plate
Photographic plate
Photographic plates preceded photographic film as a means of photography. A light-sensitive emulsion of silver salts was applied to a glass plate. This form of photographic material largely faded from the consumer market in the early years of the 20th century, as more convenient and less fragile...

s were in fact insensitive to red and barely sensitive to green, the results of this pioneering experiment were far from perfect. It was remarked in the published account of the lecture that "if the red and green images had been as fully photographed as the blue," it "would have been a truly-coloured image of the riband. By finding photographic materials more sensitive to the less refrangible rays, the representation of the colours of objects might be greatly improved."

Researchers in 1961 concluded that the seemingly impossible partial success of the red-filtered exposure was due to ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...

light. Some red dyes strongly reflect it, the red filter used does not entirely block it, and Sutton's plates were sensitive to it.

The demonstration was not of a print or transparency containing tangible colouring matter, but of colour which was photographically recorded from nature and reproduced by the same additive colour synthesis
RGB color model
The RGB color model is an additive color model in which red, green, and blue light is added together in various ways to reproduce a broad array of colors...

principle now used by all common types of colour video displays. Maxwell's purpose was not to present a method of colour photography, but to illustrate the basis of human colour perception and to show that the correct additive primaries
An additive color model involves light emitted directly from a source or illuminant of some sort. The additive reproduction process usually uses red, green and blue light to produce the other colors. Combining one of these additive primary colors with another in equal amounts produces the...

are not red, yellow and blue, as was then taught, but red, green and blue.

The three photographic plates now reside in a small museum at 14 India Street, Edinburgh, the house where Maxwell was born.

### Kinetic theory and thermodynamics

Maxwell also investigated the kinetic theory of gases. Originating with Daniel Bernoulli
Daniel Bernoulli
Daniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...

, this theory was advanced by the successive labours of John Herapath
John Herapath
John Herapath was an English physicist who gave a partial account of the kinetic theory of gases in 1820 though it was neglected by the scientific community at the time....

, John James Waterston
John James Waterston
John James Waterston was a Scottish physicist, a neglected pioneer of the kinetic theory of gases.-Early life:Waterston's father, George, was an Edinburgh sealing wax manufacturer and stationer, a relative of the Sandeman family Robert and his brother, George...

, James Joule
James Prescott Joule
James Prescott Joule FRS was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work . This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The...

, and particularly Rudolf Clausius
Rudolf Clausius
Rudolf Julius Emanuel Clausius , was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis...

, 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
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...

, 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
Kinetic theory
The kinetic theory of gases describes a gas as a large number of small particles , all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container...

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
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

led him to devise the Gedankenexperiment (thought experiment) that came to be known as Maxwell's demon
Maxwell's demon
In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the Scottish physicist James Clerk Maxwell to "show that the Second Law of Thermodynamics has only a statistical certainty." It demonstrates Maxwell's point by hypothetically describing how to...

.

In 1871, he established Maxwell's thermodynamic relations
Maxwell relations
Maxwell's relations are a set of equations in thermodynamics which are derivable from the definitions of the thermodynamic potentials. The Maxwell relations are statements of equality among the second derivatives of the thermodynamic potentials. They follow directly from the fact that the order of...

, which are statements of equality among the second derivatives of the thermodynamic potentials
Thermodynamic potentials
A thermodynamic potential is a scalar function used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. One main thermodynamic potential that has a...

with respect to different thermodynamic variables. In 1874, he constructed a plaster thermodynamic visualisation
Maxwell's thermodynamic surface
Maxwell’s thermodynamic surface is an 1874 sculpture made by Scottish physicist James Clerk Maxwell . This model provides a three-dimensional plot of the various states of a fictitious substance with water-like properties. This plot has coordinates volume , entropy , and energy...

as a way of exploring phase transitions, based on the American scientist Josiah Willard Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...

's graphical thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

papers.

### 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
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

. Here governors refer to the governor
Governor (device)
A governor, or speed limiter, is a device used to measure and regulate the speed of a machine, such as an engine. A classic example is the centrifugal governor, also known as the Watt or fly-ball governor, which uses a rotating assembly of weights mounted on arms to determine how fast the engine...

or the centrifugal governor
Centrifugal governor
A centrifugal governor is a specific type of governor that controls the speed of an engine by regulating the amount of fuel admitted, so as to maintain a near constant speed whatever the load or fuel supply conditions...

used in steam engine
Steam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...

s.

## Legacy

Maxwell was ranked 91st on the BBC
BBC
The British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...

poll of the 100 Greatest Britons
100 Greatest Britons
100 Greatest Britons was broadcast in 2002 by the BBC. The programme was the result of a vote conducted to determine whom the United Kingdom public considers the greatest British people in history. The series, Great Britons, included individual programmes on the top ten, with viewers having further...

. His name is honoured in a number of ways:
• The maxwell
Maxwell (unit)
The maxwell, abbreviated as Mx, is the compound derived CGS unit of magnetic flux. The unit was previously called a line. The unit name honours James Clerk Maxwell, who presented the unified theory of electromagnetism, and was established by the IEC in 1930.In a magnetic field of strength one...

(Mx), a compound derived CGS unit measuring magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...

.
• Maxwell Montes
Maxwell Montes
Maxwell Montes is a mountain massif on the planet Venus, part of which contains the highest point on the planet's surface.- General description :...

, a mountain range on Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...

, one of only three features on the planet that are not given female names.
• The Maxwell Gap in the Rings of Saturn
Rings of Saturn
The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...

.
• The James Clerk Maxwell Telescope
James Clerk Maxwell Telescope
The James Clerk Maxwell Telescope is a submillimetre-wavelength telescope at Mauna Kea Observatory in Hawaii. Its primary mirror is 15 metres across: it is the largest astronomical telescope that operates in submillimetre wavelengths of the electromagnetic spectrum...

, the largest submillimetre
Submillimetre astronomy
Submillimetre astronomy or submillimeter astronomy is the branch of observational astronomy that is conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands, typically taken to be between a...

-wavelength astronomical telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

in the world, with a diameter of 15 metres.
• The 1977 James Clerk Maxwell Building of the University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...

, housing the schools of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

and meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

.
• The James Clerk Maxwell building at the Waterloo campus of King's College London
King's College London
King's College London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. King's has a claim to being the third oldest university in England, having been founded by King George IV and the Duke of Wellington in 1829, and...

, in commemoration of his time as 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
The Edinburgh Academy is an independent school which was opened in 1824. The original building, in Henderson Row on the northern fringe of the New Town of Edinburgh, Scotland, is now part of the Senior School...

was opened in 2006 to mark his 175th anniversary.
• James Clerk Maxwell Road in Cambridge, which runs beside the Cavendish Laboratory
Cavendish Laboratory
The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the university's School of Physical Sciences. It was opened in 1874 as a teaching laboratory....

.
• The University of Salford
University of Salford
The University of Salford is a campus university based in Salford, Greater Manchester, England with approximately 20,000 registered students. The main campus is about west of Manchester city centre, on the A6, opposite the former home of the physicist, James Prescott Joule and the Working Class...

's main building is named after him.
• Maxwell bridge
Maxwell bridge
|- align = "center"|| A Maxwell bridge is a type of Wheatstone bridge used to measure an unknown inductance in terms of calibrated resistance and capacitance...

, a bridge circuit involving resistors, a capacitor and an inductor
• A statue on Edinburgh's George Street
• A street in Aberdeen's Kincorth area is named after him
• Thomas Pynchon
Thomas Pynchon
Thomas Ruggles Pynchon, Jr. is an American novelist. For his most praised novel, Gravity's Rainbow, Pynchon received the National Book Award, and is regularly cited as a contender for the Nobel Prize in Literature...

, an American novelist, alludes to and explains Maxwell's demon
Maxwell's demon
In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the Scottish physicist James Clerk Maxwell to "show that the Second Law of Thermodynamics has only a statistical certainty." It demonstrates Maxwell's point by hypothetically describing how to...

in The Crying of Lot 49
The Crying of Lot 49
The Crying of Lot 49 is a novel by Thomas Pynchon, first published in 1966. The shortest of Pynchon's novels, it is about a woman, Oedipa Maas, possibly unearthing the centuries-old conflict between two mail distribution companies, Thurn und Taxis and the Trystero...

.
• P J Moore, keyboard player with The Blue Nile
The Blue Nile
The Blue Nile is an adult alternative/pop band from Glasgow. The music of The Blue Nile is built heavily on synthesizers and electronic instrumentation and percussion, although later works featured acoustic guitar more prominently.-Early years:...

is developing a theatre piece based on the life of J.C.M.

## Publications

• "On the description of oval curves, and those having a plurality of foci
Focus (geometry)
In geometry, the foci are a pair of special points with reference to which any of a variety of curves is constructed. For example, foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola...

". Proceedings of the Royal Society of Edinburgh, Vol. ii. 1846.
• "Are There Real Analogies in Nature?" (February 1856)
• Illustrations of the Dynamical Theory of Gases. 1860.
• On the Theory of Compound Colours, and the Relations of the Colours of the Spectrum. 1860.
• "On physical lines of force". 1861.
• "A dynamical theory of the electromagnetic field
A Dynamical Theory of the Electromagnetic Field
"A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared...

". 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
A Treatise on Electricity and Magnetism
A Treatise on Electricity and Magnetism is a two volume treatise on electromagnetism written by James Clerk Maxwell in 1873.-See also:* On Physical Lines of Force* A Dynamical Theory of the Electromagnetic Field-External links:...

. 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 Stresses in Rarefied Gases Arising from Inequalities of Temperature". Philosophical Transactions of the Royal Society of London, Vol. 170, (1879), pp. 231–256
• On the Results of Bernoulli's Theory of Gases as Applied to their Internal Friction, their Diffusion, and their Conductivity for Heat.
• "Ether", Encyclopædia Britannica, Ninth Edition (1875–89).
• An Elementary Treatise on Electricity
An Elementary Treatise on Electricity
An Elementary Treatise on Electricity is a book by James Clerk Maxwell. The origin of the book are lecture notes Clerk Maxwell gave to members of the Cavendish Laboratory, which he founded.-External links:**...

Clarendon Press, Oxford. 1881, 1888.