Peter Guthrie Tait

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). A "non-mathematical portion of ''Treatise on Natural Philosophy''".
* ''Sketch of Thermodynamics'' (1877)

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* ''Recent Advances in Physical Science'' (1876)

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* ''Heat'' (1884)

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* ''Light'' (1884)

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* ''Properties of Matter'' (1885)

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* ''Dynamics'' (1895)

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* ''The Unseen Universe'' (1875; new edition, 1901)
* ''Scientific papers'' vol. 1 (1898–1900

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* ''Scientific papers'' vol. 2 (1898–1900

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Provisional Bibliography of Peter Guthrie Tait

. British Society for the History of Mathematics. *An Elementary Treatise on Quaternions, 1890, Cambridge University Press

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Knot Theory

Website of Andrew Ranicki in Edinburgh. * {{DEFAULTSORT:Tait, Peter Guthrie Scottish physicists Scottish mathematicians Scottish Episcopalians Thermodynamicists Fellows of the Royal Society of Edinburgh Alumni of the University of Edinburgh Alumni of Peterhouse, Cambridge Fellows of Peterhouse, Cambridge People educated at Edinburgh Academy 1831 births 1901 deaths Royal Medal winners Senior Wranglers People from Dalkeith Mathematical physicists Academics of Queen's University Belfast Academics of the University of Edinburgh 19th-century British mathematicians 20th-century British mathematicians

FRSE
Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and letters, judged to be "eminently distinguished in their subject". This s ...

(28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote with Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...

, and his early investigations into knot theory
In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

.
His work on knot theory contributed to the eventual formation of topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

as a mathematical discipline. His name is known in graph theory
In mathematics, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' ( ...

mainly for Tait's conjecture
In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 ed ...

. He is also one of the namesakes of the Tait–Kneser theorem
In differential geometry, the Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other.
The logarithmic spiral or the pictured Archimedea ...

on osculating circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point ''p'' on the curve has been traditionally defined as the circle passing through ''p'' and a pair of additional points on the curve ...

s.
Early life

Tait was born inDalkeith
Dalkeith ( ; gd, Dail Cheith, IPA: t̪alˈçe is a town in Midlothian, Scotland, on the River Esk. It was granted a burgh of barony in 1401 and a burgh of regality in 1540. The settlement of Dalkeith grew southwestwards from its 12th-cen ...

on 28 April 1831 the only son of Mary Ronaldson and John Tait, secretary to the 5th Duke of Buccleuch.
He was educated at Dalkeith Grammar School then Edinburgh Academy
The Edinburgh Academy is an independent day school in Edinburgh, Scotland, which was opened in 1824. The original building, on Henderson Row in the city's New Town, is now part of the Senior School. The Junior School is located on Arboretum R ...

. He studied Mathematics and Physics at the University of Edinburgh
The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in ...

, and then went to Peterhouse, Cambridge
Peterhouse is the oldest constituent college of the University of Cambridge in England, founded in 1284 by Hugh de Balsham, Bishop of Ely. Today, Peterhouse has 254 undergraduates, 116 full-time graduate students and 54 fellows. It is quite ...

, graduating as senior wrangler
The Senior Frog Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain."
Specifically, it is the person who ...

and first Smith's prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769. Following the reorganization in 1998, they are now awarded under the ...

man in 1852. As a fellow and lecturer of his college he remained at the University for a further two years, before leaving to take up the professorship of mathematics at Queen's College, Belfast
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. There he made the acquaintance of Thomas Andrews, whom he joined in researches on the density of ozone
Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic allotrope , breaking down in the lowe ...

and the action of the electric discharge on oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as ...

and other gases, and by whom he was introduced to Sir William Rowan Hamilton
Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Irel ...

and quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a qua ...

s.
Middle years

In 1860, Tait succeeded his old master, James D. Forbes, as professor ofnatural philosophy
Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science.
From the ancient w ...

at the University of Edinburgh, and occupied the Chair until shortly before his death. The first scientific paper under Tait's name only was published in 1860. His earliest work dealt mainly with mathematical subjects, and especially with quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a qua ...

s, of which he was the leading exponent after their originator, William Rowan Hamilton
Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Irel ...

. He was the author of two text-books on them—one an ''Elementary Treatise on Quaternions'' (1867), written with the advice of Hamilton, though not published till after his death, and the other an ''Introduction to Quaternions'' (1873), in which he was aided by Philip Kelland (1808–1879), one of his teachers at the University of Edinburgh. Quaternions was also one of the themes of his address as president of the mathematical section of the British Association for the Advancement of Science
The British Science Association (BSA) is a charity and learned society founded in 1831 to aid in the promotion and development of science. Until 2009 it was known as the British Association for the Advancement of Science (BA). The current Chie ...

in 1871.
He also produced original work in mathematical and experimental physics. In 1864, he published a short paper on thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

, and from that time his contributions to that and kindred departments of science became frequent and important. In 1871, he emphasised the significance and future importance of the ''principle of the dissipation of energy'' (second law of thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

). In 1873 he took thermoelectricity
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when ...

for the subject of his discourse as Rede lecturer at Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge beca ...

, and in the same year he presented the first sketch of his well-known thermoelectric diagram before the Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

.
Two years later, researches on "Charcoal Vacua" with James Dewar
Sir James Dewar (20 September 1842 – 27 March 1923) was a British chemist and physicist. He is best known for his invention of the vacuum flask, which he used in conjunction with research into the liquefaction of gases. He also studied at ...

led him to see the true dynamical explanation of the Crookes radiometer
The Crookes radiometer (also known as a light mill) consists of an airtight glass bulb containing a partial vacuum, with a set of vanes which are mounted on a spindle inside. The vanes rotate when exposed to light, with faster rotation for more i ...

in the large mean free path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...

of the molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

of the highly rarefied air. From 1879 to 1888, he engaged in difficult experimental investigations. These began with an inquiry into what corrections were required for thermometers operating at great pressure. This was for the benefit of thermometers employed by the ''Challenger'' expedition for observing deep-sea temperatures, and were extended to include the compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a ...

of water, glass, and mercury. This work led to the first formulation of the Tait equation, which is widely used to fit liquid density to pressure. Between 1886 and 1892 he published a series of papers on the foundations of the kinetic theory of gases
Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to:
* Kinetic theory, describing a gas as particles in random motion
* Kinetic energy, the energy of an object that it possesses due to its motion
Art and ent ...

, the fourth of which contained what was, according to Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...

, the first proof ever given of the Waterston
Waterston is a village near Milford Haven in Pembrokeshire, Wales, in the community
A community is a social unit (a group of living things) with commonality such as place, norms, religion, values, customs, or identity. Communities may s ...

- Maxwell theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

(equipartition theorem
In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. ...

) of the average equal partition of energy in a mixture of two gases. About the same time he carried out investigations into impact and its duration.
Many other inquiries conducted by him might be mentioned, and some idea may be gained of his scientific activity from the fact that a selection only from his papers, published by the Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer.
Cambridge University Pres ...

, fills three large volumes. This mass of work was done in the time he could spare from his professorial teaching in the university. For example, in 1880 he worked on the Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...

and proved that it was true if and only if no snarks were planar.
Later years

In addition, he was the author of a number of books and articles. Of the former, the first, published in 1856, was on the dynamics of a particle; and afterwards there followed a number of concise treatises onthermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

, heat, light, properties of matter and dynamics, together with an admirably lucid volume of popular lectures on Recent Advances in Physical Science.
With Lord Kelvin, he collaborated in writing the well-known '' Treatise on Natural Philosophy''. "Thomson and Tait," as it is familiarly called (" T and T' " was the authors' own formula), was planned soon after Lord Kelvin became acquainted with Tait, on the latter's appointment to his professorship in Edinburgh, and it was intended to be an all-comprehensive treatise on physical science, the foundations being laid in kinematics
Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a fi ...

and dynamics, and the structure completed with the properties of matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic pa ...

, heat, light, electricity and magnetism
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particl ...

. But the literary partnership ceased in about eighteen years, when only the first portion of the plan had been completed, because each of the members felt he could work to better advantage separately than jointly. The friendship, however, endured for the remaining twenty-three years of Tait's life.
Tait collaborated with Balfour Stewart
Balfour Stewart (1 November 182819 December 1887) was a Scottish physicist and meteorologist.
His studies in the field of radiant heat led to him receiving the Rumford Medal of the Royal Society in 1868. In 1859 he was appointed director of ...

in the ''Unseen Universe'', which was followed by ''Paradoxical Philosophy''. It was in his 1875 review of ''The Unseen Universe'', that William James first put forth his Will to Believe Doctrine. Tait's articles include those he wrote for the ninth edition of the ''Encyclopædia Britannica
The ( Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various t ...

'' on light, mechanics, quaternions, radiation, and thermodynamics, and the biographical notices of Hamilton and James Clerk Maxwell.
He died in Edinburgh on 4 July 1901. He is buried in the second terrace down from Princes Street
Princes Street ( gd, Sràid nam Prionnsan) is one of the major thoroughfares in central Edinburgh, Scotland and the main shopping street in the capital. It is the southernmost street of Edinburgh's New Town, stretching around 1.2 km (thre ...

in the burial ground of St John's Episcopal Church, Edinburgh.
Topology

TheTait conjectures
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjec ...

are three conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1 ...

s made by Tait in his study of knots. The Tait conjectures involve concepts in knot theory
In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

such as alternating knot
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. A link is alternating if it has an alternating diagram.
Many of the knots with crossing ...

s, chirality
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...

, and writhe
In knot theory, there are several competing notions of the quantity writhe, or \operatorname. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amou ...

. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture, proved by Morwen Thistlethwaite
Morwen Bernard Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory and Rubik's Cube group theory.
Biography
Morwen Thistlethwaite ...

and William Menasco William W. Menasco is a topologist and a professor at the University at Buffalo. He is best known for his work in knot theory.
Biography
Menasco received his B.A. from the University of California, Los Angeles in 1975, and his Ph.D. from the Uni ...

in 1991.
Publications

* ''Dynamics of a Particle'' (1856) * '' Treatise on Natural Philosophy'' (1867)v. 1

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The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

).
* ''An elementary treatise on quaternions'' (1867)PDF/DjVu

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Internet Archive
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Copy of the 3rd ed. at the

Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

.
* ''Elements of Natural Philosophy'' (1872); (PDF/DjVu at the PDF/DjVu

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Private life

Tait was married to Margaret Archer Porter (1839-1926), the sister of (1) William Archer Porter, alawyer
A lawyer is a person who practices law. The role of a lawyer varies greatly across different legal jurisdictions. A lawyer can be classified as an advocate, attorney, barrister, canon lawyer, civil law notary, counsel, counselor, solicitor ...

and educationist
Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty. Vari ...

who served as the Principal of Government Arts College, Kumbakonam and tutor and secretary to the Maharaja of Mysore
Mysore (), officially Mysuru (), is a city in the southern part of the state of Karnataka, India. Mysore city is geographically located between 12° 18′ 26″ north latitude and 76° 38′ 59″ east longitude. It is located at an altitude o ...

, (2) James Porter (Master of Peterhouse, Cambridge) and (3) Jane Bailie Porter, who married Alexander Crum Brown
Alexander Crum Brown FRSE FRS (26 March 1838 – 28 October 1922) was a Scottish organic chemist. Alexander Crum Brown Road in Edinburgh's King's Buildings complex is named after him.
Early life and education
Crum Brown was born at 4 Belle ...

, the Scottish organic chemist.
Tait was an enthusiastic golfer and, of his seven children, two, Frederick Guthrie Tait (1870–1900) and John Guthrie Tait (1861–1945) went on to become gifted amateur golf champions. He was an all-round sportsman and represented Scotland at international level in rugby union
Rugby union, commonly known simply as rugby, is a Contact sport#Terminology, close-contact team sport that originated at Rugby School in the first half of the 19th century. One of the Comparison of rugby league and rugby union, two codes of ru ...

. In 1891, Tait invoked the Magnus effect
The Magnus effect is an observable phenomenon commonly associated with a spinning object moving through a fluid. The path of the spinning object is deflected in a manner not present when the object is not spinning. The deflection can be exp ...

to explain the influence of spin on the flight of a golf ball
A golf ball is a special ball designed to be used in the game of golf.
Under the rules of golf, a golf ball has a mass no more than , has a diameter not less than , and performs within specified velocity, distance, and symmetry limits. Like g ...

. His daughter Edith Tait was married to Rev. Harry Reid
Harry Mason Reid Jr. (; December 2, 1939 – December 28, 2021) was an American lawyer and politician who served as a United States senator from Nevada from 1987 to 2017. He led the Senate Democratic Caucus from 2005 to 2017 and was the Senat ...

, who later became Bishop of Edinburgh.
His son William Archer Porter Tait was a civil engineer
A civil engineer is a person who practices civil engineering – the application of planning, designing, constructing, maintaining, and operating infrastructure while protecting the public and environmental health, as well as improving existing ...

.
Recognition

Tait was a lifelong friend ofJames Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and li ...

, and a portrait of Tait by Harrington Mann is held in the James Clerk Maxwell Foundation museum in Edinburgh.
There are several portraits of Tait by Sir George Reid. One, painted about 1883, is owned by the National Galleries of Scotland
National Galleries of Scotland ( gd, Gailearaidhean Nàiseanta na h-Alba) is the executive non-departmental public body that controls the three national galleries of Scotland and two partner galleries, forming one of the National Collections of ...

, to which it was given by the artist in 1902. Another portrait was unveiled at Peterhouse, Cambridge
Peterhouse is the oldest constituent college of the University of Cambridge in England, founded in 1284 by Hugh de Balsham, Bishop of Ely. Today, Peterhouse has 254 undergraduates, 116 full-time graduate students and 54 fellows. It is quite ...

in October 1902, paid for by the Master and Fellows of Peterhouse, where Tait had been an Honorary Fellow.
One of the chairs in the Department of Physics at the University of Edinburgh is the Tait professorship.
Peter Guthrie Tait Road at the University of Edinburgh King's Buildings complex is named in his honour.
See also

* Dowker–Thistlethwaite notation *Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...

* Homoeoid
* Medial graph
* Nabla symbol
References

External links

* * * *Pritchard, Chris.Provisional Bibliography of Peter Guthrie Tait

. British Society for the History of Mathematics. *An Elementary Treatise on Quaternions, 1890, Cambridge University Press

Scanned PDF

HTML version (in progress)

Knot Theory

Website of Andrew Ranicki in Edinburgh. * {{DEFAULTSORT:Tait, Peter Guthrie Scottish physicists Scottish mathematicians Scottish Episcopalians Thermodynamicists Fellows of the Royal Society of Edinburgh Alumni of the University of Edinburgh Alumni of Peterhouse, Cambridge Fellows of Peterhouse, Cambridge People educated at Edinburgh Academy 1831 births 1901 deaths Royal Medal winners Senior Wranglers People from Dalkeith Mathematical physicists Academics of Queen's University Belfast Academics of the University of Edinburgh 19th-century British mathematicians 20th-century British mathematicians