Peter Guthrie Tait (28 April 18314 July 1901) was a Scottish mathematical physicist and early pioneer in

thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

. 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 physics, mathematical physicist and engineer. Born in Belfast, he was the Professor of Natural Philosophy (Glasgow), professor of Natur ...

, and his early investigations into

knot theory In topology, knot theory is the study of knot (mathematics), 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 be und ...

. His work on knot theory contributed to the eventual formation of

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

as a mathematical discipline. His name is known in

graph theory In mathematics and computer science, 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 ...

mainly for

Tait's conjecture In mathematics, Tait's conjecture states that "Every K-vertex-connected graph, 3-connected Planar graph, planar cubic graph has a Hamiltonian cycle (along the edges) through all its Vertex (geometry), vertices". It was proposed by and disproved b ...

on cubic graphs. 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 ...

osculating circle An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has the same curvature as the curve at that point. The osculating circle provides a way to unders ...

Early life

Tait was born in

Dalkeith Dalkeith ( ; , ) 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 1541. The settlement of Dalkeith grew southwestwards from its 12th-century castle (now Dalkeith Pala ...

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 a Private schools in the United Kingdom, private day school in Edinburgh, Scotland, which was opened in 1824. The original building, on Henderson Row in Stockbridge, Edinburgh, Stockbridge, is now part of the Senior Scho ...

, where he began his lifelong friendship with

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...

. He studied mathematics and physics at the

University of Edinburgh The University of Edinburgh (, ; abbreviated as ''Edin.'' in Post-nominal letters, post-nominals) is a Public university, public research university based in Edinburgh, Scotland. Founded by the City of Edinburgh Council, town council under th ...

, and then went to

Peterhouse, Cambridge Peterhouse is the oldest Colleges of the University of Cambridge, constituent college of the University of Cambridge in England, founded in 1284 by Hugh de Balsham, Bishop of Ely. Peterhouse has around 300 undergraduate and 175 graduate stud ...

, graduating as

senior wrangler The Senior 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 achiev ...

and first

Smith's prize 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 names ...

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 The Queen's University of Belfast, commonly known as Queen's University Belfast (; abbreviated Queen's or QUB), is a public research university in Belfast, Northern Ireland, United Kingdom. The university received its charter in 1845 as part of ...

; there he made the acquaintance of

Thomas Andrews Thomas Andrews Jr. (7 February 1873 – 15 April 1912) was a British businessman and shipbuilder, who was managing director and head of the drafting department of the shipbuilding company Harland and Wolff in Belfast, Ireland. He was the naval ...

, whom he joined in researches on the density of

ozone Ozone () (or trioxygen) is an Inorganic compound, 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 , break ...

and the action of the electric discharge on

oxygen Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...

and other gases. Andrews also introduced him to Sir

William Rowan Hamilton Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathema ...

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. The algebra of quater ...

Middle years

In 1860, Tait succeeded his old master, James D. Forbes, as professor of

natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe, while ignoring any supernatural influence. It was dominant before the develop ...

at the University of Edinburgh. He 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

s, of which he was the leading exponent after their originator,

. 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 Philip Kelland PRSE FRS (17 October 1808 – 8 May 1879) was an English mathematician. He was known mainly for his great influence on the development of education in Scotland. Life Kelland was born in 1808 the son of Philip Kelland (d.1847), ...

(1808–1879). Kelland was one of his teachers and colleagues at the University of Edinburgh. Quaternions was also one of the themes of his address as president of the mathematical and physical section of the

British Association for the Advancement of Science The British Science Association (BSA) is a Charitable organization, 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 Scienc ...

in 1871. Tait also collaborated with

on ''Treatise on Natural Philosophy'' in 1867. Tait also produced original work in mathematical and experimental physics. In 1864, he published a short paper on

, 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 (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

). 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 List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...

, 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 (RSE) 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 establis ...

. Two years later, researches on "Charcoal Vacua" with

James Dewar Sir James Dewar ( ; 20 September 1842 – 27 March 1923) was a Scottish 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 studie ...

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 ...

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 that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...

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 f ...

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 The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small ...

, the fourth of which contained what was, according to

, the first proof ever given of the

Waterston Waterston is a village near Milford Haven in Pembrokeshire, Wales, in the community and parish of Llanstadwell. It lies on the B4325 road linking Neyland and Milford Haven.Ordnance Survey Demographics The built-up area had a population of 3 ...

Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...

theorem In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...

(

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

) 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 was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

, 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 shar ...

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 on

, 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 In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

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 occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, ...

. 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 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 "The Will to Believe" is a lecture by William James, first published in 1896, which defends, in certain cases, the adoption of a belief without prior evidence of its truth. In particular, James is concerned in this lecture about defending the rati ...

. Tait's articles include those he wrote for the ninth edition of the ''

Encyclopædia Britannica The is a general knowledge, general-knowledge English-language encyclopaedia. It has been published by Encyclopædia Britannica, Inc. since 1768, although the company has changed ownership seven times. The 2010 version of the 15th edition, ...

'' on light, mechanics, quaternions, radiation, and thermodynamics, and the biographical notices of Hamilton and James Clerk Maxwell.

Death

He died in Edinburgh on 4 July 1901, aged 70. He is buried in the second terrace down from

Princes Street Princes Street () 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, Edinburgh, New Town, stretching around 1.2 km (three quar ...

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

Topology

The Tait conjectures 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 or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

s made by Tait in his study of knots. The Tait conjectures involve concepts in

such as alternating knots,

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 fro ...

, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture, proved by Morwen Thistlethwaite and William Menasco in 1991.

Publications

* ''Dynamics of a Particle'' (1856) * '' Treatise on Natural Philosophy'' (1867)
v. 1
an
v. 2
(PDF/DjVu at the

Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

). * ''An elementary treatise on quaternions'' (1867)
PDF/DjVu
Copy of the 1st ed. at the

an
PDF/DjVu
Copy of the 3rd ed. at the

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

). A "non-mathematical portion of ''Treatise on Natural Philosophy''". * ''Sketch of Thermodynamics'' (1877)
PDF/DjVu
Copy at the

. * ''Recent Advances in Physical Science'' (1876)
PDF/DjVu
Copy at the

. * ''Heat'' (1884)
PDF/DjVu
Copy at the

. * ''Light'' (1884)
PDF/DjVu
Copy at the

. * ''Properties of Matter'' (1885)
PDF/DjVu
Copy at the

. * ''Dynamics'' (1895)
PDF/DjVu
Copy at the

. * ''The Unseen Universe'' (1875; new edition, 1901) * ''Scientific papers'' vol. 1 (1898–1900
PDF/DjVu
Copy at the

. * ''Scientific papers'' vol. 2 (1898–1900
PDF/DjVu
Copy at the

Private life

In 1857 Tait married Margaret Archer Porter (1839–1926). She was the sister of (1) William Archer Porter, a

lawyer A lawyer is a person who is qualified to offer advice about the law, draft legal documents, or represent individuals in legal matters. The exact nature of a lawyer's work varies depending on the legal jurisdiction and the legal system, as w ...

and

educationist Education is the transmission of knowledge and skills and the development of character traits. Formal education occurs within a structured institutional framework, such as public schools, following a curriculum. Non-formal education also fol ...

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 Indian state of Karnataka. It is the headquarters of Mysore district and Mysore division. As the traditional seat of the Wadiyar dynasty, the city functioned as the capital of the ...

, (2) James Porter (Master of Peterhouse, Cambridge), and (3) Jane Bailie Porter, who married

Alexander Crum Brown Alexander Crum Brown Fellow of the Royal Society of Edinburgh, FRSE Fellow of the Royal Society, FRS (26 March 1838 – 28 October 1922) was a Scottish Organic chemistry, organic chemist. Alexander Crum Brown Road in Edinburgh's King's Buildi ...

, 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. (In 1891, Tait invoked the

Magnus effect The Magnus effect is a phenomenon that occurs when a spin (geometry), spinning Object (physics), object is moving through a fluid. A lift (force), lift force acts on the spinning object and its path may be deflected in a manner not present when ...

to explain the influence of

spin Spin or spinning most often refers to: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...

on the flight of a

golf ball A golf ball is a ball designed to be used in 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 golf clubs, golf bal ...

.) He was an all-round sportsman and represented Scotland at international level in

rugby union Rugby union football, commonly known simply as rugby union in English-speaking countries and rugby 15/XV in non-English-speaking world, Anglophone Europe, or often just rugby, is a Contact sport#Terminology, close-contact team sport that orig ...

. His daughter, Edith, married 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 Senate, United States senator from Nevada from 1987 to 2017. He led the Senate Democratic Caucus from 2005 to 2 ...

, who later became

Bishop of Edinburgh The Bishop of Edinburgh, or sometimes the Lord Bishop of Edinburgh, is the Ordinary (officer), ordinary of the Scottish Episcopal Church, Scottish Episcopal Diocese of Edinburgh. Prior to the Reformation, Edinburgh was part of the Diocese of St ...

. Another son,

William William is a masculine given name of Germanic languages, Germanic origin. It became popular in England after the Norman Conquest, Norman conquest in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle ...

, 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 i ...

Recognition

Tait was a lifelong friend of

, and a portrait of Tait by Harrington Mann is held in the

James Clerk Maxwell Foundation The James Clerk Maxwell Foundation is a Office of the Scottish Charity Regulator, registered Scottish charity set up in 1977. By supporting physics and mathematics, it honors one of the greatest physicists, James Clerk Maxwell (1831–1879), an ...

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 The National Galleries of Scotland (, sometimes also known as National Galleries Scotland) is the executive non-departmental public body that controls the three national galleries of Scotland and two partner galleries, forming one of the Nation ...

, to which it was given by the artist in 1902. Another portrait was unveiled at

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 The King's Buildings (colloquially known as just King's or KB) is a campus of the University of Edinburgh in Scotland. Located in the suburb of Blackford, Edinburgh, Blackford, the site contains most of the schools within the University of Edin ...

complex is named in his honour. He was also given the following honours; * Fellow of the

* General Secretary of the Royal Society of Edinburgh, 1879 until 1901 * Gunning Victoria Jubilee Prize * Keith prize (twice) * Royal Medal from the

Royal Society of London The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

, in 1886 * Honorary degrees by the University of Glasgow and the University of Ireland * Honorary membership of the academies of Denmark, Holland, Sweden and Ireland.

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 PDFHTML version (in progress)

Knot Theory
Website of Andrew Ranicki in Edinburgh.
University of Edinburgh website, ''Life and Scientific Work of Peter Guthrie Tait''
online book by Cargill Gilston Knott (1898) * {{DEFAULTSORT:Tait, Peter Guthrie Scottish physicists 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 British mathematical physicists Academics of Queen's University Belfast Academics of the University of Edinburgh 19th-century Scottish mathematicians 20th-century Scottish mathematicians