Peter Guthrie Tait

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 soci ...

(28 April 1831 – 4 July 1901) was a Scottish

mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

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 of the ...

. 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. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...

, and his early investigations into

knot theory In the mathematical field of 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 ...

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

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

as a mathematical discipline. His name is known in

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

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 e ...

. 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 Archimed ...

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 i ...

Early life

Tait was born in

Dalkeith 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-cent ...

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 school (United Kingdom), independent day school in Edinburgh, Scotland, which was opened in 1824. The original building, on Henderson Row in the city's New Town, Edinburgh, New Town, is now part of the Se ...

. 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 15 ...

, 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 a ...

and first Smith's prizeman 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 , mottoeng = For so much, what shall we give back? , top_free_label = , top_free = , top_free_label1 = , top_free1 = , top_free_label2 = , top_free2 = , established = , closed = , type = Public research university , parent = ...

. There he made the acquaintance of

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

, 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 lo ...

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 wel ...

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 Irela ...

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 quatern ...

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 Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior throu ...

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

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), 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 in 1871. He 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 experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...

). 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 The Sir Robert Rede's Lecturer is an annual appointment to give a public lecture, the Sir Robert Rede's Lecture (usually Rede Lecture) at the University of Cambridge. It is named for Robert Rede, Sir Robert Rede, who was Chief Justice of the Common ...

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 bec ...

, 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 a ...

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 f ...

of water, glass, and mercury. This work led to the first formulation of the

Tait equation In fluid mechanics, the Tait equation is an equation of state, used to relate liquid density to hydrostatic pressure. The equation was originally published by Peter Guthrie Tait in 1888 in the form : \frac = \frac where P is the hydrostatic ...

, 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 enter ...

, 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 (Wales), community and parish of Llanstadwell. The built-up area had a population of 335 in 2011. Part of the village lies within the boundaries of the Dragon L ...

- 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 th ...

(

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. T ...

) 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 Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

, 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 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 Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

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 partic ...

, 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 particles ...

. 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 K ...

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 ratio ...

. 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 time ...

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

Topology

The

Tait 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 conje ...

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 19 ...

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

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, 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 Thistlethwait ...

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 Univ ...

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 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
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

Tait was married to Margaret Archer Porter (1839-1926), the sister of (1) William Archer Porter, a

lawyer 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, solic ...

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. Var ...

who served as the Principal of

Government Arts College, Kumbakonam The Government Arts College, previously known as the Government Arts College for Men, is an autonomous college based in the town of Kumbakonam in Tamil Nadu, India. This college is functioning under Bharathidasan University. The Vice-Chancellor ...

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 of ...

, (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 close-contact team sport that originated at Rugby School in the first half of the 19th century. One of the two codes of rugby football, it is based on running with the ball in hand. In its m ...

. 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 expl ...

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 Sena ...

, who later became

Bishop of Edinburgh The Bishop of Edinburgh, or sometimes the Lord Bishop of Edinburgh is the ordinary of the Scottish Episcopal Diocese of Edinburgh. Prior to the Reformation, Edinburgh was part of the Diocese of St Andrews, under the Archbishop of St Andrews ...

. 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

Peter Guthrie Tait Road, King's Buildings

Tait was a lifelong friend of

James 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 ligh ...

, and a portrait of Tait by

Harrington Mann Harrington Mann (7 October 1864 – 28 February 1937) was a Scottish portrait artist and decorative painter. He was a member of the Glasgow Boys movement in the 1880s. Art career Mann was born in Glasgow and began his studies at the Glasgow S ...

is held in the

James Clerk Maxwell Foundation The James Clerk Maxwell Foundation is a registered Scottish charity set up in 1977. By supporting physics and mathematics, it honors one of the greatest physicists, James Clerk Maxwell (1831–1879), and while attempting to increase the public ...

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, 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, the site contains most of the schools within the College of Science and Engineering, ex ...

complex is named in his honour.

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. * {{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