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 soc ...
(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. He is best known for the mathematical physics textbook ''
Treatise on Natural Philosophy
''Treatise on Natural Philosophy'' was an 1867 text book by William Thomson (later Lord Kelvin) and Peter Guthrie Tait, published by Oxford University Press.
The ''Treatise'' was often referred to as T and ''T^1'', as explained by Alexander Ma ...
'', which he co-wrote with
Lord Kelvin, 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 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 conn ...
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 on
osculating circles.
Early life
Tait was born in
Dalkeith 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. He studied Mathematics and Physics at the
University of Edinburgh, and then went to
Peterhouse, Cambridge, graduating as
senior wrangler 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. There he made the acquaintance of
Thomas Andrews, whom he joined in researches on the density of
ozone and the action of the electric discharge on
oxygen and other gases, and by whom he was introduced to Sir
William Rowan Hamilton and
quaternions.
Middle years
In 1860, Tait succeeded his old master,
James D. Forbes, as professor of
natural philosophy 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
quaternions, of which he was the leading exponent after their originator,
William Rowan Hamilton. 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
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, 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). In 1873 he took
thermoelectricity 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 becam ...
, and in the same year he presented the first sketch of his well-known thermoelectric diagram before the
Royal Society of Edinburgh.
Two years later, researches on "Charcoal Vacua" with
James Dewar 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 of the
molecule 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
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 ente ...
, the fourth of which contained what was, according to
Lord Kelvin, the first proof ever given of the
Waterston-
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 ...
theorem (
equipartition theorem) 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, 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
thermodynamics, 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
''Treatise on Natural Philosophy'' was an 1867 text book by William Thomson (later Lord Kelvin) and Peter Guthrie Tait, published by Oxford University Press.
The ''Treatise'' was often referred to as T and ''T^1'', as explained by Alexander Ma ...
''. "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 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 parti ...
, heat, light, electricity and
magnetism. 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. Tait's articles include those he wrote for the ninth edition of the ''
Encyclopædia Britannica'' 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 (three ...
in the burial ground of
St John's Episcopal Church, Edinburgh
The Church of St John the Evangelist is a Scottish Episcopal church in the centre of Edinburgh, Scotland. It is sited at the west end of Princes Street at its junction with Lothian Road, and is protected as a category A listed building.
Backgro ...
.
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 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 i ...
, 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 amoun ...
. 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 Uni ...
in 1991.
Publications
* ''Dynamics of a Particle'' (1856)
* ''
Treatise on Natural Philosophy
''Treatise on Natural Philosophy'' was an 1867 text book by William Thomson (later Lord Kelvin) and Peter Guthrie Tait, published by Oxford University Press.
The ''Treatise'' was often referred to as T and ''T^1'', as explained by Alexander Ma ...
'' (1867)
v. 1an
v. 2(PDF/DjVu at the
Internet Archive).
* ''An elementary treatise on quaternions'' (1867)
PDF/DjVuCopy of the 1st ed. at the
Internet Archive an
PDF/DjVuCopy of the 3rd ed. at the
Internet Archive.
* ''Elements of Natural Philosophy'' (1872); (PDF/DjVu at the
Internet Archive). A "non-mathematical portion of ''Treatise on Natural Philosophy''".
* ''Sketch of Thermodynamics'' (1877)
PDF/DjVuCopy at the
Internet Archive.
* ''Recent Advances in Physical Science'' (1876)
PDF/DjVuCopy at the
Internet Archive.
* ''Heat'' (1884)
PDF/DjVuCopy at the
Internet Archive.
* ''Light'' (1884)
PDF/DjVuCopy at the
Internet Archive.
* ''Properties of Matter'' (1885)
PDF/DjVuCopy at the
Internet Archive.
* ''Dynamics'' (1895)
PDF/DjVuCopy at the
Internet Archive.
* ''The Unseen Universe'' (1875; new edition, 1901)
* ''Scientific papers'' vol. 1 (1898–1900
PDF/DjVuCopy at the
Internet Archive.
* ''Scientific papers'' vol. 2 (1898–1900
PDF/DjVuCopy at the
Internet Archive.
Private life
Tait was married to Margaret Archer Porter (1839-1926), the sister of (1)
William Archer Porter
William Archer Porter (c. 1825 - d. 16 July 1890) was a British lawyer and educationist who served as the Principal of Government Arts College, Kumbakonam and tutor and secretary to the Maharaja of Mysore.
Early life and education
Porter was ...
, a
lawyer and
educationist 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 of ...
, (2)
James Porter (Master of Peterhouse, Cambridge) and (3) Jane Bailie Porter, who married
Alexander Crum Brown, the Scottish organic chemist.
Tait was an enthusiastic golfer and, of his seven children, two,
Frederick Guthrie Tait
Frederick Guthrie Tait (11 January 1870 – 7 February 1900) was an amateur golfer and Scottish soldier.
He won the Amateur Championship twice, in 1896 and again in 1898, by convincing margins. Over his short golf career, Tait recorded at lea ...
(1870–1900) and
John Guthrie Tait
John "Jack" Guthrie Tait (24 August 1861 – 4 October 1945) V.D. was a Scottish educator who became principal of the Central College of Bangalore prior to the First World War. In his early adulthood, Tait was a notable sportsman playing rugby ...
(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. In 1891, Tait invoked the
Magnus effect to explain the influence of
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
on the flight of a
golf ball. His daughter Edith Tait was married to Rev.
Harry Reid, 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 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 light ...
, and a portrait of Tait by
Harrington Mann 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
Peterhouse, Cambridge 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.
See also
*
Dowker–Thistlethwaite notation
In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite, who refined a notation origi ...
*
Four color theorem
*
Homoeoid
A homoeoid is a shell (a bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D).
When the thickness of the shell becomes negligible, it is called a thin homoeoid. The name homoeoid was coined by Lord Kelvin and P ...
*
Medial graph
In the mathematical discipline of graph theory, the medial graph of plane graph ''G'' is another graph ''M(G)'' that represents the adjacencies between edges in the faces of ''G''. Medial graphs were introduced in 1922 by Ernst Steinitz to study ...
*
Nabla symbol
The nabla symbol
The nabla is a triangular symbol resembling an inverted Greek delta:Indeed, it is called ( ανάδελτα) in Modern Greek. \nabla or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word ...
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
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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