Peter Guthrie Tait
Encyclopedia
Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
mathematical physicist
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, best known for the seminal energy physics textbook Treatise on Natural Philosophy
Treatise on Natural Philosophy
Treatise on Natural Philosophy was an 1867 text book by William Thomson and Peter Guthrie Tait, published by Oxford University Press, that did much to define the modern discipline of physics.-External links:* on Google books*...
, which he co-wrote with Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
, and his early investigations into knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
, which contributed to the eventual formation of topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
as a mathematical discipline. His name is known in Graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
mainly for Tait's conjecture
Tait's conjecture
In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 edges and 46 vertices...
.
Early years
He was born in DalkeithDalkeith
Dalkeith is a town in Midlothian, Scotland, lying on the River North Esk. It was granted a burgh of barony in 1401 and a burgh of regality in 1540...
. After attending the Edinburgh Academy
Edinburgh Academy
The Edinburgh Academy is an independent school which was opened in 1824. The original building, in Henderson Row on the northern fringe of the New Town of Edinburgh, Scotland, is now part of the Senior School...
and University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...
, he went up to Peterhouse, Cambridge
Peterhouse, Cambridge
Peterhouse is a constituent college of the University of Cambridge, England. It is the oldest college of the University, having been founded in 1284 by Hugo de Balsham, Bishop of Ely...
, graduating as senior wrangler and first Smith's prize
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in theoretical Physics, mathematics and applied mathematics at the University of Cambridge, Cambridge, England.- History :...
man in 1852. As a fellow and lecturer of his college he remained in Cambridge for two years longer, and then left to take up the professorship of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Queen's College, Belfast. There he made the acquaintance of Thomas Andrews
Thomas Andrews (scientist)
Thomas Andrews FRS was an Irish chemist and physicist who did important work on phase transitions between gases and liquids.-Life:Andrews was born in Belfast, Ireland where his father was a linen merchant...
, whom he joined in researches on the density of ozone
Ozone
Ozone , or trioxygen, is a triatomic molecule, consisting of three oxygen atoms. It is an allotrope of oxygen that is much less stable than the diatomic allotrope...
and the action of the electric discharge on oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
and other gases, and by whom he was introduced to Sir William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
and quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...
s.
Middle years
In 1860, Tait succeeded his old master, JD ForbesJames David Forbes
James David Forbes was a Scottish physicist and glaciologist who worked extensively on the conduction of heat and seismology. Forbes was a resident of Edinburgh for most of his life, educated at the University and a professor there from 1833 until he became principal of the United College of St...
, as professor of natural philosophy
Natural philosophy
Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...
at Edinburgh, and occupied that 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, which he was the leading exponent of after their originator, 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
Philip Kelland PRSE FRS was an English mathematician. He was known mainly for his great influence on the development of education in Scotland.-Early life:Kelland was born in 1808 in Dunster, Somerset, England...
(1808–1879), one of his teachers at 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
British Association for the Advancement of Science
frame|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...
in 1871.
He also produced original work in mathematical and experimental physics. In 1864, he published a short paper on thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, and from that time his contributions to that and kindred departments of science became frequent and important. In 1871, he emphasized the significance and future importance of the principle of the dissipation of energy (second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
). In 1873 he took thermoelectricity for the subject of his discourse as Rede lecturer at Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, and in the same year he presented the first sketch of his well-known thermoelectric diagram before the Royal Society of Edinburgh
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity, operating on a wholly independent and non-party-political basis and providing public benefit throughout Scotland...
.
Two years later, researches on "Charcoal Vacua" with James Dewar
James Dewar
Sir James Dewar FRS was a Scottish chemist and physicist. He is probably best-known today for his invention of the Dewar flask, which he used in conjunction with extensive research into the liquefaction of gases...
led him to see the true dynamical explanation of the Crookes radiometer
Crookes radiometer
The Crookes radiometer, also known as the light mill, consists of an airtight glass bulb, containing a partial vacuum. Inside are a set of vanes which are mounted on a spindle. The vanes rotate when exposed to light, with faster rotation for more intense light, providing a quantitative measurement...
in the large mean free path
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
of the molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
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
Challenger expedition
The Challenger expedition of 1872–76 was a scientific exercise that made many discoveries to lay the foundation of oceanography. The expedition was named after the mother vessel, HMS Challenger....
for observing deep-sea temperatures, and were extended to include the compressibility of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
, glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
, and mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
. 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 fourth of which contained what was, according to Lord Kelvin, the first proof ever given of the Waterston
John James Waterston
John James Waterston was a Scottish physicist, a neglected pioneer of the kinetic theory of gases.-Early life:Waterston's father, George, was an Edinburgh sealing wax manufacturer and stationer, a relative of the Sandeman family Robert and his brother, George...
-Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
(equipartition theorem
Equipartition theorem
In classical statistical mechanics, the equipartition theorem is a general formula that relates the temperature of a system with 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
Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
, 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
Four color theorem
In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color...
and proved that it was true if and only if no snarks
Snark (graph theory)
In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...
were planar.
Later years
In addition, he was the author of a number of books and articles. Of the former, the first, published in 1865, was on the dynamics of a particle; and afterwards there followed a number of concise treatises on thermodynamicsThermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, 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
Treatise on Natural Philosophy was an 1867 text book by William Thomson and Peter Guthrie Tait, published by Oxford University Press, that did much to define the modern discipline of physics.-External links:* on Google books*...
. "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
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
and dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
, and the structure completed with the properties of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
, heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
, light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
, electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...
and magnetism
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...
. 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
Balfour Stewart was a Scottish physicist. 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 Kew Observatory...
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
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...
. 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 Clerk Maxwell.
Chronological order of books
- Dynamics of a Particle (1865)
- Treatise on Natural Philosophy (1867); v. 1 and v. 2 (PDF/DjVu at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
). - An elementary treatise on quaternions (1867); PDF/DjVu Copy of the 3rd ed. at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Elements of Natural Philosophy (1872); http://www.archive.org/details/elementsnatural04taitgoog (PDF/DjVu at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
). A "non-mathematical portion of Treatise on Natural Philosophy". - Sketch of Thermodynamics (1877); PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Recent Advances in Physical Science (1876); PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Heat (1884); PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Light (1884); PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Properties of Matter (1885); PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Dynamics (1895); PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - The Unseen Universe (1875; new edition, 1901)
- Scientific papers vol. 1 (1898–1900) PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
. - Scientific papers vol. 2 (1898–1900) PDF/DjVu Copy at the Internet ArchiveInternet ArchiveThe Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
.
Private life
Tait was an enthusiastic golfGolf
Golf is a precision club and ball sport, in which competing players use many types of clubs to hit balls into a series of holes on a golf course using the fewest number of strokes....
er and, of his seven children, two, Frederick Guthrie Tait
Frederick Guthrie Tait
Frederick Guthrie Tait was a Scottish soldier and amateur golfer.Born in Edinburgh, the third son of eminent physicist and fanatical amateur golfer Peter Guthrie Tait, Frederick was educated at the Edinburgh Academy and Sedbergh School. He entered the Royal Military Academy Sandhurst at the second...
(1870–1900) and John Guthrie Tait
John Guthrie Tait
John "Jack" Guthrie Tait was a Scottish educator who became principal of the Central College of Bangalore prioir to the First World War. In his early adulthood, Tait was a notable sportsman playing rugby union as a forward for Cambridge University and represented the Scotland international team...
(1861–1945) went on to become gifted amateur champions. John was an all-round sportsman and represented Scotland at international level in rugby union
Rugby union
Rugby union, often simply referred to as rugby, is a full contact team sport which originated in England in the early 19th century. One of the two codes of rugby football, it is based on running with the ball in hand...
. Tait himself had, in 1891, invoked the Magnus effect
Magnus effect
The Magnus effect is the phenomenon whereby a spinning object flying in a fluid creates a whirlpool of fluid around itself, and experiences a force perpendicular to the line of motion...
to explain the influence of spin
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
on the flight of a golf ball
Golf ball
A golf ball is a ball designed to be used in the game of golf.Under the Rules of Golf, a golf ball weighs no more than 1.620 oz , has a diameter not less than 1.680 in , and performs within specified velocity, distance, and symmetry limits...
.
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)