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# Peter Guthrie Tait

Peter Guthrie Tait FRSE (28 April 1831 - 4 July 1901) was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical discipline.

Early years

He was born at Dalkeith. After attending the Edinburgh Academy and University of Edinburgh, he went up to Peterhouse, Cambridge, graduating as senior wrangler and first Smith's prizeman in 1852.[1] 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 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.

[edit] Middle years

In 1860, Tait succeeded his old master, JD Forbes, as professor of natural philosophy 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 (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 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 emphasized 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, 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 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 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 fourth of which contained what was, according to Lord Kelvin, the first proof ever given of the Waterston-Maxwell 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.

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 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. "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, 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 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 Encyclopaedia Britannica on Light, Mechanics, Quaternions, Radiation, and Thermodynamics, and the biographical notices of Hamilton and Clerk Maxwell.

Chronological order of books

A postcard from James Clerk Maxwell to Tait.

* Dynamics of a Particle (1865)

* Natural Philosophy (1867); v. 1 and v. 2 (PDF/DjVu at the Internet Archive).

* An elementary treatise on quaternions (1867); PDF/DjVu Copy of the 3rd ed. at the Internet Archive.

* Sketch of Thermodynamics (1877); PDF/DjVu Copy at the Internet Archive.

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

* Heat (1884); PDF/DjVu Copy at the Internet Archive.

* Light (1884); PDF/DjVu Copy at the Internet Archive.

* Properties of Matter (1885); PDF/DjVu Copy at the Internet Archive.

* Dynamics (1895); PDF/DjVu Copy at the Internet Archive.

* The Unseen Universe (1875; new edition, 1901)

* Scientific papers vol. 1 (1898-1900) PDF/DjVu Copy at the Internet Archive.

* Scientific papers vol. 2 (1898-1900) PDF/DjVu Copy at the Internet Archive.

Private life

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 champions. John was an all-round sportsman and represented Scotland at international level in rugby union. Tait himself had, in 1891, invoked the Magnus effect to explain the influence of spin on the flight of a golf ball.

References

1. ^ Tait, Peter Guthrie in Venn, J. & J. A., Alumni Cantabrigienses, Cambridge University Press, 10 vols, 1922–1958.

External links

* O'Connor, John J.; Robertson, Edmund F., "Peter Guthrie Tait", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Tait.html .

* 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)

* This article incorporates text from the Encyclopædia Britannica, Eleventh Edition, a publication now in the public domain.

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