Peter Guthrie Tait

Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook Treatise on Natural Philosophy, which he co-wrote with Lord Kelvin, and his early investigations into knot theory.

His work on knot theory contributed to the eventual formation of topology as a mathematical discipline. His name is known in graph theory mainly for Tait's conjecture on cubic graphs. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles.

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, where he began his lifelong friendship with James Clerk Maxwell. 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. Andrews also introduced him to Sir William Rowan Hamilton and quaternions.^{[citation needed]}

In 1860, Tait succeeded his old master, James D. Forbes, as professor of natural philosophy 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 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 (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 in 1871. Tait also collaborated with Lord Kelvin 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 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, 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.