# Dictionary of National Biography, 1912 supplement/Tait, Peter Guthrie

​TAIT, PETER GUTHRIE (1831–1901), mathematician and physicist, born on 28 April 1831 at Dalkeith, was only son in a family of three children of John Tait, secretary to Walter Francis Scott, fifth duke of Buccleuch [q. v.], by his wife Mary Ronaldson. John Ronaldson, an uncle, who was a banker at Edinburgh and an amateur student of astronomy, geology, and the recently invented photography, first interested Peter in science. At six his father died, and he removed with his mother to Edinburgh. From the grammar school of Dalkeith he passed to a private school (now defunct) in Circus Place, and thence at ten (in 1841) to Edinburgh Academy. Lewis Campbell [q. v. Suppl. II] and James Clerk Maxwell [q. v.] were his seniors there by a year. Fleeming Jenkin [q. v.] was one of his own contemporaries. During his first four years he showed promise in classics, of which he retained a good knowledge through life. But his mathematical bent soon declared itself. He was 'dux' of his class in each of his six years at the academy (1841-7). At sixteen, in 1847, he entered Edinburgh University, and joined the senior classes in mathematics and natural philosophy. Next year he left Edinburgh for Peterhouse, Cambridge, where William Hopkins [q. v.] coached him for the mathematical tripos. In January 1852 he graduated B.A. as senior wrangler—the youngest on record. He was also first Smith's prizeman. A friend and fellow countrymnan of his, William John Steele, also of Peterhouse, was second wrangler. The only previous Scottish senior wrangler was Archibald Smith [q. v.] of Jordanhill in 1836. In Edinburgh Tait's success evoked boundless enthusiasm. Obtaining a fellowship at Peterhouse immediately afterwards, he began 'coaching,' and at the same time with his friend Steele commenced a treatise on 'Dynamics of a Particle.' Steele died before the book had progressed far, and it was completed by Tait, who chivalrously published it in 1856 as the joint work of 'Tait and Steele' (MS. presented by Mrs. Tait, in Peterhouse library). A second and improved edition appeared in 1865, and a seventh edition, with further revision, in 1900. The book, which still holds its own, helped to re-establish Newton's proper position in the science of dynamics, from which the brilliant work of the French mathematicians half a century earlier had apparently displaced him.
Meanwhile Tait had removed to Belfast (September 1854) to become professor of mathematics in Queen's College. Here he remained six years, and made lasting and important friendships. These friends included his fellow professor, Thomas Andrews [q. v. Suppl. I], (Sir) Wyville Thomson, James Thomson (Lord Kelvin's brother), James McCosh (afterwards president of Princeton, U.S.A.) and above all Sir William Rowan Hamilton [q. v.], the inventor of quaternions. Tait had been fascinated by Hamilton's work on 'Quaternions' while he was an undergraduate, and he soon, to the delight of Hamilton, made great and fundamental additions to the theory, subsequently producing an 'Elementary Treatise on Quaternions' (1867; 2nd edit. 1873; 3rd edit. 1890). Still later he joined with Philip Kelland [q. v.] in a more formal 'Introduction ' (1873; 2nd edit. 1881; 3rd edit. 1904). To the end of his fife Tait returned, when he could find the leisure, to this early study. With his colleague Andrews, Tait meanwhile made researches on the density of ozone and the action of the electric discharge on oxygen and other gases, and published the results in several papers. At Belfast he married on 13 Oct. 1857 Margaret Archer, daughter of the Rev. James Porter. Two of her brothers were among Tait's friends at Peterhouse, and one of these, James, was master from 1876 to 1901.
In 1860 Tait was elected professor of natural philosophy at Edinburgh in ​succession to James David Forbes [q. v.] The candidates included Clerk Maxwell and Edward John Routh [q. v. Suppl. II]. Tait's prochvity lay towards physical rather than purely mathematical work. On his arrival in Edinburgh he was elected a fellow of the Royal Society, and four years later became one of its secretaries. Henceforth his spare time was divided between literary work and criticism, and experimental research of exceptional note in the university laboratory, the results of which were presented to the Royal Society of Edinburgh or published in Journals of other societies. Unusual thoroughness characterised all his scientific work, whether expository or experimental. He was a good linguist, French, German, and Italian being equally at command, and he was quickly conversant with the scientific work of the continent. He contributed to British scientific journals translations of valuable foreign papers, including Helmholtz's famous papers on ' Vortex Motion' (Phil. Mag. 1867) and F. Mohr's 'Views on the Nature of Heat' (ibid. 1876).
Tait early came into contact with (Sir) William Thomson (afterwards Lord Kelvin) [q. v. Suppl. II], who had become fellow of Peterhouse in 1845, but had left Cambridge next year to become professor of natural philosophy at Glasgow. In that capacity Thomson first made Tait's acquaintance. In 1861 Tait was engaged on a book on mathematical physics, and had nearly completed arrangements for publication with the Cambridge firm of Macmillan, 'when Thomson to my great delight offered to join.' The result was Thomson and Tait's Natural Philosophy.' Two books were at first intended: a handbook for students and another, 'Principia Mathematica,' which Tait referred to as 'quite unique in mathematical physics,' and 'our great work'; but Thomson's other engagements threw the bulk of the writing on Tait, and only a single 'first' volume came to birth late in 1867. The earlier portion was written by Tait. Thomson's hand is more apparent in the later portion. The work was epoch-marking, and created a revolution in scientific development. For the first time 'T & T,' as the authors called themselves, traced to Newton (Principia, Lex iii.. Scholium) the concept of the 'conservation of energy' which was just then obtaining recognition among physicists, and they showed once for all that 'energy' was the fundamental physical entity and that its 'conservation' was its predominating and all-controlling property. In Tait's words, 'Thomson and he had rediscovered Newton for the world.' Their treatise takes rank with the 'Principia,' Laplace's 'Mecanique Celeste,' and Clerk Maxwell's 'Electricity and Magnetism.' A second edition of 'Thomson and Tait' appeared in two parts, issued respectively in 1879 and 1883. No further opportunity of collaboration offered. The material which Tait had collected for the second section of the joint original design he worked up independently into volumes for students on 'Heat' (1884; new edit. 1892), 'Light' (1884; last edit. 1900), and 'Properties of Matter' (1885; 5th edit. 1907). In these educational handbooks Tait presented each subject as a connected whole, avoiding all examination methods of presentation, carrying on the student logically by experiment and general reasoning to the main truths, and only introducing mathematics when really necessary or useful to shorten some process of reasoning. 'Heat' and 'Properties of Matter' were soon translated into German.
Tait was a strenuous controversialist, especially where his friends were concerned. He actively defended his predecessor, James David Forbes, in his struggle with Tyndall, who asserted his priority to Forbes in his theory of the motion of glaciers. In Tait's second important work, 'Thermodynamics' (1868; 2nd edit. 1877), which still enjoys authority, he established against Julius Robert Mayer, the German physicist, the claim of James Prescott Joule [q. v.] to have first determined strictly the relationship between heat and work. Tait similarly defended Thomson (Lord Kelvin) against Clausius's claim in 1854 to prior discovery, both theoretically and experimentally, of the fact that Carnot's function was inversely proportional to the temperature as measured on the absolute dynamic scale (Knott's Life of Tait, p. 223).
In the spring of 1874 Tait lectured before the Edinburgh Evening Club, a gathering of congenial friends, on 'Recent Advances in Physical Science.' Tait spoke from notes, but a shorthand transcript was published in 1876 (3rd edit. 1885). The book, which holds a high place in scientific literature, was translated into French, German, and Italian. Subsequently Tait, whose religious sentiment was always strong, joined his colleague Balfour Stewart [q. v.] in an endeavour 'to overthrow materialism by a purely scientific argument.' The result, 'The Unseen Universe, or Physical Speculation on a Future State,' appeared anonymously ​ in 1875 and greatly stirred public opinion. The fourth edition, which appeared within twelve months of the first, acknowledged the authorship. The tenth edition was translated into French (1883). In order to make clearer points which readers missed, the two authors produced in 1878 a sequel entitled 'Paradoxical Philosophy.' For the 'Encyclopædia Britannica' (9th edit. 1883) Tait wrote many articles, including one, 'Mechanics,' which he afterwards developed into an advanced treatise on 'Dynamics' (1895). Here, as he wrote to Cayley, he. evolved a system, which he believed to be new, 'from general principles such as conservation and transformation of energy, least action, &c., without introducing either force, momentum, or impulse.' A. small book on 'Newton's Laws of Motion' followed in 1899.
Tait's laboratory work was at the same time of a rarely equalled magnitude and importance. To his students his manner was always that of an elder brother. Although his laboratory was not a formal institution definitely housed in College buildings till 1868, nevertheless, following the example of his predecessors, he until then used for laboratory purposes his class-room and private room in college. At first he leaned to the chemical side. He continued his investigations on the properties of ozone, which he had begun with Andrews at Belfast, and in 1862 worked with James Alfred Wanklyn [q. v. Suppl. II] on the production of electricity by evaporation and during effervescence. In 1865 he dealt with the curious motion of iron filings on a vibrating plate in a magnetic field. In 1866 he began with Balfour Stewart [q. v.] the experimental investigation of the heating of a rapidly rotating disc in vacuo, a work extending continuously through two years, being resumed after three years and again six years later. Between 1870 and 1874 he worked out and verified with his students Thomson's (Lord Kelvin's) discovery of the 'latent heat of electricity,' and his theory of thermo-electricity, and he produced the first, and still the practical, working thermo-electric diagram on Thomson's lines. When he delivered the Rede lecture before the University of Cambridge in 1873 he chose thermo-electricity for his subject. His next great work was on knots, a theme which presented itself to him as the outcome of the simple proposition that two closed plane curves which intersect each other must do so an even number of times. Begun in 1876, this research occupied him, when time allowed, till 1885, and resulted in a remarkable series of masterly papers. In 1881 he dealt with the physical side of the 'Challenger' reports, especially with the effect of pressure on the readings of thermometers used in deep-sea soundings, and on the compressibility of water and alcohol. In 1886, on the suggestion of Lord Kelvin, he undertook a searching investigation into the foundations of the kinetic theory of gases, on which he was continuously engaged for five years (it still occupied his attention in 1896). His results were published in more than twenty papers, which form collectively a 'classic' contribution to the literature of the subject. During the same period, Tait, who was an ardent votary of golf, closely studied the flight of a golf ball ('the path of a rotating spherical projectile'), which he saw was not that of a smooth heavy sphere through a resisting medium. After an endless series of experiments with the laws of impact and cognate points, he discovered the principle of the 'underspin' which gave a new development to the art of the game (cf. his paper in Badminton Magazine, 1896). Sir J. J. Thomson, in a Friday-evening discourse at the Royal Institution (18 March 1910), showed to his audience an ingenious experimental verification of Tait's general conclusions.
Tait's alertness of mind and versatile interests led to careful and abstract inquiry in every possible direction, often apparently playful, and constantly alien to his special studies. As director of the Scottish Provident Institution, he was drawn to investigate problems of life assurance. Although he had no sympathy with easy efforts to popularise science, he sought to bring true science home to the unlearned, either in articles in popular magazines like 'Good Words,' to which he contributed with Thomson a paper on 'Energy' and a series of articles on ' Cosmical Astronomy,' or in lectures to a general audience on 'Force,' 'Sensation and Science,' 'Thunderstorms,' ’Religion and Science,' 'Does Humanity require a New Revelation ?' Tait's scientific papers were collected in 2 vols. (Cambridge, 1898-1900).
Tait's eminence was widely recognised. Although he was never a fellow of the Royal Society of England, he received a Royal medal from the society in 1886. He was made hon. LL.D. of Glasgow in 1901, and hon. Sc.D. of the University of Ireland in 1875. He twice received the Keith prize from the Royal Society of ​Edinburgh as well as the Gunning Victoria Jubilee prize. He was fellow or member of the Danish, Dutch, Swedish, and Irish scientific academies. He was made hon. fellow of Peterhouse in 1885. Resigning his professorship early in 1901, Tait died at Edinburgh on 4 July 1901, and was buried there.
Sir George Reid painted three portraits of Tait: one is the property of the family; another, which has been engraved, hangs in the rooms of the Royal Society of Edinburgh, and the third is in the hall of his college, Peterhouse, Cambridge.
Two scholarships in scientific research were founded in Tait's memory at Edinburgh university, and a sum of money contributed to improve the apparatus in the natural philosophy department. A second ('Tait') chair in that department is also in process of foundation.
Of Tait's four sons the eldest, John Guthrie, is principal of the Government Central College at Mysore. The third son, Frederick Guthrie (1870-1900), born at Edinburgh on 11 Jan. 1870, after being educated at Edinburgh Academy and Sedbergh, entered Sandhurst as an Edinburgh University candidate. In 1890 he was gazetted to the Leinster regiment, and in 1894 was transferred to the Black Watch. In 1899 he volunteered for active service in South Africa. At Magersfontein (19 Dec. 1899) young Tait, 'in front of the front company,' was shot in the leg. After a few weeks in hospital he rejoined his company, and on the same day, 7 Feb. 1900, at Koodoosberg, leading a rush on the Boers' position, he was shot through the heart, and died instantly. Lieutenant Tait, known everywhere as 'Freddie Tait,' was from 1893 until he sailed for South Africa probably the most brilliant amateur golfer. He was champion golfer both in 1896 and in 1898 (Low's F. G. Tait, a Record, 1902, with characteristic portrait).
[Dr. Knott's Life and Scientific Work of P. G. Tait, Cambridge, 1911, with four portraits and bibliography enumerating some 365 papers, besides 22 vols.; family records and personal recollections.]
J. D. H. D.