Tait, Peter Guthrie

(1831-1901), physicist and mathematician

by Crosbie Smith

© Oxford University Press 2004 All rights reserved

Tait, Peter Guthrie (1831-1901), physicist and mathematician, was born on 28 April 1831 at Dalkeith, near Edinburgh, the only son among the three children of John Tait (d. c.1840), secretary to Walter Francis Scott, fifth duke of Buccleuch, and his wife, Mary Ronaldson. In his very early years Peter attended Dalkeith grammar school. On the death of her husband, Mary Tait and her children moved to Edinburgh where Peter spent about a year at Circus Place School prior to entering Edinburgh Academy in 1841. Eventually the children lived in Somerset Cottage, the home of their maternal uncle John Ronaldson. He was a banker with a keen interest in field sciences, and fostered Peter's scientific interests with geological rambles in summer, astronomical observations in winter, and experiments with the new art of photography. At the age of about thirteen, for example, Peter charted the positions of Jupiter's satellites on successive nights over a two-week period.

At the academy Tait spent his first four years studying classics under James Cumming, whose popularity inspired the formation in 1850 of the gentlemanly Cumming Club, consisting of the surviving members of the sixty-strong class of 1841. Throughout his six years at the academy, Tait headed his class as dux. In 1846 he competed against Lewis Campbell and James Clerk Maxwell (his seniors by one year) for the Edinburgh Academical Club prize; Campbell was first and Tait third overall but in mathematics the order was Tait, Campbell, Maxwell. The following year Maxwell was second and Tait third, while in mathematics Maxwell came first and Tait second. A culture of gentlemanly competition characterized the close friendship between Tait and Maxwell until the latter's death in 1879.

For his one session (1847-8) at Edinburgh University, Tait enrolled in the two highest of Philip Kelland's mathematical classes and entered himself in the highest of three divisions in James David Forbes's natural philosophy class, contrary to the advice of the professor to begin in the second division. Forbes afforded Tait an opportunity to combine mathematical and practical skills in the calculation of the sizes of wooden discs making up models of catenaries of various forms for the Natural Philosophy Museum.

Cambridge, 1848-1854
In 1848 Tait entered Peterhouse, Cambridge, where he and his fellow undergraduate William John Steele (a recent Glasgow University pupil of Professor William Thomson, also a Peterhouse graduate) were soon identified as likely high wranglers. They followed Thomson in having as their mathematical coach William Hopkins, the 'senior wrangler maker'. In the weeks leading up to the Senate House examinations Tait subjected himself to a rigorous programme of mathematical training and won the senior wranglership in January 1852, while the favourite, Steele, became second wrangler. Tait, only the second Scot to become senior wrangler, and the youngest on record, was also first Smith's prizeman.

Elected to a Peterhouse fellowship immediately after graduation, Tait spent a further two and a half years in Cambridge. His attempt to establish himself as a mathematical coach met with limited results but his one pupil, previously written off by Hopkins, emerged ahead of Hopkins's best pupil, prompting Tait to remark: 'Oh, that's nothing--I could coach a coal scuttle to be senior wrangler' (Knott, 11). Tait collaborated with Steele on A Treatise on Dynamics of a Particle, a work shaped by a tradition of mathematical textbooks for prospective Cambridge wranglers. Tait commemorated Steele's early death by publishing the work under their joint names in 1856, with a second, revised edition in 1865 and the final and seventh edition, further revised, in 1900. In later years, however, Tait recalled without enthusiasm the role of the Cambridge coaches as those who 'spend their lives in discovering which pages of a textbook a man ought to read' (Knott, 11).

Belfast, 1854-1860
Appointed professor of mathematics in Queen's College Belfast from September 1854, Tait joined a dynamic group of academics that included the chemist Thomas Andrews, the engineer James Thomson (brother of William), and James McCosh (later president of Princeton). As well as conducting his own classes, Tait supplemented the natural philosophy professor's lectures with a voluntary class for honours students interested in the higher parts of dynamics. His teaching method involved not only a regular course of lectures but also tutorial instruction with set exercises and problems followed by individual guidance. As a result he gained a reputation as an admirable teacher, clear and systematic in his treatment of the various branches taught.

While teaching at Queen's College, Tait worked closely with Andrews, whose hallmark of experimental practice was extreme accuracy. Tait undertook calculations in support of the experimental work on the density of ozone and on the action of electric discharge on oxygen and other gases. He also helped in construction of the apparatus and developed his own skills in the art of glass-blowing. As he later told Andrews's widow:

I have always regarded it as one of the most important determining factors in my own life (private as well as scientific) and one for which I cannot be sufficiently thankful, that my appointment to the Queen's College at the age of twenty-three brought me for six years into almost daily association with such a friend. (Knott, 13)
During these Belfast years Tait also devoted himself to a thorough study of William Rowan Hamilton's Lectures on Quaternions (1853). Enthusiasm for this new algebra of complex numbers in more than two dimensions (a radical departure from Cartesian methods), combined with his conviction of its utility in solving physical problems, inspired Tait to begin work on his own Elementary Treatise on Quaternions (first published in 1867 but expanded in 1873 and 1890).

From Peterhouse days Tait had been well acquainted with the sons of a Belfast clergyman of very limited means, the Revd James Porter. The Porter brothers, William Archer and James, had been students at Glasgow under Professor James Thomson (father of James and William). Following William Thomson to Peterhouse, they graduated third and seventh wranglers in 1849 and 1851 respectively. James Porter later served as master of Peterhouse (1876-1901). Tait married one of their sisters, Margaret Archer (1839-1926), on 13 October 1857. Together with James Thomson's appointment to the Queen's College chair of engineering that year, these social networks prepared the ground for Tait's long association with the Glasgow professor of natural philosophy, William Thomson, a relationship later characterized by Thomson as one of continual creative engagement: 'We never agreed to differ, always fought it out. But it was almost as great a pleasure to fight with Tait as to agree with him' (Knott, 43).

Following Forbes's retirement from the Edinburgh University chair of natural philosophy seven candidates competed for the prestigious post, including four former Cambridge wranglers (Tait, Maxwell, E. J. Routh, and Frederick Fuller). The Edinburgh Courant reported in May 1860 that neither Fuller nor Routh had 'as yet acquired a reputation for powers of scientific investigation'. Yet despite Maxwell's recognized pre-eminence in this regard, the Courant admitted that it was the deficiency of 'the power of oral exposition' in 'Professor Maxwell principally that made the curators prefer Mr Tait ... [who] has attained to great and solid scientific acquirements, and to very much of that habitual accuracy which his rival, Mr Maxwell, possesses by a sort of intuition' (Knott, 16-17). Tait had indeed a powerful presence in the lecture room, as J. M. Barrie described:

I have seen a man fall back in alarm under Tait's eyes, though there were a dozen benches between them. These eyes could be merry as a boy's, though, as when he turned a tube of water on students who would insist on crowding too near an experiment. (ibid., 17)
Energy physics
During the 1850s James and William Thomson, James Prescott Joule, W. J. M. Rankine, and James Clerk Maxwell constructed a new physics centred on the doctrines of conservation and dissipation of energy. But their informal programme had been sketched and articulated only in papers scattered in the scientific and popular periodicals of the mid-Victorian period. A late convert to energy physics, Tait quickly made the science of energy into a crusade. By the close of 1861 he had joined forces with William Thomson at Glasgow to produce a complete, state-of-the-art Treatise on Natural Philosophy which would embody North British (as Scotland was then often known) energy physics in canonical form, capable of being translated around the world.

The Treatise (known popularly as Thomson and Tait, or 'T&T' in accordance with the style used by the authors to address each other) took Newton's Principia as the sacred text of the natural philosopher and proclaimed that the 'true' Newtonian gospel was founded on the doctrine of energy conservation. A strong preference for engineering and geometrical modes of expression characterized the work. In the end, however, only one of the projected four volumes was ever written. Much of the blame lay with Thomson whose other interests, combined with his dislike of writing, delayed publication of the first volume until 1867. A second edition, prepared by George Darwin, appeared as two parts, the first in 1879 and the second in 1883.

During the 1860s John Tyndall, professor of natural philosophy at the Royal Institution in London, allied himself with T. H. Huxley and other enthusiasts for Darwin's theory of evolution. Appropriating energy conservation, Tyndall attempted to place it alongside evolution as one of the foundations of the new creed of scientific naturalism. In so doing he tried to wrest control from the North Britons whose claims to scientific authority were largely founded on the experimental work of Joule. Tyndall therefore constructed an alternative hero in the figure of the German physician Julius Robert Mayer. Taking up the cause of Joule against Mayer, Tait quickly made himself the principal crusader for a North British science of energy in scientific and popular periodicals. Tait's Thermodynamics (1868; 2nd edn, 1877), the first textbook explicitly on the subject, performed the same crusading role for students. A later book, Lectures on some Recent Advances in Physical Science (1876), reiterated many of the claims made on behalf of his friends during the previous decade.

Although Tait's efforts to promote the science of energy as a natural philosophy in harmony with Christian belief were fully endorsed by North British allies, his publication (with Balfour Stewart) of the anonymous Unseen Universe, or, Physical Speculation on a Future State (1875) and its sequel, Paradoxical Philosophy (1878), was controversial. Ostensibly directed against the materialistic determinism of Tyndall's notorious Belfast address to the British Association for the Advancement of Science (1874), the Unseen Universe, consistent with Tait's political convictions, offered a conservative rather than a progressive vision. A visible universe in temporal decay formed part of an invisible whole in which the dissipation of energy did not appear to operate as a fundamental law. This unseen and eternal whole then provided the rationale for human immortality. It was a unified vision of things material and spiritual, human and divine, which suggested a self-renewing universe (like a perfectly reversible heat engine) rather at odds with Thomson's and Maxwell's decisive separation of the material (and transitory) from the spiritual (and eternal) worlds. Unseen Universe had reached its fourth edition within a year and its tenth by 1883.

In accordance with Forbes's earlier practice, Tait at first conducted his experimental researches in the classroom and professor's private room in the college. His loyal mechanical assistant, James Lindsay, had served Forbes's predecessor John Leslie as well as Forbes himself in that capacity since 1819. Tait's research programme included a continuation of work on the properties of ozone, investigation of the motion of iron filings on a vibrating plate in a magnetic field, and the production of electricity by evaporation and during effervescence. From 1866 he collaborated with Balfour Stewart, another former Forbes's student and laboratory assistant, on a series of investigations into the heating of a rapidly rotating disc in vacuo.

Practical teaching and research
By 1867 Tait had successfully won financial support for the funding of laboratory facilities and within a year had secured accommodation for a formal laboratory through acquisition of the pathology professor's classroom, duly stripped of its benches. Opened in the autumn of 1868 and closely modelled on Thomson's well-established Glasgow physical laboratory, Tait's laboratory was open to all comers from the natural philosophy class for a voluntary course of practical physics upon payment of a fee of 2 guineas for the first session. Students, known as veterans, who chose to continue beyond the first session paid nothing more because their raison d'être was to assist the professor in his research. From 1868 until 1870 William Robertson Smith, later professor of Arabic in the University of Cambridge, served as Tait's laboratory assistant and provided students with systematic teaching in practical physics. Forbes's former private room became the centre of advanced investigation, especially into the thermoelectric properties of more than twenty metals over a considerable range of temperature.

These thermoelectric researches were closely allied to earlier work by Thomson on thermoelectricity as a branch of thermodynamics and especially to his claim that if a metal were subject to a temperature gradient then a source of electromotive power could exist between different parts of that metal (the Thomson effect). Again working closely to Thomson's agenda, for a circuit consisting of two metals Tait produced the first 'thermoelectric diagram', which represented the effects in terms of a straight-line graph (thermoelectric power plotted against temperature difference). He presented his results principally to the Royal Society of Edinburgh but also outlined his views in the 1873 Rede lecture delivered in the Senate House of the University of Cambridge at a time when Maxwell was preparing the ground for the introduction of experimental physics into an ancient university more accustomed to mathematical texts than laboratory practice.

Tait's other experimental work included investigation of the corrections needed for deep-sea temperature readings by self-recording thermometers aboard HMS Challenger, the development of a pressure-measuring instrument known as the Tait Gauge, and researches into golf-ball impact. Golf, indeed, combined Tait's love of experiment with his love of dynamics and in a series of articles published in Nature (1890-93) he revealed that underspin provided the great secret of long driving. At Edinburgh the removal of the anatomy department allowed a further expansion of the physical laboratory in 1880 by the conversion of the dissecting rooms into a junior laboratory and rooms for special magnetic and optical work. Tait's mathematical skills found their most powerful expression not only in his enthusiastic promotion of Hamilton's quaternions but also in the complexities of knots and knottiness (where he introduced a new vocabulary). Urged by Thomson, Tait devoted some years to an investigation of the foundations of the kinetic theory of gases.

Tait wrote, co-authored, and edited some twenty-two books (including two volumes of collected Scientific Papers) and published about 365 articles and reviews. He was made a fellow of the Royal Society of Edinburgh in 1860, a secretary in 1864, and general secretary from 1879 until his death. He was twice awarded the Royal Society of Edinburgh's Keith prize (1867-9 and 1871-3) and the Gunning Victoria jubilee prize (1887-90). He received a royal medal from the Royal Society of London (1886). He was fellow or member of the Danish, Dutch, Swedish, and Irish scientific academies, but never a fellow of the Royal Society. He was made an honorary ScD of the Catholic University of Ireland in 1875, an honorary fellow of Peterhouse in 1885, and an honorary LLD of Glasgow University in 1901.

His eldest son, John Guthrie, became principal of the Government Central College at Mysore. His third son, Frederick (Freddie) Guthrie Tait was Scotland's champion golfer in 1896 and 1898; a soldier in the Black Watch, he served in South Africa from 1899, was wounded at Magersfontein, recovered, but was killed instantly at Koodoosberg on 7 February 1900 leading an assault on the Boers' position. Although Professor Tait continued for another year in the Edinburgh chair, he never recovered from the blow. Little more than three months after retirement, Tait died at Challenger Lodge, Wardie, Leith, on 4 July 1901. His funeral was at St John's Episcopal Church on 6 July, with burial in the churchyard to the east of the church.


C. G. Knott, Life and scientific work of Peter Guthrie Tait (1911)
C. Smith and M. N. Wise, Energy and empire: a biographical study of Lord Kelvin (1989)
D. B. Wilson, 'P. G. Tait and Edinburgh natural philosophy, 1860-1901', Annals of Science, 48 (1991), 267-87
d. cert.

NL Scot., corresp.
U. Edin. L., corresp. and lecture notes |  Air Force Research Laboratories, Cambridge, Massachusetts, letters to Lord Rayleigh
CUL, corresp. with James Clerk-Maxwell
CUL, corresp. with Lord Kelvin
CUL, corresp. with Sir George Stokes
CUL, corresp. with William Thomson and G. G. Stokes
TCD, letters to Sir William Rowan Hamilton
U. Glas. L., corresp. with Lord Kelvin
U. St Andr. L., letters to James David Forbes

G. Reid, oils, 1882, U. Edin.
G. Reid, portrait, c.1882, Scot. NPG [see illus.]
W. Hole, etching, 1884, NPG; repro. in W. Hole, Quasi cursores: portraits of the high officers and professors of The University of Edinburgh at its tercentenary festival (1884)
G. Reid, oils, 1891, Royal Society of Edinburgh; replicas, Scot. NPG, Peterhouse, Cambridge
T. Wageman, watercolour drawing, Trinity Cam.

Wealth at death  
£24,939 5s. 5d.: confirmation, 29 Aug 1901, CCI

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