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
