and Laplace, he had discussed magnetic distributions by aid of the hydrodynamic equation of continuity. To Thomson are due the now familiar terms 'permeability' and 'susceptibility' in the consideration of the magnetic properties of iron and steel. In these years Thomson was also writing on the secular cooling of the earth, and investigating the changes of form during rotation of elastic spherical shells. At the same time he embarked with his friend Professor Peter Guthrie Tait [q. v. Suppl. II] on the preparation of a text-book of natural philosophy. Though the bulk of the writing was done by Tait, the framework of it thought and its most original parts are due to Thomson. The first part of the first volume of Thomson and Tait's 'Treatise on Natural Philosophy' was published in 1867, the second part only in 1874. No more was published, though the second edition of the first part was considerably enlarged. The book had the effect of revolutionising the teaching of natural philosophy.
Thomson's contributions to the theory of elasticity are no less important than those he made to other branches of physics. In 1867 he communicated to the Royal Society of Edinburgh a masterly paper 'On Vortex Atoms' ; seizing on Hehnholtz's proof that closed vortices could not be produced in a liquid perfectly devoid of internal friction, Thomson showed that if no such vortex could be artificially produced, then if such existed it could not be destroyed, but that being in motion and having the inertia of rotation, it would have elastic and other properties. He showed that vortex rings (like smokerings in air) in a perfect medium are stable, and that in many respects they possess qualities essential to the properties of material atoms — permanence, elasticity, and power to act on one another through the medium at a distance. The different kinds of atoms known to the chemist as elements were to be regarded as vortices of different degrees of complexity. The vortex-atom theory was linked to Ms other important researches on gyrostatic problems. Though he came to doubt whether the vortex-atom hypothesis was adequate to explain all the properties of matter, the conception bears witness to his great mental power.
In 1870 Lady Thomson, whose health had been failing for several years, died. In the same year the University of Glasgow was removed to the new buildings on Gilmore Hill, overlooking the Kelvin River. Thomson had a house here in the terrace assigned for the residences of the professors, adjoining his laboratory and lecture-room.
On 17 June 1874 he married Prances Anna, daughter of Charles F. Blandy of Madeira, whom he had met on cable-laying expeditions. In 1875 he built at Netherhall, near Largs, a mansion in the Scottish baronial style ; and in his later life, though he had a London house in Eaton Place, Netherhall was his chief home. From his youth he had been fond of the sea, and had early owned boats on the Qyde. For many years his sailing yacht the Lalla Rookh was conspicuous, and he was an accomplished navigator. His experiences at sea in cable-laying had taught him much, and in return he was now to teach science in navigation. Between 1873 and 1878 he reformed the mariners' compass, on which he undertook to write a series of articles in 'Good Words' in 1873 ; he lightened the moving parts of the compass to avoid protracted oscillations, and to facilitate the correction of the quadrantal and other errors arising from the magnetism of the ship's hull. At first the Admiralty would have none of it. Even the astronomer royal condemned it. 'So much for the astronomer royal's opinion,' he ejaculated. But the compass won its way ; and until recently was all but universally adopted both in the navy and in the mercantile marine (see, for Thomson's contributions to navigation, his Popular Lectures, vol. iii., and the Kelvin Lecture (1910) of Sir J. A. Ewing).
Dissatisfied with the clumsy appliances used in sounding, when the ship had to be stopped before the sounding line could be let down, Thomson devised in 1872 the well-known apparatus for taking flying soundings by using a line of steel piano wire. He had great faith in navigating by use of sounding fine, and delighted to narrate how, in 1877, in a time of continuous fog, he navigated his yacht all the way across the Bay of Biscay into the Solent trusting to soundings only. He also published a set of Tables for facilitating the use of Sumner's method at sea. He was much occupied with the question of the tides, not merely as a sailor, but because of the interest attending their mathematical treatment in connection with the problems of the rotation of spheroids, the harmonic analysis of their complicated periods by Fourier's methods, and their relation to hydrodynamic problems generally. He invented a tide-predicting machine, which will predict for any given port the rise and
