fall of the tides, which it gives in the form of a continuous curve recorded on paper ; the entire curves for a whole year being inscribed by the machine automatically in about four hours. Further than this, adopting a mechanical integrator, the device of his ingenious brother, James Thomson, he invented a harmonic analyser — the first of its kind — capable not only of analysing any given periodic curve such as the tidal records and exhibiting the values of the coefficients of the various terms of the Fourier series, but also of solving differential equations of any order.

Wave problems always had a fascination for Thomson, and he was familiar with the work of the mathematicians Poisson and Cauchy on the propagation of wave-motion. In 1871 Helmholtz went with him on the yacht Lalla Rookh to the races at Inverary, and on some longer excursions to the Hebrides. Together they studied the theory of waves, 'which he loved,' says Helmholtz, 'to treat as a race between us.' On calm days he and Helmholtz experimented on the rate at which the smallest ripples on the surface of the water were propagated. Almost the last publications of Lord Kelvin were a series of papers on 'Deep Sea Ship Waves,' communicated between 1904 and 1907 to the Royal Society of Edinburgh. He also gave much attention to the problems of gyrostatics, and devised many forms of gyrostat to elucidate the problems of kinetic stability. He held that elasticity was explicable on the assumption that the molecules were the seat of gyrostatic motions. A special opportunity of practically applying such theories was offered him by his appointment as a member of the admiralty committee of 1871 on the designs of ships of war, and of that of 1904-5 which resulted in the design of the Dreadnought type of battleship.

In 1871 he was president of the British Association at its meeting in Edinburgh. His presidential address ranged luminously over many branches of science and propounded the suggestion that the germs of life might have been brought to the earth by some meteorite. With regard to the age of the earth he had already from three independent lines of argument inferred that it could not be finite, and that the time demanded by the geologists and biologists for the development of life must be finite. He himself estimated it at about a hundred million of years at the most. The naturalists, headed by Huxley, protested against Thomson's conclusion, and a prolonged controversy ensued. He adhered to his propositions with unrelaxing tenacity but unwavering courtesy. 'Gentler knight there never broke a lance,' was Huxley's dictum of his opponent. His position was never really shaken, though the later researches of John Perry, and the discovery by R. J. Strutt of the degree to which the constituent rocks of the earth contain radioactive matter, the disgregation of which generates internal heat, may so far modify the estimate as somewhat to increase the figure which he assigned. In his presidential address to the mathematical and physical section of the British Association at York in 1881 he spoke of the possibility of utilising the powers of Niagara in generating electricity. He also read two papers, in one of which he showed mathematically that in a shunt dynamo best economy of working was attained when the resistance of the outer -circuit was a geometric mean between the resistances of the armature and of the shunt. In the other he laid down the famous law of the economy of copper lines for the transmission of power.

Thomson's lively interest in the practical — indeed the commercial — application of science, led him to study closely the first experiments in electric lighting. Such details as fuses and the suspension pulleys with differential gearing by which incandescent lamps can be raised or lowered absorbed some of his attention. He gave evidence before the parliamentary committee on electric fighting of 1879, and discussed the theory of the electric transmission of power, pointing out the advantage of high voltages. The introduction into England in 1881 of the Faure battery accumulator by which electricity could be economically stored excited him greatly. Thomson's various inventions — electrometers, galvanometers, siphon-recorders, and his compasses were at first made by James White, an optician of Glasgow. In White's firm, which became Kelvin & White, Limited, he was soon a partner, taking the keenest commercial interest in its operations, and frequenting the factory daily to superintend the construction. To meet demands for new measuring instruments he devised from time to time potential galvanometers, ampere gauges, and a whole series of standard electric balances for electrical engineers. His patented inventions thus grew very numerous. Up to 1900 they numbered fifty-six. Of these eleven related to telegraphy, eleven to compasses and navigation apparatus, six to dynamo machines or electric lamps.