the non-scalding property of steam issuing from a high-pressure boiler. He formulated between 1851 and 1854, with scientific precision, in a long communication to the Royal Society of Edinburgh, the two great laws of thermodynamics — (1) the law of equivalence discovered by Joule, and (2) the law of transformation, which he generously attributed to Carnot and Clausius. Clausius, indeed, had done little more than put into mathematical language the equation of the Carnot cycle, corrected by the arbitrary substitution of the reciprocal of the absolute temperature ; but Thomson was never grudging of the fame of independent discoverers. 'Questions of personal priority,' he wrote, 'however interesting they may be to the persons concerned, sink into insignificance in the prospect of any gain of deeper insight into the secrets of nature.' He gave a demonstration of the second law, founding it upon the axiom that it is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. Further, by a most ingenious use of the integrating factor to solve the differential equation for the quantity of heat needed to alter the volume and temperature of unit mass of the working substance, he gave precise mathematical proof of the theorem that the efficiency of the perfect engine working between given temperatures is inversely proportional to the absolute temperature. In collaboration with Joule, he worked at the 'Thermal Effects of Fluids in Motion,' the results appearing between 1852 and 1862 in a series of four papers in the 'Philosophical Transactions,' and four others in the 'Proceedings of the Royal Society.' Thus were the foundations of thermodynamics laid. In later years he rounded off his thermodynamic work by enunciating the doctrine of available energy.
This brilliant development and generalisation of the subject did not content Thomson. He inquired into its applications to human needs and to the cosmic consequences it involved. Thus he not only suggested the process of refrigeration by the sudden expansion of compressed cooled air, but propounded the doctrine of the dissipation of energy. If the availability of the energy in a hot body be proportional to its absolute temperature, it follows that as the earth and the sun — indeed, the whole solar system itself — cool down towards one uniform level of temperature, all life must perish and all energy become unavailable. This far-reaching conclusion once more suggested the question of a beginning of the Cosmos, a question which had arisen in the consideration of the Fourier doctrine of the flow of heat. His note-books of this time show that he had also been applying Fourier's equations to a number of outlying problems capable of similar mathematical treatment, such as the diffusion of fluids and the transmission of electric signals through long cables.
In 1852 Thomson married his second cousin Margaret, daughter of Walter Crum, F.R.S., and resigned his Cambridge fellowship. His wife's precarious health necessitated residence abroad at various times. In the summer of 1855, while they stayed at Kreuznach, Thomson sent to Helmholtz, whose acquaintance he desired to make, an invitation to come to England in September to attend the 'British Association meeting at Glasgow. On 29 July Helmholtz arrived at Kreuznach to make Thomson's acquaintance before his journey to England. On 6 August Hebnholtz wrote to his wife of the deep impression that Thomson, 'one of the first mathematical physicists of Europe,' made on him. 'He far exceeds all the great men of science with whom I have made personal acquaintance, in intelligence, and lucidity, and mobility of thought, so that I felt quite wooden beside him sometimes.' A year later Helmholtz again met Thomson at Schwalbach and described him as 'certainly one of the first mathematical physicists of the day, with powers of rapid invention such as I have seen in no other man.' Subsequently Helmholtz visited Thomson in Scotland many times, and his admiration grew steadily.
The utilisation of science for practical ends was Thomson's ambition through life. 'There cannot,' he said in a lecture to the Institution of Civil Engineers in May 1883, 'be a greater mistake than that of looking superciliously upon practical applications of science. The life and soul of science is its practical application ; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind' (see Popular Lectures and Addresses, i. 79).
