One part of the theory of capillary attraction, left defective by Laplace, namely, the action of a solid upon a liquid, and the mutual action between two liquids, was made dynamically perfect by Gauss. He stated the rule for angles of contact
between liquids and solids. A similar rule for liquids was established by Ernst Franz Neumann. Chief among recent workers on the mathematical theory of capillarity are Lord
Rayleigh and E. Mathieu.
The great principle of the conservation of energy was
established by Robert Mayer (1814–1878), a physician in
Heilbronn, and again independently by Colding of Copenhagen,
Joule, and Helmholtz. James Prescott Joule (1818–1889)
determined experimentally the mechanical equivalent of heat. Helmholtz in 1847 applied the conceptions of the
transformation and conservation of energy to the various branches of physics, and thereby linked together many well-known phenomena. These labours led to the abandonment of the corpuscular theory of heat. The mathematical treatment of thermic problems was demanded by practical considerations. Thermodynamics grew out of the attempt to determine mathematically how much work can be gotten out of a steam engine. Sadi-Carnot, an adherent of the corpuscular
theory, gave the first impulse to this. The principle known by his name was published in 1824. Though the importance of his work was emphasised by B. P. E. Clapeyron, it did not
meet with general recognition until it was brought forward by William Thomson. The latter pointed out the necessity
of modifying Carnot's reasoning so as to bring it into accord with the new theory of heat. William Thomson showed in 1848 that Carnot's principle led to the conception of an absolute scale of temperature. In 1849 he published "an account of Carnot's theory of the motive power of heat, with numerical results deduced from Regnault's experiments." In February, 1850, Rudolph Clausius (1822–1888), then in Zürich
(afterwards professor in Bonn), communicated to the Berlin Academy a paper on the same subject which contains the Protean second law of thermodynamics. In the same month William John M. Rankine (1820–1872), professor of engineering
and mechanics at Glasgow, read before the Royal Society of Edinburgh a paper in which he declares the nature of heat to consist in the rotational motion of molecules, and arrives at some of the results reached previously by Clausius. He does not mention the second law of thermodynamics, but in a subsequent paper he declares that it could be derived
from equations contained in his first paper. His proof of the second law is not free from objections. In March, 1851, appeared a paper of William Thomson which contained a