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hagen, 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