<P> The law of conservation of vis viva was championed by the father and son duo, Johann and Daniel Bernoulli . The former enunciated the principle of virtual work as used in statics in its full generality in 1715, while the later based his Hydrodynamica, published in 1738, on this single conservation principle . Daniel's study of loss of vis viva of flowing water led him to formulate the Bernoulli's principle, which relates the loss to be proportional to the change in hydrodynamic pressure . Daniel also formulated the notion of work and efficiency for hydraulic machines; and he gave a kinetic theory of gases, and linked the kinetic energy of gas molecules with the temperature of the gas . </P> <P> This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the D'Alembert's principle and Lagrangian and Hamiltonian formulations of mechanics . </P> <P> Émilie du Châtelet (1706--1749) proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum . Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem' s Gravesande in 1722 in which balls were dropped from different heights into a sheet of soft clay . Each ball's kinetic energy - as indicated by the quantity of material displaced - was shown to be proportional to the square of the velocity . The deformation of the clay was found to be directly proportional to the height the balls were dropped from, equal to the initial potential energy . Earlier workers, including Newton and Voltaire, had all believed that "energy" (so far as they understood the concept at all) was not distinct from momentum and therefore proportional to velocity . According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped from . In classical physics the correct formula is E k = 1 2 m v 2 (\ displaystyle E_ (k) = (\ frac (1) (2)) mv ^ (2)), where E k (\ displaystyle E_ (k)) is the kinetic energy of an object, m (\ displaystyle m) its mass and v (\ displaystyle v) its speed . On this basis, Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to relate it in different forms (kinetic, potential, heat ...). </P> <P> Engineers such as John Smeaton, Peter Ewart, Carl Holtzmann, Gustave - Adolphe Hirn and Marc Seguin recognized that conservation of momentum alone was not adequate for practical calculation and made use of Leibniz's principle . The principle was also championed by some chemists such as William Hyde Wollaston . Academics such as John Playfair were quick to point out that kinetic energy is clearly not conserved . This is obvious to a modern analysis based on the second law of thermodynamics, but in the 18th and 19th centuries the fate of the lost energy was still unknown . </P>

Who made the law of conservation of energy