 In 1882, Helmholtz gave an address, “The Thermodynamics of Chemical Processes,” at the Berlin Academy. Up until Helmholtz’s address, chemical reactions had been explained by “chemical forces” or “affinities” between chemical substances, measured quantitatively by the heat developed during a chemical reaction. Gustave Coriolis had clarified the notion of work as the product of force over distance in 1821, and this notion was in common use by the late 19th century. In his address, Helmholtz “proved that affinity was not given by the heat evolved in a chemical reaction but rather by the maximum work produced when the reaction was carried out reversibly” (Kragh 1993, 405). However, while kinetic and mechanical energy can be converted into heat in every case, only in restricted cases can heat be converted into kinetic and mechanical energy. Hence, the equations describing chemical processes involving heat could not always be reversed. These are the conditions under which the Legendre transform could not be applied, and thus the Hamiltonian could not be determined for that system.