defended König. Euler, rather than claiming priority, was a staunch defender of Maupertuis, and Euler himself prosecuted König for forgery before the Berlin Academy on 13 April 1752. The claims of forgery were re-examined 150 years later, and archival work by C.I. Gerhardt in 1898 and W. Kabitz in 1913 uncovered other copies of the letter, and three others cited by König, in the Bernoulli archives. Further development Euler continued to write on the topic; in his Réflexions sur quelques loix générales de la nature (1748), he called action "effort". His expression corresponds to modern potential energy, and his statement of least action says that the total potential energy of a system of bodies at rest is minimized, a principle of modern statics. Lagrange and Hamilton Much of the calculus of variations was stated by Joseph-Louis Lagrange in 1760 and he proceeded to apply this to problems in dynamics. In Mécanique analytique (1788) Lagrange derived the general equations of motion of a mechanical body. William Rowan Hamilton in 1834 and 1835 applied the variational principle to the classical Lagrangian function to obtain the Euler–Lagrange equations in their present form. Jacobi, Morse and Caratheodory In 1842, Carl Gustav Jacobi tackled the problem of whether the variational principle always found minima as opposed to other stationary points (maxima or stationary saddle points); most of his work focused on geodesics on two-dimensional surfaces. The first clear general statements were given by Marston Morse in the 1920s and 1930s, leading to what is now known as Morse theory. For example, Morse showed that the number of conjugate points in a trajectory equalled the number of negative eigenvalues in the second variation of the Lagrangian. A particularly elegant derivation of the Euler-Lagrange equation was formulated by Constantin Caratheodory and published by him in 1935. Gauss and Hertz Other extremal principles of classical mechanics have been formulated, such as Gauss's principle of least constraint and its corollary, Hertz's principle of least curvature. Disputes about possible teleological aspects The mathematical equivalence of the differential equations of motion and their integral counterpart has important philosophical implications. The differential equations are statements about quantities localized to a single point in space or single moment of time. For example, Newton's second law states that the instantaneous force F applied to a mass m produces an acceleration a at the same instant. By contrast, the action principle is not localized to