In 1870, Rudolf Clausius delivered the lecture "On a Mechanical Theorem Applicable to Heat" to the Association for Natural and Medical Sciences of the Lower Rhine, following a 20-year study of thermodynamics. The lecture stated that the mean vis viva of the system is equal to its virial, or that the average kinetic energy is equal to ⁠ 1 / 2 ⁠ the average potential energy. The virial theorem can be obtained directly from Lagrange's identity as applied in classical gravitational dynamics, the original form of which was included in Lagrange's "Essay on the Problem of Three Bodies" published in 1772. Karl Jacobi's generalization of the identity to N bodies and to the present form of Laplace's identity closely resembles the classical virial theorem. However, the interpretations leading to the development of the equations were very different, since at the time of development, statistical dynamics had not yet unified the separate studies of thermodynamics and classical dynamics. The theorem was later utilized, popularized, generalized and further developed by James Clerk Maxwell, Lord Rayleigh, Henri Poincaré, Subrahmanyan Chandrasekhar, Enrico Fermi, Paul Ledoux, Richard Bader and Eugene Parker. Fritz Zwicky was the first to use the virial theorem to deduce the existence of unseen matter, which is now called dark matter. Richard Bader showed the charge distribution of a total system can be partitioned into its kinetic and potential energies that obey the virial theorem. As another example of its many applications, the virial theorem has been used to derive the Chandrasekhar limit for the stability of white dwarf stars.