As the eighteenth century came to a close, human understanding of electrostatics approached maturity. Benjamin Franklin had already established the notion of electric charge and the conservation of charge; Charles-Augustin de Coulomb had enunciated his inverse-square law of electrostatics. In 1777, Joseph-Louis Lagrange introduced the concept of a potential function that can be used to compute the gravitational force of an extended body. In 1812, Poisson adopted this idea and obtained the appropriate expression for electricity, which relates the potential function formula_13 to the electric charge density formula_14. Poisson discovered that Laplace's equation is valid only outside of a solid. A rigorous proof for masses with variable density was first given by Carl Friedrich Gauss in 1839. Poisson's work on potential theory inspired George Green's 1828 paper, "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism". Poisson's equation is applicable in not just gravitation, but also electricity and magnetism.