This article by J. Willard Gibbs discusses the equilibrium of heterogeneous substances, presenting a general criterion for thermodynamic equilibrium. It formulates the principle that for an isolated system, equilibrium is achieved when the entropy variation is either zero or negative under constant energy, or when the energy variation is either zero or positive under constant entropy. The article also introduces the concept of a force-function, such as ψ = ε - tη, which helps determine equilibrium conditions. It explores the equilibrium of masses in contact, osmotic forces, the effect of gravity, and fundamental equations for thermodynamic systems. The article also discusses the stability of fluids, coexistent phases, and critical phases, as well as the stability of fluids with respect to continuous changes of phase. It provides a detailed analysis of the conditions for equilibrium in different phases and the stability of surfaces of discontinuity. The article also addresses the elasticity of liquid films, the electromotive force in galvanic and electrolytic cells, and the relationship between electromotive force and the changes in the cell. The study of these phenomena provides a comprehensive understanding of the equilibrium and stability of thermodynamic systems.This article by J. Willard Gibbs discusses the equilibrium of heterogeneous substances, presenting a general criterion for thermodynamic equilibrium. It formulates the principle that for an isolated system, equilibrium is achieved when the entropy variation is either zero or negative under constant energy, or when the energy variation is either zero or positive under constant entropy. The article also introduces the concept of a force-function, such as ψ = ε - tη, which helps determine equilibrium conditions. It explores the equilibrium of masses in contact, osmotic forces, the effect of gravity, and fundamental equations for thermodynamic systems. The article also discusses the stability of fluids, coexistent phases, and critical phases, as well as the stability of fluids with respect to continuous changes of phase. It provides a detailed analysis of the conditions for equilibrium in different phases and the stability of surfaces of discontinuity. The article also addresses the elasticity of liquid films, the electromotive force in galvanic and electrolytic cells, and the relationship between electromotive force and the changes in the cell. The study of these phenomena provides a comprehensive understanding of the equilibrium and stability of thermodynamic systems.