The article by J. Willard Gibbs discusses the equilibrium of heterogeneous substances, emphasizing the importance of the principle that a system will be in equilibrium when its entropy reaches a maximum. The author formulates this principle as a criterion for equilibrium, stating that for an isolated system, the variation of entropy must either vanish or be negative in all possible variations of the system's state that do not alter its energy. This criterion is expressed mathematically through equations involving energy, entropy, volume, temperature, and pressure. Gibbs further develops the concept by introducing the quantity \(\psi = \varepsilon - t\eta\) and the condition \((\delta \psi)_{t} \geqslant 0\), which is equivalent to the entropy criterion. He explains how these conditions can be applied to different masses in contact, osmotic forces, and the effect of gravity. The article also covers the stability of fluids, critical phases, and the behavior of gas mixtures with convertible components. Gibbs introduces the idea of fundamental equations, which relate the thermodynamic properties of substances, and discusses the stability of stressed solids and surfaces of discontinuity. He explores the conditions for equilibrium at these surfaces, including the concept of superficial tension. The article concludes with a discussion on liquid films and the influence of electromotive force on equilibrium conditions.The article by J. Willard Gibbs discusses the equilibrium of heterogeneous substances, emphasizing the importance of the principle that a system will be in equilibrium when its entropy reaches a maximum. The author formulates this principle as a criterion for equilibrium, stating that for an isolated system, the variation of entropy must either vanish or be negative in all possible variations of the system's state that do not alter its energy. This criterion is expressed mathematically through equations involving energy, entropy, volume, temperature, and pressure. Gibbs further develops the concept by introducing the quantity \(\psi = \varepsilon - t\eta\) and the condition \((\delta \psi)_{t} \geqslant 0\), which is equivalent to the entropy criterion. He explains how these conditions can be applied to different masses in contact, osmotic forces, and the effect of gravity. The article also covers the stability of fluids, critical phases, and the behavior of gas mixtures with convertible components. Gibbs introduces the idea of fundamental equations, which relate the thermodynamic properties of substances, and discusses the stability of stressed solids and surfaces of discontinuity. He explores the conditions for equilibrium at these surfaces, including the concept of superficial tension. The article concludes with a discussion on liquid films and the influence of electromotive force on equilibrium conditions.