The article "On the Instability of Jets" by Lord Rayleigh discusses the instability of fluid jets, particularly focusing on two causes: capillary force and dynamic forces. The capillary force causes an infinite cylinder to disintegrate into smaller masses due to the surface tension, while the dynamic force is more complex and depends on the translational motion of the jet. Rayleigh presents a detailed mathematical analysis to determine the conditions under which the cylinder becomes unstable. He uses Lagrange's method to derive expressions for the potential and kinetic energies of the motion, leading to the conclusion that the instability is maximized when the ratio of wave-length to diameter is approximately 4.508. This value is derived from the solution of a transcendental equation involving Bessel functions. The article also explores the instability caused by the translational motion of the jet, using Helmholtz's and Thomson's work on fluid discontinuities. Rayleigh applies Thomson's method to determine the law of falling away from unstable equilibrium for plane and cylindrical surfaces of separation. He provides specific solutions for different initial conditions and boundary conditions, showing how the waves on the surface of separation evolve over time. Overall, the article provides a comprehensive theoretical framework for understanding the instability of fluid jets, including both static and dynamic factors, and offers practical insights into the behavior of such jets.The article "On the Instability of Jets" by Lord Rayleigh discusses the instability of fluid jets, particularly focusing on two causes: capillary force and dynamic forces. The capillary force causes an infinite cylinder to disintegrate into smaller masses due to the surface tension, while the dynamic force is more complex and depends on the translational motion of the jet. Rayleigh presents a detailed mathematical analysis to determine the conditions under which the cylinder becomes unstable. He uses Lagrange's method to derive expressions for the potential and kinetic energies of the motion, leading to the conclusion that the instability is maximized when the ratio of wave-length to diameter is approximately 4.508. This value is derived from the solution of a transcendental equation involving Bessel functions. The article also explores the instability caused by the translational motion of the jet, using Helmholtz's and Thomson's work on fluid discontinuities. Rayleigh applies Thomson's method to determine the law of falling away from unstable equilibrium for plane and cylindrical surfaces of separation. He provides specific solutions for different initial conditions and boundary conditions, showing how the waves on the surface of separation evolve over time. Overall, the article provides a comprehensive theoretical framework for understanding the instability of fluid jets, including both static and dynamic factors, and offers practical insights into the behavior of such jets.