The paper by Horace Lamb discusses the theory of waves in an infinitely long elastic plate, building on earlier work by Pochhammer and Lord Rayleigh. The main focus is on two-dimensional waves in a solid bounded by parallel planes, with the wavelength assumed to be much larger than the thickness of the plate. Lamb examines the period equation for these waves, which is initially challenging to solve. He introduces a method to simplify the problem and provides a detailed analysis of the more important modes of vibration, including their wave lengths and wave velocities. Lamb considers both symmetrical and asymmetrical vibrations, deriving equations for the stresses and displacements. For symmetrical vibrations, he derives the period equation and finds that for long waves, the wave velocity is consistent with the ordinary theory. For very short waves, the period equation reduces to the form of Rayleigh waves. He also explores the case of incompressible materials, where the displacement function analogous to the stream function in hydrodynamics is introduced. For asymmetrical vibrations, Lamb derives the period equation and discusses the modes of vibration, including those with a rotation of matter around nodes. He also examines the influence of compressibility, showing that the numerical calculations are not significantly more complex when this hypothesis is abandoned. The paper concludes with a discussion of the physical limits to the speed of propagation of disturbances in elastic materials.The paper by Horace Lamb discusses the theory of waves in an infinitely long elastic plate, building on earlier work by Pochhammer and Lord Rayleigh. The main focus is on two-dimensional waves in a solid bounded by parallel planes, with the wavelength assumed to be much larger than the thickness of the plate. Lamb examines the period equation for these waves, which is initially challenging to solve. He introduces a method to simplify the problem and provides a detailed analysis of the more important modes of vibration, including their wave lengths and wave velocities. Lamb considers both symmetrical and asymmetrical vibrations, deriving equations for the stresses and displacements. For symmetrical vibrations, he derives the period equation and finds that for long waves, the wave velocity is consistent with the ordinary theory. For very short waves, the period equation reduces to the form of Rayleigh waves. He also explores the case of incompressible materials, where the displacement function analogous to the stream function in hydrodynamics is introduced. For asymmetrical vibrations, Lamb derives the period equation and discusses the modes of vibration, including those with a rotation of matter around nodes. He also examines the influence of compressibility, showing that the numerical calculations are not significantly more complex when this hypothesis is abandoned. The paper concludes with a discussion of the physical limits to the speed of propagation of disturbances in elastic materials.