Paper, 'On the dynamical theory of the tides of long period' by G H [George Howard] Darwin Darwin writes: 'In the following note an objection is raised against Laplace’s method of treating these tides, and a dynamical solution of the problem, founded on a paper by Sir William Thomson, is offered. Let θ, Φ be the colatitude and longitude of a point in the ocean, let ξ and η sin θ be the displacements from its mean position of the water occupying that point at the time t, let h be the height of the tide, and let ℓ be the height of the tide according to the equilibrium theory; let n be the angular velocity of the earth’s rotation, g gravity, a the earth’s radius, and γ the depth of the ocean at the point θ, Φ.' Annotations in pencil and ink throughout. Subject: Mathematics / Physics Received 5 November 1886. Read 25 November 1886. A version of this paper was published in volume 41 of the Proceedings of the Royal Society as 'On the dynamical theory of the tides of long period'. 1886