IV. On the dynamical theory of the tides of long period

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 .