On Laplace’s differential equations for the tides
This paper is an investigation of the validity of the assumptions made by Laplace in framing his well-known differential equations for the tides of the ocean. Since his time these equations have been used by all the principal workers on the dynamical theory of the tides, but in recent years it has been claimed, mainly in Norway, that they are quite inadequate. Let ω denote the angular speed of the earth’s rotation and let t denote the time; let r denote the distance of a point in the ocean from the earth’s centre, and θ the co-latitude of this point; let u, v and w denote the components of the velocity of a particle of water in the directions respectively of increasing θ, east longitude and r . Then the corresponding components of the acceleration of the particle are respectively: