The author proposes in this paper to resolve a particular case of the motion of fluids, not previously noticed, and susceptible of practical application, namely, the circumstances of the motion of an indefinitely extended non-elastic fluid, where agitated by a solid ellipsoidal body moving parallel to itself, according to any given law; always supposing the body's excursions very small compared with its dimensions. The question here stated is considered by the author to admit of an easy general solution.