It is well known that the solution of the mathematical problem of the motion of liquid arising from the motion through it of solids has been effected in comparatively few instances, and in these, such as the sphere and the ellipsoid, the surface is defined by a single equation. In the following investigation, however, we seem naturally to come across cases where the solid might be described as “a compound body,” consisting as it does of parts defined by different equations. It is possible that the method employed might lead to the solution of analogous problems in Sound, Heat, or Electricity.