, mass of fluid in whirling or rotary motion. To simplify the analysis, vortex motion usually describes motions in a frictionless fluid. In such cases the absence of friction would make it impossible to create or to destroy vortex motion. Motion in such a fluid would be a permanent flow pattern; the velocity of the fluid element instantaneously passing through a given point in space would be constant in time. Lines drawn so that their direction is that of the axis of rotation of the fluid are called vortex lines, and if these lines close on themselves they are called vortex rings. Hermann von Helmholtz was probably the first to investigate the properties of vortex motion; Lord Kelvin developed a theory of the material atom as a vortex ring; and J. C. Maxwell worked out a theory of electromagnetism, assuming that every magnetic tube of force was a vortex with an axis of rotation coinciding with the direction of the force. Many properties have been mathematically proved for the perfect frictionless fluid. In practice, however, their full realization is impossible because no frictionless fluid exists. To maintain a vortex motion a continuous energy supply to overcome friction is needed. A smoke ring is a familiar example of a typical vortex motion in which the medium is air. In this case the rings are stable for a short time because of the comparatively slight friction in air. An illustration of vortex motion in a liquid medium is the small whirlpool formed by water as it drains from a wash basin. In nature, illustrations of vortical motion on a larger scale are seen in waterspouts, whirlpools, and tornadoes. Investigations of sunspots reveal enormous vortices in the gases surrounding them. The principles of vortex motion are applied in aerodynamics, e.g., to explain the movement of air behind the trailing edge of a wing.