The geometry of slides and turns of oriented lineal elements in the plane was first studied by Kasner . Slides and turns generate whirls, which constitute a three-parameter group W
3. The product of W
3 and M
3, the three-parameter group of Euclidean displacements in the plane, yields a sixparameter group of whirl-motions
6. The geometry of turbines, and also of general series of lineal elements, under G
6 was investigated by Kasner in  and, in subsequent papers, by Kasner and DeCicco, particularly in , , , .