The “twist surfaces,” of which this is a case, stand in the same relation to the helicoid surface as the anchor-ring does to the cylinder. In the helicoid the generating line, at right angles to the axis, rotates about the axis as the point of intersection moves along it. In the twist surfaces the generating line is always at right angles to a fixed circle, and rotates about the tangent to the circle at the point of intersection, as the point of intersection moves round the circle. The species of twist surface is defined by the ratio of the angular motion of the generating line to that of the point of intersection. In the particular case illustrated by the model, the generating line turns through two right angles, while the point of intersection makes one whole revolution; that is, the rate of angular motion of the generating line is one-half of that of the point of intersection.