itself belongs to both fields, so that turning in either direction is possible from points in it. About points in a N both turnings are possible to any extent, but about points in aN' they can occur only through infinitely small angles. For so soon as turning has commenced about any of the last-mentioned points, the normal passes to one 01: the other side of the centre of motion, which is thus thrown into the field either of right- or of left-handed turning, and a glance at the figure shows that it must necessarily pass into that field which does not permit the continuance of the turning commenced.
Two Points of Restraint. If a figure have two points of restraint, as a and b Fig. 63, and their fields of turning be
separated by drawing the normals a a' and b b ', we find at once that the field of R. H. turning of a is covered throughout the angle a b between the normals by the field of L. H. turning of b, and in this way both turnings are rendered impossible. Similarly, turning can- not occur about points in the angle a! I', where again fields of right- and left- handed turning cover each other. In the angle b a' two fields of R. H. and in
a Ob' two fields of L. H. turning coincide. About points in these areas therefore (which are shaded in the figure) right- and left- handed turning are respectively possible. Thus of the two pairs of angles at the intersection of the normals, one pair (that facing the intersecting point T of the tangents) forms a field of restraint for both turnings, while the remaining pair is the field of turning, one half of it being the field of right- handed and the other half of left-handed turning. The point being common to both fields, turning in both directions may take place about it.
Fig.
If the normals to the given points of restraint be parallel and opposite in direction (i.e. at an angle of 180 to each other), the angular field becomes a strip between the normals, about points in which either right- (Fig. 64) or left-handed turning (Fig. 65)
