Let S be the class of functions w — /(« ) = z + a2 z2 + a3 23 + ... analytic and schlicht in the unit disc | z | < 1. Let ry denote the least upper bound of the radii of ali öpen discs contained in the map of w = f (z) that is schlicht for | z | < 1 and h a s/' (0) = 1. Then