The shape of the vacuum magnetic surfaces at a fixed toroidal angle in the Proto-Cleo torsatron was investigated by launching a beam of electrons along various magnetic-field lines. After completing a variable number of transits around the major axis, the beam was intercepted by a probe. The locations of the interception points for different numbers of toroidal transits trace out the minor cross section of the magnetic surfaces. A family of three experimentally measured magnetic surface cross sections are compared with computer magnetic surface cross sections. From interception-point location and corresponding time of flight data, the average rotational transform for each surface is calculated. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.