first carriage 31 is detectable for the computer via the incremental length transducer 36 the second carriage 32 is movable toward and away from the gear wheel with the aid of a control motor 37 the third carriage 33 is located resting on stops 39 of the second carriage 32 being subjected to the force of a spring 38 fig7 shows the status of the measuring apparatus after it has been levelled and the orientation sensor 34 has been positioned with respect to the center of rotation of the gear wheel as has been described above in conjunction with fig1 4 now as shown in fig8 a tooth gap is approached with the orientation sensor 34 the carriage 31 is moved by hand in the x dirrection into the appropriate position and the carriage 32 is moved with the aid of the control motor 37 in the direction toward the gear wheel to be tested until such time as the carriage 33 is raised from the stops 39 and the ball of the orientation sensor 34 thus under the force of the spring 38 is located resting on both flanks of the tooth gap it has approached in this position from the values x t and the theoretically correct radial single ball dimension m rk the angle u03c6 o is again arrived at as the positioning for a possible later measuring operation after this positioning process adjacent tooth gaps are likewise approached in the manner described above and the angle u03c6 o there is ascertained so.