A baseplate can be turned relative to a workpiece holder and concentrically to its axis. This baseplate forms in annular reference plane and has fastened to it at least one length measuring instrument. The tips of the feelers of these instruments rest on the workpiece surface to be measured. - The axes of the feeler tips run at right angles to the reference plane. At least one length measuring instrument can be displaced radially. The length measuring instruments can be inductive displacement pick-ups which transmit deviations from flatness as electrical quantities to an electronic counting and arithmetic unit.
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