Abstract: The telescoping parts of a rotary measuring arm mounted on an axis between wo centering devices enable the outer part of the measuring arm, which is equipped with a scanning roller, to be let out or pushed in by the contour of the bore as the arm is swung around by a remote control drive. During such a scan of the bore wall, an inductive or capacitive transducer provides signals representative of the radius measured to a remote location. The three legs of each centering device can be retracted or extended together by the same amount when the measuring device is removed from or set into place in the bore. A drive is also provided for retracting the measuring arm when the apparatus is being moved in the bore.