Abstract: Apparatus for controlling the position of a part, e.g. a feeler or work tool, along two orthogonal directions, the part being slideable in a first slide extending in one direction and mounted on a carriage movable along a second slide extending in the other direction and mounted on a support. The apparatus comprises a device for locating the position of the carriage on the second slide and the movable part on the first slide, a device for measuring the error in straightness of said second slide and a device for measuring the error in orthogonality of the first slide, each device comprising a laser generator for producing a laser beam parallel to the respective direction and a photoelectric detector in the path of the respective beam and subject to the respective error to be measured.