A linear gauging head, or cartridge head, comprises a casing, a spindle movable with respect to the casing along a longitudinal axis, a feeler coupled to a first end of the spindle and a differential position transducer with windings, fixed with respect to casing, and a core coupled to a second end of spindle. The spindle is guided by recirculating ball bushings with rolling elements that cooperate with the spindle and thus allow its displacement with respect to the casing.