The extremity of a brass tube, T, 0.5 to 0.6 of a meter in length and smaller in diameter than the tube to be gauged, is cut into four narrow strips a few centimeters in length. The extremity of each of these strips is bent toward the axis of the tube. Two of them, m and m', opposite each other are made very flexible, and carry, riveted to their extremities, two steel buttons, the heads of which, placed in the interior, have the form of an obtuse quoin with rounded edge directed perpendicular to the tube's axis. The other extremities of these buttons are spherical and polished and serve as caliper points in the operation of measuring. These buttons are given a thickness such that when the edges of their heads are in contact, the external diameter of the tube exceeds the distance apart of the two calibrating points by more than one millimeter. But such distance apart is increased within certain limits by inserting between the buttons a German silver wedge, L, carried by a rod, t, which traverses the entire tube, and which is maneuvered by a head, B, fixed to its extremity. This rod carries a small screw, v, whose head slides in a groove, r, in the tube, so as to limit the travel of the wedge and prevent its rotation. Beneath the head, B, the rod is filed so as to give it a plane surface for the reception of a divided scale. A corresponding slit in the top of the tube carries the index, I, of the scale. The principal divisions of the scale have been obtained experimentally, and traced opposite the index when the calibrating points were exactly 7, 8, 9 etc., millimeters apart. As the angle of the wedge is about one tenth, the intervals between these divisions are about one centimeter. These intervals are divided into ten parts, each of which corresponds to a variation in distance of one tenth of a millimeter.