long, having a hole near one end and a 1 in. slot at the other, is screwed tightly into the head of the spikes. The middle part of the bar is divided into inches and tenths of an inch. A separate brass hanger is fitted to the bar, having a vernier with its zero at the middle of the hanger and corresponding to a plumb line attached below. The hanger is moved back and forth until it coincides with the line of sight of the transit, and then the readings of the vernier are recorded. Any time that the hanger is placed on the bar and the vernier marks the same reading, the plumb line will indicate the center line of the tunnel. When, instead of one bar, two are inserted at a distance of 20 or 30 ft. apart, the plumb lines suspended from the hangers will represent the vertical plane passing through the axis of the tunnel in coincidence with the one staked out on the surface ground. [Illustration: FIG. 2.--B. R. Value’s Device for Locating the Center Line Inside of a Tunnel.] The location of the center line of a long tunnel, which is to be excavated under high mountains, is a very difficult operation, and the engineers usually leave this part of the work to astronomers, who fix the stations from which the engineers direct the work of construction. The center lines of all the great Alpine tunnels were located by astronomers who used instruments of large size. Thus, in ranging the center line of the St. Gothard tunnel, the theodolite used had an object glass eight inches in diameter.[3] Instead of the ordinary mounting a masonry pedestal with a perfectly level top is employed to support the instrument during the observations. The location is made by means of triangulation. The various operations must be performed with the greatest accuracy, and repeated several times in such a way as to reduce the errors to a minimum, since the final meeting of the headings depends upon their elimination. [3] See also the Simplon Tunnel, Chapter X. [Illustration: FIG. 3.--Triangulation System for Establishing the Center Line of the St. Gothard Tunnel.]