The St. Gothard tunnel furnishes perhaps the best illustration of careful work in locating the center line of long rectilinear tunnels of any tunnel ever built. The length of this tunnel is 9.25 miles, and the height of the mountain above it is very great. The center line was located by triangulation by two different astronomers using different sets of triangles, and working at different times. The set or system of triangles used by Dr. Koppe, one of the observers, is shown by Fig. 3; it consists of very large and quite small triangles combined, the latter being required because the entrances both at Airolo and Goeschenen were so low as to permit only of a short sight being taken. The apices of the triangles were located by means of the contour maps of the Swiss Alpine Club. Each angle was read ten times, the instrument was collimated four times for each reading, and was afterwards turned off 5° or 10° to avoid errors of graduation. The average of the errors in reading was about one second of arc. The triangulation was compensated according to the method of least squares. The probable error in the fixed direction was calculated to be 0.8″ of arc at Goeschenen and 0.7″ of arc at Airolo. From this it was assumed that the probable deviation from the true center would be about two inches at the middle of the tunnel, but when the headings finally met this deviation was found to reach eleven inches. Comparatively few tunnels are driven by working from the entrances alone, the excavation being usually prosecuted at several points at once by means of shafts. In these cases, in order to direct the excavation correctly, it is necessary to fix the center line on the bottom of the shaft. This is accomplished in two ways,--one being employed when the shaft is located directly over the center line, and the other when the shaft is located to one side of the center line. When the shaft is located on the center line two small pillars are placed on opposite edges of the shaft and collimating with the center line as shown by Fig. 4. On these two pillars the points corresponding to the center line are correctly marked, and connected by a wire stretched between them. To this wire two plumb bobs are fastened as far apart as possible. These plumb bobs mark two points on the center line at the bottom of the shaft, and from them the line is extended into the headings as the work advances. In these operations, heavy plumb bobs are used. In the New York subway plumb bobs of steel, weighing 25 lbs. each, were used, and to prevent rotation they were made with cross-sections, in the shape of a Greek cross, and were sunk in buckets filled with water. Owing to the difference between the temperature at the top and that at the bottom of the shaft, strong currents of air are produced, which keep in constant oscillation the wires to which the bobs are suspended. [Illustration: FIG. 4.--Method of Transferring the Center Line down Center Shafts.]