=Parallel Longitudinal Trenches.=--The parallel longitudinal trench method of open-cut tunneling consists in excavating two narrow parallel trenches for the side walls, leaving the center core to be removed after the side walls have been built. The diagram, Fig. 112, shows the sequence of operations in this method. The two trenches No. 1 are first excavated a little wider than the side wall masonry, and strutted as shown by Fig. 113. At the bottoms of these trenches a foundation course of concrete is laid, as shown by Fig. 114, if the ground is soft; or the masonry is started directly on the natural material, if it is rock. From the foundations the walls are carried up to the level of the springing lines of the roof arch, if an arch is used; or to the level of its ceiling, if a flat roof is used. After the completion of the side walls, the portion of the excavation shown at No. 2, Fig. 112, is removed a sufficient depth to enable the roof arch to be built. When the arch is completed, it is filled above with well-rammed earth, and the surface is restored. The excavation of part No. 3 inclosed by the side walls and roof arch is carried on from the entrances and from shafts left at intervals along the line. [Illustration: FIG. 113.--Sketch Showing Method of Timbering Open-Cut Tunnels, Double Parallel Trench Method.] [Illustration: FIG. 114.--Side-Wall Foundation Construction Open-Cut Tunnels.] A modification of the method just described was employed in constructing the Paris underground railways. It consists in excavating a single longitudinal trench along one side of the street, and building the side wall in it as previously described. When this side wall is completed to the roof, the right half of part No. 2, Fig. 112, is excavated to the line _AB_, and the right-hand half of the roof arch is built. The space above the arch is then refilled and the surface of the street restored, after which the left-hand trench is dug and the side wall and roof-arch masonry is built just as in the opposite half. Generally the work is prosecuted by opening up lengths of trench at considerable intervals along the street and alternately on the left-and right-hand sides. By this method one-half of the street width is everywhere open to traffic, the travel simply passing from one side of the street to the other to avoid the excavation. When the lining has been completed, the center core of earth inclosed by it is removed from the entrances and shafts, leaving the tunnel finished except for the invert and track construction, etc.