To determine the center line at the bottom of the shaft, the headings are first driven from both sides of the shaft, after which a transit is set up on the same alignment with the two wires, and this will indicate the vertical plane passing through the axis of construction. Two points are then fixed on the roof of the tunnel in continuation of this vertical plane. When the plumb bobs are removed from the shaft and two small plumb bobs are suspended to the two points mentioned, they will always give the same vertical plane passing through the axis of construction transferred from the surface. Because of the continuous moving of the wires, the fixing of the points on the roof of the tunnel is very troublesome, and the operation should be repeated by different men at different times before the points are permanently fixed. [Illustration: FIG. 5.--Method of Transferring the Center Line down Side Shafts.] When the shaft is placed at one side of the tunnel the pillars or bench marks are placed normal to the center line on the edges of the shaft as shown by Fig. 5. Between the points _A_ and _B_ a wire is stretched, and from it two plumb bobs are suspended, as described in the preceding case; these plumb bobs establish a vertical plane normal to the axis of the tunnel. The excavation of the side tunnel is carried along the line _BW_ until it intersects the line of the main tunnel, whose center line is determined by measuring off underground a distance equal to the distance _BO_ on the surface. By setting the instrument over the underground point _O_, and turning off a right angle from the line _BO_, the center line of the tunnel is extended into the headings. =Curvilinear Tunnels.=--There are various methods of locating the center lines of curvilinear tunnels, but the method of tangent offsets is the one most commonly employed. At the beginning the excavation is conducted as closely as may be to the line of the curve, and as soon as it has progressed far enough the tangent _AT_, Fig. 6, is ranged out. At _B_ a point is located over which to set the instrument, and the distance _AB_ is measured for the purpose of finding the ordinate of the right angle triangle _OAB_. Now _OA_ = _r_, _AB_ = _d_, and φ = angle _ABO_. Then: _r_ Tang. φ = ---. _d_ [Illustration: FIG. 6.--Method of Laying Out the Center Line of Curvilinear Tunnels.] Doubling the value of φ and making the angle _ABC_ = 2 φ, the line _BC_ will be fixed and the point _C_ located by taking _AB_ = _BC_. On _BC_ the ordinates are laid off to locate the curve. Prolong _CB_ so that _CD_ = _CB_. Then the portion of the curve _CF_ is symmetrical with _CE_, and the ordinates used to locate _EC_ may be employed to locate _CF_, by laying them off in the reverse order. In curvilinear tunnels several cases may be considered. (1) When the tunnel for almost its entire length is driven on a tangent with a curve at each end.