(2) When the tunnel begins with a curve and ends with a straight line. (3) When the whole tunnel is in curve from portal to portal. (4) The helicoidal or corkscrew tunnel. * * * * * (1) The axis of every one of the great Alpine tunnels is a straight line, with a curve at each end. To range out the center line of one of these long tunnels from a curve, no matter how accurately laid out, will certainly cause an error, which, magnified with the distance, may produce serious results. To avoid these inconveniences, the determination of the axis of the tunnel should be made from a straight line. This means that the tunnel is at first excavated on a straight line for its entire length and after the headings driven from both portals have met, the two portions of the tunnel or curve are excavated and constructed. The portions of the tunnel excavated on straight lines for conveniences of construction may then be abandoned or used in cases of accidents or repairs. When the axis of a short tunnel has a curve at each end and a straight line in the middle, it is driven directly from the entrances; first, however, excavating the curvilinear portions of the tunnel. In such a case it would be advisable to proceed in the following manner. Drive the headings on the curvilinear portions of the tunnel, staking out the center line by means of the offsets from the tangents. At the ends of the curves lay out from both fronts the rectilineal portion of the tunnel. Only very narrow headings should be excavated at first while the whole section could be enlarged near the entrances. The excavation of the headings at the front should advance very rapidly, in order that the headings may meet in the shortest possible time. When communication is established, it is comparatively easy to correct an error resulting from driving the tunnel from the curves. (2) When a tunnel begins with a curve and ends with a straight line, the work of excavation should proceed from both ends. From the straight end of the tunnel only the heading should be driven, while from the curvilinear end the whole section could be opened at once. By this arrangement the excavation progresses slowly from the curvilinear end and rapidly from the straight end of the tunnel. Once communication has been established and any error corrected, the work of enlarging the profile of the tunnel may be pushed with the same activity from both ends.