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a tangent to the exterior rail, by which it is continually in^ danger of being thrown off the track.
To counteract the influence of centrifugal force, it will be necessary to raise the exterior one, by which means the centre of gravity of the carriage is made to tend in-ward. By this means it is not only the safety of the car-. riage or train is secured, but the rubbing of the flanges of the wheels against the rails prevented. This contrivance is adopted by some, while others prefer to have the rims or edges of the wheels made slightly conical, the diameter within the tracks being greater than those without it.
A curve on a road does not matter much provided the ground is level, whatever, both abrupt curves and slopes, should, if possible, be avoided.
All curves should be on level ground; and have the straight rail slightly elevated towards the curve, to prevent a sudden shock.
On a curved railway. The wheel on the exterior curve" passes over a greater distance in the same time than' that on the interior, by which the former is partly dragged.
To make both wheels go round their respective tracks, without either of them being in danger of dragging; let" us assume the space An (fig. 28,) between the tracks equal t, d the diameter of the wheel on the interior track, D the diameter of the wheel on the exterior track, and O the centre of the curves AB and nm. It is evident the wheels must revolve an equal number of times on their respective rails, it is plain that the circumferences of the wheels must be to each other as the circumference of the rails upon which they run; but the circumferences of the wheels and rails are as their diameters; consequently, putting_no=r, and Ao=R, d: D::r:R=(r+t.) Hence D=dx().
TUNNELS, VIADUCTS, AND AQUEDUCTS.
1.-When a hill, town, river, canal, or other obstacle presents itself, so as to make it necessary to form an under-ground passage, the communication or passage is called a tunnel. The work is generally tedious and expensive; the character of its construction will depend on the nature of its soil. Among the works of this kind may be mentioned, the canal tunnel between Manchester and Hundersfield, the length of which is over three miles, and is 660 feet below the surface; the railway tunnel under Liverpool; and the road Tunnel under the Thames, which is the most stupendous work of the kind as yet attempted. This great undertaking is 38 feet in width, and in the style of double arcade.
Before commencing the excavation, a profile of the ground must accurately be made, along the central line of the tunnel. This profile must be carefully laid out on the ground by the level, or some other instrument, and pegs placed in the ground along the line, at equal intervals apart. The next thing to be done is, to find the position of the working shafts, which are vertical pits, sunk above the crown of the tunnel, through which the excavations are taken off, and also those of smaller shafts called air-shafts, which supply the tunnel with fresh air. In some soil it is not safe to sink shafts over the crown of the arch; it is recommended in such to sink them 10 or 14 feet outside the piers of the arch. The position of the shafts must depend on the nature of the soil. The height and width of the tunnel must depend on the dimensions of the carriages or boats destined to pass through it.
The excavations are now commenced by sinking the shafts to proper level; and cutting away the two faces at the entrance of the tunnel. If firm not to require arching, the shafts are sunk over the crown to the depth of 6 or 9 feet below it; a small excavation termed a heading, is driven from the bottom of each shaft to connect them, and to form a communication through the whole line for carrying out the soil, but if the soil requires to be arched, it is not safe to sink the shafts over the crown. In this case the shafts are sunk outside, to a level with the springing lines of the arch, and cross heading is driven from them to the positions of the piers; and from these points a heading is driven in the directions of each pier, sunk to the bottom of the foundations. When these headings are of sufficient dimensions, the mason-work is commenced, and carried up to the springing of the arch. Also, cross headings 6 or 7 feet wide, are driven between the piers, upon which centres are set up for turning the arches. Now the masonry and excavations are carried on from both ends until the arch is completed,
To give security and strength, every such work should be built on an inverted arch, and have its sides curved outwards. In some cases the crown only need be arched, with upright abutments of masonry. With regard to the curvature of the arches forming a tunnel, they may be segments of circles, sometimes the upper arch a parabolic, The arches are generally of good brick.
To lay out a curve in a Tunnel.-Let AC (fig. 29,) be a straight line, it is required to pass from it into the curve, suppose the radius 100 chains, Lay out CB = one chain, and at right angles to it at the point B, lay off Bm =3.96 inches; then m will be a point in the curve.
Again, erect Cn at right angles to AB, and equal to Bm, connect nm and produce it off to make mD equal 1 chain; from the point D set off the perpendicular Do equal 3.96 inches, as before; in this manner proceed to the end of the curve. It is a work of some difficulty to keep the centre of a straight tunnel in the proper direction, when the work is carried on from both ends, and from shafts at the same time. In case the shafts are not very deep, the usual method of proceeding is to fix two plum-lines in the centre line at the surface, in the mouth of each shaft, having them of a sufficient length to range from below. In some cases from the great depth, the plum-line will be of no use from the effects of air currents, then the following may be practiced. Having sunk shafts of about 20 feet in diameter, fix the centre line at these shafts on the surface, by the theodolite; then placing the instrument alternately at the two opposite points in the centre line, at the mouth of the shafts, let two points be marked below by means of the vertical arc, and these points joined and produced both ways, will give the proper direction. This method was practiced on the Great Western Railway in England, where the great depth of the shafts were from 300 to 400 feet in depth.
Viaducts. When a railroad is to be carried across a deep ravine, it is to be effected either by an embankment, or building arches to the proper height. When the road requires to be considerably elevated, it is better to conduct it across on arches, it is more permanent, cheaper, and more ornamental than an embankment, When a rail-road is to pass through a town or city, it should, if possible, be carried through a tunnel or over high arches, so as not to interfere with the houses or streets.
3. Aqueducts or Culverts. Aqueducts or culverts should be made under the road, to allow the water streams to pass from one side to another, whenever necessary.
When these are low and apt to be filled to the crown with water passing through it with rapid velocity, the crown should be supplied with vent-holes, which will prevent the destruction of the arch by the upward pressure of the fluid.
After what has been said on railway surveys, little remains to be said on the survey of a line of country for a canal.
Having made a survey of the line determined on, next it is to be levelled, and section and map prepared, exhibiting all the objects within the district; such as rivulets, mill-streams, hills and valleys, &c., which will furnish sufficient data to ascertain the number and situation of all the locks required to be erected along the line.
The section and map of the proposed canal, will enable the engineer to ascertain the most advisable summit-level of his canal, which must be commanded by so many of these head-waters as are sufficient to supply it with the required quantity of water. The required supply of water is determined by gauging all the waters which command the summit-level of the canal; and if the supply be not found sufficient, the summit-level of the canal must be lowered, or recourse must be had to some artificial means to increase the supply of water; this may be done by constructing reservoirs to receive all the rain and surface water from the surrounding eminences.