any number of equal-sized bays, depending on local circumstances, and the comparative cost of high or low piers, and that of the main chains, and the suspending-rods.

A bridge with a single bay of considerable width presents a bolder and more monumental character, and its stability, all other things being equal, is greater, the amplitude from undulations caused by a movable load being less than one of several bays.

650. A chain or rope, when fastened at each extremity to fixed points of support, will, from the action of gravity, assume the form of a catenary in a state of equilibrium, whether the two extremities be on the same or different levels. The relative height of the fixed supports may therefore be made to conform to the locality.

651. The ratio of the versed sine of the arc to its chord, or span, will also depend, for the most part, on local circumstances and the object of the suspended structure. The wider the span, or chord, for the same versed sine, the greater will be the tension along the curve, and the more strength will therefore be required in all the parts of the cable. The reverse will obtain for an increase of versed sine for the same span; but there will be an increase in the length of the curve. 652. The chains may either be attached at the extremities of the curve to the fixed supports, or piers; or they may rest upon them (Figs. 191, 192), being fixed into anchoring masses,

Fig. 191-Represents a chain arch a b c d e, resting upon two piers, and anchored at the points a and e, from which a horizontal beam m n is suspended by vertical chains, or rods.

Fig. 192-Represents the manner in which the system may be arranged when a single pier is placed between the extreme points of the bearing.

or abutments, at some distance beyond the piers. Local circumstances will determine which of the two methods will be the more suitable. The latter is generally adopted, particularly if the piers require to be high, since the strain upon them from the tension might, from the leverage, cause rup

ture in the pier near the bottom, and because, moreover, it remedies in some degree the inconveniences arising from variations of tension caused either by a movable load or changes of temperature. Piers of wood, or of cast iron, movable around a joint at their base, have been used instead of fixed piers, with the object of remedying the same inconveniences.

653. When the chains pass over the piers and are anchored at some distance beyond them, they may either rest upon saddle-pieces of cast iron, or upon pulleys placed on the piers.

654. The position of the anchoring points will depend upon local circumstances. The two branches of the chain may either make equal angles with the axis of the pier, thus assuming the same curvature on each side of it, or else the extremity of the chain may be anchored at a point nearer to the base of the pier. In the former case the resultant of the tensions and weights will be vertical and in the direction of the axis of the pier, in the latter it will be oblique to the axis, and should pass so far within the base that the material will be secure from crushing. When the cable is secured to a saddle, and the saddle is free to move horizontally on the top of the pier, the resultant forces would still be vertical if there were no frictional resistance to the movement of the saddle. In all cases, whether the inclinations of the cable on the opposite sides of the pier are equal or not, the frictional resistance under the saddle when it is moving will cause a horizontal force tending to overturn the pier.

655. The anchoring points are usually masses of masonry of a suitable form to resist the strain to which they are subjected. They may be placed either above or below the surface of the ground, as the locality may demand. The kind of resistance offered by them to the tension on the chain will depend upon the position of the chain. If the two branches of the chain make equal angles with the axis of the pier, the resistance offered by the abutments will mainly depend upon the strength of the material of which they are formed. If the branches of the chain make unequal angles with the axis of the pier, the branch fixed to the anchoring mass is usually deflected in a vertical direction, and so secured that the weight of the abutment may act in resisting the tension on the chain. In this plan fixed pulleys placed on very firm supports will be required at the point of deflection of the chain to resist the pressure arising from the tension at these points.

Whenever it is practicable the abutment and pier should be

suitably connected to increase the resistance offered by the former.

The connection between the chains and abutments should be so arranged that the parts can be readily examined. The chains at these points are sometimes imbedded in a paste of fat lime to preserve them from oxidation.

656. The chains may be placed either above or below the structure to be supported. The former gives a system of more stability than the latter, owing to the position of the centre of gravity, but it usually requires high piers, and the chain cannot generally be so well arranged as in the latter to subserve the required purposes. The curves may consist of one or more chains. Several are usually preferred to a single one, as for the same amount of metal they offer more resistance, can be more accurately manufactured, are less liable to accidents, and can be more easily put up and replaced than a single chain. The chains of the curve may be placed either side by side, or above each other, according to circumstances. 657. The cables may be formed either of chains, of wire cables, or of bands of hoop iron. Each of these methods has found its respective advocates among engineers. Those who prefer wire cables to chains urge that the latter are more liable to accidents than the former, that their strength is less uniform and less in proportion to their weight than that of wire cables, that iron bars are more liable to contain concealed defects than wire, that the proofs to which chains are subjected may increase without, in all cases, exposing these defects, and that the construction and putting up of chains is more expensive and difficult than for wire cables. The opponents of wire cables state that they are open to the same objections as those urged against chains, that they offer a greater amount of surface to oxidation than the same volume of bar iron would, and that no precaution can prevent the moisture from penetrating into a wire cable and causing rapid oxidation.

That in this, as in all like discussions, an exaggerated degree of importance should have been attached to the objections urged on each side was but natural. Experience, however, derived from existing works, has shown that each method may be applied with safety to structures of the boldest character, and that wherever failures have been met with in either method, they were attributable to those faults of workmanship, or to defects in the material used, which can hardly be anticipated and avoided in any novel application of a like character. Time alone can definitively decide

upon the comparative merits of the two methods, and how far either of them may be used with advantage in the place of structures of more rigid materials.

658. The chains of the curves may be formed of either round, square, or flat bars. Chains of flat bars have been most generally used. These are formed in long links which are connected by short plates and bolts. Each link consists of several bars of the same length, each of which is perforated with a hole at each end to receive the connecting bolts. The bars of each link are placed side by side, and the links are connected by the plates which form a short link, and the bolts.

The links of the portions of the chain which rest upon the piers may either be bent, or else be made shorter than the others to accommodate the chain to the curved form of the surface on which it rests.

659. The vertical suspension bars may be either of round or square bars. They are usually made with one or more articulations, to admit of their yielding with less strain to the bar to any motion of vibration or of oscillation. They may be suspended from the connecting bolts of the links, but the preferable method is to attach them to a suitable saddle-piece which is fitted to the top of the chain and thus distributes the strain upon the bar more uniformly over the bolts and links. The lower end of the bar is suitably arranged to connect it with the part suspended from it.

660. The wire cables are composed of wires laid side by side, which are brought to a cylindrical shape and confined by a spiral wrapping of wire. To form the cable several equal-sized ropes, or yarns, are first made. This may be done by cutting all the wires of the length required for the yarn, or by uniting end to end the requisite number of wires for the yarn, and then winding them around two pieces of wrought or of cast iron, of a horse-shoe shape, with a suitable gorge to receive the wires, which are placed as far asunder as the required length of the yarn. The yarn is firmly attached at its two ends to the iron pieces, or cruppers, and the wires are temporarily confined at intermediate points by a spiral lashing of wire. Whichever of the two methods be adopted, great care must be taken to give to every wire of the yarn the same degree of tension by a suitable mechanism. The cable is completed after the yarns are placed upon the piers and secured to the anchoring ropes or chains; for this purpose the temporary lashings of the yarns are undone, and all the yarns are united and brought to a cylindrical shape and secured throughout the extent of the cable, to within a

short distance of each pier, by a continuous spiral lashing of

wire.

The part of the cable which rests upon the pier is not bound with wire, but is spread over the saddle-piece with a uniform thickness.

661. The suspension ropes are formed in the same way as the cables; they are usually arranged with a loop at each end, formed around an iron crupper, to connect them with the cables, to which they are attached, and to the parts of the structure suspended from them by suitable saddle-pieces.

662. To secure the cables from oxidation the iron wires are coated with varnish before they are made into yarns, and after the cables are completed they are either coated with the usual paints for securing iron from the effects of moisture, or else covered with some impermeable material.

663. Piers. These are commonly masses of masonry in the shape of pillars, or columns, that rest on a common foundation, and are usually connected at the top. The form given to the pier, when of stone, will depend in some respects on the locality. Generally it is that of the architectural monument known as the Triumphal Arch; an arched opening being formed in the centre of the mass for the roadway, and sometimes two others of smaller dimensions, on each side of the main one, for approaches to the footpaths of the bridge.

Piers of a columnar, or of an obelisk form, have in some instances been tried. They have generally been found to be wanting in stiffness, being subject to vibrations from the action of the chains upon them, which in turn, from the reciprocal action upon the chains, tends very much to increase the amplitude of the vibrations of the latter. These effects have been observed to be the more sensible as the columnar piers are the higher and more slender.

Cast-iron piers, in the form of columns connected at top by an entablature, have been tried with success, as also have been columnar piers of the same material so arranged, with a joint at their base, that they can receive a pendulous motion at top to accommodate any increase of tension upon either branch of the chain resting on them.

The dimensions of piers will depend upon their height and the strain upon them. When built of stone, the masonry should be very carefully constructed of large blocks well bonded, and tied by metal cramps. The height of the piers will depend mostly on the locality. When of the usual forms, they should at least be high enough to admit the passage of vehicles under the arched way of the road.