been the idea had in view by the designers of some centres. In building the arch, it thould be commenced at each buttress at the same time, (as is generally the case,) and each side should progress equally towards the crown. In designing the framing, the effect produced by each successive layer of stone should be considered. The pressure of the stones upon one side should, by the arrangement of the struts, be counterpoised by that of the stones upon the other side.

409.-Over a river whose stream is rapid, or where it is necessary to preserve an uninterrupted passage for the purposes of navigation, the centre must be constructed without intermediate supports, and without a continued horizontal tie at the

base; such a centre is shown at Fig. 259. In laying the stones from the base up to a and c, the pieces, b d and bd, act as ties to prevent any rising at b. After this, while the stones are being laid from a and from c to b, they act as struts: the piece, fg, is added for additional security. Upon this plan, with some variation to suit circumstances, centres may be constructed for any span usual in stone-bridge building.

410.-In bridge centres, the principal timbers should abut, and not be intercepted by a suspension or radial piece between. These should be in halves, notched on each side and bolted. The timbers should intersect as little as possible, for the more

joints the greater is the settling; and halving them together is a bad practice, as it destroys nearly one-half the strength of the timber. Ties should be introduced across, especially where many timbers meet; and as the centre is to serve but a temporary purpose, the whole should be designed with a view to employ the timber afterwards for other uses. For this reason, all unnecessary cutting should be avoided.

411.-Centres should be sufficiently strong to preserve a staunch and steady form during the whole process of building; for any shaking or trembling will have a tendency to prevent the mortar or cement from setting. For this purpose, also, the centre should be lowered a trifle immediately after the key-stone is laid, in order that the stones may take their bearing before the mortar is set; otherwise the joints will open on the under side. The trusses, in centring, are placed at the distance of from 4 to 6 feet apart, according to their strength and the weight of the arch. Between every two trusses, diagonal braces should be introduced to prevent lateral motion.

412.-In order that the centre may be easily lowered, the frames, or trusses, should be placed upon wedge-formed sills; as is shown at d, (Fig. 259.) These are contrived so as to admit of the settling of the frame by driving the wedge, d, with a maul, or, in large centres, with a piece of timber mounted as a battering-ram. The operation of lowering a centre should be very slowly performed, in order that the parts of the arch may take their bearing uniformly. The wedge pieces, instead of being placed parallel with the truss, are sometimes made sufficiently long and laid through the arch, in a direction at right angles to that shown at Fig. 259. This method obviates the necessity of stationing men beneath the arch during the process of lowering; and was originally adopted with success soon after the occurrence of an accident, in lowering a centre, by which nine men were killed.

413. To give some idea of the manner of estimating the pres

sures, in order to select timber of the proper scantling, calculate (Art. 408) the pressure of the arch-stones from i to b, (Fig. 259,) and suppose half this pressure concentrated at a, and acting in the direction af. Then, by the parallelogram of forces, (Art. 258,) the strain in the several pieces composing the frame, bda, may be computed. Again, calculate the pressure of that portion of the arch included between a and c, and consider half of it collected at b, and acting in a vertical direction; then, by the parallelogram of forces, the pressure on the beams, bd and bd, may be found. Add the pressure of that portion of the arch which is included between i and b to half the weight of the centre, and consider this amount concentrated at d, and acting in a vertical direction; then, by constructing the parallelogram of forces, the pressure upon dj may be ascertained.

414. The strains having been obtained, the dimensions of the several pieces in the frames bad and b cd, may be found by computation, as directed in the case of roof trusses, from Arts. 375 to 380. The tie-beams b d, b d, if made of sufficient size to resist the compressive strain acting upon them from the load at b, will be more than large enough to resist the tensile strain upon them during the laying of the first part of the arch-stones below a and c.

415. In the construction of arches, the voussoirs, or archstones, are so shaped that the joints between them are perpendicular to the curve of the arch, or to its tangent at the point at which the joint intersects the curve. In a circular arch, the joints tend toward the centre of the circle: in an elliptical arch, the joints may be found by the following process:

416.-To find the direction of the joints for an elliptical arch. A joint being wanted at a, (Fig. 260,) draw lines from that point to the foci, ƒ and ƒ; bisect the angle, faf, with the line, ab; then ab will be the direction of the joint.

a

Fig. 261.

417.-To find the direction of the joints for a parabolic arch A joint being wanted at a, (Fig. 261,) draw a e, at right angles to the axis, eg; make cg equal to ce, and join a and g; draw a h, at right angles to ag; then a h will be the direction of the joint. The direction of the joint from b is found in the The lines, a g and bƒ, are tangents to the curve at those points respectively; and any number of joints in the curve may be obtained, by first ascertaining the tangents, and then drawing lines at right angles to them.

same manner.

JOINTS.

Fig. 202.

418.-Fig. 262 shows a simple and quite strong method of lengthening a tie-beam; but the strength consists wholly in the bolts, and in the friction of the parts produced by screwing the pieces firmly together. Should the timber shrink to even a small degree, the strength would depend altogether on the bolts. It would be made much stronger by indenting the pieces together; as at the upper edge of the tie-beam in Fig. 263; or by placing keys in the joints, as at the lower edge in

the same figure. This process, however, weakens the beam in proportion to the depth of the indents.

Fig. 263.

419. Fig. 264 shows a method of scarfing, or splicing, a the-beam without bolts. The keys are to be of well-seasoned,

Fig. 264.

nard wood, and, if possible, very cross-grained. The addition of bolts would make this a very strong splice, or even whiteoak pins would add materially to its strength.

Fig. 265.

420.-Fig. 265 shows about as strong a splice, perhaps, as can well be made. It is to be recommended for its simplicity; as, on account of there being no oblique joints in it, it can be readily and accurately executed. A complicated joint is the worst that can be adopted; still, some have proposed joints that seem to have little else besides complication to recom mend them.

421.-In proportioning the parts of these scarfs, the depths of all the indents taken together should be equal to one-third of the depth of the beam. In oak, ash or elm, the whole length of the scarf should be six times the depth, or thickness, of the beam, when there are no bolts; but, if bolts instead of indents are used, then three times the breadth; and, when both methods are combined, twice the depth of the beam. The