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eted, so as to form the surface of a pendentive ceiling; and let A b c D be the section across the diagonal; it is required to find the curvature of the springing ribs?

Draw C d perpendicular to AC, meeting AC, take the distance from C to the line AC, and set it from Con the line CA, and from this point draw a perpendicular to meet the curve Ale D of the diagonal rib; make the versid sine of the segment A dC equal to this perpendicular, and describe the segment Ad C, which is the springing line required. If from the centre C an arc be described, with a radius equal to the length of the seat of a rib, to meet the seat of the diagonal rib AD; and, if from the point of meeting a perpendicular be drawn to meet the curve A 6, the portion of the arc of the diagonal rib, intercepted between A and the perpendicular, will give the length of the rib, corresponding to the seat which was taker.. Fig. 594. The diagonal rib is a semicircle: the operation is exactly the same, and may be described in the same words.

MENSURATION OF CARPENTERS' work.

All large and plain articles in which an uniform quantity of materials and workmanship is expended, are generally measured by the square of 100 superficial feet.

Piles used in the foundations are valued at per piece, and driven by the foot run, according to their diameter, and the quality of the ground.

Keepers and planking are measured by taking the superficial contents in yards or squares.

Plain centreing is measured by the square; but as the ribs and boarding are two different qualities of work, they ought to be measured and valued separately; one dimension of the boarding being taken by girting it round the arch, the other being the length of the vault.

Centreing for groins should be measured and valued as common centreing; but in addition thereto, the angles should be paid for by the foot run, that is, the ribs and boarding ought to be measured and valued separately, according to the exact superficial contents of each; and the angles by the lineal foot for workmanship, in fitting the rib and boards, and for the waste of wood occasioned by the operation.

Wall-plates, lintels, and bond-timbers, are measured by the cubic foot, under the denomination of fir-in-bond.

Naked flooring may either be measured by the square, or by the cubic foot, according to the description of the work, and the quantity of timber employed. In forming an estimate of its value, it should be observed, that in equal cubic quantities of small and large timbers, the small tim

bers will have more superficies than the large ones, and, therefore, the saving will not be in a ratio with the solid contents; consequently the value of the workmanship will not follow the cubic quantity, or said ratio. The difficulty of handling timbers of the same length increases with the weight or solidity, as the greater quantity requires greater power to handle it, and consequently more time.

In naked flooring, where girders are introduced, the uniformity of the work is interrupted by mortises and tenons so that the sum ascertained by the cubic quantity of the girders, at the same rate per foot as the other parts, is n sufficient; not only on account of the great difference size, but the great disparity in the quantity of workmanship, occasioned by its being cut full of mortises to receive the tenons of the binding-joists; the best method, there fore, to value the labour and materials is, to measure and estimate the whole by the cubic quantity, and allow an additional rate upon every solid foot of girders; or, if the binding-joists are not inserted in the girders, at the usual distances, a fixed price for every mortise and tenon, in proportion to their size, which will keep a ratio with the area of the end of the girder.

Partitions may be measured by the cubic feet; but the cills, top-pieces, and door-heads, should be measured by themselves, according to the solid quantity, at an additional rate; because, both the uniform solidity, and the uniform quantity of workmanship are interrupted by them. In trussed partitions, the braces should be rated by the foot cube, at a superior price to that of the quarterings, for the trouble of fitting the ends of the uprights upon their upper and lower sides, and for forming the abutments at the ends.

The timbers in roofing should be measured by the cubic foot, classed as the difficulty of execution, or as the waste occasioned, may require.

Battening to walls is best measured by the square, ac cording to the dimensions and distances in the clear of the battening.

It would be endless to enumerate the various methods of measuring each particular species of carpenters' work; the leading articles only need be noticed.

When the shell of a building is finished, that is, previous to the floors being laid, or the ceilings lathed, all the timbers should be measured, that no doubt may arise as to the actual scantlings of the timbers, or of the description of the workmanship. In taking dimensions it must be observed that,

all pieces which have tenons, must be measured to the extremities of the tenons.

It is impossible to determine on any proper rate, including both materials and workmanship, as the one may be stationary, while the other is variable. With respect to materials, the value of any quantity may be easily ascertained, whatever be the price per load; but the difficulty is far greater in fixing proper rates of workmanship; however, were the time of executing every species of work known, there would be no difficulty in establishing certain uniform quantities, which would give the real value.

JOINERY.

Is the next branch of art which comes under our consideration, and comprises the practice of employing wood in the external and internal finishings of houses.

In the execution of this branch of building, it is almost unnecessary to observe that, as joinery is employed principally by way of decoration, and is liable to close inspection, it is one of the departments which demands the strictest care and attention in the workmen; and it requires the greatest ingenuity, skill, and experience, to become fully master of every subject under the joiner's consideration.

The first and most important thing to be attended to, is the judicious selection of materials; as, without a strict observance of this particular, the care, ingenuity, and exertions of the workman will be wholly frustrated.

As the temperature of the atmosphere has a great influence on wood, and more particularly in the winter season, it would be advisable to put that which is to be used in fine work over an oven for a day or two. In the different descriptions of joint used by the joiner, a hot tenacious liquid, called glue, is almost universally used, and when applied, the two surfaces of the wood, which have been previously rendered smooth, are rubbed together until the glue is nearly all forced out. One piece is then set to its situation with respect to the other.

For outside work, such as gates, doors, &c. white-lead is used in all the joints.

When a frame, consisting of several pieces, is required, the mortises and tenons are fitted together, and the joints glued all at one time, then entered to their places, and forced together by the assistance of an instrument called a cramp.

The operation of rendering a rough surface smooth, by taking away the superfluous wood, is called planing; and the tools used for this purpose are called planes.

The planes used by joiners in the primary operation of their work are called jack-planes, trying-planes, longplanes, and smoothing-planes; the respective uses of which are as follow:-The jack-plane is used for taking away the rough occasioned by the saw, and removing all superfluous and other uneven parts. The trying-plane more particularly to bring the surface perfectly level and true: the long plane succeeds, when the surface is long, and is re quired to be very straight, as in jointing long boards for the purpose of gluing them together; and the smoothingplane is used to smooth and clean off the work.

In addition to the above, termed bench-planes, others are occasionally used in forming any kind of prismatic surfaces, viz. rebating-planes, grooving-planes, moulding-planes, &c.; under which head is included the fillister and plough.

Rebating-planes are used for cutting out rebates, a kind of half groove, upon the edge of a board, or other piece of wood, formed by taking down or reducing a small part of the breadth of the board to half, more or less, of the general thickness. By this means, if a rebate be cut on the upper side of one board, and the lower side of another, the two may be made to overlap each other, without making them any thicker at the joint.

Rebates are also used for ornamenting mouldings, and for many other purposes in joiners' work. The planes for cutting them are of different kinds, some having the cutting edge at the side of the iron and stock; others at the bottom edge of the iron and the face of the stock; and others cutting in both these directions. The former are used to smooth the side of a rebate, and therefore are called side rebating-planes; the others for smoothing the bottom. A third sort of rebate-planes, called a fillister, is used for sinking or cutting away the edge of a piece of wood, to form the rebate, leaving it for the others to smooth the surfaces when cut.

The moving fillister is a rebating-plane having a ruler of wood, called the fence, fixed by screws, upon its face, in the direction of its length, and exactly parallel to the edge of the face; consequently, it covers part of the width of the cutting edge, and can be fixed at any required distance from the edge, to leave more or less of the cutting edge exposed, which will be the breadth of the rebate it will cut, because,

when used, the edge of the fence is applied against the edge of the piece to be rebated, and thus gauges the breadth its iron should cut away. The cutting-iron of this plane is not situated at right angles to the length of the stock, but has an obliquity of about forty-five degrees; the exposed side of the iron being more forward than the one next to the fence. By this obliquity, the plane has a tendency or drift to run further into the breadth of the wood; but as the fence sliding against the edge prevents this, the drift always keeps the fence in contact with the piece without the attention of the workman: it also causes the iron to cut the bottom of the rebate smoother, particularly in a transverse direction to the fibres, or where the wood is cross-grained, or where the edge is perpendicular to the sides of the plane. It is chiefly used, however, to throw the shaving into a cylindrical form, and thereby make it issue from one side of the pline. Besides this iron, there is another of smaller dimensions, called the tooth, which precedes the other, to scratch or cut a deep crack in the width of the rebate, thus making the shaving, which the iron cuts up from the bottom, separate sideways from the rest of the wood. The sash-fillister differs in many particulars from the moving filliser the fence is adapted to be moved to a considerable distance, not being fixed, as in the moving fillister, ty screvs upon the face, but sustained by two bars, fixed fast to it, pasing through the two vertical sides of the stock at right angles to the sides: these bars, when set to their intended places, are tightened by small wedges. This kind of plan is usually employed to rebate narrow pieces of wood, uch as are used in sashes; and the fence is applied against the opposite edge to that on which the rebate is to be borned.

The plough is a plane with a very narrow face, made of iron fixed beneath a wooden stock, and projecting down from the wood of the stock; the edge of the cutting-iron being the full width of the groove required: it is guided by a fene with bars like the sash-fillister, and has also a stop to regulze the depth intended for the grooves.

Molding-planes are those which have their faces and cuttin edges curved, to produce all the varieties of ornamentamouldings: they are known by the names of snipe'sbills, de snipe's-bills, beads, hollows, rounds, ovolos, and ogees. Of these there are a great variety of sizes, with which every god joiner is furnished.

The hole of these planes have their faces straight in the