angle of the width of the tread, and the other of the height of the riser. When there are both winders and flyers, two pitch-boards must be made to their respective treads, but, of course, of the same height, as all the steps rise the same. The bevel by which the edge of the plank is reduced from the right angle when the plank is sprung, is termed the spring of the plank, and the edge thus bevelled is called the sprung edge.

The bevel by which the face mould is regulated to each side of the plank, is called the pitch.

The formation of the upper and lower surfaces of a rail is called the falling of the rail; the upper surface of the rail is termed the back.

In the construction of hand-rails, it is necessary to spring the plank, and then to cut away the superfluous wood, as directed by the draughts, formed by the face-mould; which may be done by an experienced workman, so exactly, with a saw, as to require no further reduction; and when set in its place, the surface on both sides will be vertical in all parts, and in a surface perpendicular to the plan. In order to form the back and lower surface, the falling mould is applied to one side, generally the convex, in such a manner, that the upper edge of the falling mould at one end, coincides with the face of the plank; and the same in the middle, and leaves so much wood to be taken away at the other end as will not reduce the plank on the concave side; -the piece of wood to be thus formed into the wreath or twist being agreeable to their given heights.

In the following figures, we have given the method o. finding the moulds necessary for constructing a hand-rail on a circular plan.

Fig. 623, is the plan, showing part of the winders, which in this case are eight, as also the seat of the joint.

Fig. 624. Let AAA, &c. be the outside, and a a a, &c. the inside of the plan. BCD a line passing through the middle of the breadth, BC being straight, and CD one-fourth of the circumference of the circle, the point E in the middle of the arc CD, B at one extremity of the line BCED, and D at the other.

Divide the quadrant CD into any number of equal parts, which in this example are four. Draw the straight line MN, and make MN equal to the developement of the quadrant AAA, &c. on the convex side. Draw MO perpendicular to MN, and make MO equal to the height of a step; draw OP parallel to MN, and make OP equal in length to the width of a step, and join PM.

Draw Ns perpendicular to MN. In Ns make N o equal to the height of four of the winders, and join o M curve off the angle at M, in the manner shown below, by intersection of lines: Through o draw x y perpendicular to Mo, make o r and oy each equal to half the width of the falling mould, and draw the upper and lower edges of the mould.

Join DE. Fig. 624, and produce DE to F. Draw DG and EL. Make DG equal to one-fourth (or any part of) the height from N to the upper edge of the falling mould, Fig. 625, and EL equal to one-fourth, or the same part, of the height from Q to the upper edge of the falling mould. Join GL and produce it to meet DE in F, join the dotted line BF. Draw IK, through the centre F, perpendicular to BF. Draw a b, ab, &c. meeting IK. At any convenient distance from KI draw c d parallel to IK. Make the perpendicular of the face-mould equal to its corresponding height on the falling mould, and draw the straight line ce; then draw ordinates A b, A b, &c. continue them until they meet ce, and from the points of intersection draw perpendiculars to ce, and set off the distances as shown by corresponding letters. Then by tracing a curve through these points the face mould will be completed.

The top line rrr, &c. is left on the falling mould, to regulate its position when bent upon the convex surface, as the line rrr, and will fall into the plane surface of the top of the plank. This line is obtained by making the perpendiculars fr, 2r, fr, &c. equal to the corresponding perpendiculars fb, fb, &c. Fig. 624. To find the face-mould of a staircase, so that when set to its proper rake it will be perpendicular to the plan whereon it stands for a level landing.

Fig. 626. Draw the central line, a b, parallel to the sides of the rail, on the right line a b apply the pitch-board of a flyer, from b to c draw ordinates n m, o p, qr, s t, uv, at discretion, observing to draw one from the point r, so that you may obtain the same point exactly in the facemould; then take the parts which the ordinates give on the line a b, and apply them at Fig. 627, and take the distances mn, p o, &c. and transfer them to Fig. 627, and a curve through these points will be the face-mould required.

To find the falling mould.

Fig. 626. Divide the radius of the circle into four equal parts, and set three of these parts from 4 to a; through a y, the extremities of the diameter of the rail, draw ax and a y, producing them till they touch the tangent AB; then will AB be the circumference of the semicircle by, which is applied from A to B, Fig. 628, as a base line. Make A a the height of a step; draw the hypotenuse a B, apply the pitch board of a flyer at a b c, and B d e, then curve off the angle by intersection of lines, and draw a line parallel to it, for the upper edge of the mould.

MEASURES CUSTOMARY IN JOINERS' WORK.

Prepared boarding is measured by the foot superficial; the following being the different distinctions :-edges shot; edge shot, ploughed, and tongued; wrought on one side, and edges shot; wrought on both sides, and edges shot; wrought on both sides, ploughed, and tongued; boards keyed and clamped, mortise-clamped, and mortise and mitre-clamped. The prices are regulated according to the thickness. If the boards be glued, an additional price per foot is allowed; if tongued, still more, according to the description of tongue. In boarded flooring, the dimensions are taken to the extreme parts, from which the squares are to be computed. Deductions for chimneys, stair-cases

&c. are taken from this. The price depends on the surface, whether wrought or plain, the manner of the longitudinal and heading-joints, the thickness of stuff, whether the boards be laid one after the other, or folded, or whether the floor be laid with boards, battens, or wainscot.

Skirting, when wide, is also measured by the foot superficial; the price depending upon the position, whether level, raking, or ramping, or upon the manner of finishing, whether plain, torus, or rebated, or scribed to the floor, or to the steps, or upon the plan, whether straight or circular.

Weather-boarding, is measured by the square of 100 superficial feet.

Boarded partitions are measured by the square, from which must be deducted the doors and windows, except an agreement be made to the contrary.

The price of all kinds of framing depends on the thickness, or whether the framing be plain or moulded; and if moulded, the description of moulding, whether struck on the solid, or laid in, mitred, or scribed; as also upon the number of panels in a given height and breadth, and upon the nature of the plan.

The different kinds of wainscotting, as window linings, door linings, back linings, partitions, doors, shutters, &c. are all measured by the superficial foot.

Windows are in general valued by the foot superficial; though sometimes by the window. When measured, the dimensions are taken for height, from the top of the cill to the under side of the head, allowing seven inches for the head and cill; and for width in clear of pulley-stiles, allowing eight inches. The sash and frame are either measured together or separately.

Skylights are measured by the foot superficial, their price depending on the plan and elevation. Framed grounds at per foot run.

Ledged doors by the foot superficial, dado by the superficial foot; the price depending whether the plan be straight or circular, or the elevation level or inclined.

In measuring stair-cases, the risers, treads, and carriages, are generally classed together, and measured by the foot superficial: the price varying as the steps are flyers or winders, as the risers are mitred into the string-board, the treads dove-tailed for balusters, and the nosings returned, or whether the bottom of the risers be tongued into the treads. The curtail step is generally valued as a whole. Returned nosings at so much each; and if circular, double the price of straight