The inside falling-mould will be found as follows: take the stretch-out of the curve abcd, No. 1, and draw the straight line ad, No. 4, which make equal to the said curve. Divide AD, No. 3, and ad, No. 4, each into the same number of equal parts, the more the truer the work will be effected. We shall here suppose that sixteen equal parts will be sufficient; therefore each of the lines AD, ad, being divided into sixteen parts, at the points 1, 2, 3, 4, &c. Through all the points 1, 2, 3, 4, &c., No 3, draw lines perpendicular to AD, cutting the upper curve at the points 5, 6, 7, 8, &c., and the under curve at the points, 9, 10, 11, &c. Again, through the points 1, 2, 3, 4, in the line ad, No. 4, draw perpendiculars 1-5, 2-9-6, 3-10-7, 4-11-8, &c. Make 1-5, 2-6, 3-7, 4-8, &c., in No. 4, respectively equal to 1-5, 2-6, 3-7, 4-8, &c., No. 3; then, through all the points 5, 6, 7, 8, &c., draw a curve; also draw as, in No. 4, perpendicular to ad, and join the point s to the curve: this being done, will complete the upper edge of the fallingmould, for the concave side of the rail: then, through the point a, draw another curve; which, being done, will form the under line of the said falling-mould.

The falling-mould, No. 3, is applied to the convex side of the said piece of the wood; and the other mould, No. 4, to the concave side of the said piece. The joint is made at the line Cc, and the remaining part of the scroll is made out of a single level block; but part of each fallingmould, No. 3, and No. 4, is used as far as the line Aa; the remaining part of the block from the line Aa being level.

208. In Elliptical Stairs, where the steps are not equally divided next the well-hole, the stretch-out of the line, representing the ends of the steps on the plan, must have the places of the risers marked upon it, and a perpendicular being drawn to each of these places, and made equal to the height of the corresponding step above the plan, the line drawn through extremities of the perpendiculars will give the form of the edge of the falling-mould.

The upper and lower edges of the falling-mould will always be a curved line when the steps are not equally divided at the well-hole, but we think the extra trouble this occasions is fully compensated for by the stairs being so much more agreeable in use, when divided as we have recommended in art. 156, fig. 3, plate LXXIII.

The face-moulds for steps, divided unequally at the well-hole, are found in the same manner as when they are equally divided, (see art. 205, and pl. LXXXIII,) the only differences being, that BF, bf, in No. 3, and AF, ae, in No. 2, are curved lines found in the manner we have described in the first part of this article.

To draw the Form of a Hand-Rail upon the Plank by continued Motion.

209. If a plank be placed in the true position in respect to the plane of the plan, and distance from the centre of the well-hole; then, if the well-hole be a part of a circle on the plan, let a cylindrical rod be fixed, as an axis, in the centre of the circle, and in a vertical position, with an arm of sufficient length that will slide up or down on the rod, and turn round on it as on an axis. The arm should have a slider with a pencil, in order that the point of the pencil may be adjusted to the proper distance from the centre; and the hole in the arm through which the axis passes, should be of sufficient length to keep it truly at right angles to the rod.

Let the pencil be adjusted to the proper distance from the centre, and commencing at the upper end of the plank, if the pencil be moved round the axis, it will descend and describe on the plank the curve of one side of the rail; and by setting the pencil again, the other side may be described. By turning the pencil point upwards, the under side of the plank may have the lines drawn upon it in like manner.

210. The form of the rail for elliptical stairs may also be described by continued motion by fixing a trammel (see Carpentry, art. 8,) on the top of a square bar, which bar should be made to slide up and down in the centre of the well-hole.

All these contrivances are, however, more expensive, and generally more troublesome to the workman than the ordinary method by finding points in the curves; though we think that the attempt to apply them in practice gives very accurate notions of the forms and properties of hand-rails.

211. The curved parts of hand-rails, for either circular or elliptical well-holes, may be described by continued motion by the trammel, when it is placed in the same plane with the plank. The centre of the well-hole being found in that plane, draw a line through the centre on the plan, and perpendicular to the line of intersection between the plane of the plank and the plane of the plan; and, from the point in which the perpendicular meets the intersecting line, draw a line through the centre found in the plane of the plank; this line will be the larger axis of the ellipsis, the shorter one will be at right-angles to it, and the lengths are easily found by the methods of finding the points in the curves of hand-rails. These particulars being found, the portions of ellipses may be described by the trammel.

OF FIXING JOINERS' WORK.

212. THE methods of fixing joiners' work, so that it may be firm, preserve its form, and not be liable to split by shrinking, are of considerable importance; as however well a piece of work may have been prepared, if it be not properly fixed, it cannot fulfil its intended purpose in a manner creditable to the workman.

We have treated very fully on the expansion and contraction of timber, in Carpentry, art. 201, and those following it; and we have also shown how timber should be cut, so that the boards may preserve their form, and we now have to apply the truths, there stated, to the fixing of wood-work.

Of Fixing Grounds.

213. The architraves, dado, skirtings, and surbase mouldings, and, indeed, nearly all the apparent surfaces in joinery, are fixed to pieces of wood called Grounds; and, as the straightness and accuracy of these mouldings and surfaces must depend upon the care that has been taken to fix the grounds truly, it will appear, that fixing grounds, which is a part often left to inferior workmen, in reality requires much skill and attention. Besides, grounds are almost always the guide for the plasterer, and, consequently, the accuracy of his work also depends

on them.

When plasterers' work joins to the edges of grounds, they should have small grooves ploughed in the edges, to form a key for the plaster, as is sufficiently illustrated in the various figures we have given in the plates.

The thickness of the grounds should be equal to the thickness of the plastering and laths, and it is from three-quarters of an inch to an inch, according as the plasterers' work is done, in an inferior or in the best manner.

The faces and edges of grounds should be fixed exactly plumb and level; or, as the more scientific carpenters may express it, the faces and edges should be fixed exactly in vertical and horizontal planes.

Of Fixing Dado, Skirtings, &c.

214. If the piece of joiners' work to be fixed consist of boards jointed together, but not framed, it should be fixed so that it may shrink, or swell without splitting, and the quantity allowed for motion must depend on the dryness of the timber.

The nature of the work will generally determine how this may be effected. Let us suppose that a plain piece of dado of considerable breadth is to be fixed. Let us suppose that the dado has been prepared as described in art. 45, and that it is kept straight by a dovetailed key. Now let the dado be firmly nailed at the upper edge, and let a narrow skirting ground, with a groove and cross tongue in its upper edge, be fixed to bond timbers or plugs in the wall, the tongue being inserted also into a corresponding groove in the lower edge of the dado. It is obvious, that the tongue being loose, the dado may contract or expand, as a pannel in a frame. The backs and elbows of windows should be fixed in the same manner.

In the principal rooms of a mansion, the skirting is usually grooved into the floor, and fixed only to the narrow ground, called the skirting ground. By fixing in this manner, the skirting never shows an open joint. Sometimes in inferior rooms the skirting is scribed and nailed fast to the floor, and grooved into the base-moulding, and, when either method is adopted, there cannot be an open joint between the skirting and floor, as is too frequently the case in houses.

When it is considered, that an open joint, in such a situation, must become a receptacle for dust, and a harbour for insects, the importance of adopting those methods of fixing skirtings will be apparent.

It is a good plan to fix skirtings only in a temporary manner till a house has become seasoned, and all the timbers have shrunk and settled to their proper bearings; but a due attention to the methods here proposed will render this precaution less necessary.

In fixing any board that exceeds about 5 inches in width it is necessary to take precautions to prevent it from splitting, or deranging the form of the work; and, in general, it may be fixed along one edge, and the other may be confined by grooves or similar means, that have the property of allowing it to expand and contract. Sometimes both edges are left at liberty, and the board is fixed in the middle. Any joiner who has examined the state of work in a house, after it has been inhabited for about a couple of years, will be able fully to appreciate the value of an attention to those seemingly minute precautions.

Wide plain surfaces, such as landings of stairs, tops of tables, and the like, are frequently fixed down by buttons screwed to the under-side so as to turn into grooves in the joists, bearers, o frames. Then, when the wood shrinks or expands, the buttons slide a little in the grooves, and no splitting takes place.

The very general introduction of the method of ploughing and tongueing the parts of woodwork together is one of the most important improvements in modern joinery; it is an easy, effectual, and useful mode of combination, both in as far as it provides against the greatest defect of wood-work, its shrinkage, and the scope it affords for obtaining variety of outline at a comparatively small expense of either labour or material.