METHODS OF TAKING DIMENSIONS AND SETTING OUT WORK.

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forms methods of his own, and, merely from his being most familiar with his own processes, he will, following his own methods, do his work in a better manner than by strange ones, even if to an unprejudiced mind the methods he followed were evidently inferior.

The end and aim of a joiner, in all these operations, is to avoid the peculiar imperfections and disadvantages of his materials, and to do this at the least expense of time and wood. The straightness of the fibres of wood renders it unfit for curved surfaces, at least, when the curvature is considerable. Hence, short pieces are glued together as nearly in the form desired as can be, and the apparent surfaces are covered with thin veneers; or the work is glued up in pieces that are thin enough to bend to the required form. Sometimes a thin piece of wood is bent to the proposed form, upon a saddle or solid cylinder; and blocks are jointed, and glued upon the back; the whole is then allowed to become completely dry, and it will preserve the form that has been given to it by the saddle. But, when a piece of work is glued up in parts, it should be extremely well done; and, not as frequently happens with the joints black and irregular, and springing open in places. The difficulty of doing work of this kind well, has led to the trial of a variety of other methods.

48. If a piece of wood be boiled in water for a certain time, then taken out, and bent while hot into the proposed form, and it be retained in that form by screws or wedges till it be perfectly dry, it is found to preserve nearly the same figure that has been given to it. The quantity it springs back, when relieved, is not easily allowed for; and it is equally uncertain how long it may continue to return towards its natural straightness.

49. The same effect may be produced by steaming, as by boiling wood; and, indeed, more effectively. Both methods have been long practised, to a considerable extent, in the art of ship-building; but we are not aware that any general principles have yet been discovered either by experiment or otherwise, that would enable us to apply it with that degree of certainty and precision which is required in joinery. It has frequently been tried to bend wood by these means for the joiner's purpose, but we still want to know what relation there is between the curve to which it may be bent, and that which it will retain; and also the degree of bending we may with safety give to a piece of wood of a given thickness; for it clearly must not be bent so as to injure the grain of the wood.

The time that a piece of wood should be boiled or steamed, in order that it may be in the best state for bending, should also be made the subject of inquiry by experiment; and this being determined, the relation between the time and the thickness of the pieces should be ascertained.

For the purposes of joinery, we think that the process might be improved by saturating the pores of the convex side of each piece with a strong solution of clear glue immediately after bending it; for, by filling in this manner the extended pores, and allowing the glue to harden thoroughly before relieving the pieces, they would retain their shape better.

METHODS OF TAKING DIMENSIONS AND SETTING OUT WORK.

50. TAKING dimensions of plain square work is so simple, that we need not consider it; but, when irregular figures are to be framed, it requires more skill. The methods to be followed, in such cases, depend upon the method of describing a triangle, when its three sides are given. Thus, let ABC (fig. 6, pl. XLVII,) be the three given sides of a triangle; in any convenient

place draw the straight line DE, equal to the given line A, and from D, with the straight line B, as a radius, describe an arc at F; and, from E, with the straight line C, as a radius, describe another arc, cutting the former in F; join DF and EF: then will DEF be the triangle required. In order to take the dimensions of a place which is to receive a piece of framing, make an eyesketch, as in fig. 7, No. 1; and upon each line mark the dimensions of the sides; then make a scale, fig. 8, and take the lengths of the sides from the scale; and, on No. 2, find the angular points of the triangle, as was done in constructing the triangle, fig. 6.

Having cut each piece of wood to its proper length, scribe each edge down to its place; then lay together the ends which are to meet, one piece being on the top of the other, and draw the shoulders of the joints. When the place which is to receive the framing consists of more than three sides, sketch the figure, as before; draw lines from one corner to every other corner, and mark the dimensions upon these lines, and the dimensions of each side of the figure upon its respective line. This is fully exemplified in figures 9 and 10, No. 2, in each figure, being set out from the same scale.

METHODS OF ENLARGING AND DIMINISHING MOULDINGS.

51. THESE methods depend entirely on the proportion which any two lines, of different lengths, have to one another, when divided in the same ratio.

Euclid proves, and indeed it is self-evident, that, if a line be drawn parallel to one side of a triangle, and if lines be drawn from the opposite angle, through any number of points taken in one of the parallels, to cut the other, these two parallels will be divided in the same ratio. This is one of the principles of proportioning cornices.

Another method of proportion, emanating from a similar principle, proved by the same geometrician, and which is equally evident, is, that when any number of straight lines are drawn parallel to one side of a triangle, so as to cut each of the other two sides in as many points, each of the two sides thus divided have their corresponding segments in the same proportion. Hence we have only to construct a triangle, which shall have two of its sides given; for, if the divisions in one of these lines be given, we may divide the other in the same ratio, by drawing lines parallel to the third side of the triangle: or, according to the first principle, if a straight line be drawn parallel to one side of a triangle, this straight line will divide the triangle into two similar triangles; therefore, if the triangle to be divided be equilateral, the smaller triangle, when divided, will also be equilateral. Therefore, if the divided line be greater than the undivided line, we have only to construct an equilateral triangle, and set the length of the undivided line from one of the angular points upon one of the sides, and draw a straight line through the point of extension, parallel to the side opposite to that angular point; then, placing the parts of the divided line on the greatest of the two parallel lines, we have only to draw lines, through the points of division, to the opposite angle, and the lesser parallel line will be divided in the same proportion.

52. Let AB, fig. 1, plate XLVIII, be the height of a cornice, divided by the height of the members into as many parts. Upon AB describe the equal sided on equilateral triangle ABE; from the points of division in AB draw lines to E. On the side EB or EA, of the triangle, make EH or EG equal to the height of the intended cornice, and draw GH parallel to AB; then GH will contain the heights of the members of the new cornice. The projections are found thus: AC, being the lower line of the cornice, produce AC to D; and, from all the points of

Produce DB to b, and draw Cb perpendicular to Db; also, make AC perpendicular to CB, and a C perpendicular to b C. Set off Ca equal to C A, and join a b; then the inclined moulding must be drawn on lines parallel to b a. Draw EF perpendicular to DB, and let 1, 2, 3, 4, &c. be any number of points in the given section of the level moulding; from each of these points draw a line parallel to DE, to meet the line EF; also draw E c perpendicular to a b, and draw lines parallel to a b from each point to cut E c. Set off the points of division on EF, at the same distances, respectively, from the line E c as the corresponding points 1, 2, 3, 4, &c. are from the line EB, and through the points 1', 2', 3', &c. draw the moulding. The moulding thus found will mitre with the given one; also, supposing the inclined moulding to be given, the level one be found in like manner.

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If the angle CBD be less than a right angle, the whole process remains the same, but when it is a right angle, CB coincides with C b, and the method of describing the moulding becomes the same as that usually given: as it does not then require the preparatory steps which are necessary when the angle is any other than a right angle. It having several times happened that we have had occasion to find the inclined moulding for octagonal buildings, we thought it desirable to give a method which suits for any angle whatever.

56. When a building with mouldings or a horizontal cornice, crowning the walls, has a pediment, with a similar cornice upon the rake, the upper mouldings are mitred together, so that the mitre-plane may be perpendicular to the horizon: the question then is, having the section of the one, how to find the section of the other. And, since in this case, the horizontal cornices are generally wrought first, the section of the horizontal moulding at the top is given, in order to find that of the pediment.

Therefore, in fig. 2, there is given the horizontal section, a b c d e f g, to find the section of the inclined moulding. Let the points a, b, c, d, e, f, g, be any number of points taken at pleasure; draw lines through these points, parallel to the rake; and, also, draw lines through the same points, perpendicular to the horizontal cornice, so that all shall cut any horizontal line in the points h, i, j, k, l, m, n. Transfer the distances between the points h, i, j, k, l, m, n, any where upon the raking line, to h', i', j', k', l', m', n'; and, from these points, draw lines perpendicular to the rake, cutting the inclined lines at the points, a', b', c', d', e', f', g' ; then, through the points a', b', c', d', e', f', g', draw a curve, which will be the section of the inclined moulding.

Again, suppose it were required to return the moulding upon the rake to a level moulding at the top, as is sometimes done in open pediments. Upon any horizontal line, transfer the distances between the points h, i, j, k, l, m, n, to h", i", j", l'",m", n"; and, from these points, draw lines perpendicular to the level cornice, cutting the raking-lines before drawn at the points a”,b”,c" d", e",f", g'; then, through the points a", b′′, c", d′′, e", ƒ", g′′, draw a curve, which will form the return-moulding at the top.

Figure 3.-The lower section is the horizontal part, and the upper section is that of the upper return-moulding, found in a similar manner to fig. 2, excepting that, as the mouldings themselves are circular, the lines drawn through the points b, c, d, must also be circular; and, instead of laying the parts between the points, b, c, d, &c., upon the raking-line, they must be laid upon a straight line, which is a trangent to the circle.

Figure 4 shows the method of finding the return-mouldings for a raking ovolo; the lower section being the given moulding, and the upper one that of the return horizontal moulding. Figure 5 exhibits the method of finding the return of a raking cavetto.

57. Plate L, fig. 1, shows the steps of a stair, where the base-moulding continues along the rake, and returns both at the bottom and top of the stair. Figure 2 exhibits the moulding