In Fig. 103 is shown how to develop the tangents of the face mould. Reproduce the tangents and curve of the plan in full size. Fix point 3 at a height equal to 3 risers from the floor line; at this point place the pitch-board of the flight to determine the pitch over the curve as shown from 3 through b" to the floor line. From the newel, draw a line to w, square to the floor line; and from iv, square to the pitch-line b", draw the line w in; connect in to n. This last line is the development of the bottom plan tangent a.; and the line b" is the development of the plan tangent b; and the angle between the two lines a" and b" will give each line its true direction as required on the face-mould for squaring the joints of the wreath. as shown at m to connect square wi th the newel, and at 3 to nect square to the rail of the connecting flight.
Tile wreath in this ex ample follows the nosingline of the steps without being ramped as it was in the examples shown in Figs. 100 and 101. In those figures the bottom tangent a was level, while in Fig. 103 it inclines equal to the pitch of the upper tangent b" and of the flight adjoining. In other words, the method shown in Fig. 101 is applied to a construction in which the wreath is ramped; while in Fig. 103 the method is applicable to a wreath following the nosing line all along the curve to the newel.
The stair-build er is supposed to know how to con struct a wreath under both conditions, as the conditions are usually Jetermined by tie Architect.
The foregoing examples cover all conditions of tangents that are likely to turn up in practice, and, if clearly understood, will enable the student to lay out the face-moulds for all kinds of curves.
Bevels to Square the Wreaths. The next process in the construc tion of a wreath that the handrailer will be called upon to perform, is to find the bevels that will, by being applied to each end of it, give the correct angle to square or twist it when winding around the well hole from one flight to another flight, or from a flight to a landing, as the case may be.
The wreath is first cut from the plank square to its surface as shown in Fig. 104. After the application of the bevels, it is twisted, as shown in Fig: 105, ready to be moulded; and when in position, ascending from one end of the curve to the other end, over the clined plane of the section around the well-hole, its sides will be plumb, as shown in Fig. 106
at b. In this ure, as also in Fig. 105, the wreath a lies in a horizontal position in which its sides appear to be out of plumb as much as the bevels are out of plumb. In the upper part of the figure, the wreath b is shown placed in its position upon the plane of the section, where its sides are seen to be plumb. It is evident, as shown in the relative posi tion of the wreath in this figure, that, if the bevel is the correct angle of the plane of the section whereon the wreath b rests in its ascent over the well hole, the wreath will in that case have its sides plumb all along when in position. It is for this purpose that the bevels are needed.
A method of finding the bevels for allwreaths (which is considered rather difficult) will now be explained : First Case. In Fig. 107 is shown a case where the bottom tangent of a wreath is inclining, and the top one level, similar to the top wreath shown in Fig. 9S. It has already been noted that the plane of the section for this kind of wreath inclines to one side only; therefore one bevel only will be required to square it, which is shown at d, Fig. 107. A view of this plane is given in Fig. 10S; and the bevel d, as there shown, indicates the angle of the inclination, which also is the bevel required to square the end d of the wreath. The bevel is shown applied to the end of the landing rail in exactly the same manner in which it is to be applied to the end of the wreath. The true bevel for this wreath is found at the upper angle of the pitch-board. At the end a, as already stated, no bevel is required, owing to the plane inclining in one direction only. Fig. 109 shows a face-mould and bevel for a wreath with the bottom tangent level and the top tangent inclining, such as the piece at the bottom connecting with the landing rail in Fig. 94.
Second Case. It may be required to find the bevels for a wreath having two equally inclined tangents. An example of this kind also is shown in Fig. 94, where both the tangents c" and d" of the upper wreath incline equally. Two bevels are required in this case, because the plane of the section is inclined in two directions; but, owing to the inclinations being alike, it follows that the two will be the same. They are to be applied to both ends of the wreath, and, as shown in Fig. 105, in the same direction—namely, toward the inside of the wreath for the tom end, and toward the outside for the upper end.