Fig. 102. Bottom Steps with Obtuse-Angle Plan.

Fig. 103. Developing Face Mould, Obtuse-Angle Plan.

Fig. 104. Cutting Wreath from Plank.

In all the preceding examples, the tangents on the plan were at right angles; that is, they were square to one another. Fig. 100 is a plan of a few curved steps placed" at the bottom of a stairway with a curved stringer, which is struck from a center o. The plan tangents a and b are shown to form an acute angle with each other. The rail above a plan of this design is usually ramped at the bottom end, where it intersects the newel post, and, when so treated, the bottom tangent a will have to be level.

In Fig. 101 is shown how to find the angle between the tangents on the face-mould that gives them the correct direction for squaring the joints of the wreath when it is determined to have it ramped. This figure must be drawn full size. Usually an ordinary drawing-board will answer the purpose. Upon the board, reproduce the plan of the tangents and curve of the center line of rail as shown in Fig. 100. Measure the height of 5 risers, as shown in Fig. 101, from the floor line to 5; and draw the pitch of the flight adjoining the wreath, from 5 to the floor line. From the newel, draw the dotted line to w, square to the floor line; from w, draw the line w m, square to the pitch-line b". Now take the length of the bottom level tangent on a trammel, or on dividers if large enough, and extend it from n to m, cutting the line drawn previously from w, at m. Connect m to n as shown by the line a". The intersection of this line with b" determines the angle between the two tangents a" and b" of the face-mould, which gives them the correct direction as required on the face-mould for squaring the joints. The joint at m is made square to tangent a"; and the joint at 5, to tangent b".

Fig. 105. Wreath Twisted, Ready to be Moulded.

Fig. 106. Twisted Wreath Raised to Position, with Sides Plumb.

In Fig. 102 is presented an example of a few steps at the bottom of a stairway in which the tangents of the plan form an obtuse angle with each other. The curve of the central line of the rail in this case will be less than a quadrant, and, as shown, is struck from the center o, the curve covering the three first steps from the newel to the springing.

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 w, square to the pitch-line b", draw the line w m; connect m 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 with the newel, and at 3 to connect square to the rail of the connecting flight.

Fig. 107. Finding Bevel, Bottom Tangent Inclined, Top One Level.

Fig. 108. Application of Bevels in Fitting Wreath to Rail.

The wreath in this example follows ' the nosing line 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-builder is supposed to know how to construct a wreath under both conditions, as the conditions are usually determined by the Architect.

Fig. 109. Face-Mould and Bevel for Wreath, Bottom Tangent Leve Top One Inclined.

Fig. 110. Finding Bevels for Wreath with Two Equally Inclined Tangents.

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.