The construction of wreaths is based on a few geometrical problems—namely, the projection of straight and curved lines into an oblique plane; and the finding of the angle of inclination of the plane into which the lines and curves are projected. This angle is called the bevel, and by its use the wreath is made to twist.
In [Fig. 84] is shown an obtuse-angle plan; in [Fig. 85], an acute-angle plan; and in [Fig. 86], a semicircle enclosed within straight lines.
Projection. A knowledge of how to project the lines and curves in each of these plans into an oblique plane, and to find the angle of inclination of the plane, will enable the student to construct any and all kinds of wreaths.
The straight lines a, b, c, d in the plan, [Fig. 86], are known as tangents; and the curve, the central line of the plan wreath.
The straight line across from n to n is the diameter; and the perpendicular line from it to the lines c and b is the radius.
A tangent line may be defined as a line touching a curve without cutting it, and is made use of in handrailing to square the joints of the wreaths.
Tangent System.
The tangent system of handrailing takes its name from the use made of the tangents for this purpose.
In [Fig. 86], it is shown that the joints connecting the central line of rail with the plan rails w of the straight flights, are placed right at the springing; that is, they are in line with the diameter of the semicircle, and square to the side tangents a and d.