Fig. 92. Finding Angle between Tangents.
[Fig. 93] is another view of these tangents in position placed over and above the plan tangents of the well-hole. It will be observed that this figure is made up of [Figs. 88] and [91] combined. [Fig. 88], as here presented, is shown to connect with a level-landing rail at a. The joint having been made square to the level tangent, a will butt square to a square end of the level rail. The joint at h is shown to connect the two wreaths and is made square to the inclined tangent m of the lower wreath, and also square to the inclined tangent c″ of the upper wreath; the two tangents, aligning, guarantee a square butt-joint. The upper joint is made square to the tangent d″, which is here shown to align with the rail of the connecting flight; the joint will consequently butt square to the end of the rail of the flight above.
The view given in this diagram is that of a wreath starting from a level landing, and winding around a well-hole, connecting the landing with a flight of stairs leading to a second story. It is presented to elucidate the use made of tangents to square the joints in wreath construction. The wreath is shown to be in two sections, one extending from the level-landing rail at a to a joint in the center of the well-hole at h, this section having one level tangent a and one inclined tangent m; the other section is shown to extend from h to n, where it is butt-jointed to the rail of the flight above.
Fig. 93. Laying Out Line of Wreath to Start from
Level-Landing Rail. Wind around Well-Hole, and
Connect at Landing with Flight to Upper Story.
This figure clearly shows that the joint at a of the bottom wreath—owing to the tangent a being level and therefore aligning with the level rail of the landing—will be a true butt-joint; and that the joint at h, which connects the two wreaths, will also be a true butt-joint, owing to it being made square to the tangent m of the bottom wreath and to the tangent c″ of the upper wreath, both tangents having the same inclination; also the joint at n will butt square to the rail of the flight above, owing to it being made square to the tangent d″, which is shown to have the same inclination as the rail of the flight adjoining.