In Fig. 89 is shown the geometrical solu tion—the one necessary to find the angle between the tangents as required on the face mould to square the joints of the wreath. The figure is shown to be similar to Fig. 87, except that it has an additional portion marked "Section." This section is the true shape of the oblique plane whereon the wreath ascends, a view of which is given in Fig. 88. It will be observed that one side of it is the developed tangent in; another side, the developed tangent a" (= a).
The angle between the two as here presented is the one required on the face mould to square the joints.
In this example, Fig. 89, owing to the plane being oblique in one direction only, the shape of the section is found by merely drawing the tangent a" at right angles to the tangent m, making it equal in length to the level tangent a in the plan. By drawing lines parallel to a" and m respectively, the form of the section will be found, its outlines being the por jections of the plan lines; and the angle between the two tangents, as already said, is the angle required on the face-mould to square the joints of the wreath.
The solution here presented will enable the student to find the correct direction of the tangents as required on the face-mould to square joints, in all cases of practical work where one tangent of a wreath is level and the other tangent is inclined, a condition usually met with in level-landing stairways.
Fig. 90 exhibits a condition of tangents where the two are equally inclined. The plan here also is taken from Fig. 86. The inclination of the tangents is made equal to the inclination of tangent b in Fig. 86, as shown at In in Figs. 87, 88, and 89.
In Fig. 91, a view of Fig. 90 is given, showing clearly the inclination of the tangents c" and d" over and above the plan tangents c and d. The central line of the wreath is shown extending along the sectional plane, over and above its plan lines, from one joint to the other, and, at the joints, made square to the inclined tangents c" and d". It is evident from the view here given, that the condition necessary to square the joint at each ell(' vvoimo pie to find the true angle between the tangents c" and d", wructi wont. give the correct direction to each tangent.
In Fig. 92 is shown how to find this angle correctly as required on the face-mould to square the joints. in this figure is shown the
same plan as in Figs. 90 and 91, and the same inclination to the tangents as in Fig. 90, so that, except for the portion marked "Section," it would be similar to Fig. 90.
To find the correct angle for the tangents of the face-mould, draw the line in from d, square to the inclined line of the tangents c' d"; revolve the bottom inclined tangent c' to cut line In in ii, where the joint is shown fixed ; and from this point draw the line c" to w. The intersection of this line with the upper tangent d" forms the correct angle as required on the face-mould. By drawing the joints square to these two lines, they will butt square with the rail that is to connect with them, or to the joint of another wreath that may belong to the cylinder or well-hole.
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. SS and 91 com bined. Fig. SS, as here presented, is shown to con nect 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 in is shown to connect the two wreaths and is made square to the inclined tan gent 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 It, this section having one level tangent a and one inclined tangent m; the other tion is shown to extend from h to n, where it is butt-jointed to the rail of the flight above.