This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
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First-Floor Plan Shown on Opposite Page.
Now, from point n, draw a few treads and risers as shown; and along the nosing of the steps, draw the pitch-line; continue this line over the tangents d", c", and m, down to where it connects with the bottom level tangent, as shown. This gives the pitch or inclination to the tangents over and above the we11-h o1 e. The same line is shown in Fig. 93, folded around the w e 11-h o 1 e, from n, where it connects with the flight at the upper end of the well-hole, to a, where it connects with the level-landing rail at the bottom of the well-hole. It will be observed that the upper portion, from joint n to joint h, over the tangents c" and d", coincides with the pitch-line of the same tangents as presented in Fig. 92, where they are used to find the true angle between the tangents as it is required on the face-mould to square the ioints of the wreath at h.
In Fig. 89 the same pitch is shown given to tangent m as in Fig. 94; and in both figures the pitch is shown to be the same as that over and above the upper connecting tangents c" and d", which is a necessary condition where a joint, as shown at h in Figs. 93 and 94, is to connect two pieces of wreath as in this example.
In Fig. 94 are shown the two face-moulds for the wreaths, placed upon the pitch-line of the tangents over the well-hole. The angles between the tangents of the face-moulds have been found in this figure by the same method as in Figs. 89 and 92, which, if compared with the present figure, will be found to correspond, excepting only the curves of the face-moulds in Fig. 94.
Fig. 95. Well-Hole Connecting Two Flights, with Two Wreath-Pieces, Each Containing Portions of Unequal Pitch.
The foregoing explanation of the tangents will give the student a fairly good idea of the use made of tangents in wreath construction. The treatment, however, would not be complete if left off at this point, as it shows how to handle tangents under only two conditions - namely, first, when one tangent inclines and the other is level, as at a and m; second, when both tangents incline, as shown at c" and d".
In Fig. 95 is shown a well-hole connecting two flights, where two portions of unequal pitch occur in both pieces of wreath. The first piece over the tangents a and b is shown to extend from the square end of the straight rail of the bottom flight, to the joint in the center of the well-hole, the bottom tangent a" in this wreath inclining more than the upper tangent b". The other piece of wreath is shown to connect with the bottom one at the joint h" in the center of the well-hole, and to extend over tangents c" and d" to connect with the rail of the upper flight. The relative inclination of the two tangents in this wreath, is the reverse of that of the two tangents of the lower wreath. In the lower piece, the bottom tangent a", as previously stated, inclines considerably more than does the upper tangent b"; while in the upper piece, the bottom tangent c" inclines considerably less than the upper tangent d".
Fig. 96. Finding Angle between Tangents for Bottom Wreath of Fig. 95.
Fig. 97. Finding Angle between Tangents for Upper Wreath of Fig. 95.
The question may arise: What causes this? Is it for variation in the inclination of the tangents over the well-hole? It is simply owing to the tangents being used in handrailing to square the joints.
The inclination of the bottom tangent a" of the bottom wreath is clearly shown in the diagram to be determined by the inclination of the bottom flight. The joint at a" is made square to both the straight rail of the flight and to the bottom tangent of the wreath; the rail and tangent, therefore, must be equally inclined, otherwise the joint will not be a true butt-joint. The same remarks apply to the joint at 5, where the upper wreath is shown jointed to the straight rail of the upper flight. In this case, tangent d" must be fixed to incline conformably to the inclination of the upper rail; otherwise the joint at 5 will not be a true butt-joint.
The same principle is applied in determining the pitch or inclination over the crown tangents b" and c". Owing to the necessity of joint-ing the two wreaths, as shown at h, these two tangents must have the same inclination, and therefore must be fixed, as shown from 2 to 4, over the crown of the well-hole.
The tangents as here presented are those of the elevation, not of the face-mould. Tangent a" is the elevation of the side plan tangent a; tangents b" and c" are shown to be the elevations of the plan tangents b and c; so, also, is the tangent d" the elevation of the side plan tangent d.
If this diagram were folded, as Fig. 94 was shown to be in Fig. 93, the tangents of the elevation - namely, a", b", c", d" - would stand over and above the plan tangents a, b, c, d of the well-hole. In practical work, this diagram must be drawn full size. It gives the correct length to each tangent as required on the face-mould, and furnishes also the data for the lay-out of the mould.