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].
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″.
Fig. 96. Finding Angle between Tangents
for Bottom Wreath of [Fig. 95].
Fig. 97. Finding Angle between Tangents
for Upper Wreath of [Fig. 95].
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″.