Fig. 117. Upper Tangent Inclined. Lower
Tangent Level, Over Acute-Angle Plan.
Third Case. In this example, two unequal tangents are given, the upper tangent inclining more than the bottom one. The method shown in [Fig. 110] to find the bevels for a wreath with two equal tangents, is applicable to all conditions of variation in the inclination of the tangents. In [Fig. 112] is shown a case where the upper tangent d″ inclines more than the bottom one c″. The method in all cases is to continue the line of the upper tangent d″, [Fig. 112], to the ground line as shown at n; from n, draw a line to a, which will be the horizontal trace of the plane. Now, from o, draw a line parallel to a n, as shown from o to d, upon d, erect a perpendicular line to cut the tangent d″, as shown, at m; and draw the line m u o″. Make u o″ equal to the length of the plan tangent as shown by the arc from o. Put one leg of the dividers on u; extend to touch the upper tangent d″, and turn over to 1; connect 1 to o″; the bevel at 1 is to be applied to tangent d″. Again place the dividers on u; extend to the line h, and turn over to 2 as shown; connect 2 to o″, and the bevel shown at 2 will be the one to apply to the bottom tangent c″. It will be observed that the line h represents the bottom tangent. It is the same length and has the same inclination. An example of this kind of wreath was shown in [Fig. 95], where the upper tangent d″ is shown to incline more than the bottom tangent c″ in the top piece extending from h″ to 5. Bevel 1, found in [Fig. 112], is the real bevel for the end 5; and bevel 2, for the end h″ of the wreath shown from h″ to 5 in [Fig. 95].
Fig. 118. Finding Bevels
for Wreath of Plan, [Fig. 117].
Fourth Case. In [Fig. 113] is shown how to find the bevels for a wreath when the upper tangent inclines less than the bottom tangent. This example is the reverse of the preceding one; it is the condition of tangents found in the bottom piece of wreath shown in [Fig. 95]. To find the bevel, continue the upper tangent b″ to the ground line, as shown at n; connect n to a, which will be the horizontal trace of the plane. From o, draw a line parallel to n a, as shown from o to d; upon d, erect a perpendicular line to cut the continued portion of the upper tangent b″ in m; from m, draw the line m u o″ across as shown. Now place the dividers on u; extend to touch the upper tangent, and turn over to 1, connect 1 to o″; the bevel at 1 will be the one to apply to the tangent b″ at h, where the two wreaths are shown connected in [Fig. 95]. Again place the dividers on u; extend to touch the line c; turn over to 2; connect 2 to o″; the bevel at 2 is to be applied to the bottom tangent a″ at the joint where it is shown to connect with the rail of the flight.
Fifth Case. In this case we have two equally inclined tangents over an obtuse-angle plan. In [Fig. 102] is shown a plan of this kind; and in [Fig. 103], the development of the face-mould.
In [Fig. 114] is shown how to find the bevel. From a, draw a line to a′, square to the ground line. Place the dividers on a′; extend to touch the pitch of tangents, and turn over as shown to m; connect m to a. The bevel at m will be the only one required for this wreath, but it will have to be applied to both ends, owing to the two tangents being inclined.