Fig. 114. Finding Bevel Where Tangents Incline
Equally over Obtuse-Angle Plan.
Fig. 115. Same Plan as in Fig. 114,
but with Bottom Tangent Level.
Second Case. It may be required to find the bevels for a wreath having two equally inclined tangents. An example of this kind also is shown in [Fig. 94], where both the tangents c″ and d″ of the upper wreath incline equally. Two bevels are required in this case, because the plane of the section is inclined in two directions; but, owing to the inclinations being alike, it follows that the two will be the same. They are to be applied to both ends of the wreath, and, as shown in [Fig. 105], in the same direction—namely, toward the inside of the wreath for the bottom end, and toward the outside for the upper end.
Fig. 116. Finding Bevels
for Wreath of Fig. 115.
In [Fig. 110] the method of finding the bevels is shown. A line is drawn from w to c″, square to the pitch of the tangents, and turned over to the ground line at h, which point is connected to a as shown. The bevel is at h. To show that equal tangents have equal bevels, the line m is drawn, having the same inclination as the bottom tangent c″, but in another direction. Place the dividers on o′, and turn to touch the lines d″ and m, as shown by the semicircle. The line from o′ to n is equal to the side plan tangent w a, and both the bevels here shown are equal to the one already found. They represent the angle of inclination of the plane whereon the wreath ascends, a view of which is given in [Fig. 111], where the plane is shown to incline equally in two directions. At both ends is shown a section of a rail; and the bevels are applied to show how, by means of them, the wreath is squared or twisted when winding around the well-hole and ascending upon the plane of the section. The view given in this figure will enable the student to understand the nature of the bevels found in [Fig. 110] for a wreath having two equally inclined tangents; also for all other wreaths of equally inclined tangents, in that every wreath in such case is assumed to rest upon an inclined plane in its ascent over the well-hole, the bevel in every case being the angle of the inclined plane.