## Obtaining Oblique Cuts

tion, which arc the usual drawings given, will show that the true length of the line required, a'-b, is not shown in either drawing. If, however, we conceive the edge a lifted up until it is level with b, the point b remaining tixed, we should then have the surface parallel with the plan, and, drawn thus, its true shape would be disclosed.

To do this, set off on Fig. 7, the real width of the piece B, obtained at a-b, Fig. 9, and draw the developed edge parallel to its original position, a -ax. Intersect this line at a' by a projector perpendicular to it, from point a ; this locates point a in its new position, and as point h has not moved, if we join a'-b, obviously we obtain the true shape of the bevel or cut to fit against the piece A.

In Figs. to to 12 are shown a plan and two elevations of a vertical piece A, standing at an angle of 58° with the edge of its base, and a doubly inclined piece B, fitting against it ) the oblique cuts a-b and c d are required. To obtain these a similar method is pursued. It may be well to describe first the method of making the orthographic projections. The essential data are: the width of base is 14 in.; angle between vertical piece and edge of base, 58°; angle between base and brace or inclined piece, 40 0; height of top of brace, 2 ft.; front edge of brace to be 5 in. lower than back edge. Proceed to draw Figs. 10 and 12 to these conditions, then project the elevation Fig. 11 from them, as indicated by the dotted projectors. Having found position of point a in Fig. 11, draw the front edge of B at the required angle from it and the back edge parallel thereto. Next project points c and d i'lto the plan, and draw the joint c" d'. This completes the projections and we can proceed with the developments.

The first thing required is the true width of piece B, which neither of the projections show. To obtain this, turn the piece A into the vertical plane by taking point b" as centre and a"-b" as radius; describe the arc a"-a2, then project this point into the vertical plane as shown, and intersect it at a* by a horizontal projector from point a. Join a3~b', and the real length of the line a-b' is seen. Set off this length 