PRACTICAL PROBLEMS IN SHEET-METAL WORK. To describe a pattern for a square tapering article. The plan and vertical height or elevation are shown in Fig. 147. Draw the diagonals and take the distance from the center a to b, and mark off the same from g to d. Take the distance from a to 1 or k, and mark off the same from h to e. Draw a line through the points d, e, to cut the perpendicular line at f. Then draw the perpendicular line af, Fig. 148, and take the radius fd, Fig. 147, and with it describe the arc of a circle hdk, Fig. 148. With the radius fe in Fig. 147, and with f in Fig. 148 as a center, draw the smaller arc e. Take the length of one side b, Fig. 147, and mark off the of the base from c to same four times on the circle hdk at h, g, d, i, k. Draw through these points to the center f, join these points hg, gd, di, and ik. Also join the points on the smaller circle in the same manner, which will complete the pattern. To describe the pattern for a rectangular taper-sided tray. The vertical height and one-half the plan are shown in Fig. 149. Draw the horizontal line bd and the perpendicular line op as in Fig. 150. a Fig. 149. Draw the m Fig. 150. rectangle efgh the same size as efgh in Fig. 149. Take the length ab as in Fig. 149 and mark off a corresponding distance from e to b, h to d, and o to p, as in Fig. 150, and draw through the points b, p, and d the lines at right angles as bq, st, and dr. Transfer the length il to bq and to dr, also the length ul from p to s, and from p to t. Then draw the lines qf, sf, tg, and rg, which will complete one-half of the pattern. To describe the pattern for a hexagon tray with tapering sides. The elevation and one-half the plan are shown in Fig. 151. To develop the pattern draw the perpendicular bc, Fig. 152, and draw the halfhexagon efghi, of the same size as efghi in Fig. 151. Divide the lines hg and gf into two equal parts and draw the lines ak and am through the points of bisection, then carry the length ab, Fig. 151, from 1 to k in Fig. 152. Draw through k the line no parallel to hg. Then take the kl, Fig. 151, and mark off the same from k to n and from k to o, and draw the lines hn and go. Proceed in the same manner to draw the remainder, which will complete one-half of the pattern. To describe the pattern for a diamond-shaped tapering body. The plan for the size and shape of top and bottom and the vertical height fi are shown in Fig. 153. Transfer the lengths ac and ae from f to g and f to h respectively, also the distances from a to b and a to d, to il and ik, and draw through g and 1 a line to cut the perpendicular at m and another line through h and k to m. With the lengths mg, mh, ml, and mk, Fig. 153, as radii, describe the curves g, h, 1, k from the center m, Fig. 154. Transfer the ec, Fig. 153, from g to r and from g to n, Fig. 154, also from n to o and r to b, and draw lines from r, b, n, and o to the center m. Connecting the points br, rg, gn, and no, also ds, sl, lt, and tu will complete the pattern. To describe the pattern for an oblique pyramid. The lengths of the sides are shown projected, a'b to Cb', and a'a to Cc' giving for the true lengths a'b' and a'c'. Take the length a'c' in Fig. 155, and with it strike the radius a'c in Fig. 156. With the length a'b' in Fig. 155, strike the radius a'b in Fig. 156. Take the length of one side as ba in Fig. 155, and set it off from e to a, and from a to c, from c to b, and from b to e. Connect the points of intersections of the arcs |