Practical Carpentry

Problem 28.—The axes of an ellipse being given, to draw the curve by intersections: Let AC (Fig. 53) be the major axis, and DB half the minor axis. On the major axis construct the parallelogram AEFC, and make its height equal to DB. Divide AE and EB each into the same number of equal parts, and number the divisions from A and E, respectively; then join Al, 12, 23, etc., and their intersections will give points through which the curve may be drawn.

Problem 29.—To describe with a compass a figure resembling the ellipse: Let AB (Fig. 54) be the given axis, which divide into three equal parts at the points fg. From these points as centers, with the radius Fa, describe circles which intersect each other, and from the points of intersection through f and g, draw the diameters CgE, CfD. From C as a center, with the radius CD, describe the arc DF, which completes the semi-ellipse. The other half of the ellipse may be completed in the same manner, as shown by the dotted lines.

Problem 30.—Another method of describing a figure approaching the ellipse with a compass: The proportions of the ellipse may be varied by altering the ratio of the divisions of the diameter, as thus: Divide the major axes of the ellipse AB (Fig. 55), into four equal parts, in the points

fgh. On fh construct an equilateral triangle fCh, and produce the sides of the triangle Cf, Ch in definitely, as to D and E. Then from the centers f and h, with the radius Af, describe the circles ADg, BEg; and from the center C, with the radius CD, describe the arc DE to complete the semi-ellipse. The other half may be completed in the same manner. By this method of construc tion the minor axis is to the major axis as 14 is to 22.

Problem 31.—To find how far apart to saw kerfs to spring a board or moulding: Let ab (Fig. 56) be the curve, around which it is desired to spring a piece of stock. Take a piece of stock dg of the thickness which is to be used. Lay it down so that the edge shall pass through the center c, and mark from c to g, and also at e.

Now, with the saw which is to be used, make a kerf nearly through the piece of stock at c. Keeping this piece on the line cg, spring down the end d until the kerf is closed, then mark the point. f : of will be the distance apart to saw kerfs.