A B D C in Fig. 376 shows the plan of the article at the base, IKLMHGFE represents the shape at the top, E3 H2 D2 C2 is an elevation of one side. In order to obtain the slant hight of the octagonal sides it will be necessary to construct a diagonal section or elevation. Therefore extend the lines of the base C3 D2 and top E2H2, as shown, to the left, through which draw a vertical line, as R1 C2 Upon the line of the base set off each way from C1a distance equal to A R or R D of the plan. In like manner upon the line of the top, set off from R1 each way a distance equal to one-half

I G. Draw I1 A1 and G1D1, thus completing a diagonal section. If it is desired to complete a diagonal elevation, set off E2 F2 equal to E F of the plan and draw lines to C5, as shown.

To obtain the pattern of one of the smaller sides. produce the diagonal line R C, upon which set off the length or stretchout of I1 A1, as shown by N C1, and draw the measuring line E1' F1 By means of the T-square, as indicated by the dotted lines, set off E1 F1 equal to E F of the plan and draw C1 E1 and C1 F1. Then E1 C1 F1 is the pattern of one of the smaller sides of the article. For the pattern of one of the larger sides, draw R P perpendicular to the side A C, upon which set off O P, in length equal to E3 C3 of the elevation, at right angles to which through O and P draw measuring lines.

Fig. 377. - Pattern in One Piece.

By means of the T-square, as shown by the dotted lines, make A2 C4 equal to A C of the plan. In like manner make I2 E4 equal to I E of the plan. Connect A2 F2 and C4 E4. Then A2 I2 E4 C4 will be the pattern of one of the larger sides of the article. If for any reason the pattern is desired to be all in one piece the shapes of the different sides may be laid off adjacent to each other, the large and small sides alternating, all us indicated by i i1 a a1, Fig. 377.

Fig. 376. - Elevations, Plan and Patterns.

A Tapering Article Which is Square at the Base and Octagonal at the Top.

The Patterns of a Finial, the Plan of which is Octagon with Alternate Long: and Short Sides.

In Fig. 378, let A L M N O P B S T be the elevation of the finial corresponding to the plan which is shown immediately below it. The elevation is so drawn as to show the profile of one of the long sides. for the pattern of which proceed in the usual manner. Divide the profile A L M N O P into any number of convenient spaces, as shown by the small figures, and from the points thus obtained drop lines across the corresponding section in the plan, cutting the miter lines D E C and D2 F C, as shown. A duplicate of the part E C F of the plan is shown below by E1 C2 F1. and in the demonstration C2 E1 and C2 F1 are to be considered the same in all respects as C E and C F. The same may be said of the two parts of the stretchout line bearing like letters; the division having been made on account of the extreme length which the pattern would have if made in one piece. Perpendicular to D D2 lay off a stretchout, as shown by G H, through the points in which draw measuring lines in the usual manner. Place the T-square parallel to the stretchout line, and, bringing it against each of the several points in D E C and D2 F C, cut the corresponding measuring lines. Then a line traced through these points of intersection will be the pattern sought.

For the pattern of the short sides a somewhat different course is to be pursued. As the distance from C to the line K E is greater than that from C to E F a profile of the piece as it would-appear if cut on the line C D must first be obtained. To do this proceed as follows; From the points in C E. dropped from the profile, carry lines parallel to E K across C D, cutting C K, as shown. At any convenient place lay off B1 P1, Fig. 379, in length equal to C D of the plan, on which lay off points corresponding to the points obtained in C D, and for convenience in the succeeding operations number them to correspond with the numbare in the profile from which they arc derived. At B1 erect the perpendicular B1 A1, equal to B A of the elevation. From the several points in the profile of the elevation draw horizontal lines cutting the central vertical line A B, as shown. Setoff points in A1 B1 in Fig. 379 to correspond, and through these points draw horizontal lines, which number for convenience of identification in the following steps. From the several points in B1 P1 carry lines vertically, intersecting corresponding horizontal lines. Then a line traced through these points, as shown by A1 L1 M1 N1 O1 P1, will be the profile of the short side on the line C D of the plan.

Fig. 378. - Elevation, Plan and Patterns.

Fig. 379. - Diagonal Section.

The Patterns of a Finial, the Plan of Which is Octagon with Alternate Long and Short Sides.

After obtaining the profile as here described, for the pattern of the short side proceed as follows: Perpendicular to K E of the short side, or on C D extended, lay off a stretchout of the diagonal section A1 O1 of Fig. 379, as shown by C1 D1, through the points in which draw measuring lines in the usual manner. Place the T-square parallel to the stretchout line, and, bringing it against the several points in the miter lines D K C and DEC bounding the short side in the plan, cut the corresponding measuring lines. Then a line traced through these points, as shown in the diagram, will be the required pattern.