In the central portion of Fig. 374 is shown the plan B C D E F G H, upon which it is required to construct a finial, the only other view given being a section through one of the sides, being that numbered 1 on the plan.

The section of side ABC, or No. 1, is shown above and in line with the plan of the same, and is marked Profile No. 1, and is a section on the line A M, which is drawn at right angles to B C of the plan. To obtain the pattern of A B C of plan, or No. 1, divide the profile K L in the usual manner, and, with the T-square placed parallel with C B of plan and brought successively against the several points in profile K L, drop: lines cutting the miter lines A B and A C.

On A M extended, as Al Ml, lay off a stretchout of K L of profile, through the points in which draw the customary measuring lines. Place the T-square parallel to the stretchout line Al Ml, and, bringing it against the several points in the miter lines A B and A C, cut corresponding measuring lines. Tracing lines through the points thus obtained, as shown by Al C1 Bl, will give the pattern of part of article shown on plan by A B C.

Fig. 374. - Pattern for a Finial, the Plan of Which is an Irregular Polygon.

Since the point A in the plan is not equidistant from all the sides of the same, when measured on lines at right angles to each - that is, since AN, AO and A P, drawn at right angles respectively to C D, D E and E P, differ in length from each other and from A M - a correct section must be obtained for each of the other sides before their patterns can be developed.

These different sections can be most conveniently obtained at one operation in the following manner:

With the T-square placed parallel with D C, and brought successively against the points in A C, draw lines cutting A D and A N. Then the points in A N can be used to obtain a profile of section No. 2. Also continue the points from A D across the third section of the plan, and parallel with D E, and produce them until they cut A E, also A O, which is drawn from A at right angles to D O produced. Then A O contains the points necessary in obtaining a profile of the third section. Continue the points from A E across the fourth section of the plan, and parallel with E F, cutting A P and A F. Then the points in A P can be used to obtain a profile of section No. 4.

While the projection of the several points in each of the new profiles can be obtained respectively from the lines A N, A O and A P, the hights of the several points must be the same in all and must be derived from the normal profile K L. Therefore continue J L, which represents a horizontal line of profile No. 1, in either direction, as shown by L4 L2. From the several points in profile No. 1 draw lines parallel with L4 L2, extending them indefinitely in either direction. At any convenient position on L4 L2 set off points corresponding to the points in A N of the plan, as shown at J2 L2, numbering them to correspond with the points in A N and in the normal profile. From each of the points in J2 L2 erect lines perpendicular to the same, intersecting lines of corresponding number drawn from K L. Then a line traced through the points of intersection, as shown from K2 to L2, will be the correct section on A N of the plan, from which to obtain a stretchout of piece No. 2.

The sections of pieces No. 3 and No. 4 are obtained in a similar manner from A O and A P. J3 L3 is a duplicate of A O and J4 34 of A P. Perpendiculars are erected from each of the points cutting horizontal lines of corresponding number, thus developing K3 L3 and K4 L4.

To obtain the pattern of ADC (No. 2) continue A N downward indefinitely, upon which lay off a stretchout of K2 L2, as shown by A2 N2, through the points in which draw the usual measuring lines. Place the T-square parallel with A2 N2, and, bringing it against the several points in A C and A D, cut measuring lines of corresponding numbers. Lines traced through these points, as shown by A2 C2 and by A2 D2, will be the pattern sought.

The stretchouts for pieces Nos. 3 and 4 are taken respectively from profiles 3 and 4. A3 03 is the stretchout of K3 L3 and is laid off on a continuation of A O, while A4 P4 is taken from K4 L4 and is set off on a continuation of A P. The remaining operations are the same as those employed in obtaining the other pieces.