In Fig. 536, A C D E represents the side elevation of the article, F H K L the end elevation, and M N R P in Fig. 537 the plan. By inspection of these it will be seen that the portion represented upon the end elevation by G L K is simply a flat triangular surface, while the corners of the vessel, shown by B C D of the side view and N R of the plan, are quarters of the envelope of an inverted scalene cone.

Fig. 536. - Side and End Elevations of Oblong Vessel with Semicircular End.

To obtain the patterns proceed as follows: Divide one-half of the end of the plan into any convenient number of equal spaces, all as shown by small figures 1, 2, 3, 4, etc., in N R. From each of the points thus determined draw lines to the point N, the apex of the cone in plan, all as shown in the engraving. Proceed next to construct the diagram of triangles shown in Fig. 538, of which the lines just drawn in the plan are the liases and B D is the common altitude. Draw A B, in length equal to D B of Fig. 536, and at right angles to it draw B C, which produce indefinitely. From B along B C set off spaces equal to the distances from N of the plan to the several points in the boundary line. That is, make B 5 of Fig. 538 equal to N 5 of Fig. 537, and B 4 equal to N 4, and so on. And from each of the points in B C draw lines to A. Then the distances from A to the various points in B C will he the distances from the apex of the scalene cone to the various points assumed in its base, and will be the radii of the arcs shown between D F and E in Fig. 539. For convenience erect any perpendicular, as A1 Dof Pig. 539, upon which set off distances equal to the length of the lines in the diagram drawn from A, or, in other words, make A1 1 equal to A 1 of the diagram, Pig, 538; A1 2 equal to A 2 of the diagram, and so on. From A' as center, with radius A1 D, describe the arc D E indefinitely. In like manner, from the same center, with radius A' 2, describe a corresponding arc, and proceed in this way with each of the other points lying in the line A1 D.

Fig. 537. - Plan of Oblong Vessel with Semicircular End.

Fig. 538. - Diagram of Triangles.

Fig. 539. - Pattern of End Pieces.

From any convenient point upon arc 6, as F, draw A1 F, which will represent the side of the pattern corresponding to B D of the side elevation. With the dividers set to the space used in stepping off the arc N R of the plan, place one foot at the point F of the pattern and step from one arc to the next until all the arcs are reached, and draw A1 E. Then A1 F E will be one portion of the required pattern. From E as center, with radius E A1, describe the arc A1 G indefinitely. Make the chord A1 G equal to L K of the end elevation, Fig. 536, and draw E G. Then A1 E G will be the pattern of that portion shown by L G K of the end view and NRP of the plan. Duplicate the part A1 F E, as shown by G H E, thus completing the pattern of the entire end.