In Fig. 600, let D G F E be the side elevation of the article and K N M one-half of the plan of the base. The half plan of the top is shown by K W L, the base and top being tangent in plan at the point K. The conditions and method of procedure in this problem do not differ materially from those of Problem 184.

Fig. 600.   Elevation and Plan of an Irregular Flaring Article with Elliptical Base and Round Top.

Fig. 600. - Elevation and Plan of an Irregular Flaring Article with Elliptical Base and Round Top.

Fig. 601. - Diagrams of Triangles Obtained from Fig. 600.

The surface of this article may be divided into measurable triangles in the following manner: Divide the plans of top and base into the same number of equal parts, as shown by 1, 2, 3, etc., in the base and 11, 21, 31 etc., in the top, and connect similar points in the two by solid lines, as shown by 6 61, 5 51, etc. Also connect each point in the plan of the top with the next lower number in the plan of the base, as shown by the dotted lines in the engraving, as 6 71, 5 6l, etc.

Next construct the diagrams of triangles, as shown in Fig. 601 at the right of the elevation, making A U in hight equal to D E of the elevation, and lay off U T at right angles to it. Let A represent all points in the circle representing the plan of the top of the article. Lay off from U upon U T the distance from each of the several points in the circle to the corresponding point in the ellipse. Thus make D 7 equal to 71 7 of the plan, U 6 equal to 61 6, etc., and draw the radial lines A 2, A 3, etc. In like manner construct a corresponding diagram, as shown by C B V, using for the spaces in B V the lengths of the dotted lines between the circle and the ellipse in the plan, and draw C 2, C 3, C 4, etc. By means of these two sets of lines, converging at A and C respectively, and the stretchouts of the two curves of the plan, the actual dimensions of the triangles into which the surface of the article has been divided can be accurately measured.

These are to be used in describing the pattern as follows: At any convenient place draw the straight line P R in Fig. 602, in length equal to G F of the elevation, or, what is the same, equal to A 7 of the first diagram. As but half of the plan of the article is shown, the pattern will also appear as one-half of the whole shape, and therefore P R will form its central line. From P as center, with radius C 6 of the second diagram, describe an arc, which intersect by a second arc struck from R as center, with radius 7 6 of plan, thus establishing the point 6 of the pattern. Then with radius A 6 of the first diagram, from 6 of the pattern as center, describe an arc, which cut with another arc struck from 71 of the pattern as center, and 71 61 of the plan as radius, thus locating the point 61 of the pattern. Continue this process, locating in turn 5, 51, 4, 41, etc., until points corresponding to all the points laid off in the plan are established. Lines traced through the points 7, 6, 5, etc., and 71, 61, 51, etc., will, with P R and O S, form the pattern of one-half the article.

Fig. 602.   Pattern for Article shown in Fig. 600.

Fig. 602. - Pattern for Article shown in Fig. 600.