In Fig. 654 are shown the elevations and plan of a hood of a style which is usually hinged to the top of an oil tank, or can. The plan shows a curve of something more than a semicircle, H' G F', while the curve F K H of the back view is slightly less than a half circle, the problem being to determine the shape of a piece of metal to fill the space between the two curves, as shown by A B C of the side view.

Divide one-half of the plan into any number of equal parts, as shown by the small figures 1, 2, 3, etc. From the points established in the plan cany lines upward until they cut the base line of the required piece, as indicated by the points between A and B. From the points thus established carry lines parallel to A C until they cut the line representing the back of the hood, as shown between C and B, thence carry them horizontally until they cut the profile of the back of the hood, as shown by the points between K and F. From the points in K F drop lines vertically on to the base line F E, establishing points in it, as shown. Lay off spaces in the line F' E' of the plan corresponding to those of F E in the back, and from the points thus established draw solid lines to those of corresponding numbers laid off in the plan from G to F'. These lines represent the bases of a series of right angled triangles whose altitudes are shown by the dotted lines of the back view, and whose hypothenuses will give the correct distances between points of similar number in the plan.

As the altitudes of these triangles are also shown in C B of the side elevation, that view is here made use of for the purpose of obtaining the required hypothenuses. However, since the solid lines drawn across the plan are not parallel to G E', the distances

1 B, 2 B, etc., representing them in the base line of the side view will not be the correct bases of the triangles, therefore set off on A B, measuring each time from B, the correct lengths of the several solid lines of the plan, as indicate by the points near 1, 2, 3, etc., on the line A B, from which points draw lines (shown dotted) to points of similar number in B C. Then the dotted lines 1 1. 2 2, etc., of the side view will be the correct hypothennses of the triangles whose bases are indicated by the solid lines drawn across the plan. To complete the measurements accessary for obtaining the pattern connect the points in the opposite sides of the plan diagonally, as, for example, 0 of the front and 1 of the back, and 1 of the front with 2 of the back, as shown by the dotted lines. These dotted lines represent the bases of a second set of triangles, to be constructed in the same manner as the former set, all as shown, Fig. 655. Draw A B and B C at right angles to each other and upon C B set off the several hights shown in C B of Fig. 654. Upon A B lay off B 0, corresponding in length to 1 0 in the plan. Make B 1 of the diagram equal to 2 1 of the plan, and in the same manner make B 2 and B 3 of the diagram equal to 3 2 and 4 3 of the plan respectively. From the points thus established in the base line of the diagram draw lines to points of next higher number in the vertical line. These hypothenuses will then represent lengths of lines measured on the face of the hood corresponding to the diagonal dotted lines in the plan. To develop the pattern, first draw any line, as 0 0 of Fig. 656, equal in length to A C of side, Fig. 654. From 0, at the right of the pattern, as center, with the distance between the points 0 to 1 in the profile F K of the back as radius, describe a short arc.

Fig. 654. - Elevations and Plan of Hood fur an Oil Tank, Showing System of Triangulation.

Fig. 665, - Diagram of triangles Based upon the Dotted Lines of the Plan.

Fig. 656. - Pattern for the Top of Hood.

Next take in the dividers the distance 0 1 of Fig. 855, and from the opposite end of the center line describe a short arc, intersecting the one already drawn at the point 1, thus establishing that point. From 1 as center, with dotted line 1 1 of the side view as radius, describe another short are, which in turn intersect by an are struck from 0 of the left hand side of the pattern with 0 1 of the plan as radius. This will establish the point 1 of the opposite side of the pattern. Continue in this way, intersecting the hypothenuse of the triangles whose bases are the dotted lines of the plan with the measurements taken from the back view, and the hypothenuse of the triangles which are shown by the solid lines of the plan with the measurements taken from the circumference of the plan. In this manner all points in the profile of the pattern neces sary to its delineation will be established. A freehand line drawn through these points will give one half the required pattern, all as shown in Fig. 656. The other half may be obtained by any convenient method of duplication.

The shape of patterns forming the back and the vertical sides of the hood are clearly shown in the engraving and need no further explanation.