In the same manner as some circular tapering articles are formed as portions of round oblique cones (Chapter xviii (Articles Of Unequal Overhang. Oblique Cone).), so we may have square objects coming out as parts of square oblique pyramids. Fig. 53 is an illustration of the latter. The top and bottom of the hood are square, and also parallel; but it will be seen from the plan that their centres do not come on the same vertical lines. If the corner lines in plan are produced, they will meet in the common point t, this being the plan of the apex of the oblique pyramid of which the hood is a frustum. To set out the pattern: Produce the side lines in the elevation, and obtain T, the apex of the cone (this should come exactly over t in the plan). From t' mark the lengths t 1, t 2, t 3, and t 4, along the base line, so fixing the points 1', 2', 3', and 4'. Join these latter to T, and then draw the arcs to the radii T 1', T 2', etc., as shown. Open out the compasses to the length of the side of the square, say i to 2, and, commencing at 1 (on the arc drawn through 1'), step around from curve to curve the points 2, 3, 4, and 1.

Fig. 53.

Join these up to each other and T. This figure would give the pattern for the complete oblique pyramid. We now want to cut away the part of pattern that corresponds to the top of the pyramid. Take T again as centre, and as radii the distances down to where the respective lines cross the top line or top line produced, and swing around on to the corresponding lines. Thus T 2° will be equal to T 2", T 4° to T 4", and so with the other lines.

If it is a large hood, then the plates can be set out separately, as in the former cases.

No allowances for jointing have been put on the above pattern, as this will depend upon the size of hood and the number of plates into which the complete pattern is divided.

Whilst the construction, as shown above, is for a square oblique pyramid, it should be borne in mind that the same principle will apply to any other shaped article that comes out as a frustum of an oblique pyramid.

Fig. 54.