There are so many different kinds of the above class of work that there is some difficulty in making a selection of typical examples sufficiently broad to cover the general run of this character of work. In giving some representative cases it will perhaps be best to commence with a

Square, Equal Tapering Cap

This form of cap, or bonnet, is what is known in geometry as a square pyramid (Fig. 48), each face being triangular in shape and equal-sided.

To readily set out the pattern for a pyramid (having either four or more sides) the true length of one of the edges should first be obtained, and then used as the radius for the pattern circle. To do this a half-elevation is drawn (Fig. 49) by marking up the height, b t, and half the base, b a. The line a c is now drawn square to a t, and cut off equal to a b; then t c will give the true lengths of the edges, or the radius of the pattern circle. It might also be remembered that the triangle a t c gives the half-shape of one of the pyramid faces, or pattern triangles. After describing the arc C C C, to the radius t c, the compasses should be set to the length of the cap-base (twice b a), and this distance used to step around the arc. It will be seen that five lengths have been marked around; the last two being halved and joined up to T to form a seam line. It is always a good plan in pyramid work of this character, when the seam is required to come up the middle of a side, to set along the arc one more length than the number of sides that the cap has, and cut away half of each end triangle; this method insuring the correct position of the joints.

Square Equal Tapering Cap 53

Fig. 48.

The above is also exemplified in Fig. 50, where the pattern for an

Equal Tapering Square Article is shown set out. Here also a half-side elevation is drawn. The apex of the pyramid, of which this article is a frustum, can be found by producing a d to meet the centre line in t.

Square Equal Tapering Cap 54

Fig. 49.

The pattern for the complete pyramid is first struck out, as previously explained. The line d f is drawn square to a t, and the compasses set to the length t f; the arc which passes through F F, on the pattern, then being described.

Large articles, like hoppers and hoods, would, of course, be made up in parts, with joints running down the corners; or, in the case of very large jobs, perhaps two or three plates for each side. No difficulty, however, should be met with in these cases, when it is remembered that the shape of one side of the hopper will be E F F E on the pattern, or, for half a side, the figure a d f e on the elevation.