A square spout for a jug, as seen in Fig. 267, represents a good example of flat sheet surfaces fitting on to a conical surface. It may be applied in a variety of ways other than in the case shown. The setting out of the pattern is illustrated by Fig. 268, in which an elevation of the jug neck and spout is also shown. Before the pattern can be laid out, the line n l must first be obtained, this being done as follows: From the centre, o, describe the arc k t, and draw n m equal to half the width of the spout. Produce a b to c, and bisect b c in d. Draw f e square to o e, passing through d, and on this describe an arc of circle to meet the line d i in i. Now draw d g perpendicular to b c, and equal in length to d i. A quarter-ellipse should now be described on d b and d g, as shown. The line s h is next drawn parallel to a c, and at a distance from it equal to m n, to cut the ellipse in h. The perpendicular h l is then dropped on to a c to fix the point l, and thus determine the line n l.

Fig. 268.

The pattern is projected as shown, L H being equal to l h, and R N equal to r n, the curve H B H being, of course, twice the part of ellipse represented by b h on the elevation. To fit exactly on to the conical surface, the edge H N should be slightly hollow; but this, if found necessary, can be put right when bending the flange over. If a not very particular job, there is really no need to cut away the part H B H, as the edge H H can be curved around the neck at the part where it fits.

Fig. 269.