If a cylindrical pipe fits on to a conical pipe, both having the same centre line, it will be manifest that the cylindrical pipe will be cut square at the joint, and that the conical pipe will come out as a frustum of a cone. If, however, their centre lines do not coincide, but are some distance apart, and parallel, the two pipes will fit together as shown in Fig. 308.

Before attempting to mark out the pattern it will be necessary to first draw in the elevation of a joint curve. To do this, construct the semicircle, as seen in plan, Fig. 308, and divide it into six equal parts, running lines up through each division point square to the base line. Now, taking b as centre, and b 1, b 2, etc., as radii, swing on to the base line, thus determining the points 1' 2', etc. From these last points run perpendiculars up to intersect the outside lines of the cone in 0", 1", 2", etc., and then from these draw lines across parallel to the base line to meet the perpendiculars already drawn from the points on the semicircle. The points of intersection of these two lines will lie on the joint curve.

Fig. 308.

The complete conical pattern is first marked out in the usual way, and a centre line, A 0", drawn. Along this the distances from a 0" in the elevation are set; that is, A 5" equals a b", A 4" equals a 4", and so on. With A as centre, arcs are then drawn through the points 5", 4", etc. The lengths of these are carefully measured off equal to that of the corresponding arc on the semicircle in plan. Thus 1" 1° equals 1 1', the arc 2" 2° is the same length as 2 2', and so on for the others. The points so found when joined up with an even curve will give the cut required.

For the cylindrical pipe the pattern will be marked out in the usual way, the lengths of the construction lines being measured from the top end down to the joint curve.