If the conical pipe has to fit on the middle of the spherical dome, it will at once be seen that the cut on the end of the cone must be square to its centre line. But if the conical pipe fits on the side of the dome, as in Fig. 345, then the setting out of the pattern becomes a much more difficult matter.
To set out the pattern for the latter case, it will be necessary to first of all obtain points on the elevation of the joint line. To do this the principle adopted is to imagine horizontal cuts taken through the cone and sphere. These sections would of course be circles, and where they intersect each other would give points on the joint line. The arcs shown on Fig. 345 represent parts of the section circles. Thus, to obtain one point: With centre c (on the centre line of sphere) and radius c b, the arc b e is drawn; then with centre d (on the centre line of the cone) and radius d a, the arc a e is drawn; from the point e, where the two arcs intersect, a perpendicular is dropped on to the line a c, giving f, this being one point on the joint line. In the same manner, as many other points as are required can be obtained. Through each point so found, a line from the apex of the cone is drawn down to the base.
and then from the base on to the semicircle as shown. The lengths of arcs on the semicircle are then set around for the girth of the pattern curve, as 0, 1, 2, etc., and the radial lines drawn; these latter are then cut by swinging the lengths around from the side of the cone. When the points so found are joined up, the pattern is complete.