If the centre lines of these two conical surfaces coincide, it is evident that each part will come out as a frustum of cone; but if the centre lines are not common to each, but parallel, then the two parts will fit together as shown in Fig. 309. In the latter case the problem becomes somewhat more difficult.

The setting out of the patterns is shown in Fig. 310. Just as in most other cases that we have dealt with, the first thing to be done is to obtain an elevation of the joint curve. For this purpose an elevation and half-plan of the dome and pipe is constructed. Through the points 0" and 6" lines parallel to the base line are drawn, cutting the centre line of the large cone in the points e and a. Then line e a is divided into, say, four equal parts, giving points b c and d. Cross lines are then drawn through each of these points to cut the centre line of the small cone in f, g, h, and i. Now taking b as centre, and b k as radius, draw an arc of a circle; then, with h as centre, and h l as radius, construct another arc to cut the former in m. From m drop a perpendicular on to b l, thus obtaining n, which will be a point on the joint curve. In the same manner, circular arcs can be described on the lines passing through c and d, and further points on the joint curve obtained. These being carefully joined up will give the elevation of the joint curve as required for getting the lengths of the pattern construction lines.

Fig 309.

Fig. 310.

For the conical pipe pattern it will be most convenient to produce the sides down to the base line, and on this describe a, semicircle, dividing it into six equal parts, as shown. Perpendiculars are then run up from each division point to the base and joined to the apex, c, of the cone. Where these radial lines cross the joint curve, lines square to the centre line are run to the outside of the cone, giving the points 5', 4', 3', etc. The lengths c 5', c 4', etc., are then transferred by running the arcs around on to the correspondingly numbered radial line of the complete cone pattern, thus giving points for the pattern cut. These being connected with a fair curve will give the required pattern cut for the conical pipe.

In the same manner the pattern for the conical dome can be struck out. The semicircle in plan is divided as before, perpendiculars run up, and radial lines drawn. From the points where these latter intersect the joint curve, cross lines are drawn to meet the outside line of the conical dome in the points 5°, 4°, 3°, etc. Then for the pattern, these lengths are marked off on the construction lines. That is T 5°, T 4°, etc., on the pattern will respectively equal t 5°, t 4°, etc., on the elevation. Any laps for jointing can, of course, be added as required for either of the patterns.