The intersection of an oblique cone with a cylinder, as shown in Fig. 322, presents a way by which a circular-mouthed hood can be run into a vertical pipe.

The determination of the joint line and the method of getting the lengths of the pattern lines will be shown for one point only. The plan and elevation of the oblique cone and the setting out of the full pattern are just the same as shown in Chapter XVIII (Articles Of Unequal Overhang. Oblique Cone). A line is first run up from b to b', joined to t' and cut through at the point a' by a line run up from a. Now using t as centre draw the arcs a c and b B; joining B to t' and drawing a line up from c to cut B t' in A (or A can be found by drawing a line across from a' to cut B t'). The line T A on the pattern is then marked off equal to t' A in the elevation. In the same way the other points for the pattern can be obtained.

Fig. 322.

The shape of hole for the cylindrical pipe can be drawn by making D E and D F respectively equal to d e and d f, and the distance E A equal in length to the arc e a. In a similar manner the other widths of the hole can be determined.