In Fig. 335, let A B C represent the plan of a drum or cylinder, and B E D C the plan of rectangular pipe, the profile of which is shown by F G H I. In the elevation, J K L M represents the drum, N O P Q the rectangular pipe, and K n O the tingle at which they are to intersect. Draw the end view, or plan, of circular drum in line with the elevation, as shown. Also extend O n and P q so a line dropped from point C of plan will cut them, as shown by N and Q. Then n NQq is the joint between the drum and pipe, as shown in elevation. For the pattern of rectangular pipe proceed as follows: Divide B C of plan into any convenient number of equal parts, and from these points carry lines horizontally cutting E D. Also from the points in C B drop lines vertically catting Q P and N O. On O P extended lay off a stretchout of profile F G H I, as shown by I I'. transferring the spaces in E D to H G and F I', and through the points in it draw the usual measuring lines, as shown. Place the T-square parallel with the stretchout line I I', and, bringing it successively against the points in the miter lines N n Q q, cut the corresponding measuring lines, as indicated by the dotted lines. Lines traced through the points thus obtained, as indicated by i h g f i', will give the desired pattern. It will be observed that I II A i is a duplicate of O P Q N, and that G F f g is also a duplicate, only in a reversed position. The points in h g of pattern arc derived from Q q, as the points in f i' of pattern are derived from N n. If the size of the work-is such as to render it inconvenient to drop points from the elevation to the pattern by means of the T-square, the stretchout line I I' can be drawn where convenient, the usual measuring lines erected and the distances from O P to points in N n and Q q transferred by means of the dividers to lines of similar number drawn from the stretchout line.

For the pattern or shape of opening in drum, proceed as follows: On I, M extended, as R U, lay off a

Pattern Problems, 147 stretchout of B C of plan, and from the points thus obtained erect the usual measuring lines, as shown. Place the T-square parallel with M L, and, bringing it successively against the points N n and Q q, cut measuring lines of corresponding number. Through the points thus obtained trace the lines V W and Y X; then V W X Y will be the shape of the required opening in the side of the drum.

Fig. 335. - Patterns for Rectangular Pipe Intersecting a Cylinder Obliquely.