In Fig. 345 J K L M is the side elevation of the round pipe and K F G H that of the elliptical pipe joining the larger pipe at the angle FGJ. In the end elevation T S I shows the profile of the round pipe and U R S T the intersection of the elliptical pipe whose profile is shown at A B C D and N O P Q, respectively, in the side and end views. From an inspection of the drawings it will be seen that the side elevation shows the narrow view of the elliptical pipe, while the end elevation shows its broad view, or in other words, that the profile of the elliptical pipe is so placed that its major axis crosses the round or larger pipe. In Fig. 346 the elevations show the same pipes intersecting at the same angle,, but with the difference that the profile of the elliptical pipe is so placed that its minor axis crosses the round pipe. The reference letters and figures are the same in the two drawings and the following demonstration will apply equally well to either:

Fig. 345 - The Joint between an Elliptical Pipe and a Round Pipe of Larger Diameter at Other than Right Angles. First Case. The Major Axis of the Elliptical Pipe Crossing the Round Pipe.

By way of getting ready to lay out the miter, it will first be necessary to obtain a correct elevation of the miter line or intersection between the two pipes, as shown, from II to G. To do this divide the two profiles ABCD and N O P Q into the same number of equal parts, commencing at the same points in each. Draw lines from the points in NOPQ, parallel with U T, cutting T S. In a similar manner draw lines indefinitely from the points in A B C D, parallel with

H E, as shown. From the points in T S draw lines parallel with M J which produce until corresponding lines from the two profiles intersect. Through the several points of intersection thus obtained draw the miter line H G. For the pattern of E F G H proceed as follows: On E F extended, as V W, lay off a stretchout of profile A B C D, through the points in which draw the usual measuring lines at right angles to the stretchout line. With the T-square placed at right angles with H E, or parallel with V W, and brought successively against the points in the miter line H G, cut corresponding measuring lines. A line traced through the points thus obtained, as shown by X Y Z, will give the miter cut required, and V W X Y Z shows the entire pattern.

Fig. 346. - Second Case. The Minor Axis of the Elliptical Fipe Crossing the

Round Pipe.

The method of obtaining the shape of the opening in the round pipe is exactly similar to that described in the several preceding problems.