In Fig. 588 are shown front and side views and lan of an article forming a transition between a rect-angular pipe at one end and a round pipe at the other, and forming at the same time an angle between the two pipes. A B F C of the front view shows the size of the rectangular pipe, while Q B H D shows the opening to receive the round pipe. In the side view a c shows the vertical rectangular end. and b d shows the angle at which the round end is placed, b l d being a half profile of the round end. As will be seen by an inspection of the front, view, each quarter of the circular opening is treated as the base of a portion of a scalene cone whose apex is in the adjacent angle of the rectangle, the intermediate surfaces being flat triangular pieces. Thus B G and G D are the quarter bases of scalene cones whose apices are respectively at A and C; A B E and C D F are triangles whose altitudes or profiles are shown respectively by a b and e d of the side view; and A G C is a triangle whose profile appears at o u in the plan.

Fig. 583. - Front and Side Views and Plan of an Article Forming a Transition Between a Rectangular Pipe and a Round Pipe, at an Angle.

Divide each quarter of the profile b l and l d of Fig. 583 into any number of equal spaces, as shown by the small figures; also draw a duplicate of this half profile in proper relation to the plan, as shown by m g x, which divide as before, numbering the points in each to correspond, as shown. From the points in b l p drop lines at right angles to b d, cutting the same. From the points in m g x carry lines indefinitely to the left parallel to the center line gf, and intersect them by lines of corresponding number erected vertically from the points in b d. A line traced through the points of intersection will give a correct plan view of the opening in the round end. To avoid confusion of lines the intersections from the points between b and h or the upper half of the opening are shown only in the near or lower half of the plan from t to u, while the points belonging to the lower half (h to d) are shown only in the further half of the plan from p to q.

From each of the points in p q of the plan draw lines to s, which is the projection of e of the side view or apex of the cone in the lower half, and from the points in t u draw lines to o, the apex of the cone of the upper half of the article. These lines represent only the horizontal distances from s and o to the points in the opening t u q p of the plan or B G D of the front view. To ascertain the real distances between these points it will be necessary to first ascertain their vertical hights from an assumed horizontal plane and then to construct from these measurements a series of right angled triangles whose hypothenuses will give the desired distances.

From the points in b h of the side view drop lines vertically, cutting a horizontal line drawn from a, as shown between v and j; and from the points in h d drop lines to w z drawn horizontally from e. To construct the triangles required in the top part, first draw the right angle R O K, as shown in Fig. 584, and from O on O R set off the length of lines in b h j v of side view, as indicated by the small figures. From O on O K set off the length of lines in o t u of plan of top, also as indicated by the small figures. Connect the points in O R with those of similar number in O K, as shown. To obtain the triangles required for the bottom part, proceed in a similar manner. Draw the right angle W S L, as shown in Fig. 585. From S on S W set off the length of lines in h d z w of side view, as indicated by the small figures. From S on S L set off the length of lines in s p q of plan of top, also as indicated by the small figures. Connect the points in S W with those of similar number in S L, as shown.

For the pattern proceed as shown in Fig. 586. Draw the line O O', in length equal to A B of front view or u k of plan. Bisect O O' in C, and erect the perpendicular C D, in length equal to a b of side view, and draw O D, D O'. These lines are equal in length to R K of first diagram of triangles. With O of pattern as center, and 2 2' in R O K as radius, describe a small arc, 2, which intersect with one struck from point

D of pattern as center, and b 2 in b l of profile as radius, thus establishing point 2 of pattern. Proceed in this manner, using the length of lines in R O K for distances from O of pattern, and the stretchout between points in b l of profile of side view for the distance between points in D G of pattern; then draw D G and G O. With point G of pattern as center, and 5 5' in W S L of triangles as radius, strike a small arc, E, which intersect with one struck from point O of pattern as center and a e of side view as radius, thus establishing point E of pattern. Draw G E and E O. With point E of pattern as center, and 6 6' of triangle in W S L as radius, strike a small arc, 6, which intersect with one struck from point G of pattern as center, and l 6 of profile as radius, thus establishing point 6 of pattern. Proceed in this manner, using the length of lines in W S L as distance from E of pattern, and the stretchout between points in l d of profile of side view for the distance between points in G H of pattern, and draw G H and H E. With point H of pattern as center, and e d of side view as radius, strike a small arc, C, which intersect with one struck from point E of pattern as center, and o f of plan, or C O of pattern, as radius, thus establishing point C of pattern; then draw H C and C E. From E and C erect the perpendiculars E R and C F, in length equal to c e of side view, and draw F R. With O of pattern as center, and a c of the side view as radius, strike a small arc, which intersect with one struck from E of pattern as center and e c of the side view as radius, thus establishing point K of pattern, and draw O K and K E. Then DGHFREKC represents the half pattern of article. The other half can be obtained in the same manner or by duplication, as may be found convenient.

Fig. 586. - Pattern for Transition Piece Shown in Fig. 583.

Fig. 584. - Diagram, of Triangles in Top Half.

Fig. 585. - Diagram of Triangles in Bottom Half.