The centre lines of the pipes may be arranged to meet at any required angle; but, for the sake of simplification, a square elbow (Fig. 19) will be taken first.

In work of this character the important thing is to accurately set out a side elevation of the elbow, so as to obtain the correct position of the joint line. This is done by first drawing in the centre lines at the required angle, and then from their point of intersection describing a circle (shown dotted in Fig. 19) equal in diameter to the cylindrical pipe. The outside lines of the pipes are afterwards drawn to touch this circle, and where they intersect will give the ends of the joint line. Thus, in Fig. 19, the cone and cylinder intersect respectively in a and 6; hence the straight line a 6 will be the side elevation of the joint. It will save confusion to remember that this joint line does not pass through the point of intersection of the centre lines. The shape of the section made by the cut to form the junction of the two pipes will, of course, be elliptical, and by careful measurement it will be found that the size of the ellipses on the conical and cylindrical pipes will be exactly the same; hence the two pipes should fit together correctly. A cone base may be taken at any convenient position; but in the case of the square elbow it is, perhaps, best to produce the under side of the conical pipe until it meets the back of the straight pipe, and then use the line 0 6 as the cone-base. A semicircle is described as shown, divided into six equal parts, and lines drawn square to the cone-base, these being then joined up to the cone-apex c. From the points where the radial lines intersect the joint a 6, lines are run parallel to the cone-base on to the outside line of cone, thus obtaining the points 0', 1', 2', etc. For the pattern, the compasses are first set to the distance c 6, and, with C as centre, the arc 0 0 described, its length being obtained by stepping along the length of one of the arcs from the semicircle twelve times. To obtain points for the pattern curve, the compasses are respectively set to the lengths c0', cV1', c2', etc., these being marked from C along the correspondingly numbered lines on the pattern. Thus - to take one case only - the line C4" on the pattern will be the same length as c4' on the elevation. After marking all the points, they are joined up with an even curve. The cut for the other end of pattern is obtained by describing the curve B B from centre C with the radius c b from the elevation.

Fig. 19.

If the elbow is made of galvanised sheet iron, an allowance for jointing can be put on as shown by the dotted line 4" D, the width of this depending upon the thickness of sheet metal used.

The cylindrical pipe pattern is not shown, as this will be struck out as before explained; but it should be noted that the allowance for jointing must be added to the back of pattern to correspond to that put on the throat portion of conical pipe.

In plate work more care will have to be taken to allow for thickness of metal in jointing. In setting out the elevation, the middle line of the metal thickness should form the outline of the figure. Suppose it is required to flange the tapered pipe over on to the cylindrical one; then the cone at the dotted circle portion should be made twice the thickness of the metal greater in diameter than the straight pipe. On the other hand, if the cylindrical pipe is to be flanged on to the conical part, then the former should be made two thicknesses in diameter greater.

Before proceeding to lay any lines down for a pattern or template, the arrangement of jointing should first be settled, as by a little forethought any method of connecting can be allowed for, and often much subsequent trouble avoided.
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