Where a junction of two pipes of unequal diameter is formed, as in Fig. 12, it will be necessary first of all to obtain an elevation of the joint line, or of points upon the same. This can be done by drawing a semicircle on the main pipe and on the bottom line of this pipe a quarter-circle of radius, equal to half the diameter of branch pipe. The quarter-circle is divided into three equal parts, and lines drawn up to cut the semicircle in 0', 1', 2', and 3'. Lines are drawn up through these points parallel to the centre line of the top pipe, and where they intersect with the lines drawn through the corresponding points on the semicircle on branch pipe will give points on the joint curve. Great care should be exercised to obtain these points correctly, as the accuracy of the patterns depend upon the lines on the branch pipe being cut off to their proper lengths. In setting out the pattern for branch pipe the girth is, as usual, measured along 0 0, lines drawn up from all the points, and distances marked up these lines equal in length to the line with the same number on branch pipe in elevation.

To mark out the shape of the hole is somewhat more difficult than in the previous cases. Drop a perpendicular line from 3 on joint line to the bottom line of pipe. This in elevation is denoted by 3 a. To obtain points on curve of hole draw any line down the paper, and mark a point on it 0'. Set above and below this point the distance 0' 1', obtained by measuring along between 0' 1' on the semicircle on main pipe in elevation. In the same way set along the lengths V 2' and 2' 3'. Lines at right angles to the line 3' 3' are now drawn through these points, and the corresponding lengths measured on each side of 3 a in the elevation marked along. Thus 0' 0 will equal a 0 and 0' 6 equal a 6, 1' 1 will be the same as b 1 and 1/ 5 as b 5. In the same way, 2' 2 and 2' 4 will respectively equal c 2 and c 4. The points found will, of course, now be joined up with an even-flowing curve, and the shape of the hole is completed.

Facility in marking out the shapes of holes should be acquired by every sheet and plate metal worker, as it will save endless cutting, chiselling, and filing after the plate or sheet is bent into shape.

Nothing has been said so far as to any allowance that should be made for the thickness of sheet or plate; but this will be dealt with in later chapters.