The methods applied to obtain the patterns in the last cases can with some little modification be used for all sorts of made-up bends. We will now explain the application to a three-way piece, as shown in Fig. 251. This kind of job can be made up in three pieces, the two side parts which form the waist and outside of legs, and one part which forms the inside of legs, or it can be formed of five pieces, three as above, together with a triangular gusset on each side.

Fig. 250.

The patterns as set out in Fig. 252 are to buildup the bend in three pieces. A half-side and half-end elevation of the bend is drawn, and it should be remembered in connection with this that the area of the waist pipe circle should be equal to the areas of the two leg-pipe circles added together. The leg-pipe being 4 in. diameter, the diameter of the waist-pipe will be equal to -

= 5.7 = 5¾ in. (nearly).

Instead of bothering to calculate, the size of waist-pipe can readily be found by construction. Set out A B and B C at right angles (Fig. 253), each respectively equal to the radius of the leg-pipes, whether they are the same size or not; then A C will be the radius of the waist-pipe. In connection with this figure it is worth while noting that if A B, B C, C D, and D E are equal and drawn to form right-angled triangles, then the lines A B, A C, A D, and A E will give the radii of circles whose areas are as 1 is to 2 is to 3 is to 4.

Fig. 251.

To draw in the neutral lines (Fig. 252), their positions on the waist and leg-pipes are calculated as explained in connection with the quarter-bend.

For the waist and outside leg pattern, make the centre line equal in length to the neutral line, and across its ends draw lines square, and cut these off equal to half the circumference of waist and leg-pipes respectively. Set compasses to E F on the end elevation, and with centre L on the pattern describe the arc K G, making it equal in length to the line 0 H on the elevation. Join L to G, and draw the side curve, and the net pattern is complete.

Fig. 252.

The pattern for the inside of legs will be equal in length to the neutral line for that portion, and its width made equal to half the circumference of the leg-pipe.

Fig. 258.