This section is from the book "The Tinman's Manual And Builder's And Mechanic's Handbook", by Isaac Ridler Butt. Also available from Amazon: The Tinman's Manual And Builder's And Mechanic's Handbook.
[Drawn for this work by L.W. Truesdell, Tinman, Owego,N. T.] Original.
Describe two circles UX and V'S, the curves desired for the elbow, having the distance from U to V' equal to the diameter; then divide the circle V', W, R and S, into as many sections as desired; then construct a rectangle, Fig. 8, ADEB, the width equal to the width of one section V'W, Fig. 7, and the length equal to the circumference of the elbow; then span the dividers from the point R to the point P at the dotted line, Fig. 7, and with the dividers thus spanned mark the points FF' Fig. 8, from points A and D, and draw the lines FG and F'G'; from point I draw the two diagonal lines IF and IG, span the dividers so as to divide one of these diagonal lines into six equal parts, viz. I, L,0, T, 0, V, G; from the point L erect a perpendicular line produced until it intersects the line IH produced; from the point of intersection M, as a centre, describe the arc NIO for the top of the elbow; with the same sweep of the dividers describe the arcs NO and NO; then draw an indefinite straight line PQ tangent to the arcs NO and NI, having the points of contact at S and S; on this tangent line erect a perpendicular line passing through the point N (same as in Fig. 5), produced until it intersects the line BE produced; then place one foot of the dividers on the point of intersection and span them over the dotted line to the point T, (same as in Fig. 5), and with the dividers spanned describe the arcs TS, TS, TS, and TS; these arcs and the arcs NO, NIO and ON, will be one side of the section, and by the same rule the other side of the section may be described at the same time, which will be a pattern to cut the other sections by.