A survey by Professor A. F. Barker of Leeds University tracing how mathematics came to be applied to yarn and cloth construction from about 1880-1890 onward. It covers Ashenhurst's yarn diameter rule and cloth geometry, the idea of twist defined by angle rather than turns per inch, and graphs and nomograms that relate twist angle, yarn count and turns per inch. It closes with the confusing variety of regional textile units and the groupings needed to set up a loom for figured cloth. Illustrated with diagrams of thread interlacing, twist charts, a nomograph and two-fold yarn twist types.