We are concerned with the important class of Youden rectangles, or incomplete latin squares, with treatments in cyclic order. The most economical way to write such a design is to conceive the treatments of the first block, or row, in ascending order and the forward differences of that row. By a special algorithm involving diagonal addition of the differences, it is possible to determine rapidly whether a given arrangement of such differences, and hence of treatments, will give rise to a Youden rectangle.
