ABSTRACT Diagrams demonstrating principles of formal arrangement (what is commonly called composition or design) were pervasive in the production and interpretation of pictorial art in the United States throughout the first half of the twentieth century. This essay surveys three of the most influential: a Japan-inspired design manual written by art educator Arthur Dow and first published in 1899; a WWI-era proportional scheme devised by illustrator and amateur classical archeologist Jay Hambidge, and a series of essays from 1926 on the ‘mechanics of form organization’ by painter (and, at the time, Art Students League of New York instructor), Thomas Hart Benton. These and similar devices were an integral part of the relentless standardization and self-conscious modernization of artists’ methods modeled on industrial processes of mass production and pursued between the Civil War and the Great Depression by educators and policy-makers interested in establishing the teaching of art in the United States on a more practical basis than that provided by the European academic tradition. Despite their once near-ubiquity and pivotal role in the development of several generations of American modernists, including Georgia O’Keeffe, George Bellows and Jackson Pollock, as described here, these hugely popular devices are almost entirely forgotten today.