From “Origin of Vertical Files” (Library History Buff Blog):
Research by the Early Office Museum makes a strong case that the first vertical file cabinets were produced by Library Bureau, the library and office supply company founded by Melvil Dewey. The earliest advertisement for a vertical file cabinet was found by the Museum in a 1900 Library Bureau catalog. Information in this catalog indicates that vertical files utilized the same technology pioneered in library card catalog cabinets which were also produced by Library Bureau.
