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While researching the links between mnemonics and shorthand, I just came across "A complete guide to the improvement of the memory or the science of memory simplified: with practical applications to languages, history, geography, music, prose, poetry, shorthand, etc." written by James Henry Bacon and published by Sir Isaac Pitman & Sons, London. https://archive.org/details/b21293405 (Third Edition, 1890). The major system appears on page 59, though it has a few transposed letters/numbers compared to more modern versions of the system.

Isaac Pitman, who published the book, was also the inventor of Pitman shorthand which was introduced in 1837 and is structurally similar to the Major System.

The book seems to be based on Bacon's prior work "The Science of Memory Simplified and Explained: Or, A Rational System for Improving the Memory, Etc" written in 1861.

Josh, if you feel it appropriate, you can also add the book above to http://blog.artofmemory.com/free-books-on-mnemotechnics-581.html