The green-bordered version first appeared in 1928 and stood for both company and field grade officers.
Volume 8 of the Master Regs, containing the seat cover regs, which I am referring to was printed in 1940, so further updates to the cover regs must have produced the square versions, etc. Also such details as the anchor color on general's covers (gold in my references) appear as red in the 1940 sailor's manual, so I assume another change occurred in 1940 at least. That manual also says the base color was black instead of dark blue.
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