Regarding the cartridge designation on the barrel, the approximate years of change were:
32 Winchester CTG from 1899 until 1914
32 W.C.F. CTG from 1914-1922
32-20 CTG from 1922 until the end of production, c. 1930.
Note - none of these alterations closely corresponds to engineering changes.

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Jack
SWCA #2475, SWHF #318