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Hopkins and Allen purchased Forehand Arms in 1902, so sometime between then and 1915 when the company closed.
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If the shotgun is marked Hopkins and Allen Manufacturing Company, Norwich Conn. it was made between circa 1880-1885 and 1898. If marked Hopkins and Allen Arms Company, it was manufactured between 1898 and 1915. No records are available to give a more exact date of manufacture.
If it is Hopkins & Allen MFG Co, sometime between 1868 and 1898. Hopkins & Allen ARMS Co would be from 1898 to 1915. A 16 gauge would more likely (but not certainly) have been made after 1900.
1870-1910 or so
1884
A copy of the Blue Book of Gun Values might help.
10-1000 USD depending on specifics
Provide the serial number.
Sometime between 1902 (their factory was destroyed in a fire and rebuilt ) and 1916, when they closed. Actual production records are pretty slim.
No definitive sn data published.