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SGW ! !
"DOM" = date of manufacture
The crossed weapons with a crown above is a legally-required proofmark indicative of the Birmingham (England) proof house, used 1868-1925.
A Charles Shelley was a British military man from around 1900 (+/-), so the gun might have had his name applied when he either bought or commissioned the gun.
If you dismount the barrels, there should be identifying marks (more proof marks, date marks and maybe a maker's mark) located on several different surfaces.
Investigate & photograph the action water table flats, the barrel's underside flats, the underside of the barrels and on the top of the rib.
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