Mark,
Congratulations on having your Great Great Grandfather's Parker.
It's a Grade 0 Hammergun made in 1883. The 18033 on the barrel flats is the order number. You should see 29884 on the side of the barrel lug which would match the receiver and forarm. If that's not the case, the barrels are not original.
It should be a 12ga with 30" Twist barrels and a capped pistol grip stock. Your's has a straight gripped stock and doesn't look like a factory straight Parker stock so I believe it's been replaced. Also it looks like the Doll's Head and extension have been either replaced or repaired.
I would have the gun checked out by a gunsmith familiar with vintage shotguns before attempting to shoot it. If he say's it's ok, use only low pressure loads.
Good luck,
Chuck Bishop
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