Mesa, you'll probably get more answers about strange and/or antique arms on Harley Nolden's Institute for Firearms Research.
This type arm, the various Remington Rolling Block, is FAR outside my limited knowledge. I trust other members will come up with a lot more data. Just to get you started, though - -
From your description, the rifle in question could be either a Remington No. 1-1/2 Sporting Rifle or a No. 2 Sporting Rifle.
No. 1-1/2 A reduced scale version of the No. 1 Sporting rifle, one of the first mass produced breechloaders. The little 1-1/2 was chambered in .22 Short, .22 Long, or Extra Long, plus some larger rimfire cartridges and the pistol caliber WCF cartridges. Barrels were part octogon, part round. Manufactured 1869 to 1902. In GOOD condition, one could be worth $600.
No. 2 Similar to above, but I can't find an image of either. Chambered in various lower-powered rinfire and centerfire cartridges. Made 1873 to 1910. In GOOD condition, possible value around $425.
Could also be a No. 4, or, if a takedown rifle, a No. 6. The later models become worth progressively less. If it has or has had a Lyman combination rear sight, even a No. 7, which could still be worth up to, perhaps, $1000.
For a positive ID, you really need a lot more information, and if at al possible, a series of photos.
Does this rifle have ANY original finish left on the metal or wood? If not, and with such a poor bore, even a No. 1-1/2 might not be worth $100.
Most of my information comes from Stoeger's Gun Trader's Guide, 25th Edition.
Good luck in your quest for information.
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Blog: Expert Witness