When Identifying LC Smith guns, the first thing you do is check the address atop the barrels; with that serial number it most likely says "Syracuse, NY". If so, there are no existing serial number records for that period; therefore you won't find a ship/manufacture date, but we speculate the gun was likely produced sometime around 1885-86. This is the most likely senario, as we have no hammer gun serial number records below #277XX for Smith guns with a Fulton, NY address; and 10-bore hammer guns were not being produced when the sequential serial number sequence began in 1918-19. As to value, unless your hammer gun is higher than a Grade 3; or otherwise, unless it remains in near new factory original condition, it will command very little collector interest (which is the primary determinant of gun value, but then the sky is the limit for the nimrod who hasn't done his homework and has a lot of accumulated cents).
