From the photographs, your Ballard Number 2 Sporting Rifle would have been made sometime between 1881 and 1891. It appears to be a typical Number 2 Sporting Rifle. The tang mounted peep sight is a good one, it is a Marlin Gallery Peep Sight and is very desirable to collectors.
The firing pin appears to either be broken or a homemade replacement as the shape for the reversible firing pin is not correct. You need to find a copy of John Dutcher's extraordinary book, BALLARD: The Great American Single Shot Rifle. On page 296, you will find a photograph of the correct shape for the reversible firing pin.
There are very little records for the Ballard rifles, and what do exist are intermixed with the Marlin Model 1881 lever action repeating rifle. The Ballard serial numbers that are listed in the records are reproduceded in both Brophy's Marlin book and Dutcher's Ballard book. Only one appears to be a Number 2 Sporting Rifle and it was shipped in 1903. (a gun that sat in the warehouse a long time or was returned for repairs and then listed in the records for some reason as that serial number is not amoung the other Ballard rifles that are listed!)
I hope this helps.
Due to the increasing cost of ammunition, there be no warning shot!
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