I think it's 30-40 Krag. The barrel is a custom barrel with a short cylinder before the taper begins. That's something Ackley did for custom guns. The caliber marking would have have A.I. (Ackley Improved).
Of course, you can always do a chamber cast to see if it has the customary 40 degree shoulder of the A.I. cartridge. Even then, it should be safe to fire a normal 30-40 as they were fire formed to fit the A.I. chamber.
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