A couple of years ago the Shotgun News ran an article about some scientists out at Dugway Proving Grounds in western Utah that tried firing old blackpowder cartridge rifles (.45-70, 50-90, etc.) at very long range to test the old stories of the extreme accuracy possible with those guns, like the Sharps buffalo rifles.
They were amazed at the results. I didn't keep the issue of SGN, but I think they claimed 2-3 minute of angle accuracy out to over a mile (!). You might do a search of the SGN website and see if the article is online.
I'll have to look that up. That's just un-fricking-believable.