Q: Is this a M1860 Spencer Carbine, with 22" barrel? If so, it is chambered for the #56 cartridge, aka .56-.56, which are the external dimensions of the cartridge. The groove diameter of the barrel tapers from .545 at the breech to .535 at the muzzle! The bullets used in the original rimfire cartridges were of the "heel" type, and externally lubed. The later model Spencers (Burnside manufacture) and post-War models were chambered for the .56-.50 and used an inside lubed bullet. Bullet diameter for that round was about .515". Christopher Spencer did not like the military version of the cartridge, claiming it had too much crimp. His solution was to come out with a more bottlenecked case, but using the same bullet diameter, and designated .56-.52. That round was completely interchangeable with the .56-.50 round. As a matter of fact, these two rounds could be fired in the older guns, although the bullet might rattle down the barrel, unless it slugged up to fit. As both guns were issued to cavalry companies on the Western frontier, so there might be some mixup in the ammo available if companies were in a firefight against Indians at the same time!
The 3rd Infantry was the only infantry unit West of the Mississippi issued Spencer M1860 rifles. Lt. Fred Beecher was the Acting Assistant Quartermaster for the 3rd. There were also 7th Cavalry companies stationed at the same post. When Maj. Sandy Forsyth was organizing his scouts, Spencers were issued, and was the difference in survival at the Battle of Beecher Island (where the young lieutenant was killed). But a question I've never been able to answer is, were some of the scouts actually issued Spencer rifles out of 3rd Inf. stores? If the carbines were M1860's, they would have taken the same identical ammo as the rifles. Beecher, himself, also had a Henry rifle, and the Scouts had at least three Springfield rifles, cal. 50-70.
Hope this of interest. Stay well, Pard!