That's not a .50 caliber pistol bullet, it's a 50-70 rifle bullet. After the Civil War the gov. had tons of left over muzzleloading Springfield Rifle Muskets, and the army was in need of a breech loader. So along came the Allyn conversion. They sleeved the rifle musket down to .50 caliber and installed the breech loading mechanism that collectors today call the "trapdoor." The frontier army was armed with muzzleloaders, and Red Cloud had been kicking army butt, defeating Fetterman etc. Then a shipment of the 50-70 conversions arrived, and a wood cutting detail was armed with them. They were attacked by Red Cloud and defeated the Indians using those breech loading rifles. Then in 1873 the army adopted the single shot 45-70 Springfield as their standard arm, which was basically the same as the Allyn conversion in a smaller caliber. Early on the 45-70 cartridges were inside primed center fire. The case was made of copper "guilding metal," and a primer cup was inserted inside and then the cup was crimped into place. You can see those crimps in the photo of your cartridges and the empty cases. Once the inside primer was in place, the case was then loaded with 70 grains of black powder and a 405 grain bullet was seated on top. The Cavalry fired a shorter version of the rifle, called a model 1873 45-55 Springfield Carbine. They fired a cartridge that looked exactly like the 45-70, 405 grain bullet, same length case, same crimp etc. But because the carbine was lighter the 45-70 bullet caused the carbine to have more "kick" when fired. So they were loaded down to 55 grains of black powder, and because there can't be an air gap between the bullet and black powder, there were cardboard fillers placed between the bullet and the powder. These cartridges couldn't be told apart by looking at them, so sometimes the enlisted men thought it would be a joke to put rifle cartridges in the Cavalry officers bullet pouch to be fired in his carbine, so for a short time the army didn't have any head stamps on the rifle rounds, but there was a raised "C" head stamp on the carbine cartridges, however there were lots of carbine cartridges that couldn't be told from a rifle round. These carbine marked cartridges are very rare and would be quite a find. Later on, the army head stamped these cartridges with dates and arsenal where they were loaded, and later yet, with R for rifle and C for carbine, and several times changed the weight of the bullets, finally using primers like are on modern cartridges today, making them reloadable, but that's all a different story from what you are finding. In the era you are searching the army also used the .45 caliber colt revolver. Again, same story on head stamps and priming, but pistol length brass. Your cartridge finds appear to be late 1860's (50-70) and early 1870's inside primed, no head stamped cases. The US Army used the 45-70 cartridge longer than any other, it being in use from 1873 until WWI when it was still in use in National Guard units.
