Hello,
It looks the cartridge is the .58 Berdan Musket.
Remington converted a lot of the Model 1861 and 1863 Springfield Muskets after the Civil War to Rolling Block Rifles. Below is a photo of two of them that are in my collection. They were made by taking a musket and cutting the wood and the barrel before the lock plate and in back of the lock plate. All of the parts were then fitted to the rolling block receiver. Since the muskets were .58 caliber, Remington left the caliber the same instead of sleeving them to .50 caliber, which would added to the cost of the rifle.
Have a Good Day,
Matt