The length of the case is approximately 3/4 inch. The cartridges were found with associated pottery sherds, suggesting that the cartridges were used during the Indian Wars in the SW. Another collector who emailed suggested the following:
“You have a very typical 44 Henry rimfire case that has been fired in either a Henry or an 1866 Winchester rifle or carbine. I have metal-detected many Indian War battle sites in the westen states and have found hundreds of these. They are typically found in 3 lengths - .82”, .90", and .96". It appears you have the short one, which is the most common.
They were first manufactured in 1860. Indians used them extensively up until the late 1880s or early 1890s. They were manufactured into the early 1900s so there is no way to date them any closer than that. Most that are found at battle sites are from the 1870s, such as the battle of the Little Bighorn, where they were the primary cartridge used by the Indians."