These are U.S. military-issued single-shot ball-and-powder pistols of .54 caliber
Shown at bottom is a Model 1836 flintlock, manufactured in 1842 by Robert Johnson of Middletown, CT under contract to the U.S. government. This is the last of a series of flintlock pistols used by the U.S. military. This model would have been used in the Mexican war.
At top is a Model 1842 percussion lock, manufactured in 1850 under contract to the U.S. government by Henry Aston of Middletown, CT. It is the first of the percussion pistols to be used by U.S. military. Some early models of this gun would have been used in the Mexican War, but later were used in the early days of the Civil War.
Both pistols used a unique swivel ramrod that prevented it from being misplaced or dropped, especially during battle.