They were cartridges made for the Civil War Burnside carbine. Dixie Gun works sells reproductions of the cases for reloading for anyone having the rifles.
The Burnside carbine was a breech-loading [carbine] that saw widespread use during the [American Civil War] .
The carbine was designed and patented by [Ambrose Burnside] , who resigned his commission in the U.S. Army to devote himself full time to working on the weapon. The carbine used a special brass [cartridge] , also invented by Burnside. Pressing the weapon's two trigger guards opened the breech block and allowed the user to insert a cartridge. When the trigger was pulled, the [hammer] struck a [percussion cap] and caused a spark; a hole in the base of the cartridge exposed the [black powder] to this spark. The unique, cone-shaped cartridge sealed the joint between the [barrel] and the breech. Most other breech-loading weapons of the day tended to leak hot gas when fired, but Burnside's design eliminated this problem.
In 1857, the Burnside carbine won a competition at West Point against 17 other carbine designs. In spite of this, few of the carbines were immediately ordered by the government, but this changed with the outbreak of the Civil War, when over 55,000 were ordered for use by Union [cavalrymen] . This made it the third most popular carbine of the Civil War; only the [Sharps carbine] and the [Spencer carbine] were more widely used. They saw action in all theatres of the war. There were so many in service that many were captured and used by Confederates. A common complaint by users was that the unusually shaped cartridge sometimes became stuck in the barrel after firing.
By using ordnance returns and ammunition requisitions, it has been estimated that 43 Union cavalry regiments were using the Burnside carbine during the 1863-1864 period. Additionally, 7 Confederate cavalry units were at least partially armed with the weapon during this same period.
Here is aphoto of it.
Nice Burnside Carbine Cartridge Brass Case & Bullet in Unfired Condition
Hope this helps