Parrott Round
This artillery round would have been fired from a Parrott Rifle, a highly accurate type of cannon used during the Civil War.
Designed by Captain Robert Parker Parrott, the gun was longer than the Napoleon and was distinguishable by a thick band of iron, which was wrapped around the breech of the gun.
The Parrott had a 3-inch bore, which became standard military issue in the Union army after 1863; prior to this the Parrott had a 2.9-inch bore.
The gun also came in 20 and 32 pounder sizes. The Confederates copied this gun as they did with many other weapons throughout the war, and the Parrott gun or a version of it could often be found in Confederate artillery batteries. 
Information courtesy of Civil War Academy.