Mystery bullets from Civil War site

To assist in figuring this out, some research will help you.
1. The exact location where you found the bullets.
(You did not reveal that to us.)
2. A look at the official records of the army of the republic should describe whether this was a campground or battle site. Also, the units both federal and confederate and the officers that were there. The records are online.
3. Once you know which units were engaged, you can find out what weapons had been issued to them and pin down exactly what bullets were used at your site.
The grand army of the republic had unlimited men and supplies. This allowed them the luxury of keeping meticulous records and detailed after action reports. The confederate armies had neither the men or resources. Thus the record keeping was not near the level of the federal armies.
Somebody will probably be on here to quickly eyeball identify this but the above process is how my historian friend does this.

Probably going to need some better pictures.

Tried to enlarge picture. I measured the lengths and they averaged .800.

There is a lot going on in the pictures with all the shadowing and blurriness. Looks like you might be trying to take pics thru glass? If so, try taking them out and getting a nice picture of each.

https://www.armyoftennesseerelics.com/civil-war-cartridges

Scroll down to "U.S. Burnside Cavalry Carbine Cartridge .54 Cal."

That's one possibility.

Here's more stuff: https://www.armyoftennesseerelics.com/civil-war-bullets-vol-1