Yak1366 is correct on every point. Excellent reply.
More specifically, your bullet's ID is a yankee generic "Springfield" 3-groove Minie-bullet, a .58-caliber one, intended primarily for use in a Springfield Rifle, but it would also fit a .577 Enfield Rifle.
Your bullet is badly smashed because it was fired at very close range into one of the rocks or boulders in Chattanooga's famously boulder-riddled soil. (Long ago when I lived in North Georgia I used to go relic-digging around Lookout Mountain, so I know what you're dealing with.)
Before it was fired, it probably looked like the one in the photo below.
Rdh5832, here's some very basic civil war bullet info for you, since that is the first one you've ever found:
Civil war relic diggers tend to call this type a "3-ringer" but in actuality the bullet has 3 grooves... not rings, which are raised above the bullet's cylindrical body, like a wedding ring on your finger. Your bullet is made of 100%-pure lead, which is why long-buried ones develop greyish-white Lead Oxide ("lead rust") patina. Please be careful to NOT scrape it off when you clean a dug bullet, because that paper-thin patina layer is the proof of your of your bullet's age. If the patina is removed, the bullet cannot be distinguished from a modern Reproduction of a civil war bullet. (Accurate reproductions are made for modern Blackpowder rifle shooters and game-hunters -- you can see some at the bottom of the webpage here:
Ol' Buffalo Bullet Mold Tables )
Yak1366, what you are calling a "skirted base" is formed by a slight miss-fit between the body of the bulletcasting mold and the cavity-forming insert part of the mold. In other words, there is a separate part of the mold (containing the cone shape) which fits into the bottom of the "hollow" for the bullet's body in the main mold. If the cone-forming part is not aligned EXACTLY right, the result is an indented line and/or a bit of "flashing" on the cast bullet's base. I regret that I don't have a photo showing that type of mold, and thus I've tried to paint a picture with words. Thus comes the old saying, "A picture is worth a thousand words (of description)".