You PM'ed me a request to ID your flat-solid-base 3-groove bullet. Congratulations... you've found your first civil war US Merrill .54 Carbine bullet. The Merrill as a breechloader ...so, although your bullet's precision measurement is .560, it is for a .54-caliber firearm.
Explanation, just in case you don't already know:
Muzzle-loading bullets were always a bit smaller than the firearm's bore-diameter. However, Breechloader bullets can be a bit larger than the firearm's bore, because the bullet gets loaded into the back end of the barrel. That rule also applies to revolving pistols, because even though the bullet goes into the cylinder, it still enters the barrel from the back end. For example, unfired revolver bullets (such as Colt, Bartholow, etc) typically measure .01 to .02 larger than the barrel's bore-diameter. When fired, the breechloading bullet gets squeezed down to the same size as the barrel's bore, of course.