Connie:

I am NOT an expert at this, so please defer anything I may say to someone who is more knowledgeable. It sounds like a ball which would have been fired from a Napoleon-type gun, which was the most ocmmon field artillery in the Civil War era. The hitch is that some of the shot were fused, that is bored out with a powder charge in the hollowed space inside, and then closed with a plug to hold the explosive inside, with a fuse. The usual explosive of the era was black powder, which can still retain its explosive capacity, and in fact becomes very unstable as it ages. The problem was that Civil War era fuses were not very reliable, and lots of them (particularly Confederate ordnance) failed to go off and explosde like they were designed. Duds.

Other balls, however, were solid shot and not fused to explode at all. (We had one when I was a kid -- many years ago -- and used it as a shot put. Hey! If you don't have the money or inclination to buy a real shot put, a cannon ball can do nicely!) If your cannon ball is not badly corroded, you can tell from a brief visual inspection if there is a plug; if there is not, you know you are safe. (Even if there is a plug, the great probablily is that there is no charge inside.)

If you have a neighbor who served in the miltary, he or she may have the expertise to look at it for you. If you call the local law enforcement, they will go into full panic mode, call the bomb disposal squad, and generally ruin your day. I would very much doubt if what you have is still live. If you didn't set the thing off digging it up, there is a very small chance that it has any explsoive potential, but I would set it aside until someone can look at it for you. Even if its got a charge, it can be defused. They are great conversation pieces. Just don't use it as a shot put until someone who is in the know can look at it for you.

Good luck.