Nick79, thank you for providing your iron ball find's precisely measured diameter and weight, as requested by my friend ARC.
Actually you gave us the ball's circumference instead of the diameter. Doing the match.. circumference of 7.75-inches divided by Pi (3.1516) equals 2.48" diameter. You said it weighs 1 pound 7 ounces (approx 1.4 pounds).
I'll save you the effort of hunting through the Shot Tables charts at the link given in my previous post, helpfully provided by vpnavy. (Thanks, VPN.)
Unfortunately, no cannonball or grapeshot-ball or canister-ammo ball used in the United States from the Colonial era through the civil war matches up with the diameter or the weight of your iron ball.
www.civilwarartillery.com/shottables.htm
A helpful tip:
When you (anybody) think you've found a cannonball, it's always helpful to ask, "Was a cannon ever at the location where I found the ball?" More often than not, the answer from the historical records of the location is No... which greatly tends to exclude the possibility that the ball is a cannonball.