You didn't say anything about what metal the ball is made of. Does a magnet stick to it?
For anybody here who doesn't already know:
If the ball is iron, look for an extremely close match-up with the ball's very-precise diameter & weight measurements here:
Cannon bore, shot, and shell diameters for smoothbore guns
Also for anybody here who doesn't already know:
The data charts at that site are from the 1861 US Ordnance Manual, telling the very-precise diameter and weight of artillery balls (cannonballs, grapeshot balls, and canister-ammo balls) used in the US from the Revolutionary War through the Civil War. The Ordnance Department established those very precise size and weight requirements because the ammunition (balls) HAD to fit into the cannon's barrel precisely, being not even slightly too large or too small. In combat, you don't want to discover that the ammo you've been issued doesn't fit the gun properly.
Mcogan, your ball's size-measurement of 27mm translate to 1.06-inches. That puts it within the tolerance-range for a 12-pounder Field Howitzer canister-ball. But, the ball's 78-grams weight translates to 2.75 ounces (.172 pounds)... which is slightly heavier than a 1.06-inch ball made of cast-iron.
In the photo you posted the ball looks corroded-away in some places. If that is correct, it means the ball now weighs a bit less than it did before it got corroded. Steel is about 10% heavier than cast-iron. The corroded 1.06-inch ball's current weight versus its diameter indicates it is made of steel. There were no steel canister-balls. So, based on the precise size-&-weight measurements you've provided, I have to say that that ball is not an artillery ball.
