[Slamfire]

You are asking what is essentially, a structural soundness opinion.

What vintage of rifle, blackpowder or smokeless. If blackpowder I would not consider it safe, even in like new condition, with smokeless loads.

How large are the cracks?

I don't know the safety factors built into those barrels. The fact that it is cracked indicates to me that the metal was either defective or at some point of its life, it has been exposed to pressures that exceeded the ultimate tensile strength of the barrel. If either is true, I would not consider the barrel to be "safe". Whatever margin the barrel had, it has less right now.

If you plan to pass this down to another generation I would have the barrel replaced. Future generations may not know enough not to fire rounds in the barrel and a descendant of yours may lose a hand or an eye.

If this was a question about a car and worn out brakes, you know what the answer would be before you let your Son drive the car. (Fix the brakes!) I don’t consider this any different.

Maybe the SASS types know a source for barrels. I would have the barrel replaced with a modern tube. A web search will find barrel blanks, then another web search you will need to find a gunsmith who will turn that blank, chamber it, and put it on the receiver.

That's my opinion.