To ball iron is to manipulate a semi-solid mass of purified metal inside a puddling furnace until it forms a cohesive lump. The operator uses a long iron bar to gather the pasty iron particles together at welding heat. Once the metal is properly balled, it is extracted from the furnace and immediately taken to a hammer or squeezer to expel the trapped liquid slag.
Heard on the job
You need to ball that iron tight before you pull it, or it will fall apart under the hammer.