Tree doesn't know the proper term other than 'giving them a drink'. When offering them a drink, they will not refuse it whether offered on a sponge on a spear or one tied to a stick. After a few hours stretched on the cross, their will to resist has long passed, especially on a sunny day.
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Often the soldiers have spears, needed to guard the condemned from an attempted rescue or (lords' forgive!) an mercy kill. Often they would not have thought to bring a pole or stick to raise the sponge to the prisoner's mouth, so a spear would have to do. It is a wonderful tool for the task. Remember the condemned has her arms and feet nailed to the cross and the point of the spear can make drinking from sponge difficult at best.
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There is talk about giving the condemned prisoner wine or vinegar. Remember the wine was brought for the soldiers' refreshment, not the prisoner's. And as for carrying vinegar to the site, why bother? After a few hours hanging from her cross under the blazing sun, she will drink anything.
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So drop your trowels and piss on the sponge. She drink
anything.
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...and it will remind her what you think of her!