They actually decided on moonshine as the best binder, since it was the best source of pure alcohol around. In order to get it, they had to head out to John Eye Blevin's place up in the hills. Blevin was a worker in the mine but was injured in an accident where huge amounts of stone fell and one piece of the slate cut off a big chunk of one of his feet. Because he was injured in a mine accident, the owners of the mine have allowed him to remain when most non-mine workers are expected to leave.
So the boys head up to the house and end up accepting John's offer of a drink so they are quite drunk when they leave. Apparently it doesn't take much pure alcohol to send them flying!