How does Dimmesdale try to purify his body in Scarlet Letter?

Dimmesdale, since he did commit adultery with Hester, saw himself as a failure. He thought that he had commited a great sin and the only way to make things any better in the light of God was for him to be exposed to the town. However, he couldn't bring himself to admit to it in front of the town until the end of the book. He wanted Hester to reveal him; to show him to the town. She promised him that she wouldn't. So he continued to torture himself, and to make himself pay for the wrong that he did until he admited to it before he died.