By the end of chapter 12, the reader has experienced two incidents of "the scaffold".
What happens in both the first and second experience, and why is each experience crucial to the novel as it unfolds?
The second scaffold scene continues to develop Dimmesdale's "cowardice" --- his inability to accept responsibility for what he has done. In the first scene, Hester bears the scorn of the entire community (hypocritical though it may be) for her failing; she bore everything in the full light of the day. Dimmesdale imitates Hester's punishment, but it is just foolishness.
"It is done!" muttered the minister, covering his face with his hands. "The whole town will awake, and hurry forth, and find me here!"
But it was not so. The shriek had perhaps sounded with a far greater power, to his own startled ears, than it actually possessed.
When Mr. Wilson walks by, Hawthorne tells us,
Good Heavens! Had Mr. Dimmesdale actually spoken? For one instant, he believed that these words had passed his lips. But they were uttered only within his imagination. The venerable Father Wilson continued to step slowly onward, looking carefully at the muddy pathway before his feet, and never once turning his head towards the guilty platform.
Perhaps the most telling question comes from little Pearl:
"Wilt thou stand here with mother and me, to-morrow noontide?" inquired Pearl.
"Nay; not so, my little Pearl!" answered the minister; for, with the new energy of the moment, all the dread of public exposure, that had so long been the anguish of his life, had returned upon him; and he was already trembling at the conjunction in which--with a strange joy, nevertheless--he now found himself. "Not so, my child. I shall, indeed, stand with thy mother and thee one other day, but not to-morrow!"
Dimmesdale is no more ready to come clean about his actions at the second scaffold scene than he was when he questioned Hester at the first. He wants forgiveness, but he still wants it for "free." Hester, who has paid dearly for her "peace" witnesses the whole scene, but can do nothing for him. Ironically, he is led away from the scaffold by Chillingworth who met Hester shortly after her ordeal.
In the beginning of the book, Hester is standing on the scaffold with the infant Pearl. In the second incident, Rev. Dimesdale is on the scaffold with Hester and Pearl. The first incident shows the reader the determination of Hester to live her life and accept her punishment. The second incident shows the character of Rev. Dimesdale. He has seen how the Scarlett Letter has affected Hester. He is ready to take responsibility for his actions.