How do Danforth and Hathorne attempt to get Proctor to drop the charge that Mary Warren has lied in The Crucible by Arthur Miller? Why do they want him to do so? Why does Proctor refuse?
The two judges during the Salem Witch Trials in The Crucible by Arthur Miller are Danforth and Hathorne. Both men are convinced they are doing a holy work by identifying and punishing the witches, ridding the town of its most sinful elements. Unfortunately, they have gotten so caught up in their passion for sin-finding that they see the accusers (Abigail and the other girls) as right all the time and without question. When Proctor and his little entourage come to court and want to cast doubt on the veracity of the girls' testimony, the judges' integrity is at stake and they act in their own defense rather in the best interests of justice and the accused.
The first thing Danforth does after Proctor announces that Mary Warren will testify that the girls are lying is refuse to accept her deposition. If he does not have it, he does not have to deal with it. His panic can be seen in the stage directions surrounding this refusal.
Danforth, instantly: No, no, I accept no depositions. He is rapidly calculating this; he turns from her to Proctor. Tell me, Mr. Proctor, have you given out this story in the village?
When Proctor persists, Danforth tries another tactic: he tries to intimidate both Proctor and Mary Warren. He says,
Do you know, Mr. Proctor, that the entire contention of the state in these trials is that the voice of Heaven is speaking through the children?
Proctor is not intimidated (of course Mary is, at least a bit) and Danforth continues his questioning. Now Danforth is a bit baffled, because he was sure he could make them recant and go away; however, they are still here and he has to deal with this potentially damning testimony that will make not only the girls but him look bad. And of course, Parris is in the background of this entire dialogue, hoping to make Proctor look like a revenge-seeking lunatic.
Danforth then sends a mixed message. He is willing to hear what they have to say, but he needs to try intimidation again before he will let them present their evidence. This time he hopes to scare Mary, and he does.
[I]t strike hard upon me that she will dare come here with such a tale. Now, Mr. Proctor, before I decide whether I shall hear you or not, it is my duty to tell you this. We burn a hot fire here; it melts down all concealment.
When he continues this line of questioning and Proctor still insists on presenting his evidence, Danforth finally resorts to a personal attack. He questions Proctor's motives and character. When that does not dissuade Proctor, Danforth tries to bribe Proctor by promising to let Elizabeth--who has just been discovered to be pregnant--live at least another year IF Proctor will drop the charges.
Understandably, Proctor hesitates, but of course the issue is greater than just his own family and he has to decline the offer. Now Danforth turns in a hard-nosed judge who wants to do everything precisely by the book. No more games and no more offers. Now it is all going to be brought into the open and then Danforth will do what he does best--pronounce judgment.