In Act IV of The Crucible, what is the significance of the judges' responses to Proctor's confession?
I think that the fundamental significance of the judges' revelry at Proctor's "confession" is an affirmation that they won. Throughout the trial, there had been the feeling that there was no real and distinct pursuit of justice. Rather, it had been an exercise of power. When Corey refuses to do what the court says, he is imprisoned because he does not acquiesce. When Proctor defies the court, it is taken as a sign of disrespect to the court. When Francis Nurse presents the petition of signatures affirming his wife's character, the court wants to interrogate those 91 individuals. The court had always set itself up as an instrument of power as opposed to one committed to the drive for justice.
When Proctor breaks down and signs the confession, it is a sign that the court has won. Someone with the standing of Proctor in the community has been able to affirm that the court was right. The judges are elated with this because it will prove instrumental in demonstrating that their power should be seen as absolute and vital to the town's interests. Proctor's confession is representative of a momentum changing event in how the town perceives the trials. With Abigail's departure and embezzlement, Parris' lack of positive reception, Andover's rejection of their own witchhunts, and good people like Rebecca Nurse and Giles Corey having to suffer death and humiliation, the judges were looking for something to lend credence and validation to their endeavors and Proctor's confession gave this to them. In this, their excitement and enthusiastic reaction resided.