Final answer:
Deputy Governor Danforth exemplifies the theme of self-preservation in Act III of The Crucible by defending the court's authority and his reputation.
Step-by-step explanation:
In Act III of The Crucible, Deputy Governor Danforth exemplifies the theme of self-preservation most prominently. Danforth is in charge of the court and becomes increasingly defensive of its proceedings as the act progresses.
Self-preservation is evident when Danforth says, "I am innocent to a witch. I know not what a witch is." This defensive stance is an attempt to maintain the court's authority and his reputation, in spite of evidence that might suggest the innocence of the accused.
Moreover, his resistence to consider the evidence brought by Proctor, that could overturn previous convictions, indicates that Danforth prioritizes the integrity of the court—and by extension, his own power—over justice.
This is further supported by his insistence on signed confessions, which provide physical evidence of the court's supposed justification for its actions, and his reluctance to postpone the executions.