Answer:
- He wants to make sure that no one else knows that the girls could be lying and Danforth doesn't want to lose his position of authority.
Step-by-step explanation:
In the context of 'The Crucible III,' the key reason for thinking that Danforth was disturbed regarding whether Proctor had informed anyone else regarding the lies of the girls is that 'he didn't wish to lose his position of authority.' He had an inner threat that he might lose his authority and therefore, he wanted to ensure that nobody else comes to know about the lies told by the girls in order to safeguard his position.