Elizabeth is talking quietly to get Proctor to cooperate and do what she wants him to do.Proctor is talking quietly because he is struggling with his thoughts, because he is lying to her.
Explanation:
The difference between each character's motivations to speak quietly in this moment is that Elizabeth is talking QUIETLY to get Proctor to cooperate and do what she wants ,desire or wish him to do.
While Proctor is talking QUIETLY because he is struggling with his thoughts, because he is lying to her which was the reason they both tend to use the word QUIETY in Lines 147–153
