When Proctor first arrives at Reverend Parris's house, it seems as though has come in order to find Mary Warren, the girl employed by him and his wife, to help in their home. He says to her, "I forbid you to leave the house, did I not? Why shall I pay you? I am looking for you more often than my cows!" However, he also seems to have heard the rumors about Betty and has come, in addition, to satisfy his curiosity about her.
When the Putnams arrive, Mr. Putnam first seems interested in comparing Betty Parris's health to his own daughter's condition. He notes that Betty's eyes are closed while Ruth's are open. However, he is also very concerned that a witch has infiltrated the town and is hurting their children, and he is anxious to convince Parris that this is true. He says, "Mr. Parris, I have taken your part in all contention here, and I would continue; but I cannot if you hold back in this. There are hurtful, vengeful spirits layin' hands on these children." Putnam is clearly motivated by a desire to have Parris recognize and publicize the existence of such spirits, as he declares that he will no longer be able to support Parris if the minister will not.
Reverend Hale seems to be motivated by an earnest desire to discover if the Devil really has shown himself in Salem, as well as by pride in his ability to make such a discovery. When describing his books "with a tasty love of intellectual pursuit," he says, "Here is all the invisible world, caught, defined, and calculated. In these books the Devil stands stripped of all his brute disguises [....]. Have no fear now -- we shall find him out if he has come among us, and I mean to crush him utterly if he has shown his face!" Despite the fact that the Devil, for the Puritans, is an incredibly powerful and persuasive entity, Hale never questions his ability to recognize, resist, and destroy him. He is motivated by the desire to do so.
Tituba is motivated by her desire to avoid punishment. Parris threatens his slave with death by whipping if she does not confess, and Putnam insists that she should be hanged. She is so frightened that she seems willing to say anything to prevent these outcomes, and so when Hale speaks kindly to her, she responds positively-- probably because no one ever speaks kindly to her. When Hale takes her hand, "She is surprised." He tells her, "we will bless you, Tituba" and she is "deeply relieved." He tells her that God will protect her, and she seems to want to believe that. After all, she needs protection. Thus, Tituba seems mostly motivated by the need for safety.
Giles Corey seems to be mainly motivated by curiosity. Almost the moment he enters Parris's house, he asks, "Is she going to fly again? I hear she flies." There is a rumor in Salem that Betty Parris flew over a neighbor's barn, and Giles clearly seems to believe it. He doesn't ask after Betty's health, and only appears to only be interested in satisfying his curiosity.
Reverend Parris seems mostly motivated by a personal desire to retain his position and authority in the town. He tells Abigail, "if you trafficked with spirits in the forest I must know it now, for surely my enemies will, and they will ruin me with it." He speaks of "a faction that is sworn to drive [him] from [his] pulpit." He does seem to show some concern for his daughter, Betty, but his concerns about his own position seem to weigh more heavily on his mind.