While Reverend Parris is clearly concerned about his reputation and position within the town, I think it is important that we not shortchange his true grief for and anxiety about his daughter, Betty, and her frightening condition. Miller describes him: "Quaking with fear, mumbling to himself through his sobs, he goes to [Betty's] bed and gently takes [her] hand." He then speaks softly and gently to his supine, silent child, begging her to open her eyes and wake up before he "kneel[s] again," one would assume to pray. He has already sent one of his daughter's friends to the town doctor; likewise, he has sent to Reverend Hale, a minister from nearby Beverly who is supposed to be an expert in witchcraft and can examine Betty to confirm that the cause of her illness is not unnatural. It seems, then, that his daughter's health is foremost in his mind, at least as important as his concern for himself and his authority. When he speaks to her in private, before Abigail enters, his language and tone are affectionate and kind, and they appear to reveal his very real fear and concern for her condition. He prays, then, at least as much for her as he does for himself.
He certainly is praying for Betty's return to health, but he most certainly is praying for his reputation, for not only did he witness his daughter in the woods but also his niece and slave. When the townspeople become aware of this - that the devil apparently has taken such a firm hold in the minister's family - his reputation and ministry in Salem will likely be over. Some of the residents, such as John Proctor, have already shunned going to church because of Parris and his fire and brimstone attitude of preaching, so it is easy to see why Parris is so worried about this whole incident from the very start.