Whether it is lawful for a man to kill his wife if she be discovered in the act of adultery?

Objections

Objection 1 : It would seem lawful for a man to kill his wife if she be discovered in the act of adultery. For the Divine law commanded adulterous wives to be stoned. Now it is not a sin to fulfill the Divine law. Neither therefore is it a sin to kill one's own wife if she be an adulteress.
Objection 2 : Further, that which the law can rightly do, can be rightly done by one whom the law has commissioned to do it. But the law can rightly kill an adulterous wife or any other person deserving of death. Since then the law has commissioned the husband to kill his wife if she be discovered in the act of adultery, it would seem that he can rightly do so.
Objection 3 : Further, the husband has greater power over his adulterous wife than over the man who committed adultery with her. Now if the husband strike a cleric whom he found with his wife he is not excommunicated. Therefore it would seem lawful for him even to kill his own wife if she be discovered in adultery.
Objection 4 : Further, the husband is bound to correct his wife. But correction is given by inflicting a just punishment. Since then the just punishment of adultery is death, because it is a capital sin, it would seem lawful for a husband to kill his adulterous wife.