John Wesley on Genesis 24:2

His eldest servant - Probably Eliezer of Damascus, one whose conduct and affection he had had long experience of: he trusted him with this great affair, and not Isaac himself, because he would not have Isaac go at all into that country, but marry thither by proxy; and no proxy so fit as the steward of his house. This matter is settled between the master and the servant with a great deal of care and solemnity. The servant is bound by an oath to do his utmost to get a wife for Isaac among his relations, Ge 24:3,4. Abraham swears him to it, both for his own satisfaction, and for the engagement of his servant to all possible care and diligence. Thus God swears his servants to their work, that, having sworn, they may perform it. Swearing being an ordinance, not peculiar to the church, but common to mankind, is to be performed by such signs as are the common usages of our country.