Jamieson, Fausset and Brown on Genesis 15:9-21

9-21. Take me an heifer, &c.--On occasions of great importance, when two or more parties join in a compact, they either observe precisely the same rites as Abram did, or, where they do not, they invoke the lamp as their witness. According to these ideas, which have been from time immemorial engraven on the minds of Eastern people, the Lord Himself condescended to enter into covenant with Abram. The patriarch did not pass between the sacrifice and the reason was that in this transaction he was bound to nothing. He asked a sign, and God was pleased to give him a sign, by which, according to Eastern ideas, He bound Himself. In like manner God has entered into covenant with us; and in the glory of the only-begotten Son, who passed through between God and us, all who believe have, like Abram, a sign or pledge in the gift of the Spirit, whereby they may know that they shall inherit the heavenly Canaan.