Commentary on the Bible, by Adam Clarke, [1831], at sacred-texts.com
The law of the peace-offering in general, Lev 3:1-5. That of the peace-offering taken from the flock, Lev 3:6-11; and the same when the offering is a goat, Lev 3:12-17.
Peace-offering - שלמים shelamim, an offering to make peace between God and man; see on Leviticus 7 (note), and Gen 14:18 (note).
Lay his hand upon the head of his offering - See this rite explained in Exo 29:10 (note), and Lev 1:4 (note). "As the burnt-offering, (Leviticus 1).," says Mr. Ainsworth, "figured our reconciliation to God by the death of Christ, and the meat-offering, (Leviticus 2)., our sanctification in him before God, so this peace-offering signified both Christ's oblation of himself whereby he became our peace and salvation, (Eph 2:14-16; Act 13:47; Heb 5:9; Heb 9:28), and our oblation of praise, thanksgiving, and prayer unto God."
The fat that covereth the inwards - The omentum, caul or web, as some term it. The fat that is upon the inwards; probably the mesentery or fatty part of the substance which connects the convolutions of the alimentary canal or small intestines.
Aaron's sons shall burn it - As the fat was deemed the most valuable part of the animal, it was offered in preference to all other parts; and the heathens probably borrowed this custom from the Jews, for they burnt the omentum or caul in honor of their gods.
The whole rump, it shall he take off hard by the backbone - To what has already been said on the tails of the eastern sheep, in the note on Exo 29:22, we may add the following observation from Dr. Russel concerning the sheep at Aleppo. "Their tails," says he, "are of a substance between fat and marrow, and are not eaten separately, but mixed with the lean meat in many of their dishes, and also often used instead of butter." He states also that a common sheep of this kind, without the head, fat, skin, and entrails, weighs from sixty to seventy English pounds, of which the tail usually weighs fifteen pounds and upwards; but that those of the largest breed, when fattened will weigh one hundred and fifty pounds, and their tails fifty, which corresponds with the account given by Ludolf in the note referred to above. The sheep about Jerusalem are the same with those in Abyssinia mentioned by Ludolf, and those of Syria mentioned by Dr. Russel.
It is the food of the offering - We have already remarked that God is frequently represented as feasting with his people on the sacrifices they offered; and because these sacrifices were consumed by that fire which was kindled from heaven, therefore they were considered as the food of that fire, or rather of the Divine Being who was represented by it. "In the same idiom of speech," says Dodd, "the gods of the heathens are said, Deu 32:38, to eat the fat and drink the wine which were consumed on their altars.
A goat - Implying the whole species, he-goat, she-goat, and kid, as we have already seen.
That ye eat neither fat nor blood - It is not likely that the fat should be forbidden in the same manner and in the same latitude as the blood. The blood was the life of the beast, and that was offered to make an atonement for their souls; consequently, this was never eaten in all their generations: but it was impossible to separate the fat from the flesh, which in many parts is so intimately intermixed with the muscular fibres; but the blood, being contained in separate vessels, the arteries and veins, might with great ease be entirely removed by cutting the throat of the animal, which was the Jewish method. By the fat therefore mentioned here and in the preceding verse, we may understand any fat that exists in a separate or unmixed state, such as the omentum or caul, the fat of the mesentery, the fat on the kidneys, and whatever else of the internal fat was easily separable, together with the whole of the tail already described. And probably it was the fat of such animals only as were offered to God in sacrifice, that was unlawful to be eaten. As all temporal as well as spiritual blessings come from God, he has a right to require that such of them should be dedicated to his service as he may think proper to demand. He required the most perfect of all the animals, and the best parts of these perfect animals. This he did, not that he needed any thing, but to show the perfection of his nature and the purity of his service. Had he condescended to receive the meanest animals and the meanest parts of animals as his offerings, what opinion could his worshippers have entertained of the perfection of his nature? If such imperfect offerings were worthy of this God, then his nature must be only worthy of such offerings. It is necessary that every thing employed in the worship of God should be the most perfect of its kind that the time and circumstances can afford. As sensible things are generally the medium through which spiritual impressions are made, and the impression usually partakes of the nature of the medium through which these impressions are communicated; hence every thing should not only be decent, but as far as circumstances will admit dignified, in the worship of God: the object of religious worship, the place in which he is worshipped, and the worship itself, should have the strongest and most impressive correspondence possible.