Leviticus 3
Barnes' Notes
And if his oblation be a sacrifice of peace offering, if he offer it of the herd; whether it be a male or female, he shall offer it without blemish before the LORD.
The peace-offering (like the burnt-offering, Leviticus 1:3, and the Minchah, Leviticus 2:1) is here spoken of as if it was familiarly known before the giving of the Law. "Peace-offering" seems preferable to "thank-offering," which occurs in several places in the margin of our Bible. "thank-offering" appears to be the right name for a subordinate class of peace-offering.

And he shall lay his hand upon the head of his offering, and kill it at the door of the tabernacle of the congregation: and Aaron's sons the priests shall sprinkle the blood upon the altar round about.
Kill it at the door ... - See Leviticus 1:3. Tradition says that the peace-offerings might be killed in any part of the court.

And he shall offer of the sacrifice of the peace offering an offering made by fire unto the LORD; the fat that covereth the inwards, and all the fat that is upon the inwards,
"The fat that covereth the inwards" refers to the caul or transparent membrane which has upon it a network of fatty tissue: "the fat upon the inwards" refers to the small lumps of suet found upon the intestines of healthy animals.

And the two kidneys, and the fat that is on them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away.
The caul above the liver - Probably the membrane covering the upper part of the liver.

And Aaron's sons shall burn it on the altar upon the burnt sacrifice, which is upon the wood that is on the fire: it is an offering made by fire, of a sweet savour unto the LORD.
Upon the burnt sacrifice - Upon the ashes of the continual burnt-offering Exodus 29:38, in accordance with Leviticus 6:12.

And if his offering for a sacrifice of peace offering unto the LORD be of the flock; male or female, he shall offer it without blemish.
If he offer a lamb for his offering, then shall he offer it before the LORD.
A lamb - A sheep. The word signifies a full-grown sheep, in its prime.

And he shall lay his hand upon the head of his offering, and kill it before the tabernacle of the congregation: and Aaron's sons shall sprinkle the blood thereof round about upon the altar.
See Leviticus 1:4-5 notes.

And he shall offer of the sacrifice of the peace offering an offering made by fire unto the LORD; the fat thereof, and the whole rump, it shall he take off hard by the backbone; and the fat that covereth the inwards, and all the fat that is upon the inwards,
The whole rump - The whole fat tail: i. e., the tail of the kind of sheep well known in the East, and often weighing 15 lbs. and even as much as 50 lbs., when the sheep has been increased by artificial fattening.

And the two kidneys, and the fat that is upon them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away.
And the priest shall burn it upon the altar: it is the food of the offering made by fire unto the LORD.
Burn it - See Leviticus 1:9 note.

And if his offering be a goat, then he shall offer it before the LORD.
See Leviticus 1:10 note. Birds were not accepted as peace-offerings, most probably because they were, by themselves, insufficient to make up a sacrificial meal.

And he shall lay his hand upon the head of it, and kill it before the tabernacle of the congregation: and the sons of Aaron shall sprinkle the blood thereof upon the altar round about.
And he shall offer thereof his offering, even an offering made by fire unto the LORD; the fat that covereth the inwards, and all the fat that is upon the inwards,
And the two kidneys, and the fat that is upon them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away.
And the priest shall burn them upon the altar: it is the food of the offering made by fire for a sweet savour: all the fat is the LORD'S.
Rather, as food of an offering made by fire for a sweet savour, shall all the fat be for Yahweh. Our bodily taste and smell furnish figures of the satisfaction with which the Lord accepts the appointed symbols of the true worship of the heart. All that was sent up in the fire of the altar, including the parts of the sin-offering Leviticus 4:31, as well as the burnt-offering (Leviticus 1:9, etc.), was accepted for "a sweet savour": but the word food may here have a special fitness in its application to the peace-offering, which served for food also to the priests and the offerer, and so symbolized communion between the Lord, His ministers, and His worshippers.

The fat is the Lord's - The significance of this appears to consist in the fact that its proper development in the animal is, in general, a mark of perfection.

It shall be a perpetual statute for your generations throughout all your dwellings, that ye eat neither fat nor blood.
Blood - See Leviticus 17:11 note.

Throughout all your dwellings - The suet was neither to be eaten in sacrificial meals in the sanctuary, nor in ordinary meals in private houses.

Notes on the Bible by Albert Barnes [1834].
Text Courtesy of Internet Sacred Texts Archive.

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