There are priests that offer gifts according to the law: who serve unto the example and shadow of heavenly things.'--Hebrews 8:4, 5.
It is a curious fact, but sadly significant, that modern Judaism should declare neither sacrifices nor a Levitical priesthood to belong to the essence of the Old Testament; that, in fact, they had been foreign elements imported into it--tolerated, indeed, by Moses, but against which the prophets earnestly protested and incessantly laboured. The only arguments by which this strange statement is supported are, that the Book of Deuteronomy contains merely a brief summary, not a detailed repetition, of sacrificial ordinances, and that such passages as Isaiah 1:11, etc., Micah 6:6, etc., inveigh against sacrifices offered without real repentance or change of mind. Yet this anti-sacrificial, or, as we may call it, anti-spiritual, tendency is really of much earlier date. For the sacrifices of the Old Testament were not merely outward observances--a sort of work-righteousness which justified the offerer by the mere fact of his obedience--since it is not possible that the blood of bulls and of goats should take away sins' (Heb 10:4).
Symbolism of the Sacrifices
The sacrifices of the Old Testament were symbolical and typical. An outward observance without any real inward meaning is only a ceremony. But a rite which has a present spiritual meaning is a symbol; and if, besides, it also points to a future reality, conveying at the same time, by anticipation, the blessing that is yet to appear, it is a type. Thus the Old Testament sacrifices were not only symbols, nor yet merely predictions by fact (as prophecy is a prediction by word), but they already conveyed to the believing Israelite the blessing that was to flow from the future reality to which they pointed. Hence the service of the letter and the work-righteousness of the Scribes and Pharisees ran directly contrary to this hope of faith and spiritual view of sacrifices, which placed all on the level of sinners to be saved by the substitution of another, to whom they pointed. Afterwards, when the destruction of the Temple rendered its services impossible, another and most cogent reason was added for trying to substitute other things, such as prayers, fasts, etc., in room of the sacrifices. Therefore, although none of the older Rabbis has ventured on such an assertion as that of modern Judaism, the tendency must have been increasingly in that direction. In fact, it had become a necessity--since to declare sacrifices of the essence of Judaism would have been to pronounce modern Judaism an impossibility. But thereby also the synagogue has given sentence against itself, and by disowning sacrifices has placed itself outside the pale of the Old Testament.
Sacrifices the Centre of the Old Testament
Every unprejudiced reader of the Bible must feel that sacrifices constitute the centre of the Old Testament. Indeed, were this the place, we might argue from their universality that, along with the acknowledgment of a Divine power, the dim remembrance of a happy past, and the hope of a happier future, sacrifices belonged to the primeval traditions which mankind inherited from Paradise. To sacrifice seems as natural' to man as to pray; the one indicates what he feels about himself, the other what he feels about God. The one means a felt need of propitiation; the other a felt sense of dependence.
The Idea of Substitution
The fundamental idea of sacrifice in the Old Testament is that of substitution, which again seems to imply everything else--atonement and redemption, vicarious punishment and forgiveness. The firstfruits go for the whole products; the firstlings for the flock; the redemption-money for that which cannot be offered; and the life of the sacrifice, which is in its blood (Lev 17:11), for the life of the sacrificer. Hence also the strict prohibition to partake of blood. Even in the Korban,' gift (Mark 7:11) or free-will offering, it is still the gift for the giver. This idea of substitution, as introduced, adopted, and sanctioned by God Himself, is expressed by the sacrificial term rendered in our version atonement,' but which really means covering, the substitute in the acceptance of God taking the place of, and so covering, as it were, the person of the offerer. Hence the Scriptural experience: Blessed is he whose transgression is forgiven, whose sin is covered . . . unto whom the Lord imputeth not iniquity' (Psa 32:1, 2); and perhaps also the Scriptural prayer: Behold, O God, our shield, and look upon the face of Thine Anointed' (Psa 84:9). Such sacrifices, however, necessarily pointed to a mediatorial priesthood, through whom alike they and the purified worshippers should be brought near to God, and kept in fellowship with Him. Yet these priests themselves continually changed; their own persons and services needed purification, and their sacrifices required constant renewal, since, in the nature of it, such substitution could not be perfect. In short, all this was symbolical (of man's need, God's mercy, and His covenant), and typical, till He should come to whom it all pointed, and who had all along given reality to it; He whose Priesthood was perfect, and who on a perfect altar brought a perfect sacrifice, once for all--a perfect Substitute, and a perfect Mediator (Heb 10:1-24).
The Paschal Lamb
At the very threshold of the Mosaic dispensation stands the sacrifice of the Paschal Lamb connected with the redemption of Israel, and which in many respects must be regarded as typical, or rather anticipatory, of all the others. But there was one sacrifice which, even under the Old Testament, required no renewal. It was when God had entered into covenant relationship with Israel, and Israel became the people of God.' Then Moses sprinkled the blood of the covenant' on the altar and on the people (Exo 24). On the ground of this covenant-sacrifice all others rested (Psa 50:5). These were, then, either sacrifices of communion with God, or else intended to restore that communion when it had been disturbed or dimmed through sin and trespass: sacrifices in communion, or for communion with God. To the former class belong the burnt- and the peace-offerings; to the latter, the sin- and the trespass-offerings. But, as without the shedding of blood there is no remission of sin, every service and every worshipper had, so to speak, to be purified by blood, and the mediatorial agency of the priesthood called in to bring near unto God, and to convey the assurance of acceptance.
Bloody and Unbloody Offerings
The readiest, but perhaps the most superficial, arrangement of sacrifices is into bloody and unbloody. The latter, or Minchah,' included, besides the meat- and drink-offering, the first sheaf at the Passover, the two loaves at Pentecost, and the shewbread. The meat-offering was only brought alone in two instance--the priest's offering (Lev 7:12) and that of jealousy (Num 5:15), to which Jewish tradition adds the meat-offerings mentioned in Leviticus 2. If in Leviticus 5:11 a meat-offering is allowed in cases of extreme poverty as a substitute for a sin-offering, this only further proves the substitutionary character of sacrifices. From all this it will be evident that, as a general rule, the meat-offering cannot be regarded as separate from the other or bloody sacrifices. In proof of this, it always varied in quantity, according to the kind of sacrifice which it accompanied (Num 15:1-12; 28:1-12; 39:1, etc.).
The Requisites of Sacrifice
The general requisites of all sacrifices were--that they should be brought of such things, in such place and manner, and through such mediatorial agency, as God had appointed. Thus the choice and the appointment of the mode of approaching Him, were to be all of God. Then it was a first principle that every sacrifice must be of such things as had belonged to the offerer. None other could represent him or take his place before God. Hence the Pharisees were right when, in opposition to the Sadducees, they carried it that all public sacrifices (which were offered for the nation as a whole) should be purchased, not from voluntary contributions, but from the regular Temple revenues. Next, all animal sacrifices were to be free of blemishes (of which the Rabbis enumerate seventy-three), and all unbloody offerings to be without admixture of leaven or of honey; the latter probably because, from its tendency to fermentation or corruption, it resembled leaven. For a similar reason salt, as the symbol of incorruption, was to be added to all sacrifices. 
Hence we read in Mark 9:49--'For every one shall be salted with fire, and every sacrifice shall be salted with salt'; that is, as the salt is added to the sacrifice symbolically to point to its incorruption, so the reality and permanence of our Christian lives will be brought out by the fire of the great day, when what is wood, hay, and stubble shall be consumed; while that which is real shall prove itself incorruptible, having had the fire applied to it.
The Creatures Appointed
In Scripture three kinds of four-footed beasts--oxen, sheep, and goats; and two of birds--turtle-doves and young pigeons--are appointed for sacrifices. 
The latter, except in certain purifications, are only allowed as substitutes for other sacrifices in case of poverty. Hence also no direction is given either as to their age or sex, though the Rabbis hold that the turtle-doves (which were the common birds of passage) should be fully grown, and the domestic pigeons young birds. But, as in the various sacrifices of oxen, sheep, and goats there were differences of age and sex, the Jews enumerate twelve sacrifices, to which as many terms in Scripture correspond. The Paschal lamb and that for the trespass-offerings required to be males, as well as all burnt- and all public sacrifices. The latter made void the Sabbath and defilement,' i.e. they superseded the law of Sabbath rest (Matt 12:5), and might be continued, notwithstanding one kind of Levitical defilement--that by death.
The Eleven Sacrifices of the Rabbis
The Rabbis, who are very fond of subtle distinctions, also speak of public sacrifices that resembled the private, and of private sacrifices that resembled the public, in that they also made void the Sabbath and defilement.' Altogether they enumerate eleven public sacrifices, viz. the daily sacrifices; the additional for the Sabbath; for the New Moon; the Passover sacrifices; the lamb when the sheaf was waved; the Pentecostal sacrifices; those brought with the two first loaves; New Year's; Atonement Day sacrifices; those on the first day of, and those on the octave of Tabernacles.' Private sacrifices they classify as those on account of sins by word or deed; those on account of what concerned the body (such as various defilements); those on account of property (firstlings, tithes); those on account of festive seasons; and those on account of vows or promises. Yet another division of sacrifices was into those due, or prescribed, and those voluntary. For the latter nothing could be used that had previously been vowed, since it would already belong unto God.
Holy and Less Holy
But of far greater importance is the arrangement of sacrifices into the most holy and the less holy, which is founded on Scripture (Lev 6:17; 7:1; 14:13). Certain meat-offerings (Lev 2:3, 10; 6:17; 10:12), and all burnt-, sin-, and trespass-sacrifices, as well as all public peace-offerings, were most holy. Such were to be offered or sacrificed in one of the more holy places; they were slain at the north side of the altar  (the less holy at the east or south side); and they were either not partaken of at all, or else only by the officiating priests, and within the court of the Temple.
The skins of the most holy sacrifices, except such as were wholly burnt, belonged to the priests; those of the less holy to the offerers. In the latter case they also partook of their flesh, the only exception being the firstlings, which were eaten by the priests alone. The Rabbis attach ten comparative degrees of sanctity to sacrifices; and it is interesting to mark that of these the first belonged to the blood of the sin-offering; the second to the burnt-offering; the third to the sin-offering itself; and the fourth to the trespass-offering. Lastly, all sacrifices had to be brought before actual sunset, although the unconsumed flesh might smoulder on the altar till next dawn.
The Acts of Sacrifice
The Rabbis mention the following five acts as belonging to the offerer of a sacrifice: the laying on of hands, slaying, skinning, cutting up, and washing the inwards. These other five were strictly priestly functions: catching up the blood, sprinkling it, lighting the altar fire, laying on the wood, bringing up the pieces, and all else done at the altar itself.
The whole service must have been exceedingly solemn. Having first been duly purified, a man brought his sacrifice himself before the Lord'--anciently, to the door of the Tabernacle' (Lev 1:3; 4:4), where the altar of burnt-offering was (Exo 40:6), and in the Temple into the Great Court. If the sacrifice was most holy, he entered by the northern; if less holy, by the southern gate. Next he placed it so as to face the west, or the Most Holy Place, in order thus literally to bring it before the Lord. To this the apostle refers when, in Romans 12:1, he beseecheth us to present our bodies a living sacrifice, holy, acceptable unto God.'
Laying on of Hands
But this was only the commencement of the service. Women might bring their sacrifices into the Great Court; but they might not perform the second rite--that of laying on of hands. This meant transmission and delegation, and implied representation; so that it really pointed to the substitution of the sacrifice for the sacrificer. Hence it was always accompanied by confession of sin and prayer. It was thus done. The sacrifice was so turned that the person confessing looked towards the west, while he laid his hands between the horns of the sacrifice,  and if the sacrifice was brought by more than one, each had to lay on his hands.
It is not quite a settled point whether one or both hands were laid on; but all are agreed that it was to be done with one's whole force'--as it were, to lay one's whole weight upon the substitute. 
If a person under vow had died, his heir-at-law took his place. The only public sacrifices in which hands were laid on were those for sins of public ignorance (Lev 4:15; 16:21), when the elders' acted as representing the people--to which some Rabbinical authorities add public sin-offerings in general (on the ground of 2 Chron 29:23)--and the scapegoat on the Day of Atonement, on which the high-priest laid his hands. In all private sacrifices, except firstlings, tithes, and the Paschal lamb, hands were laid on, and, while doing so, the following prayer was repeated: I entreat, O Jehovah: I have sinned, I have done perversely, I have rebelled, I have committed (naming the sin, trespass, or, in case of a burnt-offering, the breach of positive or negative command); but I return in repentance, and let this be for my atonement (covering).' According to Maimonides, in peace-offerings a record of God's praise, rather than a confession of sins, was spoken. But, as the principle prevailed that frequent confession even without sacrifice was meritorious, another formula is also recorded, in which the allusion to sacrifices is omitted.
Closely connected with this was the lifting and waving' of certain sacrifices. The priest put his hands under those of the offerer, and moved the sacrifice upwards and downwards, right and left; according to Abarbanel also forwards and backwards.' The lamb of the leper's trespass-offering was waved before it was slain (Lev 14:24); private peace-offerings, only after they had been slain; while in public peace-offerings, the practice varied.
Sacrifices Slain by Priests Only
Under ordinary circumstances all public sacrifices, and also always that of the leper, were slain by the priests. 
The Talmud declares the offering of birds, so as to secure the blood,  to have been the most difficult part of a priest's work.
For the death of the sacrifice was only a means towards an end, that end being the shedding and sprinkling of the blood, by which the atonement was really made. The Rabbis mention a variety of rules observed by the priest who caught up the blood--all designed to make the best provision for its proper sprinkling. 
Thus the priest was to catch up the blood in a silver vessel pointed at the bottom, so that it could not be put down, and to keep it constantly stirred, to preserve the fluidity of the blood. In the sacrifice of the red heifer, however, the priest caught the blood directly in his left hand, and sprinkled it with his right towards the Holy Place: while in that of the leper one of the two priests received the blood in the vessel; the other in his hand, from which he anointed the purified leper (Lev 4:25).
The Application of the Blood
According to the difference of sacrifices, the blood was differently applied, and in different places. In all burnt-, trespass-, and peace-offerings the blood was thrown directly out of the vessel or vessels in which it had been caught, the priest going first to one corner of the altar and then to the other, and throwing it in the form of the Greek Letter gamma, so that each time two sides of the altar were covered. Any blood left after these two gifts,' as they were called (which stood for four), was poured out at the base of the altar, whence it flowed into the Kedron. In all sin-offerings the blood was not thrown, but sprinkled, the priest dipping the forefinger of his right hand into the blood, and then sprinkling it from his finger by a motion of the thumb. According to the importance of the sin-offering, the blood was so applied either to the four horns of the altar of burnt-offering, or else it was brought into the Holy Place itself, and sprinkled first seven times towards the veil of the Most Holy Place (Lev 4:6, 17), and then on the four horns of the golden altar of incense, beginning at the north-east. Finally, on the Day of Atonement the blood was sprinkled within the Most Holy Place itself. From all sin-offerings the blood of which was sprinkled on the horns of the altar of burnt-offering certain portions were to be eaten, while those whose blood was brought into the Holy Place itself were wholly burnt. But in the sacrifices of firstlings, of tithes of animals, and of the Paschal lamb, the blood was neither thrown nor sprinkled, and only poured out at the base of the altar.
On the shedding of blood, which was of the greatest importance--since, according to the Talmud, whenever the blood touches the altar the offerer is atoned for'--followed the flaying' of the sacrifice and the cutting up into his pieces.' All this had to be done in an orderly manner, and according to certain rules, the apostle adopting the sacrificial term when he speaks of rightly dividing the word of truth' (2 Tim 2:15). The inwards' and legs' having been washed (Lev 1:9), and dried with sponges, the separate pieces of the sacrifice were brought up by various priests: the calculation of the Rabbis being, that in the case of a sheep or a she-goat six priests carried the sacrifice, one more the meat-, and another the drink-offering (in all eight); while in that of a ram twelve, and in that of a bullock four-and-twenty priests were needed for the service. Next, the sacrificial salt was applied, and then the pieces were first confusedly thrown and then arranged upon the fire.  This latter part of the service requires explanation.
The common idea that the burning either of part or the whole of the sacrifice pointed to its destruction, and symbolised the wrath of God and the punishment due to sin, does not seem to accord with the statements of Scripture. The term used is not that commonly employed for burning, but means causing to smoke,' and the rite symbolises partly the entire surrender of the sacrifice, but chiefly its acceptance on the part of God. Thus the sacrifice consumed by a fire which had originally come down from God Himself--not by strange fire--would ascend for a sweet savour unto the Lord' (Lev 1:9; 4:31). Even the circumstance that the fire for the altar of incense was always taken from that on the altar of burnt-offering, shows that, while that fire might symbolise the presence of a holy Jehovah in His house, it could not refer to the fire of wrath or of punishment. 
As already stated, those parts of the sin-, trespass-,  and public peace-offerings, which were allowed to be eaten, could only be partaken of by the priests (not their families) during their actual ministry, and within the Temple walls.
The flesh of these offerings had also to be eaten on the day of the sacrifice, or in the night following; while in other offerings the permission extended to a second day. The Rabbis, however, restrict the eating of the Paschal lamb to midnight. Whatever was left beyond the lawful time had to be burned.
New Testament View of Sacrifice Agrees with the Synagogue
It is deeply interesting to know that the New Testament view of sacrifices is entirely in accordance with that of the ancient Synagogue. At the threshold we here meet the principle: There is no atonement except by blood.' In accordance with this we quote the following from Jewish interpreters. Rashi says (on Lev 17:11): The soul of every creature is gave it to atone for the soul of man--that one soul should come and atone for the other.' Similarly Aben Ezra writes: One soul is a substitute for the other.' And Moses ben Nachmann: I gave the soul for you on the altar, that the soul of the animal should be an atonement for the soul of the man.' These quotations might be almost indefinitely multiplied. Another phase of Scriptural truth appears in such Rabbinical statements as that by the imposition of hands: The offerer, as it were, puts away his sins from himself, and transfers them upon the living animal'; and that, as often as any one sins with his soul, whether from hate or malice, he puts away his sin from himself, and places it upon the head of his sacrifice, and it is an atonement for him.' Hence, also, the principal laid down by Abarbanel, that, after the prayer of confession (connected with the imposition of hands) the sins of the children of Israel lay on the sacrifice (of the Day of Atonement).' This, according to Maimonides, explains why every one who had anything to do with the sacrifice of the red heifer or the goat on the Day of Atonement, or similar offerings, was rendered unclean; since these animals were regarded as actually sin-bearing. In fact, according to Rabbinical expression, the sin-bearing animal is on that ground expressly designated as something to be rejected and abominable. The Christian reader will here be reminded of the Scriptural statement: For He has made Him to be sin for us who knew no sin, that we might be made the righteousness of God in Him.'
There is yet one other phase on which the Synagogue lays stress. It is best expressed in the following quotation, to which many similar might be added: Properly speaking, the blood of the sinner should have been shed, and his body burned, as those of the sacrifices. But the Holy One--blessed be He!--accepted our sacrifice from us as redemption and atonement. Behold the full grace which Jehovah--blessed be He!--has shown to man! In His compassion and in the fulness of His grace He accepted the soul of the animal instead of his soul, that through it there might be an atonement.' Hence also the principle, so important as an answer to the question, Whether the Israelites of old had understood the meaning of sacrifices? He that brought a sacrifice required to come to the knowledge that that sacrifice was his redemption.'
In view of all this, the deep-felt want so often expressed by the Synagogue is most touching. In the liturgy for the Day of Atonement we read: While the altar and the sanctuary were still in their places, we were atoned for by the goats, designated by lot. But now for our guilt, if Jehovah be pleased to destroy us, He takes from our hand neither burnt-offering nor sacrifice.' We add only one more out of many similar passages in the Jewish prayer-book: We have spoken violence and rebellion; we have walked in a way that is not right . . . Behold, our transgressions have increased upon us; they press upon us like a burden; they have gone over our heads; we have forsaken Thy commandments, which are excellent. And wherewith shall we appear before Thee, the mighty God, to atone for our transgressions, and to put away our trespasses, and to remove sin, and to magnify Thy grace? Sacrifices and offerings are no more; sin- and trespass-offerings have ceased; the blood of sacrifices is no longer sprinkled; destroyed is Thy holy house, and fallen the gates of Thy sanctuary; Thy holy city lies desolate; Thou hast slain, sent from Thy presence; they have gone, driven forth from before Thy face, the priests who brought Thy sacrifices!' Accordingly, also, the petition frequently recurs: Raise up for us a right Intercessor (that it may be true), I have found a ransom (an atonement, or covering).' And on the Day of Atonement, as in substance frequently on other occasions, they pray: Bring us back in jubilee to Zion, Thy city, and in joy as of old to Jerusalem, the house of Thy holiness! Then shall we bring before Thy face the sacrifices that are due.'
The Eve of Day of Atonement
Who shall make answer to this deep lament of exiled Judah? Where shall a ransom be found to take the place of their sacrifices? In their despair some appeal to the merits of the fathers or of the pious; others to their own or to Israel's sufferings, or to death, which is regarded as the last expiation. But the most melancholy exhibition, perhaps, is that of an attempted sacrifice by each pious Israelite on the eve of the Day of Atonement. Taking for males a white cock,  and for females a hen, the head of the house prays: The children of men who dwell in darkness and in the shadow of death, bound in misery and iron--them will He bring forth from darkness and the shadow of death, and break their bonds asunder. Fools, because of their transgressions and because of their iniquities, are afflicted; their soul abhorreth all manner of meat, and they draw near unto the gates of death. Then they cry unto the Lord in their trouble, that He save them out of their distresses. He sends His word and heals them, and delivers them from their destruction. Then they praise the Lord for His goodness, and for His marvellous works to the children of men. If there be an angel with Him, an intercessor, one among a thousand, to show unto men his righteousness, then He is gracious unto him, and saith, Let him go, that he may not go down into the pit; I have found an atonement (a covering).'
Next, the head of the house swings the sacrifice round his head, saying, This is my substitute; this is in exchange for me; this is my atonement. This cock goes into death, but may I enter into a long and happy life, and into peace!' Then he repeats this prayer three times, and lays his hands on the sacrifice, which is now slain.
This offering up of an animal not sanctioned by the law, in a place, in a manner, and by hands not authorised by God, is it not a terrible phantom of Israel's dark and dreary night? and does it not seem strangely to remind us of that other terrible night, when the threefold crowing of a cock awakened Peter to the fact of his denial of the Lamb of God which taketh away the sin of the world'?
And still the cry of the Synagogue comes to us through these many centuries of past unbelief and ignorance: Let one innocent come and make atonement for the guilty!' To which no other response can ever be made than that of the apostle: Such an High-Priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens'! (Heb 7:26)
 The Rabbis speak of the so-called salt of Sodom,' probably rock salt from the southern end of the Dead Sea, as used in the sacrifices.  The birds' used at the purification of the leper (Lev 14:4) cannot be regarded as sacrifices.  The reason of this is obscure. Was it that the north was regarded as the symbolical region of cold and darkness? Or was it because during the wilderness-journey the Most Holy Place probably faced north--towards Palestine?  If the offerer stood outside the Court of the Priests, on the topmost of the fifteen Levitical steps, or within the gate of Nicanor, his hands at least must be within the Great Court, or the rite was not valid.  Children, the blind, the deaf, those out of their minds, and non-Israelites, were not allowed to lay on hands.'  The Hebrew term used for sacrificial slaying is never applied to the ordinary killing of animals.  In the case of birds there was no laying on of hands.  The Rabbis mention five mistakes which might render a sacrifice invalid, none of them the least interesting, except, perhaps, that the gullet might never be wholly severed.  Whatever was laid upon the altar was regarded as sanctified' by it, and could not be again removed, even though it should have become defiled. This explains the words of Christ in Matthew 23:19.  Compare the article in Herzog's Encyc. vol. x. p. 633. Some of the sacrifices were burned on the altar of burnt-offering, and some outside the gate; while in certain less holy sacrifices it was allowed to burn what was left anywhere within the city.  Except those for the whole people and for the high-priest, which had to be burned outside the gate.  Because the Hebrew word for man' (Gever) is used in the Talmud for a cock,' and white,' with reference to Isaiah 1:18.