Fausset's Bible Dictionary
Numbers 19. The ordinance was for cleansing, not atonement. Contact with death, the visible penalty of sin (Genesis 2:17), was a defilement requiring purgation before one could have communion with the congregation of the living Israel (Isaiah 4:3). The defilement being but ceremonial (though at the same time conveying instruction as to real defilement) needed only ceremonial cleansing. The victim was a female, whereas the greater offerings for sin were male. No part came on the altar; even the blood was not sprinkled there, but before the tabernacle, and not by the high priest but by his son. No charge was given as to its being burnt in a clean place, but simply "without the camp," entire with skin and dung. The "red" pointed not so much to the blood of Christ as to the earth color (adam ) or "red earth"), the flesh being the object of the purifying; also to sin, deep dyed as "scarlet," and associated with the flesh (Isaiah 1:18).
The Mishna, Parah 3:2, states that the children sent to fetch water for the red heifer sacrifice from Siloam were mounted on bulls in order to have their feet off the ground, so as to escape pollution. Not the blood but the "ashes" were what purified the flesh; the blood-sprinkling before the tabernacle indicated a connection with atonement. The priest and the gatherer of the ashes remained unclean until evening, because the whole rite referred to defilement. A portion of the ashes mixed with running water was sprinkled on the unclean person, on the third and seventh days (a week, one revolution of time, being required before the cleansing was complete), with a bunch of hyssop; cedar wood and a bit of scarlet were also thrown into the fire that burnt the heifer.
The hyssop's supposed detergent properties were the reason for its use; cedar from its durability and its odor counteracting corruption; scarlet, as being the life color and used as medicine to strengthen the heart, symbolized life. The meaning of the rite is divinely declared in Hebrews 9:13, "if the ashes of an heifer sprinkling the unclean sanctifieth to the purifying of the flesh, how much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, purge your conscience from dead works to serve the living God?" The Egyptian priests, the Persians according to the Zendavesta, the Romans, and Greeks, and the modern New Zealanders, have had strict rules as to defilement by contact with the dead.
The widespread deaths in the camp owing to Korah's rebellion and its sequel suggested the enactment of a ceremony presently after, relieving the people of the dread of further penalty because of the defilement contracted by the presence of so many corpses, the sad evidences of sin's awful penalty, and perpetually teaching them to look forward to a deeper purgation by a greater atonement. The sinless Antitype had to bear the reproach of associating with sinners (Luke 5:30; Luke 15:2). As the heifer was east "without the camp," so Christ was cut off from fellowship with the representatives of the theocracy, and crucified between two thieves outside of Jerusalem (Hebrews 13:11-12).
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Fausset, Andrew R. Entry for 'Heifer, Red'. Fausset's Bible Dictionary. https://www.studylight.org/dictionaries/eng/fbd/h/heifer-red.html. 1949.