BAY COW
This was also a sin offering, and has a unique character. The red heifer was killed outside the camp, and its blood was sprinkled by the priest seven times directly before the Tabernacle.
Then the whole animal was burned, and the priest would put cedar wood, hyssop, and scarlet wood on the pyre where the cow was burned. The ashes were collected and placed in a clean place outside the camp.
When the ashes were used, a clean person mixed the ashes in a vessel with running water, then moistened a swab with it, and sprinkled this mixture on the person, tent, etc., that was contaminated. It was the water of separation, a purification from sin.
The sorrel heifer ordinance was an exceptional form of the sin offering. It does not consider the atonement, but the purification through water of those who, having their dwelling and place in the camp, where the sanctuary of Jehovah was, had become defiled along the way (cf. Num. 5:1-4).
It corresponds to Jn. 1:9 on the basis that sin was condemned on the cross. The washing of feet of those who are already clean, as the Lord taught in Jn. 13, has this character of cleaning with water.
The Holy Spirit applies, through the Word, the truth of the condemnation of sin on the cross of Christ to the heart and conscience, to purify the believer, without applying the blood again (Num. 19:1-22; Heb. 9 :13).
But John 13 goes further. The Lord applies the truth of his departure from this world to the Father to the very walk of his disciples.