Complete Commentary on the Whole Bible, by Matthew Henry, at sacred-texts.com
(Num 19:1-10) The ashes of a heifer.
(Num 19:11-22) Used to purify the unclean.
The heifer was to be wholly burned. This typified the painful sufferings of our Lord Jesus, both in soul and body, as a sacrifice made by fire, to satisfy God's justice for man's sin. These ashes are said to be laid up as a purification for sin, because, though they were only to purify from ceremonial uncleanness, yet they were a type of that purification for sin which our Lord Jesus made by his death. The blood of Christ is laid up for us in the word and sacraments, as a fountain of merit, to which by faith we may have constant recourse, for cleansing our consciences.
Why did the law make a corpse a defiling thing? Because death is the wages of sin, which entered into the world by it, and reigns by the power of it. The law could not conquer death, nor abolish it, as the gospel does, by bringing life and immortality to light, and so introducing a better hope. As the ashes of the heifer signified the merit of Christ, so the running water signified the power and grace of the blessed Spirit, who is compared to rivers of living water; and it is by his work that the righteousness of Christ is applied to us for our cleansing. Those who promise themselves benefit by the righteousness of Christ, while they submit not to the grace and influence of the Holy Spirit, do but deceive themselves; we cannot be purified by the ashes, otherwise than in the running water. What use could there be in these appointments, if they do not refer to the doctrines concerning the sacrifice of Christ? But comparing them with the New Testament, the knowledge to be got from them is evident. The true state of fallen man is shown in these institutions. Here we learn the defiling nature of sin, and are warned to avoid evil communications.