Numbers 19 gives the recipe for concocting the water of purification from the ashes of a burnt red heifer and some other ingredients. We expect a Reformed theologian like Edwards to reach immediately for Christological analogies. Instead, the heifer becomes a type of the martyr church ( Notes on Scripture , 280-1):

“It was to be an heifer on which never had come yoke Numbers 19:2], which most fitly represents the spirit and practice of God’s true church in the time of persecution from her enemies, which refuses to submit to the yoke, that they would oppose whatever cruelties they exercise them with. She will not call any man on earth master or lord, won’t be subject to their impositions, won’t forsake the commands of God nor be subject to the commandments of men, will ‘follow the Lamb whithersoever he goeth’ [Revelation 14:4], will not worship the beast, nor his image, nor receive his mark in their foreheads nor in their hand [Revelation 20:4], stand fast in the liberty wherewith Christ hath made them free, not submitting to the yoke of bondage (Galatians 5:1). This heifer was sacrificed to God; so are the martyrs represented as sacrificed. They offer up themselves a sacrifice to God through the Holy Spirit, and the souls of the martyrs are represented as souls under the altar [Revelation 6:9]. She was to be burnt ‘without the camp’ [v. a], as the martyrs, especially suffering under Antichrist, are rejected and cast out of the communion of their persecutors as not being of the church of Christ. ‘Her skin, and her flesh, and her blood, with her dung’ Numbers 19:5], were to be burnt; the sufferings of the martyrs burns up their carnality and corruption, and cleanses all their filthiness.”

Even the purgative properties of the heifer point to the martyrs: The peculiar use of the ashes of the red heifer Numbers 19:17–19] was to purge from pollutions by dead bodies. So the use for which God designs the suffering and persecutions of his church is to rouse his people from coldness and deadness in religion, and from carnality, and worldly- or fleshly-mindedness, whereby men become as dead carcasses, for he or she that liveth in pleasure is dead while he liveth. Carnal things are well compared to dead carcasses, for they are fleshly, and they are filthy and loathsome like stinking flesh.”