Shall bring down the heifer unto a rough valley - איתן נחל nachal eythan might be translated a rapid stream, probably passing through a piece of uncultivated ground where the elders of the city were to strike off the head of the heifer, and to wash their hands over her in token of their innocence. The spot of ground on which this sacrifice was made must be uncultivated, because it was considered to be a sacrifice to make atonement for the murder, and consequently would pollute the land. This regulation was calculated to keep murder in abhorrence, and to make the magistrates alert in their office, that delinquents might be discovered and punished, and thus public expense saved.
Eared - i. e., plowed; compare Genesis 45:6 note and references. The word is derived from the Latin, and is in frequent use by English writers of the fifteenth and two following centuries.
Strike off the heifer‘s neck - Rather, “break its neck” (compare Exodus 13:13). The mode of killing the victim distinguishes this lustration from the sin-offering, in which there would be of course shedding and sprinkling of the blood.