The state of being the first-born among several sons of the same parents. The exclusive right held by the eldest son, particularly his exclusive right to succeed to the estate of his ancestor, to the exclusion of his younger brothers.1  The British rule of primogeniture was followed in the American colonies in cases where a father died intestate, but had no weight where the will of the decedent was known.  The practice lost favor in America after the Revolutionary War, and was outlawed by the states.

1Black's Law Dictionary, 4th Edition.