A hearth son was, in medieval England, a younger son of a landed knight or baron, who due to the laws of feudal inheritance, did not have his own land. Unlike in Anglo-Saxon times, when land was split between surviving sons, during the Middle Ages the eldest son of a landed family inherited the estate entire. As such, younger sons had no income, and resided in a family member's home. There they would live out the rest of their days, most likely unmarried due to the undesirability of an unlanded groom, and waiting for a chance to make it on their own. This term first appears in English lawbooks and is further discussed in the book "William Marshal" by David Crouch.
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