In "The Custom House," in The Scarlett Letter, what did the son inherit from his father, and why did the narrator say he took "shame" upon himself?
In the Introduction to The Scarlet Letter, called "The Custom House," which was a separate short story that Hawthorne adapted to use in The Scarlet Letter, Hawthorne tells the background of Salem within which the story of Hester is set. It was an original colonist by the name of Briton who is distantly related to the narrator and who left behind him a son bred in the persecutory Puritan traits--both good and bad, as Hawthorne says--which is the inheritance he received from his father: the ability to mercilessly persecute on religious grounds. In other words, the zealous trait of persecuting and abusing individuals or groups of people who held religious beliefs other than Puritan beliefs was included within the genetic inheritance of the son of the founder of the Briton family in Salem. Take note that the narrator is not that son.
The narrator, although a descendant of the original Briton, is separated from both him and his son by the "past" and the "histories" that bear the story of their persecutions and the "stain" on thier "dry old bones," which must have "crumbled utterly to dust." Regardless of this unspecified but extensive separation of time between the original and his son and the narrator of the story, the narrator feels a family guilt and responsibility--he clearly has not inherited the persecutory trait--and for that and for his recognition of great wrong done, he is willing to take on the shame that the early family members brought upon the family name by their acts of cruelty and persecution. In other words, he recognizes the truth and willing to take the blame upon himself, thus acknowledging their guilt, and he prays that the curses they brought upon the family may be removed.