under what authority does the duke claim ownership of the dead whale

Ishmael details a story about a Fast-Fish secured by whalemen that the Lord Warden attempted to take as his own under the law, despite the whalemen's poverty. Ishmael inquires on what principle the Sovereign is invested the right to part of the whale. According to Plowdon, the whale belongs to the King and Queen because of its superior excellence.

The duke claims the authority over the dead whales based on the English law which says that the king gets the head, the queen gets the tail, and the rest belongs to someone in England because the whale caught on English shores is, in fact, English.

It's quite reasonable.😀