The master - The person who is here meant was the helmsman, who occupied in ancient ships a conspicuous place on the stern, and steered the ship, and gave directions to the crew.
The owner of the ship - Probably a different person from “the master.” He had the general command of the ship as his own property, but had employed “the master,” or the pilot, to direct and manage it. His counsel in regard to the propriety of continuing the voyage would be likely to be followed.