Ahab’s call for the great measure of grog in Chapter 36: The Quarter-Deck provokes some extra excitement among the crew, and cries of ‘drink and swear’, echoed from the mad captain, provide for these men the kind of mystical drunkenness necessary to embark on so mad a quest.
Our use of the Measure, to denote turn order outside of the hunt, is simply the representation of a physical totem that is, by it’s nature, passed around. Hunts can be furied, long, even somewhat earth-shattering for players. By the time a whale is taken or lost, it can be easy to have forgotten who drew what, and whose turn it is at the Mast-head, so leave the Measure where it lays until the hunt is over. Obviously use a real measure of grog if you are outfitted and inclined to do so.