Regarding navigational matters and the ship's deck log while underway, who is the assistant to the officer of the deck?

The assistant to the officer of the deck while underway is the quartermaster of the watch. This position is crucial as the quartermaster is responsible for navigating the ship and maintaining accurate records of the ship's course and position. They assist the officer of the deck by providing vital navigational information and ensuring that the ship's deck log is accurately maintained. This includes recording the ship's movements, relevant navigational data, and any significant events that occur while the ship is underway.

The other roles listed do not specifically fit this responsibility: the boatswain's mate generally oversees deck operations and maintenance, the master at arms maintains order and discipline aboard the ship, and the coxswain typically commands the small boats or manages boat operations. None of these positions encompass the navigational focus and record-keeping responsibility that is integral to the role of the quartermaster of the watch.