Answer: The phrase "farthest extremity" refers to the point or boundary that is located at the greatest distance or furthest point from a given reference point. It can refer to physical locations, such as the farthest extremity of a continent or the farthest extremity of a building, or it can refer to abstract concepts, such as the farthest extremity of an argument or the farthest extremity of a belief system. In general, the term is used to describe something that is located at the very edge or outermost limit of a particular area or concept.
Explanation: In the context of this passage, "farthest extremity" refers to the furthest point on the path of the British battleship Bismarck's journey, where it crossed the path of the American battleship patrol. This means that Bismarck was at the outermost limit of the area where the American battleships were patrolling.