When it is necessary, then, for seamen to sail their ships entirely by “dead reckoning” they are always anxious to check up their positions by any outside aids that are available. It was for this reason that our captain, on the imaginary voyage we took from Philadelphia to Havana in the last chapter, sailed so close to Diamond Shoal Lightship instead of crossing the Gulf Stream and heading out to sea. I shall add but one more thing before I end this brief and incomplete explanation of navigation and its related subjects. Navigation and dead reckoning we have touched upon. Piloting still remains untouched. This branch of navigation, if branch it really is, shows the navigator the position of his ship by reference to objects ashore. Let us suppose that a ship has crossed the ocean and is approaching a harbour entrance. While at sea an error of half a mile or so meant little, but as he approaches shore he wants to know _exactly_ where he is. On each side of the harbour entrance let us suppose that there is a lighthouse. The navigator gets out his large-scale chart of the vicinity and lays it on his chart table. This chart shows the harbour entrance and shows the positions of the lighthouses. Then he determines the direction of these two lighthouses according to his compass. Let us suppose one lies exactly northwest and the other exactly southwest. On the chart, then, he draws two lines, one through the point marking each of the lighthouses. From the lighthouse to the northwest he draws a line extending southeast (the opposite direction) out to sea. From the lighthouse to the southwest he draws a line to the northeast. These two lines cross, and he knows that his ship was exactly at the intersection when he took his bearings. As this can be done in a minute or two the position is very accurate, unless his ship is sailing very rapidly, which it probably would not be. This is known as the “cross bearing” method of learning one’s position, and is one of the simplest problems in piloting. Suppose, however, that a ship is sailing along the shore, and but one prominent object can be seen on the land. The navigator watches until the object (a lighthouse, perhaps) is “four points off his bow”—that is, until the angle between his course and the direction of the object is 45 degrees. From that moment the log is watched carefully, until the object is directly at right angles to the ship’s course. The distance sailed during that time is the same as the distance from the ship to the object ashore at the time the second bearing is secured, and if a compass bearing is taken when the ninety-degree bearing has been taken, a line drawn on the chart from the position of the object ashore can be marked with the distance in miles, and the navigator will know exactly the position of his ship at that moment. This is known as “bow and beam bearings.” There are other similar methods of obtaining the desired result.