Note 12 — Chapter XVII · TWENTY-FOUR HOURS IN TRALEE BAY

As this phrase is not self-explanatory—like cross-bearings from two points ashore—some readers may like to be reminded of the elementary geometry involved in the method here referred to of determining a position by the aid of a single known point. Having got his four-point (45°) bearing, he would proceed on the same course till he got an eight-point (90°) bearing. In a right-angled triangle, of which one of the other angles is 45°, the remaining angle is also 45°. The sides opposite these equal angles are also equal. That is to say, the distance from the rock (which is what he wants to know) is equal to the distance run between the times of taking the two bearings (which he can determine by log-speed and allowances for current, etc.).