In the simplest case the position of the boat may be found by taking the compass bearings of two known objects on shore. For example, A and B in Fig. 37 may represent the positions of two prominent objects whose position is marked upon an ordnance map of the neighbourhood, or they may be flagstaffs specially set up and noted on the map; and let C represent the boat from which the bearings of A and B are taken by a prismatic compass, which is marked from 0 to 360°. Let the magnetic variation be N. 15° W., and the observed bearings A 290, B 320, then the position stands as in Fig. 38, or, correcting for magnetic variation, as in Fig. 39, from which it will be seen that the true bearing of C from A will be 275-180=95° East of North, or 5° below the horizontal, and the true bearing of C from B will be 305-180=120° East of North, or 35° below the horizontal. These directions being plotted will give the position of C by their intersection. Fig. 40 shows the prismatic compass in plan and section. It consists practically of an ordinary compass box with a prism and sight-hole at one side, and a corresponding sight-vane on the opposite side. When being used it is held horizontally in the left hand with the prism turned up in the position shown, and the sight-vane raised. When looking through the sight-hole the face of the compass-card can be seen by reflection from the back of the prism, and at the same time the direction of any required point may be sighted with the wire in the opposite sight vane, so that the bearing of the line between the boat and the required point may be read. If necessary, the compass-card may be steadied by pressing the stop at the base of the sight vane. In recording the bearings allowance must in all cases be made for the magnetic pole. The magnetic variation for the year 1910 was about l5 1/2° West of North, and it is moving nearer to true North at the rate of about seven minutes per annum. [Illustration: FIG. 37.--POSITION OF BOAT FOUND BY COMPASS BEARINGS.] [Illustration: FIG. 38.--REDUCTION OF BEARINGS TO MAGNETIC NORTH.] [Illustration: FIG. 39.--REDUCTION OF BEARINGS TO TRUE NORTH.] There are three of Euclid's propositions that bear very closely upon the problems involved in locating the position of a floating object with regard to the coast, by observations taken from the object. They are Euclid I. (32), "The three interior angles of every triangle are together equal to two right angles"; Euclid III. (20), "The angle at the centre of a circle is double that of the angle at the circumference upon the same base--that is, upon the same part of the circumference," or in other words, on a given chord the angle subtended by it at the centre of the circle is double the angle subtended by it at the circumference; and Euclid III. (21), "The angles in the same segment of a circle are equal to one another." [Illustration: Fig. 40.--Section and Plan of Prismatic Compass.]