Rock with less than 6 feetl. Signifies no bottom found 10 100 Wreck , partially or wholy Rocks with limiting under water 54 Rock or Shoal, the Position B.P.D OP.D Fishing Stakes GENERAL REMARKS Charts are generally drawn on the true meridian; if otherwise, a true meridian is given on the chart. The datum to which the soundings are reduced is mean low water spring tides, unless otherwise stated in the title of the chart. Soundings are expressed in feet or fathoms, as stated in the title of the chart. 1 fathom 6 feet = 1.828766 mètres. Underlined figures, on rocks and banks which uncover, express the heights in feet above low water of ordinary springs, unless otherwise stated. All heights (except those expressed in underlined figures) are given in feet above high water springs, or, in places where there is no tide, above the level of the sea. The natural scale is the proportion which the scale of the chart bears to the actual distance represented, and is shown thus- 12,150 A sea inile is the length of a minute of latitude at the place, and a cable is assumed to be a tenth part of a sea mile. The figures in brackets in the bottom right-hand corner of a chart, thus—(38.43 X 25.49) are the dimensions of the plate in inches between the innermost graduation or border lines. All loagitudes are referred to the meridian of Greenwich. B THE STATION POINTER The theory of the Station Pointer is founded on the twenty-first proposition of the Third Book of Euclid, which proves that the angle subtended by any chord will be the same from any part of the same segment of a circle. In Fig. 1, if the line A B subtend an angle of, say, 30° at C, it will subtend the same А angle at D or anywhere on the arc ADC B. Therefore it follows that the position of observer can only be found by taking a bearing of one of the points. The Station Pointer is useful in fixing a point by means of the "three-point problem’ or “two points " in transit and one angle. The instrument (see Fig. 2) consists of a disc about 6 inches in diameter. From a central ring proceed three arms about 12 inches long. The Fig. 1. central arm is fixed and its bevelled edge coincides with the zero of the graduations. The otber two arms can be moved to any required angle and can be fixed by a clamping screw. The Fig.2. 11 Ca Quo 51 OH STATION POINTER instrument is graduated in degrees to the right and left of the fixed arm, which is the zero of the instrument. Method of using.—The legs of the instrument are clamped at the observed angles and the bevelled edge of the central leg is placed over the middle object, then the instrument is moved about, still keeping the central leg on the centre object, until the bevelled edges of the other two legs coincide with the other two objects or points observed. When the three legs lie over the three points (as shown in Fig. 2), the pricking point at the centre of the instrument being pressed down will mark the position of the observer on the chart. The fix by station pointer is good If the three points are in the same straight line. too small If the observer's position is within the triangle formed by the points. If the points are nearly equidistant from the observer and the angles not less than 70° If one angle is large and the other small, and the small angle is made with an outer object far behind the central object. The angles should be sensitive on a change of position of observer. If the centre of the instrument can be moved without displacing one of the objects the "fix" is bad. When two points are in line they are said to be in transit. THE INDETERMINATE CASE When the sum of the observed angles is equal to the supplement of the angle at the central object, B, the position of the observer is indeterminate. It can, however, be determined by taking a bearing of one of the objects. (180° B) In Fig. 3 if (x + y) = (A + C), it is proved in Euclid II]. 22 that the four points A, B, C, and P must be on the circumference of a circle and P may be anywhere on the arc A P. C. This is known as being on the circle. When two circles can be drawn the position of the observer is where the two circles cut each other. If, then, in any case, the observed angles be nearly equal to the supplement of the angle at the central object, the two circles will nearly coincide and the “ fix” will be a bad one. Fig. 3. If no station pointer is at hand the centres of the circle on which the observer is situated can be found in the following manner : Fig. 4. W'hen the angle is acute.--In Fig. 4 let A B subtend an angle of 60°; from each end of the line A B lay off an angle of 30°, and at C, their point of intersection, is the centre of the required circle. The angle at D being less than a right angle, the segment A D B is greater than a semicircle (Euc. III. 31), therefore the centre of the circle and the observer are on the same side of the line A B. Also D being obtuse the segment A D B is less than a semicircle (Euc. III. 31), therefore the centre of the circle is on the side of A B remote from D, and the arc on which the observer is situated is the lesser The accuracy of the graduations of the station pointer can be tested in the following manner segment, ADB. Let A B C (Fig. 6)represent any angle 0 Take B A equal to the given radius. Describe the arc A C. Draw the chord A C. Bisect the angle A B C by the straight line B E; this will also bisect the chord AC at right angles (Euc. I. 26). B Fig. 6. Now by plane trigonometry, E C = B C x sin. . And AC = 2 EC NI* : AC = 2 B C x sin. Therefore chord = 2 radius x sin. of half the given angle. Example.—Test the angle of 45°, using a radius of 24 inches. For a radius of 24 inches the length of the chord is 18-37 inches. The length can also be found by multiplying 48 in. by the nat. sin. of 22}°. |