instrument will then represent the exact position of the ship, and should be marked down on the chart through the small hole c, Fig. 28, especially made for that purpose. Thus the ship's position is determined quickly and accurately without the least aid of the compass. 104. Examining the Station Pointer.-Before using a station pointer it should be examined, and in doing so proceed as follows: First find whether the arms are exactly in the center of the instrument or not. This is done by placing the movable arms on opposite sides of, and as close as possible to, the zero arm; one of the arms is then clamped tight, while the other is tightened enough so as to allow a slight force to move it; the latter is then moved gently around the whole graduated circle and returned back to its original position. Proceed similarly with the other arm. If the arms when thus moved meet with nearly uniform resistance they are well centered; if not, the centering of the instrument needs adjustment. 105. This complied with, the graduations of the instrument should be attended to. This is done as follows: Place one of the arms, for instance, the right, at reading 180° and clamp it. Then draw a light pencil line along the edges of the clamped arm and also along the zero arm, and make a dot through the hole at the center. Remove the station pointer and place a ruler on the paper so that its edge coincides with the pencil line drawn along the zero arm. The continuation of the edge of the ruler should then pass through the central point and coincide with the pencil line that was drawn along the edge of the clamped right arm. Test the other arm similarly, and if both are found satisfactory, set the right arm to 90° and the left to 270°; replace the instrument on the paper, and along the edge of each arm draw pencil lines as before; remove the instrument and place the edge of a ruler along the two lines. If these graduations are correct, the edge should coincide exactly with the two lines and the central point. This done, the arms are set perpendicularly to each other so as to read 10° and 100°, respectively; then, at 20° and 110°, at 50° and 140°, and so on; at each setting the instrument is so placed with its center on the central point on the paper so that the edge of one of the movable arms coincides with one of the original pencil lines; the edge of the other movable arm should then coincide with the pencil line, which is perpendicular to the pencil line along the edge of the other arm. If in all cases this condition is satisfied, the graduation of the instrument is perfect. 106. For navigational purposes, the graduations of the circumference of a station pointer to whole and half degrees are sufficient. The diameter of the circle should be about 5 inches and the length of the arms about 10 inches. Lengthening bars should accompany the instrument. 107. The Position Finder.-A still simpler form of the station pointer is an instrument recently invented and called the position finder. This instrument is absolutely independent of both compass and sextant; each of its three arms are fitted with small steel pointers, and at the center is affixed a sight vane. The bearings are taken directly by the instrument, each arm in the direction of an object; the movable arms are then clamped and the instrument placed on the chart in exactly the same manner as the station pointer, the time required for the whole operation being about 4 or 5 minutes. 108. As a substitute for the station pointer and position finder, an instrument called the radiograph is recommended. This consists of a graduated circular piece of ground glass on which the radii subtending the measured angles are drawn with a pencil. Should, however, the lastnamed instrument not be available, common tracing paper will prove an excellent substitute and in particular cases almost preferable to the station pointer itself. For instance, when the objects used for angles are very near the observer they may, on the chart, come within the metal circle of the instrument and be more or less hidden by it. By using tracing paper on which a graduated circle is either drawn or printed, this inconvenience is at once removed. NAVIGATION (PART 3) THE SAILINGS CLASSIFICATION OF METHODS 1. We will now consider the methods of calculation used to determine the position of a ship at sea by keeping account of the courses and distances that she sails. These methods, usually known as the sailings, are named as follows: Plane sailing, parallel sailing, middle-latitude sailing, Mercator's sailing, and great-circle sailing. Other sailings are simply a modification or combined application of these. PLANE SAILING EXPLANATION AND PRINCIPLES 2. Plane sailing is usually defined as being the art of navigating a ship on the supposition that the earth is a flat surface. This definition should not be taken literally. In all sailings, the earth's surface is regarded to be what it really is-spherical; yet, the distance run during a day by an ordinary vessel is so insignificant in comparison with the enormous surface of the earth that it may, for all practical purposes, be represented by a straight line on a plane surface. This will appear more clearly by examining an ordinary good-sized globe, representing the earth; a day's run, or the distance made good by a ship during a day, may on such a globe be represented by a straight line of not more than perhapsor of an inch in length. If the space in which this For notice of copyright, see page immediately following the title page line was embodied was cut out and placed on a flat surface, the difference in length between the two lines would be so small as not to be perceptible to the naked eye, and the curvature of the meridians and latitude parallels, contained in the space, would be practically inappreciable. We do not, therefore, assume that the surface actually sailed upon is a plane, with the meridians parallel straight lines; but, for reasons mentioned above, we find that we may practically replace the small part of the spherical surface sailed over by a plane surface, and consider, without committing any appreciable error, the meridians as straight parallel lines that intersect the latitude parallels at right angles, forming perfect squares, as shown in Fig. 1. Hence, we derive the term plane sailing. 3. From previous statements, we know that when a ship. steers a straight, continuous course, her track, or rhumb line, will intersect all meridians at the same angle. Therefore, in plane sailing, if a ship sails, for instance, from a to b, Fig. 1, her track, or path, a b will form, with the meridian ac and the parallel cb, a right-angled triangle abc. The same thing will occur when the ship sails from a to d, or from a to e, or in any other direction except when the course is true north and south or true east and west. Hence, in plane sailing, we have only a plane right-angled triangle to deal with, and the most elementary acquaintance with plane trigonometry will suffice in solving problems relating to this sailing. 4. Formulas Relating to Plane Sailing.-Referring to the triangle a cb, Fig. 1, the elements that enter into this sailing are readily recognized; the angle cab is the course, the hypotenuse a b is the distance, the side cb is the departure, and the side ac is the difference of latitude. Then, by the first principles of plane trigonometry, we have the following relations between the different parts of the triangle: From Plane Trigonometry, we know that sin C= and cos C= 1 cosec C' Hence, instead of dividing by the cose 1 sec C cant, we may multiply by the sine of the same angle, or vice versa; and, similarly, instead of dividing by the cosine we may multiply by the secant of the same angle, and so on. 5. From the foregoing, and by referring to the formulas and rearranging them into tabular form, we obtain the following result: |