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changing the course accordingly, one cannot fail to keep the ship at the required distance from the rocks.

37. Illustrative Example. -Suppose you are bound from Grand Haven to Whitehall, Mich., and that about SSW, 2 miles from White River Light, at the entrance to White Lake, lies the wreck of a sunken steamer R, Fig. 16, in 10 fathoms of water. The masts of the steamer are gone but the top of its smokestack is just awash. Its position. which is marked on the chart, is therefore difficult to locate

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unless close to the wreck. You do not care to go inside of the wreck, but prefer to pass it on the outside at a safe distance of, say, } statute mile. On the shore there are two conspicuous marks, the yellow octagonal brick tower of the White River Lighthouse and a bluff B just below and south of Duck Lake, that can be used for forming a horizontal danger angle for passing the wreck , mile outside of it. It is required to find that danger angle, in order to do which proceed as follows: With R as a center and statute mile (taken from the scale) as a radius, describe a circle; connect the most seaward point of that circle with the two objects on shore by means of straight lines. The angle formed by these lines is the required horizontal danger angle, and when measured by a protractor will be found to contain 70°. Hence, by setting the sextant to that angle and keeping the objects in contact, as explained in the preceding article, the wreck may be rounded at the required distance.

38. Comparison of the Two Methods. – When circumstances permit the selection of a vertical and a horizontal danger angle, the latter should always be preferred as being much more accurate than the former. This is so on account of the horizontal angle being much larger than the vertical angle, and because the recorded heights of lights and other objects on shore are not always reliable and can be considered as being only approximately correct. Furthermore, it is evident that the horizontal danger angle may be used during both night and day, whenever two lights are in sight, whereas the use of the vertical angle is limited to the day only.

39. Cautionary Remarks. – It must be remembered that, before using the danger angle in the actual practice of navigating a ship past a danger, the student should be efficient in its use.

Do not try to experiment with it in places where actual danger exists. Practice it at first with imaginary

re of being able to utilize it with ease and confidence.

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40. In connection with the use of charts and determining the position of a ship while in sight of known objects, many instruments have been introduced to facilitate and simplify such operations. Among them the station pointer is important. This instrument, which does away with the possibility of committing errors in applying compass corrections, besides saving considerable time in fixing a position, is shown in Fig. 17. It consists of a graduated circle of metal having three arms attached to its center c; of these, ce is fixed while the other two are movable. The latter are fitted with clamping screws s and s' so that they can be set and secured to any required angle, the center line of the fixed arm serving as

the zero point. The instrument is made in different sizes and more

re or less perfect in detail; like the tant, some are fitted with tangent screws and reading microscopes. As a whole the instrument is simple, easy to handle and adjust, and has no complicated mechanism to get out of order.

sex

Right

Left

on

e

FIG. 17

41. How to Use the Station Pointer. - Select three objects on shore, the positions of which are known, and which are to be found

the chart. Let these three objects be represented in Fig. 18 by a, b, and c; the angles between a and b and b and C

are then measured by a sextant, either in quick succession by one observer, or separately by two observers at the same instant. This done, take the station pointer, holding the arms from you, and set the left arm so that the angle subtended by it and the fixed leg will be equal to the measured angle between a and b. Similarly, set the right arm so that the angle between it and the zero arm is equal to the measured angle between b and c. Then place the instrument on the chart so that the center of the fixed arm passes through the object b, while the other arms pass through a and c, respectively. The center p of the instrument will then represent the exact position of the ship and should be marked down on the chart through the small hole ç, Fig. 17, especially made for that purpose. Thus the ship's position is determined quickly and accurately without the least aid of the compass.

42. 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 a sight vane at

Zero Arm

FIG. 18

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the center. The bearings are taken directly by the instrument and are placed on the chart in exactly the same manner as with the station pointers, the time required for the whole operation being about 4 or 5 minutes.

43. As a substitute for the station pointer and position finder, an instrument called the radiograph is mended. 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 or tracing cloth will prove excellent substitutes, and in particular cases are 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 cloth on which a graduated circle is either drawn or printed, this inconvenience is at once removed.

DETERMINING THE POSITION OF A SHIP

WHEN NOT IN SIGHT OF LAND

INTRODUCTORY REMARKS

44. We shall now consider the methods used to determine the position of a ship when it is not in sight of land or any known permanent object. Of these methods there are several, but only those adapted for navigating the Great Lakes will be considered here. They are plane sailing, parallel sailing, and middle-latitude sailing.

The accuracy of the result attained by any of these methods will depend on the accuracy of the account kept of the courses and distances run. In other words, when a navigator knows exactly what courses have been steered and what distances have been run on each course, and appropriate allowance has been made for the influence of wind, the exact position of his vessel may be determined at any time by the methods about to be described.

an

PLANE SAILING

EXPLANATION AND PRINCIPLES

45.

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

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