CHAPTER I. DEFINITIONS RELATING TO NAVIGATION. 1. That science, generally termed Navigation, which affords the knowledge necessary to conduct a ship from point to point upon the earth, enabling the mariner to determine, with a sufficient degree of accuracy, the position of his vessel at any time, is properly divided into two branches: Navigation and Nautical Astronomy. 2. Navigation, in its limited sense, is that branch which treats of the determination of the position of the ship by reference to the earth, or to objects thereon. It comprises (a) Piloting, in which the position is ascertained from visible objects upon the earth, or from soundings of the depth of the sea, and (b) Dead Reckoning, in which the position at any moment is deduced from the direction and amount of a vessel's progress from a known point of departure. 3. Nautical Astronomy is that branch of the science which treats of the determination of the vessel's place by the aid of celestial objects-the sun, moon, planets, or stars. 4. Navigation and Nautical Astronomy have been respectively termed GeoNavigation and Celo-Navigation, to indicate the processes upon which they depend. 5. As the method of piloting can not be employed excepting near land or in moderate depths of water, the navigator at sea must fix his position either by dead reckoning or by observation of celestial objects; the latter method is more exact, but as it is not always available, the former must often be depended upon. 6. THE EARTH.-The Earth is an oblate spheroid, being a nearly spherical body slightly flattened at the poles; its longer or equatorial axis measures about 7,927 statute miles, and its E shorter axis, around which it rotates, about 7,900 statute miles. The Earth (assumed for purposes of illustration to be a sphere) is represented in figure 1. The Axis of Rotation, usually spoken of simply as the Axis, is PP'. The Poles are the points, P and P', in which the axis intersects the surface, and are designated, respectively, as the North Pole and the South Pole. Р G N ימ T' N n T W Q M M' P' FIG. 1. The Equator is the great circle EQMW, formed by the intersection with the earth's surface of a plane perpendicular to the axis; the equator is equidistant from the poles, every point upon it being 90° from each pole. Meridians are the great circles PQP', PMP, PM'P', formed by the intersection with the earth's surface of planes secondary to the equator (that is, passing through its poles and therefore perpendicular to its plane). Parallels of Latitude are small circles NTn, N'n'T', formed by the intersection with the earth's surface of planes passed parallel to the equator. The Latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. Latitude is reckoned North and South, from the equator as an origin, through 90° to the poles; thus, the latitude of the point T is MT, north, and of the point T', M'T', north. The Difference of Latitude between any two places is the arc of a meridian intercepted between their parallels of latitude, and is called North or South, according to direction; thus, the difference of latitude between T and T' is Tn' or T'n, north from T or south from T'. The Longitude of a place on the surface of the earth is the arc of the equator intercepted between its meridian and that of some place from which the longitude is reckoned. Longitude is measured East or West through 180° from the meridian of a designated place, such meridian being termed the Prime Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich, England. If, in the figure, the prime meridian be PGQP', then the longitude of the point T is QM, east, and of T', QM', east. The Difference of Longitude between any two places is the arc of the equator intercepted between their meridians, and is called East or West, according to direction; thus, the difference of longitude between T and T' is MM', east from M or west from M'. The Departure is the linear distance, measured on a parallel of latitude, between two meridians; unlike the various quantities previously defined, departure is reckoned in miles; the departure between two meridians varies with the parallel of latitude upon which it is measured; thus, the departure between the meridians of T and T' is the number of miles corresponding to the distance Tn in the latitude of T, or to n'T' in the latitude of T'. The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equiangular Spiral. In the figure this line is represented by TrT'. The constant angle which this line makes with the meridians is called the Course; and the length of the line between any two places is called the Distance between those places: The unit of linear measure employed by navigators is the Nautical or Sea Mile, or Knot. This unit is defined in the United States of America as being 6,080.27 feet in length and equal to one-sixtieth part of a degree of a great circle of a sphere whose surface is equal in area to the area of the surface of the earth. The nautical mile is not exactly the same in all countries, but, from the navigator's standpoint, the various lengths adopted do not differ materially. Since, upon the ocean, latitude has been capable of easier and more accurate determination than longitude, it might naturally be expected that there exists an intimate fixed relation between the nautical mile and the minute of latitude (or the length of that portion of a meridian which subtends at the earth's center the angular measure of one minute); but on account of the fact that the earth is not a perfect sphere, a fixed relation does not exist, and the arc of a meridian that subtends an angle of 1' at the center of the earth varies slightly in length from the Equator_to the poles, being 6,045.95 feet at the Equator and 6,107.85 feet at the poles. Its average length is 1,852.201 meters, or 6,076.82 feet. Accordingly in France, Germany, and Austria the nautical mile is 1,852 meters, 2,025.41 yards, or 6,076.23 feet. For purposes of navigation the nautical mile is assumed to be equal to a minute of latitude in all parts of the world; and, hence, when a vessel changes her position to the north or south by 1 nautical mile, it may always be considered that the latitude has changed 1'. Owing to the fact that the meridians converge toward the poles, the difference of longitude produced by a change of position of 1 mile to the east or west will vary with the latitude; thus, a departure of 1 mile will equal a difference of longitude of 1' at the Equator, but of more than 1' at any higher latitude, being in fact equal to 1'.1 of longitude in latitude 30° and to 2' of longitude in latitude 60°. In England the nautical mile, corresponding to the Admiralty knot, is regarded as having a length of 6,080 feet. The statute mile of 5,280 feet, which is employed in land measurements, is commonly used in navigating river and lake vessels. This is notably the case on the Great Lakes of America, but with the recognition of the advantages to be gained by the practice of nautical astronomy in the navigation of these vessels, the use of the nautical mile is extending. The Great Circle Track or Course between any two places is the route between those places along the circumference of the great circle which joins them. In the figure this line is represented by TgT'. From the properties of a great circle (which is a circle upon the earth's surface formed by the intersection of a plane passed through its center) the distance between two points measured on a great circle track is shorter than the distance upon any other line which joins them. Except when the two points are on the same meridian or when both lie upon the equator, the great circle track will always differ from the rhumb line, and the great circle track will intersect each intervening meridian at a different angle. CHAPTER II. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. DIVIDERS OR COMPASSES. 7. This instrument consists of two legs movable about a joint, so that the points at the extremities of the legs may be set at any required distance from each other. It is used to take and transfer distances and to describe arcs and circles. When used for the former purpose it is termed dividers, and the extremities of both legs are metal points; when used for describing arcs or circles, it is called a compass, and one of the metal points is replaced by a pencil or pen. PARALLEL RULERS. 8. Parallel rulers are used for drawing lines parallel to each other in any direction, and are particularly useful in transferring the rhumb-line on the chart to the nearest compass-rose to ascertain the course, or to lay off bearings and courses. PROTRACTOR. 9. This is an instrument used for the measurement of angles upon paper; there is a wide variation in the material, size, and shape in which it may be made. (For a description of the Three Armed Protractor, see art. 428, Chap. XVII.) THE CHIP LOG. 10. This instrument, for measuring the rate of sailing, consists of three parts; viz, the log-chip, the log-line, and the log-glass. A light substance thrown from the ship ceases to partake of the motion of the vessel as soon as it strikes the water, and will be left behind on the surface; after a certain interval, if the distance of the ship from this stationary object be measured, the approximate rate of sailing will be given. The log-chip is the float, the log-line is the measure of the distance, and the log-glass defines the interval of time. The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with lead on the circular edge sufficiently to make it float upright in the water. There is a hole in each corner of the log-chip, and the log-line is knotted in the one at the apex; at about 8 inches from the end there is seized a wooden socket; a piece of line of proper length, being knotted in the other holes, has seized into its bight a wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as the line is checked this peg pulls out, thus allowing the log-chip to be hauled in with the least resistance. The log-line is about 150 fathoms in length, one end made fast to the log-chip, the other to a reel upon which it is wound. At a distance of from 15 to 20 fathoms from the log-chip a permanent mark of red bunting about 6 inches long is placed to allow sufficient stray line for the log-chip to clear the vessel's eddy or wake. The rest of the line is divided into lengths of 47 feet 3 inches called knots, by pieces of fish-line thrust through the strands, with one, two, three, etc., knots, according to the number from stray-line mark; each knot is further subdivided into five equal lengths of two-tenths of a knot each, marked by pieces of white rag. The length of a knot depends upon the number of seconds which the log-glass measures; the length of each knot must bear the same ratio to the nautical mile of a degree of a great circle of the earth, or 6,080 feet) that the time of the glass does to an hour. In the United States Navy all log-lines are marked for log-glasses of 28 seconds, for which the proportion is: 3600 6080=288 : x, x=47ft.29, or 47ft 3in. The speed of the ship is estimated in knots and tenths of a knot. The log-glass is a sand glass of the same shape and construction as the old hourglass. Two glasses are used, one of 28 seconds and one of 14 seconds; the latter is employed when the ship is going at a high rate of speed, the number of knots indicated on a line marked for a 28-second glass being doubled to obtain the true rate of speed. 11. The log in all its parts should be frequently examined and adjusted; the peg must be found to fit sufficiently tight to keep the log-chip upright; the logline shrinks and stretches and should often be verified; the log-glass should be compared with a watch. One end of the glass is stopped with a cork, by removing which the sand may be dried or its quantity corrected. 12. A ground log consists of an ordinary log-line, with a lead attached instead of a chip; in shoal water, where there are no well-defined objects available for fixing the position of the vessel and the course and speed are influenced by a tidal or other current, this log is sometimes used, its advantage being that the lead marks a stationary point to which motion may be referred, whereas the chip would drift with the stream. The speed, which is marked in the usual manner, is the speed over the ground, and the trend of the line gives the course actually made good by the vessel. THE PATENT LOG. 13. This is a mechanical contrivance for registering the distance actually run by a vessel through the water. There are various types of patent logs, but for the most part they act upon the same principle, consisting of a registering device, a fly or rotator, and a log or towline; the rotator is a small spindle with a number of blades extending radially in such manner as to form a spiral, and, when drawn through the water in the direction of its axis, rotates about that axis after the manner of a screw propeller; the rotator is towed from the vessel by means of a log or towline from 30 to 100 fathoms in length, made fast at its apex, the line being of special make, so that the turns of the rotator are transmitted through it to the worm shaft of the register, to which the inboard end of the line is attached; the registering device is so constructed as to show upon a dial face the distance run, according to the number of turns of its worm shaft due to the motion of the rotator; the register is carried at some convenient point on the vessel's quarter; it is frequently found expedient to rig it out upon a small boom, so that the rotator will be towed clear of the wake. 14. Though not a perfect instrument, the patent log affords a means of determining the vessel's speed through the water. It will usually be found that the indications of the log are in error by a constant percentage, and the amount of this error should be determined by careful experiment and applied to all readings. Various causes may operate to produce inaccuracy of working in the patent log, such as the bending of the blades of the rotator by accidental blows, fouling of the rotator by seaweed or refuse from the ship, or mechanical wear of parts of the register. The length of the towline has much to do with the working of the log, and by varying the length the indications of the instrument may sometimes be adjusted when the percentage of error is small; it is particularly important that the line shall not be too short. The readings of the patent log can not be depended upon for accuracy at low speeds, when the rotator does not tow horizontally, nor in a head or a following sea, when the effect depends upon the wave motion as well as upon the speed of the vessel. 15. Electrical registers for patent logs are in use, the distance recorded by the mechanical register being communicated electrically to some point of the vessel 16. A number of instruments based upon different physical principles have been devised for recording the speed of a vessel through the water and have been used with varying degrees of success. Of these the hydraulic speed indicator, known as the Nicholson Ship Log, affords an instance. 17. The revolutions of the screw propeller afford in a steamer the most valuable means of determining a vessel's speed through the water. The number of revolutions per knot must be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foulness of bottom. THE LEAD. 18. This device, for ascertaining the depth of water, consists essentially of a suitably marked line, having a lead attached to one of its ends. It is an invaluable aid to the navigator in shallow water, particularly in thick or foggy weather, and is often of service when the vessel is out of sight of land. Two leads are used for soundings-the hand-lead, weighing from 7 to 14 pounds, with a line marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to 100 pounds, the line being 100 fathoms or upward in length. Lines are generally marked as follows: 2 fathoms from the lead, with 2 strips of leather. 10 fathoms from the lead, with leather having a 13 fathoms from the lead, same as at 3 fathoms. 15 fathoms from the lead, same as at 5 fathoms. 17 fathoms from the lead, same as at 7 fathoms. Fathoms which correspond with the depths marked are called marks; the intermediate fathoms are called deeps; the only fractions of a fathom used are a half and a quarter. A practice sometimes followed is to mark the hand-lead line in feet around the critical depths of the vessel by which it is to be used. Lead lines should be measured frequently while wet and the correctness of the marking verified. The distance from the leadsman's hand to the water's edge should be ascertained in order that proper allowance may be made therefor in taking soundings at night. 19. The deep-sea lead may be armed by filling with tallow a hole hollowed out in its lower end, by which means a sample of the bottom is brought up. THE SOUNDING MACHINE. 20. This machine possesses advantages over the deep-sea lead, for which it is a substitute, in that soundings may be obtained at great depths and with rapidity and accuracy without stopping the ship. It consists essentially of a stand holding a reel upon which is wound the sounding wire, and which is controlled by a suitable brake. Crank handles are provided for reeling in the wire after the sounding has been taken. Attached to the outer end of the wire is the lead, which has a cavity at its lower end for the reception of the tallow for arming. Above the lead is a cylindrical case containing the depth-registering mechanism; various devices are in use for this purpose, all depending, however, upon the increasing pressure of the water with increasing depths. 21. In the Lord Kelvin machine a slender glass tube is used, sealed at one end and open at the other, and coated inside with a chemical substance which changes color upon contact with sea water; this tube is placed, closed end up, in the metal cylinder; as it sinks the water rises in the tube, the contained air being compressed with a force dependent upon the depth. The limit of discoloration is marked by a clearly defined line, and the depth of the sounding corresponding to this line is read off from a scale. Tubes that have been used in comparatively shallow water may be used again where the water is known to be deeper. 22. A tube whose inner surface is ground has been substituted for the chemical |