Produced by Viv, Ted Garvin and the Online Distributed Proofreading Team at http://www.pgdp.net [Transcriber's Note:- Words and phrases surrounded by underscores are italicised. There are four symbols which are denoted by :- (.) Circle surrounding a centred dot - Right Ascension of the Meridian; (+) Circle surrounding a cross - Earth's Central Progress; (_) Circle with centre dot and line under - Observed altitude of sun's lower limb; -(-)- Circle with line through - True Altitude. ] LECTURES IN NAVIGATION Prepared for Use as a Text Book at the OFFICERS' MATERIAL SCHOOL NAVAL AUXILIARY RESERVE by Lieutenant ERNEST G. DRAPER, U.S.N.R.F. Head of the Department of Navigation Officers' Material School, Naval Auxiliary Reserve COPYRIGHT BY ERNEST G. DRAPER FOREWORD These Lectures have been compiled as speedily as possible to meet the demand for some quick but fairly comprehensive method whereby large bodies of men, divided into small classes, might learn the elements of Navigation and thus assume, without delay, their responsibilities as Junior Officers of the deck, Navigators and Assistant Navigators in the United States Naval Auxiliary Reserve. I realize that the haste with which the book has been written is apparent in many places, and it is hoped that many evidences of this haste will disappear in case further editions are printed. Besides acknowledging the help and information which was secured from the list of navigational works, mentioned on another page, I wish to mention particularly Prof. Charles Lane Poor's book, entitled "Nautical Science," from which was secured practically all of the information in the Lecture on Planets and Stars (Tuesday--Week V); Commander W. C. P. Muir's book, "Navigation and Compass Deviations," and Lieutenant W. J. Henderson's book, "Elements of Navigation," the text of which was followed closely in discussing Variation and Deviation and Traverse Sailing. I desire to express my gratitude to Lieutenant Commander R. T. Merrill, 2nd, U. S. N., for suggesting a detailed outline of the whole course; to Lieutenant Commander B. O. Wills, U. S. N., for his valuable criticisms and almost daily help during the preparation of these Lectures; to Lieutenant (j. g.) C. D. Draper, U. S. N. R. F.; Lieutenant (j. g.) R. Brush, U. S. N. R. F., and Lieutenant (j. g.) P. C. McPherson, U. S. N. R. F., for many criticisms and suggestions; and to Captain Huntington, Seamen's Church Institute, for suggesting helpful diagrams, particularly the one on page 44. This opportunity is also taken for thanking the many Instructors in the School for their opinions on various questions that have come up in connection with the course and for assistance in eliminating errors from the text. E. G. D. LIST OF BOOKS CONSULTED AMERICAN PRACTICAL NAVIGATOR, BOWDITCH NAVIGATION AND COMPASS DEVIATIONS, MUIR NAUTICAL SCIENCE, POOR ELEMENTS OF NAVIGATION, HENDERSON WRINKLES IN PRACTICAL NAVIGATION, LECKY WHYS AND WHEREFORES OF NAVIGATION, BRADFORD EPITOME OF NAVIGATION, NORIE NAVIGATION, HOSMER FINDING A SHIP'S POSITION AT SEA, SUMNER GENERAL ASTRONOMY, YOUNG PREFACE TO THOSE TAKING THIS COURSE IN NAVIGATION: These lectures have been written with the idea of explaining, in as simple language as possible, the fundamental elements of Navigation as set forth in Bowditch's American Practical Navigator. They will be given you during the time at the Training School devoted to this subject. At present this time includes two morning periods of one and a half hours each, separated by a recess of fifteen minutes. In general the plan is to devote the first period to the lecture and the second period to practical work. Not many examples for practical work have been included in this book, but one example, illustrating each new method, has been worked out. If you understand these examples you should be able to understand others similar to them. Toward the end of the course a portion of each second period will be devoted to handling the sextant, work with charts, taking sights, etc. In short, every effort will be made to duplicate, as nearly as possible, navigating conditions on board a modern merchant ship. DEPARTMENT OF NAVIGATION, _Officers' Material School_, _Naval Auxiliary Reserve_ CONTENTS WEEK I--PILOTING _Tuesday_--The Compass 1 _Wednesday_--Pelorus; Parallel Rulers; The Lead, Sounding Machine, Dividers and Log 6 _Thursday_--The Chart 10 _Friday_--The Protractor and Sextant 13 _Saturday_--Fixes, Angles by Bearings and Sextant 16 WEEK II--DEAD RECKONING _Tuesday_--Latitude and Longitude 20 _Wednesday_--Useful Tables--Plane and Traverse Sailing 23 _Thursday_--Examples on Plane and Traverse Sailing (Continued) 27 _Friday_--Mercator Sailing 28 _Saturday_--Great Circle Sailing--The Chronometer 30 WEEK III--CELESTIAL NAVIGATION _Tuesday_--Celestial Co-ordinates, Equinoctial System, etc. 34 _Wednesday_--Time by the Sun--Mean Time, Solar Time, Conversion, etc. 36 _Thursday_--Sidereal Time--Right Ascension 43 _Friday_--The Nautical Almanac 47 _Saturday_--Correction of Observed Altitudes 52 WEEK IV--NAVIGATION _Tuesday_--The Line of Position 55 _Wednesday_--Latitude by Meridian Altitude 58 _Thursday_--Azimuths of the Sun 61 _Friday_---Marc St. Hilaire Method by a Sun Sight 63 _Saturday_--Examples on Marc St. Hilaire Method by a Sun Sight 66 WEEK V--NAVIGATION _Tuesday_--A Short Talk on the Planets and Stars--Identification of Stars--Time of Meridian Passage of a Star 66 _Wednesday_--Latitude by Meridian Altitude of a Star--Latitude by Polaris 73 _Thursday_--Marc St. Hilaire Method by a Star Sight 74 _Friday_--Examples: Latitude by Meridian Altitude of a Star; Latitude by Polaris; Marc St. Hilaire Method by a Star Sight 75 _Saturday_--Longitude by Chronometer Sight of the Sun 76 WEEK VI--NAVIGATION _Tuesday_--Longitude by Chronometer Sight of a Star 79 _Wednesday_--Examples on Longitude by Chronometer Sight of a Star 80 _Thursday_--Latitude by Ex-Meridian Altitude of the Sun 81 _Friday_--Examples: Latitude by Ex-Meridian Altitude of the Sun 83 _Saturday_--Finding the Watch Time of Local Apparent Noon 83 WEEK VII--NAVIGATION _Tuesday_--Compass Error by an Azimuth 88 _Wednesday_--Correcting Longitude by a Factor 89 _Thursday_--The Navigator's Routine--A Day's Work at Sea 91 _Friday_--Day's Work 105 _Saturday_--Day's Work 105 WEEK VIII--NAVIGATION _Monday to Thursday_--Day's Work 107-108 _Additional Lecture_--Compass Adjustment 109 WEEK I--PILOTING TUESDAY LECTURE THE COMPASS Everyone is supposed to know what a compass looks like. It is marked in two ways--the old way and the new way. Put in your Note-Book this diagram: [Illustration] The new way marked on the outside of the diagram, starts at North with 0°, increases toward the right through East at 90°, South at 180°, West at 270° and back to North again at 360° or 0°. The old way, marked on the inside of the diagram, starts at North with 0°, goes to the right to 90° at East and to the left to 90° at West. It also starts at South with 0°, goes to the right to East at 90° and to the left to West at 90°. A Compass Course can be named in degrees, according to either the new or old way. For instance, the new way is just 45°. The old way for the same course is N 45° E. New way--100°. Old way for same course--S 80° E. There is another way to name a compass course. It is by using the name of the point toward which the ship is heading. On every ship the compass is placed with the lubber line (a vertical black line on the compass bowl) vertical and in the keel line of the ship. The lubber line, therefore, will always represent the bow of the ship, and the point on the compass card nearest the lubber line will be the point toward which the ship is heading. The compass card of 360° is divided into 32 points. Each point, therefore, represents 11-1/4°. The four principal points are called _cardinal_ points. They are--North, East, South, West. Each cardinal point is 90° from the one immediately adjacent to it. It is also 8 points from the one adjacent to it, as 90° is 8 points, i.e., 11-1/4° (one point) times 8. Midway between the cardinal points are the inter-cardinal points. They are--N E, S E, S W, N W, and are 45° or 4 points from the nearest cardinal point. Midway between each cardinal and inter-cardinal point--at an angular distance of 22-1/2° or 2 points, is a point named by combining a cardinal point with an inter-cardinal point. For instance, NNE, ENE, ESE, SSE, SSW, WSW, WNW, NNW. Midway between the last points named and a cardinal or inter-cardinal point, at an angular distance of 11-1/4°, is a point which bears the name of that cardinal or inter-cardinal point joined by the word _by_ to that of the cardinal point nearest to it. As, for instance, N by E, E by N, E by S, S by E, S by W, W by S, W by N, N by W. Also NE x N, NE x E, SE x E, SE x S, SW x S, SW x W, NW x W, NW x N. The angular distance between each and every whole point is divided into 4 parts called half and quarter points and each representing an angular measure of approximately 2° 49'. In mentioning fractional points, the U. S. Navy regulations are to name each point from North and South toward East and West except that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point: For instance, N 1/2 E, N x E 1/2 E, NE 1/2 N, NW 1/2 N, NW 1/4 W, NW 3/4 W, NW 1/4 N. Boxing the compass is naming each point and quarter-point in rotation, i.e., starting at North and going around to the right back to North again. Every man should be able to identify and name any point or quarter-point on the compass card. In changing a point course into a degree course, for either new or old compass, a guide is herewith furnished you. This should be pasted into the front of your Bowditch Epitome. It shows, from left to right, the name of the point course, its angular measure in the new compass and its angular measure in the old compass. It also shows at the bottom, the angular measure of each division of one point. In understanding this guide, remember that each course is expressed in degrees or degrees and minutes. Put in your Note-Book: In Navigation, each degree is written thus °. Each fraction of a degree is expressed in minutes and written thus '. There are 60' in each degree. Each fraction of a minute is expressed in seconds and is written ". There are 60" in each minute. Four degrees, ten minutes and thirty seconds would be written thus: 4° 10' 30". Although this guide just given you is given as an aid to quickly transfer a point course into a new or old compass course--or vice versa--you should learn to do this yourself, after awhile, without the guide. Put in your Note-Book: --------------+-----------+------------+-------------- Ship's Head | New | Old | By Point --------------+-----------+------------+-------------- NE | 45° | N 45° E | NE 90° | 90° | N 90° E | EAST SE × E | 123° 45' | S 56° E | SE × E S 20° E | 160° | S 20° E | S x E 3/4 E S 2 pts. E | 157° 30' | S 22° 30' E| SSE NW 3/4 W | 306° 34' | N 53° W | NW 3/4 W 289° 41' | 289° 41' | N 70° W | WNW 1/4 W --------------+-----------+------------+-------------- I will show you just how each one of these courses is secured from the guide just given you. Note to Instructor: After explaining these courses in detail, assign for reading _in the class room_ the following articles in Bowditch: Arts. 25-26-27-28-29-30-31-32, 74-75-76-77-78-79-80-81-82. Every compass, if correct, would have its needle point directly to the real or _true_ North. But practically no compass with which you will become familiar will be correct. It will have an error in it due to the magnetism of the earth. This is called Variation. It will also have an error in it due to the magnetism of the iron in the ship. This is called Deviation. You are undoubtedly familiar with the fact that the earth is a huge magnet and that the magnets in a compass are affected thereby. In other words, the North and South magnetic poles, running through the center of the earth, do not point true North and South. They point at an angle either East or West of the North and South. The amount of this angle in any one spot on the earth is the amount of Variation at that spot. In navigating a ship you must take into account the amount of this Variation. The amount of allowance to be made and the direction (i.e. either East or West) in which it is to be applied are usually indicated on the chart. On large charts, such as those of the North Atlantic, will be found irregular lines running over the chart, and having beside them such notations as 10° W, 15° W, etc. Some lines are marked "No Variation." In such cases no allowance need be made. On harbor charts or other small charts, the Variation is shown by the compass-card printed on the chart. The North point of this card will be found slewed around from the point marking True North and in the compass card will be some such inscription as this: "Variation 9° West in 1914. Increasing 6' per year." Now let us see how we apply this Variation so that although our compass needle does not point to true North, we can make a correction which will give us our true course in spite of the compass reading. Note these diagrams: [Illustration] The outer circle represents the sea horizon with the long arrow pointing to true North. The inner circle represents the compass card. In the diagram to the left, the compass needle is pointing three whole points to the left or West of True North. In other words, if your compass said you were heading NE x N, you would not actually be heading NE x N. You would be heading true North. [Illustration] In other words, standing in the center of the compass and looking toward the circumference, you would find that every true course you sailed would be three points to the _left_ of the compass course. That is called Westerly Variation. Now look at the diagram to the right. The compass needle is pointing three whole points to the right or East of True North. In other words, standing in the center of the compass and looking toward the circumference, you would find that every true course you sailed would be three points to the _right_ of the compass course. That is called Easterly Variation. Hence we have these rules, which put in your Note-Book: _To convert a compass course into a true course_ When the Variation is westerly, the true course will be as many points to the left of the compass course as there are points or degrees of Variation. When the Variation is easterly, the true course will be as many points or degrees to the right of the compass course. _To convert a true course into a compass course_ The converse of the above rule is true. In other words, Variation westerly, compass to the right of true course; variation easterly, compass course to the left. DEVIATION As stated before, Deviation causes an error in the Compass due to the magnetism of the iron in the ship. When a ship turns, the compass card does not turn, but the relation of the iron's magnetism to the magnets in the compass is altered. Hence, every change in course causes a new amount of Deviation which must be allowed for in correcting the compass reading. It is customary in merchant vessels to have the compasses adjusted while the ship is in port. The adjuster tries to counteract the Deviation all he can by magnets, and then gives the master of the ship a table of the Deviation errors remaining. These tables are not to be depended upon, as they are only accurate for a short time. Ways will be taught you to find the Deviation yourself, and those ways are the only ones you can depend upon. Put in your Note-Book: Westerly Deviation is applied exactly as westerly Variation. Easterly Deviation is applied exactly as easterly Variation. The amount of Variation plus the amount of Deviation is called the Compass Error. For instance, a Variation of 10° W plus a Deviation of 5° W equals a compass error of 15° W, or a Variation of 10° W plus a Deviation of 5° E leaves a net compass error of 5° W. LEEWAY Leeway is not an error of the compass, but it has to be compensated for in steaming any distance. Hence it is mentioned here. A ship steaming with a strong wind or current abeam, will slide off to the leeward more or less. Hence, her course will have to be corrected for Leeway as well as for Variation and Deviation. Put in your Note-Book: Leeway on the starboard tack is the same as westerly Variation. Leeway on the port tack is the same as easterly Variation. This is apparent from the following diagram: [Illustration] As the wind, blowing from the North, hits the left hand ship, for instance, on her starboard side, it shoves the ship to the left of her true course by the number of points or degrees of leeway. Leave a space and put the following heading in your Note-Book: I. Complete rule for converting a compass course into a true course: 1. Change the compass course into a new compass reading. 2. Apply Easterly Variation and Deviation +. 3. Apply Westerly Variation and Deviation -. 4. Apply port tack Leeway +. 5. Apply starboard tack Leeway -. II. Complete rule for converting a true course into a compass course: 1. Reverse the above signs in applying each correction. I will now correct a few courses, and these are to be put into your Note-Book: ---------+------+-------------+--------+--------+-------+--------- C Cos | Wind | Leeway | Dev. | Var. | New | Old ---------+------+-------------+--------+--------+-------+--------- N x E | NW | 1/2 pt. | 5° E | 10° W | 12° | N 12° E S 67° E | S | 1 pt. | 3° W | 5° E | 104° | S 76° E E x N | SE | 1/2 pt. | 5° W | 10° E | 78° | N 78° E W x N | NW | 1-1/2 pts. | 1° E | 15° E | 280° | N 80° W ---------+------+-------------+--------+--------+-------+--------- Assign for Night Work the following arts. in Bowditch: 36-8-10-13-14-15-16-17-18-19-20-21-22-23-24. WEDNESDAY LECTURE PELORUS, PARALLEL RULERS, THE LEAD, SOUNDING MACHINE, DIVIDERS AND LOG _I. The Pelorus_ This is an instrument for taking bearings of distant objects, and for taking bearings of celestial bodies such as the sun, stars, etc. It consists of a circular, flat metallic ring, mounted on gimbals, upon a vertical standard. The best point to mount it is in the bow or on the bridge of the ship, where a clear view for taking bearings can be had. The center line of the pelorus should also be directly over the keel line of the ship. The inner edge of the metallic ring is engraved in degrees--the 0° or 360° and the 180° marks indicating a fore-and-aft line parallel to the keel of the ship. Within this ring a ground glass dial is pivoted. This ground glass dial has painted upon it a compass card divided into points and sub-divisions and into 360°. This dial is capable of being moved around, but can also be clamped to the outside ring. Pivoted with the glass dial and flat ring is a horizontal bar carrying at both of its extremes a sight vane. This sight vane can be clamped in any position independently of the ground glass dial, which can be moved freely beneath it. An indicator showing the direction the sight vane points can be read upon the compass card on the glass dial. If the glass dial be revolved until the degree of demarcation, which is coincident with the right ahead marking on the flat ring, is the same as that which points to the lubber's line of the ship's compass, then all directions indicated by the glass dial will be parallel to the corresponding directions of the ship's compass, and all bearings taken will be compass bearings, i.e., as though taken from the compass itself. In other words, it is just as though you took the compass out of its place in the pilot house, or wherever it is regularly situated, put it down where the pelorus is, and took a bearing from it of any object desired. In taking a bearing by pelorus, two facts must be kept in mind. First, that when the bearing is taken, the exact heading, as shown by the ship's compass, is the heading shown by the pelorus. In other words, if the ship is heading NW, the pelorus must be set with the NW point on the lubber line when the bearing is taken of any object. Second, it must be remembered that the bearing of any object obtained from the pelorus is the bearing _by compass_. To get the true bearing of the same object you must make the proper corrections for Variation and Deviation. This can be compensated for by setting the glass dial at a point to the right or left of the compass heading to correspond with the compass error; then the bearing of any object will be the true bearing. But naturally, you will not be able to make compensation for these errors unless you have immediately before found the correct amount of the compass error. _Parallel Rulers_ The parallel rulers need no explanation except for the way in which they are used on a chart. Supposing, for instance, you wish to steam from Pelham Bay to the red buoy off the westerly end of Great Captain's Island. Take your chart, mark by a pencil point the place left and the place to go to and draw a straight line intersecting these two points. Now place the parallel rulers along that line and slide them over until the nearest edge intersects the center of the compass rose at the bottom or side of the chart. Look along the ruler's edge to find where it cuts the circumference of the compass rose. That point on the compass rose will be the _true_ compass course, and can be expressed in either the new or old compass, as, for instance, 60° or N 60° E. Remember, however, that this is the _true_ course. In order to change it into the compass course of your ship, you must make the proper corrections for the compass error, i.e., Variation and Deviation and for Leeway, if any. _The Lead and Sounding Machine_ The lead, as you know, is used to ascertain the depth of the water and, when necessary, the character of the bottom. There are two kinds of leads: the hand lead and deep-sea lead. The first weighs from 7 to 14 pounds and has markings to 25 fathoms. The second weighs from 30 to 100 pounds and is used in depths up to and over 100 fathoms. Put in your Note-Book: Fathoms which correspond with the depths marked are called _marks_. All other depths are called _deeps_. The hand lead is marked as follows: 2 fathoms--2 strips of leather. 3 fathoms--3 strips of leather or blue rag. 5 fathoms--A white rag. 7 fathoms--A red rag. 10 fathoms--A piece of leather with one hole in it. 13 fathoms--Same as at 3. 15 fathoms--Same as at 5. 17 fathoms--Same as at 7. 20 fathoms--2 knots or piece of leather with 2 holes. 25 fathoms--1 knot. 30 fathoms--3 knots. 35 fathoms--1 knot. 40 fathoms--4 knots. And so on up to 100 fathoms. The large hand leads are hollowed out on the lower end so that an "arming" of tallow can be put in. This will bring up a specimen of the bottom, which should be compared with the description found on the chart. All up-to-date sea-going ships should be fitted with Sir William Thompson's Sounding Machine (see picture in B. J. Manual). This machine consists of a cylinder around which are wound about 300 fathoms of piano wire. To the end of this is attached a heavy lead. An index on the side of the instrument records the number of fathoms of wire paid out. Above the lead is a copper cylindrical case in which is placed a glass tube open only at the bottom and chemically colored inside. The pressure of the sea forces water up into this tube, as it goes down, a distance proportionate to the depth, and the color is removed. When hoisted, the tube is laid upon a prepared scale, and the height to which the water has been forced inside shows the depth in fathoms on the scale. DIVIDERS The dividers are nothing but an instrument for measuring distances, etc., on the chart. THE LOG There are two kinds of logs--the chip log, used for measuring the speed of the ship, and the patent log, used for measuring distance run. The chip log consists of a reel, line, toggle and chip. Usually a second glass is used for measuring time. The chip is the triangular piece of wood ballasted with lead to ride point up. The toggle is a little wooden case into which a peg, joining the ends of the two lower lines of the bridle, is set in such a way that a jerk on the line will free it, causing the log to lie flat so that it can be hauled in. The first 10 or 15 fathoms of line from the log-chip are called "stray line," and the end of this is distinguished by a mark of red bunting. Its purpose is to let the chip get clear of the vessel's wake. The marks on the line (called knots) are pieces of fish line running through the strands of the reel line to the number of two, three, four, etc. A piece of white bunting marks every two-tenths of a knot. This is because the run of the ship is recorded in knots and tenths. The knots of fish line are 47 feet 4 inches from each other. The log glass measures 28 seconds in time. For high rates of speed, a 14 second glass is used. Then the number of knots shown by the log line must be doubled. The principle of the chip log is that each division of the log line bears the same ratio to a nautical mile that the log glass does to the hour. In other words, if 10 knots or divisions of the log line run out while the 28 second glass empties itself, the ship's speed is 10 knots per hour. If ten knots or divisions run out while the 14 second glass empties itself, the ship's speed is 20 knots per hour. The patent or towing log consists of a dial, line and rotator. The large circle of the dial records the knots and the small circle tenths of knots. When changing course, read the log and enter it in the log book. When changing course again, read the log again. The difference between the two readings will be the distance run. Both logs are liable to error. A following sea makes them under-rate, a head sea over-rate. With both logs you must allow for currents. If a current is against you--and you know its rate--you must deduct its rate from that recorded in the log and vice versa. The reason for this is that your log measures your speed through the water. What you must find is your actual distance made good over the earth's surface. Put in your Note-Book: Between Sandy Hook and Fort Hamilton, bound due North, speed by chip-log was 10 knots, tidal current setting North 2 knots per hour; what did the ship make per hour? Answer: 12 knots. At sea in North Sea ship heading S x W, patent log bet. 8 A.M. and 12 M. registered 32 miles, current running N x E 2 knots per hour; what was the actual distance made good? Answer: 24 miles. Directions for allowing for a current setting diagonally across a ship's course will be given in the proper place. Assign for Night Work the following articles in Bowditch: Arts. 161-162-163-164-165. THURSDAY LECTURE THE CHART _Aids to Navigation_ A chart is a map of an ocean, bay, sound or other navigable water. It shows the character of the coast, heights of mountains, depths at low water, direction and velocity of tidal currents, location, character, height and radius of visibility of all beacon lights, location of rocks, shoals, buoys, and nature of the bottom wherever soundings can be obtained. The top of the chart is North unless otherwise noted. When in doubt as to where North is, consult the compass card printed somewhere on the chart. On sea charts, such as those of the North Atlantic, only the true compass is printed, with the amount and direction of Variation indicated by lines on the chart. Parallels of latitude are shown by straight lines running parallel to each other across the chart. The degrees and minutes of these parallels are given on the perpendicular border of the chart. Meridians of longitude are shown by straight lines running up and down, perpendicular to the parallels of latitude, and the degrees and minutes of these meridians are given on the horizontal border of the chart. Put in your Note-Book: A minute of latitude is always a mile, because parallels of latitude are equidistant at all places. A minute of longitude is a mile only on the equator, for the meridians are coming closer to each other as they converge toward either pole. They come together at the North and South poles, and here there is no longitude. * * * * * I can explain this very easily by reference to the following illustration: [Illustration] As every parallel of latitude is a circle of 360° the distance from A to B will be the same number of degrees, minutes and seconds whether measured upon parallel AA' or EE', but it will not be the same number of miles as the meridians of longitude are gradually converging toward the poles. On the other hand, the distances from A to C, C to D, D to E, etc., must be the same because the lines AA', CC', DD', EE' are all parallel. That is why the distance is always measured on the latitude scale (i.e. on the vertical border of the chart), and a minute of latitude is always a mile on the chart, no matter in what locality your ship happens to be. You should be able to understand any kind of information given you on a chart. For instance, what are the various kinds of buoys and how are they marked? Put in your Note-Book: 1. In coming from seaward, red buoys mark the starboard side of the channel, and black buoys the port side. 2. Dangers and obstructions which may be passed on either hand are marked by buoys with red and black horizontal stripes. 3. Buoys indicating the fairway are marked with black and white vertical stripes and should be passed close to. 4. Sunken wrecks are marked by red and black striped buoys described in No. 2. In foreign countries green buoys are frequently used to mark sunken wrecks. 5. Quarantine buoys are yellow. 6. As white buoys have no especial significance, they are frequently used for special purposes not connected with Navigation. 7. Starboard and port buoys are numbered from the seaward end of the channel, the black bearing the odd and red bearing the even numbers. 8. Perches with balls, cages, etc., will, when placed on buoys, be at turning points, the color and number indicating on which side they shall be passed. 9. Soundings in plain white are in fathoms; those on shaded parts are in feet. On large ocean charts fathom curves, showing the range of soundings of 10, 20, 30, 40, etc., fathoms are shown. 10. A light is indicated by a red and yellow spot. F. means fixed, Fl., flashing; Int., intermittent; Rev., revolving, etc. 11. An arrow indicates a current and its direction. The speed is always given. 12. Rocks just under water are shown by a cross surrounded by a dotted circle; rocks above water, by a dotted circle with dots inside it. Practically all charts you will use will be called Mercator charts. Just how they are constructed is a difficult mathematical affair but, roughly, the idea of their construction is based upon the earth being a cylinder, instead of a sphere. Hence, the meridians of longitude, instead of converging at the poles, are parallel lines. This compels the parallels of latitude to be adjusted correspondingly. Although such a chart in any one locality is out of proportion compared with some distant part of the earth's surface, it is nevertheless in proportion for the distance you can travel in a day or possibly a week--and that is all you desire. The Hydrographic Office publishes blank Mercator charts for all latitudes in which they can be used for plotting your position. It makes no difference what longitude you are in for, on a Mercator chart, meridians of longitude are all marked parallel. It makes a great difference, however, what latitude you are in, as in each a mile is of different length on the chart. Hence, it will be impossible for you to correctly plot your course and distance sailed unless you have a chart which shows on it the degrees of latitude in which you are. For instance, if your Mercator chart shows parallels of latitude from 30° to 40° that chart must be used when you are in one of those latitudes. When you move into 41° or 29°, you must be sure to change your plotting chart accordingly. In very high latitudes and near the North pole, the Mercator chart is worthless. How can you steer for the North pole when the meridians of your chart never come together at any pole? For the same reason, bearings of distant objects may be slightly off when laid down on this chart in a straight line. On the whole, however, the Mercator chart answers the mariner's needs so far as all practical purposes are concerned. The instruments used in consulting a chart, i.e., parallel rulers, dividers, etc. have already been described. The only way to lay down a course and read it is by practice. The one important thing to remember in laying down a course, is that what you lay down is a true course. To steam this course yourself, you must make the proper correction for your compass error. Assign for Night Work in Bowditch, Arts. 9-239-240-241-243-244-245-246-247-248-249-251-252-253-254-255-256-257-258. If any time in class room is left, spend it in laying down courses on the chart and reading them; also in answering such questions as these: 1. I desire to sail a true course of NE. My compass error is 2 points Westerly Variation and 1 point Easterly Deviation. What compass course shall I sail? 2. I desire to sail a true course of SW x W. My Variation is 11° W, Deviation 2 pts. W and Leeway 1 pt. starboard. What compass course shall I sail? 3. I desire to sail a true course of 235°. My compass error is 4 pts. E Variation, 27° W Deviation, Leeway 1 pt. port. What compass course shall I sail? 4. I desire to sail a true course of S 65° W. My compass error is 10° E Variation, 3° E Deviation, Leeway 1/4 point starboard. What compass course shall I sail? FRIDAY LECTURE THE PROTRACTOR AND SEXTANT The protractor is an instrument used to shape long courses. There are many kinds. The simplest and the one most in use is merely a piece of transparent celluloid with a compass card printed on it and a string attached to the center of the compass card. To find your course by protractor, put the protractor down on the chart so that the North and South line on the compass card of the protractor will be immediately over a meridian of longitude on the chart, or be exactly parallel to one, and will intersect the point from which you intend to depart. Then stretch your string along the course you desire to steam. Where this string cuts the compass card, will be the direction of your course. Remember, however, that this will be the _true_ course to sail. In order to convert this true course into your compass course, allow for Variation and Deviation according to the rules already given you. In case you know the exact amount of Variation and Deviation at the time you lay down the course--and your course is not far--you can get your compass course in one operation by setting the North point of your protractor as far East or West of the meridian as the amount of your compass error is. By then proceeding as before, the course indicated on the compass card will be the compass course to sail. This method should not be used where your course in one direction is long or where your course is short but in two or more directions. The reason for this is that in both cases, either your Variation or Deviation may change and throw you off. Practically all navigation in strange waters in sight of land and in all waters out of sight of land depends upon the determination of angles. The angle at which a lighthouse is seen from your ship will give you much information that may be absolutely necessary for your safety. The angular altitude of the sun, star or planet does the same. The very heart of Navigation is based upon dealing with angles of all kinds. The instrument, therefore, that measures these angles is the most important of any used in Navigation and you must become thoroughly familiar with it. It is the sextant or some member of the sextant family--such as the quadrant, octant, etc. The sextant is the one most in use and so will be described first. Put in your Note-Book: The sextant has the following parts: (Instructor points to each.) 1. Mirror 2. Telescope 3. Horizon Glass 4. Shade Glasses 5. Back Shade Glasses 6. Handle 7. Sliding Limb 8. Reading Glass 9. Tangent Screw 10. Arc In getting angles of land-marks or buoys, the sextant is held by the handle No. 6 in a horizontal position. The vernier arrow in the sliding limb is set on zero. Now, suppose you wish to get the angular distance between two lighthouses as seen from the bridge of your ship. (Draw diagram.) [Illustration] Look at one lighthouse through the line of sight and true horizon part of the horizon glass. Now, move the sliding limb along the arc gradually until you see the other lighthouse in the reflected horizon of the horizon glass. When one lighthouse in the true horizon is directly on top of the other lighthouse in the reflected horizon, clamp the sliding limb. If any additional adjustment must be made, make it with the tangent screw No. 9. Now look through the reading glass No. 8. You should see that the arc is divided into degrees and sixths of degrees in the following manner: 11° 10° | | -------------+-----------------| | | ----|--+--+--+--+--+--|--+--+--+ | | | | | | | | | | ----+--+--+--+--+--+--+--+--+--+ Now, as every degree is divided into sixty minutes, one-sixth of a degree is 10 minutes. In other words, each of the divisions of a degree on this arc represents 10 minutes. Now on the vernier in the sliding limb, directly under the arc, is the same kind of a division. But these divisions on the vernier represent minutes and sixths of a minute, or 10 seconds. To read the angle, the zero point on the vernier is used as a starting point. If it exactly coincides with one of the lines on the scale of the arc, that line gives the measurement of the angle. In the following illustration the angle is 10-1/2 degrees or 10° 30': 10° 9° ----------------+-----------------------+ | | ---------|---+---+---|---+---+---|---+---+---| | | | | | | | | | | -+---+---+---+---+---+---+---+---+---+---+---+ | | ^ ----+---+---+ 0 If however, you find the zero on the vernier has passed a line of the arc, your angle is more than 10° 30' as in this: 11° 10° ------------+-----------------------+ | | ------------|---+---+---|---+---+---| | | | | | | | ------------+---+---+---+---+---+---+ | | | ^ ------------+---+---+---+ 0 You must then look along the vernier to the left until you find the point where the lines do coincide. Then add the number of minutes and sixths of a minute shown on the vernier between zero and the point where the lines coincide to the number of degrees and minutes shown on the arc at the line which the vernier zero has passed, and the sum will be the angle measured by the instrument. Now in measuring the altitude of the sun or other celestial body, exactly the same process is gone through except that the sextant is held vertically instead of horizontally. You look through the telescope toward that part of the sea directly beneath the celestial body to be observed. You then move the sliding limb until the image of the celestial body appears in the horizon glass, and is made to "kiss" the horizon, i.e., its lowest point just touching the horizon. The sliding limb is then screwed down and the angle read. More about this will be mentioned when we come to Celestial Navigation. Every sextant is liable to be in error. To detect this error there are four adjustments to be made. These adjustments do not need to be learned by heart, but I will mention them: 1. The mirror must be perpendicular to the plane of the arc. To prove whether it is or not, set the vernier on about 60°, and look slantingly through the mirror. If the true and reflected images of the arc coincide, no adjustment is necessary. If not, the glass must be straightened by turning the screws at the back. 2. The horizon glass must be perpendicular to the plane of the arc. Set the vernier on zero and look slantingly through the horizon glass. If the true and reflected horizons show one unbroken line, no adjustment is necessary. If not, turn the screw at the back until they do. 3. Horizon glass and mirror must be parallel. Set the vernier on zero. Hold the instrument vertically and look through the line of sight and horizon glass. If the true and reflected horizons coincide, no adjustment is necessary. If they do not, adjust the horizon glass. 4. The line of sight (telescope) must be parallel to the plane of the arc. This adjustment is verified by observing two stars in a certain way and then performing other operations that are described in Bowditch, Art. 247. Do not try to adjust your sextant yourself. Have it adjusted by an expert on shore. Then, if there is any error, allow for it. An error after adjustment is called the Index Error. Put in your Note-Book: How to find and apply the IE (Index Error): Set the sliding limb at zero on the arc, hold the instrument perpendicularly and look at the horizon. Move the sliding limb forward or backward slowly until the true horizon and reflected horizon form one unbroken line. Clamp the limb and read the angle. This is the IE. If the vernier zero is to the left of the zero on the arc, the IE is minus and it is to be subtracted from any angle you read, to get the correct angle. If the vernier zero is to the right of the zero on the arc, the IE is plus and is to be added to any angle you read to get the correct angle. Index error is expressed thus: IE + 2' 30" or IE - 2' 30". Quadrants, octants and quintants work on exactly the same principles as the sextant, except that the divisions on the arc and the vernier differ in number from the sixth divisions on the arc and vernier of the sextant. If any time is left, spend it in marking courses with the protractor and handling the sextant. Assign for Night Work the following Arts. in Bowditch: 134-135-136-138-142-144-145-151-152-157-158-159-160-161-162-163. SATURDAY LECTURE FIXES, ANGLES BY BEARINGS AND SEXTANT There are five good ways of fixing your position (obtaining a "fix," as it is called) providing you are within sight of landmarks which you can identify or in comparatively shoal water. Put in your Note-Book: 1. Cross bearings of two known objects. 2. Bearing and distance of a known object, the height of which is known. 3. Two bearings of a known object separated by an interval of time, with a run during that interval. 4. Sextant angles between three known objects. 5. Using the compass, log and lead in a fog or in unfamiliar waters. 1. Cross bearings of two known objects. Select two objects marked on the chart, so far apart that each will bear about 45° off your bow but in opposite directions. These bearings will be secured in the best way by the use of your pelorus. Correct each bearing for Variation and Deviation so that it will be a true bearing. Then with the parallel rulers carry the bearing of one object from the chart compass card until you can intersect the object itself and draw a line through it. Do exactly the same with the other object. Where the two lines intersect, will be the position of the ship at the time the bearings were taken. [Illustration] Now supposing you wish to find the latitude and longitude of that position of the ship. For the latitude, measure the distance of the place from the nearest parallel with the dividers. Take the dividers to the latitude scale at the side of the chart and put one point of them on the same parallel. Where the other point touches on the latitude scale, will be the latitude desired. For the longitude, do exactly the same thing, but use a meridian of longitude instead of a parallel of latitude and read from the longitude scale at the top or bottom of the chart instead of from the side. 2. Bearing and distance of a known object, the height of which is known. Take a bearing of, say, a lighthouse the height of which is known. The height of all lighthouses on the Atlantic Coast can be found in a book published by the U.S. Dept. of Commerce. Correct the bearing, as mentioned in case No. 1. Now read the angle of the height of that light by using your sextant. Do this by putting the vernier 0 on the arc 0, sliding the limb slowly forward until the top of the lighthouse in the reflected horizon just touches the bottom of the lighthouse in the true horizon. With this angle and the known height of the light, enter Table 33 in Bowditch. At the left of the Table will be found the distance off in knots. This method can be used with any fairly perpendicular object, the height of which is known and which is not more than 5 knots away, as Table 33 is not made out for greater distances. 3. Two bearings of the same object, separated by an interval of time and with a run during that interval. Take a compass bearing of some prominent object when it is either 2, 3 or 4 points off the bow. Take another bearing of the same object when it is either 4, 6 or 8 points off the bow. The distance run by the ship between the two bearings will be her distance from the observed object at the second bearing. "The distance run is the distance off." A diagram will show clearly just why this is so: [Illustration] The ship at A finds the light bearing NNW 2 points off her bow. At B, when the light bears NW and 4 points off, the log registers the distance from A to B 9 miles. 9 miles, then, will be the distance from the light itself when the ship is at B. The mathematical reason for this is that the distance run is one side of an isosceles triangle. Such triangles have their two sides of equal length. For that reason, the distance run is the distance off. Now the same fact holds true in running from B, which is 4 points off the bow, to C, which is 8 points off the bow, or directly abeam. The log shows the distance run between B and C is 6.3 miles. Hence, the ship is 6.3 miles from the light when directly abeam of it. This last
{'title': 'Lectures in Navigation by Ernest Gallaudet Draper', 'source': 'Project Gutenberg', 'lang': 'en'}