`
`THE
`AMERICAN
`PRACTICAL NAVIGATOR
`
`AN EPITOME OF NAVIGATION
`
`ORIGINALLY BY
`NATHANIEL BOWDITCH, LL.D.
`
`2002 BICENTENNIAL EDITION
`
`Prepared and published by the
`NATIONAL IMAGERY AND MAPPING AGENCY
`Bethesda, Maryland
`
`© COPYRIGHT 2002 BY THE NATIONAL IMAGERY AND MAPPING AGENCY, U. S. GOVERNMENT.
`NO DOMESTIC COPYRIGHT CLAIMED UNDER TITLE 17 U.S.C. ALL RIGHTS RESERVED.
`
`*7642014014652*
`NSN 7642014014652
`NIMA REF. NO. NVPUB9V1
`For sale by the Superintendant of Documents, U.S. Government Printing Office
`Internet: bookstore.gpo.gov Phone: toll free (866) 512-1800; DC area (202) 512-1800
`Fax: (202) 512-2250 Mail Stop: SSOP, Washington, DC 20402-0001
`
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`Last painting by Gilbert Stuart (1828). Considered by the family of Bowditch to be the best of
`various paintings made, although it was unfinished when the artist died.
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`NATHANIEL BOWDITCH
`(1773-1838)
`
`Nathaniel Bowditch was born on March 26, 1773, in
`Salem, Mass., fourth of the seven children of shipmaster
`Habakkuk Bowditch and his wife, Mary.
`Since the migration of William Bowditch from
`England to the Colonies in the 17th century, the family had
`resided at Salem. Most of its sons, like those of other
`families in this New England seaport, had gone to sea, and
`many of them became shipmasters. Nathaniel Bowditch
`himself sailed as master on his last voyage, and two of his
`brothers met untimely deaths while pursuing careers at sea.
`Nathaniel Bowditch’s father is said to have lost two
`ships at sea, and by late Revolutionary days he returned to
`the trade of cooper, which he had learned in his youth. This
`provided insufficient income to properly supply the needs
`of his growing family, who were often hungry and cold. For
`many years the nearly destitute family received an annual
`grant of 15 to 20 dollars from the Salem Marine Society. By
`the time Nathaniel had reached the age of 10, the family’s
`poverty forced him to leave school and join his father in the
`cooper’s trade to help support the family.
`Nathaniel was unsuccessful as a cooper, and when he
`was about 12 years of age, he entered the first of two ship-
`chandlery firms by which he was employed. It was during
`the nearly 10 years he was so employed that his great mind
`first attracted public attention. From the time he began
`school Bowditch had an all-consuming interest in learning,
`particularly mathematics. By his middle teens he was recog-
`nized in Salem as an authority on that subject. Salem being
`primarily a shipping town, most of the inhabitants sooner or
`later found their way to the ship chandler, and news of the
`brilliant young clerk spread until eventually it came to the
`attention of the learned men of his day. Impressed by his de-
`sire to educate himself, they supplied him with books that he
`might learn of the discoveries of other men. Since many of
`the best books were written by Europeans, Bowditch first
`taught himself their languages. French, Spanish, Latin,
`Greek and German were among the two dozen or more lan-
`guages and dialects he studied during his life. At the age of
`16 he began the study of Newton’s Principia, translating
`parts of it from the Latin. He even found an error in that clas-
`sic text, and though lacking the confidence to announce it at
`the time, he later published his findings and had them ac-
`cepted by the scientific community.
`During the Revolutionary War a privateer out of Beverly,
`a neighboring town to Salem, had taken as one of its prizes an
`English vessel which was carrying the philosophical library of
`a famed Irish scholar, Dr. Richard Kirwan. The books were
`brought to the Colonies and there bought by a group of
`educated Salem men who used them to found the
`
`Philosophical Library Company, reputed to have been the best
`library north of Philadelphia at the time. In 1791, when
`Bowditch was 18, two Harvard-educated ministers, Rev. John
`Prince and Rev. William Bentley, persuaded the Company to
`allowBowditchtheuseofitslibrary.Encouragedbythesetwo
`men and a third, Nathan Read, an apothecary and also a
`Harvard man, Bowditch studied the works of the great men
`who had preceded him, especially the mathematicians and the
`astronomers. By the time he became of age, this knowledge,
`acquired when not working long hours at the chandlery, had
`made young Nathaniel the outstanding mathematician in the
`Commonwealth, and perhaps in the country.
`In the seafaring town of Salem, Bowditch was drawn
`to navigation early, learning the subject at the age of 13
`from an old British sailor. A year later he began studying
`surveying, and in 1794 he assisted in a survey of the town.
`At 15 he devised an almanac reputed to have been of great
`accuracy. His other youthful accomplishments included the
`construction of a crude barometer and a sundial.
`When Bowditch went to sea at the age of 21, it was as
`captain’s writer and nominal second mate, the officer’s berth
`beingofferedhimbecauseofhisreputationasascholar.Under
`Captain Henry Prince, the ship Henry sailed from Salem in the
`winter of 1795 on what was to be a year-long voyage to the Ile
`de Bourbon (now called Reunion) in the Indian Ocean.
`Bowditch began his seagoing career when accurate time
`was not available to the average naval or merchant ship. A
`reliable marine chronometer had been invented some 60
`years before, but the prohibitive cost, plus the long voyages
`without opportunity to check the error of the timepiece, made
`the large investment an impractical one. A system of
`determining longitude by “lunar distance,” a method which
`did not require an accurate timepiece, was known, but this
`productof theminds ofmathematicians andastronomers was
`so involved as to be beyond the capabilities of
`the
`uneducated seamen of that day. Consequently, ships were
`navigated by a combination of dead reckoning and parallel
`sailing(asystemofsailingnorthorsouthtothelatitudeofthe
`destination and then east or west to the destination). The
`navigational routine of the time was “lead, log, and lookout.”
`To Bowditch, the mathematical genius, computation of
`lunar distances was no mystery, of course, but he
`recognized the need for an easier method of working them
`in order to navigate ships more safely and efficiently.
`Through analysis and observation, he derived a new and
`simplified formula during his first trip.
`John Hamilton Moore’s The Practical Navigator was
`the leading navigational text when Bowditch first went to
`sea, and had been for many years. Early in his first voyage,
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`however, the captain’s writer-second mate began turning
`up errors in Moore’s book, and before long he found it
`necessary to recompute some of the tables he most often
`used in working his sights. Bowditch recorded the errors he
`found, and by the end of his second voyage, made in the
`higher capacity of supercargo, the news of his findings in
`The New Practical Navigator had reached Edmund Blunt,
`a printer at Newburyport, Mass. At Blunt’s request,
`Bowditch agreed to participate with other learned men in
`the preparation of an American edition of the thirteenth
`(1798) edition of Moore’s work. The first American edition
`was published at Newburyport by Blunt in 1799. This
`edition corrected many of the errors that Moore had
`included.
`Although most of the errors were of little significance
`to practical navigation because they were errors in the fifth
`and sixth places of logarithm tables, some errors were
`significant.The most significant mistake was listing the
`year 1800 as a leap year in the table of the sun’s declination.
`The consequence was that Moore gave the declination for
`March 1, 1800, as 7°11'. Since the actual value was 7° 33',
`the calculation of a meridian altitude would be in error by
`22 minutes of latitude, or 22 nautical miles.
`Bowditch’s principal contribution to the first American
`edition was his chapter “The Method of Finding the
`Longitude at Sea,” which discussed his new method for
`computing lunar distances. Following publication of the first
`American edition, Blunt obtained Bowditch’s services in
`checking the American and English editions for further
`errors. Blunt then published a second American edition of
`Moore’s thirteenth edition in 1800. When preparing a third
`American edition for the press, Blunt decided that Bowditch
`had revised Moore’s work to such an extent that Bowditch
`should be named as author. The title was changed to The
`New American Practical Navigator and the book was
`published in 1802 as a first edition. Bowditch vowed while
`writing this edition to “put down in the book nothing I can’t
`teach the crew,” and it is said that every member of his crew
`including the cook could take a lunar observation and plot
`the ship’s position.
`Bowditch made a total of five trips to sea, over a period
`of about nine years, his last as master and part owner of the
`three-masted Putnam. Homeward bound from a 13-month
`voyage to Sumatra and the Ile de France (now called
`Mauritius)
`the Putnam approached Salem harbor on
`December 25, 1803, during a thick fog without having had
`a celestial observation since noon on the 24th. Relying
`upon his dead reckoning, Bowditch conned his wooden-
`hulled ship to the entrance of the rocky harbor, where he
`had the good fortune to get a momentary glimpse of Eastern
`Point, Cape Ann, enough to confirm his position. The
`Putnam proceeded in, past such hazards as “Bowditch’s
`Ledge” (named after a great-grandfather who had wrecked
`his ship on the rock more than a century before) and
`anchored safely at 1900 that evening. Word of the daring
`
`feat, performed when other masters were hove-to outside
`the harbor, spread along the coast and added greatly to
`Bowditch’s reputation. He was,
`indeed,
`the “practical
`navigator.”
`His standing as a mathematician and successful
`shipmaster earned him a well-paid position ashore within a
`matter of weeks after his last voyage. He was installed as
`president of a Salem fire and marine insurance company at
`the age of 30, and during the 20 years he held that position
`the company prospered. In 1823 he left Salem to take a
`similar position with a Boston insurance firm, serving that
`company with equal success until his death.
`From the time he finished the “Navigator” until 1814,
`Bowditch’s mathematical and scientific pursuits consisted of
`studies and papers on the orbits of comets, applications of
`Napier’s rules, magnetic variation, eclipses, calculations on
`tides,andthechartingofSalemharbor.Inthatyear,however,he
`turned to what he considered the greatest work of his life, the
`translation into English of Mecanique Celeste, by Pierre
`Laplace. Mecanique Celeste was a summary of all the then
`known facts about the workings of the heavens. Bowditch
`translated four of the five volumes before his death, and
`published them at his own expense. He gave many formula
`derivations which Laplace had not shown, and also included
`further discoveries following the time of publication. His work
`made this information available to American astronomers and
`enabled them to pursue their studies on the basis of that which
`was already known. Continuing his style of writing for the
`learner, Bowditch presented his English version of Mecanique
`Celeste in such a manner that the student of mathematics could
`easily trace the steps involved in reaching the most complicated
`conclusions.
`Shortly after the publication of The New American
`Practical Navigator, Harvard College honored its author
`with the presentation of the honorary degree of Master of
`Arts, and in 1816 the college made him an honorary Doctor
`of Laws. From the time the Harvard graduates of Salem first
`assisted him in his studies, Bowditch had a great interest in
`that college, and in 1810 he was elected one of its Overseers,
`a position he held until 1826, when he was elected to the
`Corporation. During 1826-27 he was the leader of a small
`groupofmenwhosavedtheschoolfromfinancialdisasterby
`forcing necessary economies on the college’s reluctant
`president. At one time Bowditch was offered a Professorship
`in Mathematics at Harvard but this, as well as similar offers
`from West Point and the University of Virginia, he declined.
`In all his life he was never known to have made a public
`speech or to have addressed any large group of people.
`Many other honors came to Bowditch in recognition of
`his
`astronomical,
`mathematical,
`and
`marine
`accomplishments. He became a member of the American
`Academy of Arts and Sciences, the East India Marine
`Society,
`the Royal Academy of Edinburgh,
`the Royal
`Society of London, the Royal Irish Academy, the American
`Philosophical Society, the Connecticut Academy of Arts
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`the Royal
`the Boston Marine Society,
`and Sciences,
`Astronomical Society, the Palermo Academy of Science,
`and the Royal Academy of Berlin.
`Nathaniel Bowditch outlived all of his brothers and
`sisters by nearly 30 years. He died on March 16, 1838, in
`his sixty-fifth year. The following eulogy by the Salem
`Marine Society indicates the regard in which this distin-
`guished American was held by his contemporaries:
`“In his death a public, a national, a human benefactor has
`departed. Not this community, nor our country only, but the
`
`whole world, has reason to do honor to his memory. When the
`voice of Eulogy shall be still, when the tear of Sorrow shall
`cease to flow, no monument will be needed to keep alive his
`memory among men; but as long as ships shall sail, the needle
`point to the north, and the stars go through their wonted
`courses in the heavens, the name of Dr. Bowditch will be
`reveredasofonewhohelpedhisfellow-meninatimeofneed,
`who was and is a guide to them over the pathless ocean, and of
`one who forwarded the great interests of mankind.”
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`Original title page of The New American Practical Navigator, First Edition, published in 1802.
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`PREFACE
`
`The Naval Observatory library in Washington, D.C., is
`unnaturally quiet. It is a large circular room, filled with
`thousands of books. Its acoustics are perfect; a mere
`whisper from the room’s open circular balcony can be
`easily heard by those standing on the ground floor. A
`fountain in the center of the ground floor softly breaks the
`room’s silence as its water stream gently splashes into a
`small pool. From this serene room, a library clerk will lead
`you into an antechamber, beyond which is a vault
`containing the Observatory’s most rare books. In this vault,
`one can find an original 1802 first edition of the New
`American Practical Navigator.
`One cannot hold this small, delicate, slipcovered book
`without being impressed by the nearly 200-year unbroken
`chain of publication that it has enjoyed. It sailed on U.S.
`merchantmen and Navy ships shortly after the quasi-war
`with France and during British impressment of merchant
`seamen that led to the War of 1812. It sailed on U.S. Naval
`vessels during operations against Mexico in the 1840’s, on
`ships of both the Union and Confederate fleets during the
`Civil War, and with the U.S. Navy in Cuba in 1898. It went
`around the world with the Great White Fleet, across the
`North Atlantic to Europe during both World Wars, to Asia
`during the Korean and Vietnam Wars, and to the Middle
`East during Operation Desert Storm. It has circled the globe
`with countless thousands of merchant ships for 200 years.
`As navigational requirements and procedures have
`changed throughout the years, Bowditch has changed with
`them. Originally devoted almost exclusively to celestial
`navigation, it now also covers a host of modern topics. It is
`as practical today as it was when Nathaniel Bowditch,
`master of the Putnam, gathered the crew on deck and taught
`them the mathematics involved in calculating lunar
`distances.
`It
`is
`that practicality that has been the
`publication’s greatest
`strength, and that makes
`the
`publication as useful today as it was in the age of sail.
`Seafarers have long memories. In no other profession
`is tradition more closely guarded. Even the oldest and most
`cynical acknowledge the special bond that connects those
`who have made their livelihood plying the sea. This bond is
`not comprised of a single strand; rather, it is a rich and
`varied tapestry that stretches from the present back to the
`birth of our nation and its seafaring culture. As this book is
`a part of that tapestry, it should not be lightly regarded;
`rather, it should be preserved, as much for its historical
`importance as for its practical utility.
`Since antiquity, mariners have gathered available
`navigation information and put it into a text for others to
`follow. One of the first attempts at this involved volumes of
`
`Spanish and Portuguese navigational manuals translated
`into English between about 1550 to 1750. Writers and
`translators of the time “borrowed” freely in compiling
`navigational texts, a practice which continues today with
`works such as Sailing Directions and Pilots.
`Colonial and early American navigators depended
`exclusively on English navigation texts because there were
`no American editions. The first American navigational text,
`Orthodoxal Navigation, was completed by Benjamin
`Hubbard in 1656. The first American navigation text
`published in America was Captain Thomas Truxton’s
`Remarks, Instructions, and Examples Relating to the
`Latitude and Longitude; also the Variation of the Compass,
`Etc., Etc., published in 1794.
`The most popular navigational text of the late 18th
`century was John Hamilton Moore’s The New Practical
`Navigator. Edmund M. Blunt, a Newburyport publisher,
`decided to issue a revised copy of this work for American
`navigators. Blunt convinced Nathaniel Bowditch, a locally
`famous mariner and mathematician, to revise and update
`The New Practical Navigator. Several other learned men
`assisted in this revision. Blunt’s The New Practical
`Navigator was published in 1799. Blunt also published a
`second American edition of Moore’s book in 1800.
`By 1802, when Blunt was ready to publish a third
`edition, Nathaniel Bowditch and others had corrected so
`many errors in Moore’s work that Blunt decided to issue the
`work as a first edition of the New American Practical
`Navigator. It is to that 1802 work that the current edition of
`the American Practical Navigator traces its pedigree.
`The New American Practical Navigator stayed in the
`Bowditch and Blunt family until the government bought the
`copyright in 1867. Edmund M. Blunt published the book
`until 1833; upon his retirement, his sons, Edmund and
`George, took over publication.The elder Blunt died in
`1862; his son Edmund followed in 1866. The next year,
`1867, George Blunt sold the copyright to the government
`for $25,000. The government has published Bowditch ever
`since. George Blunt died in 1878.
`Nathaniel Bowditch continued to correct and revise the
`book until his death in 1838. Upon his death, the editorial
`responsibility for the American Practical Navigator passed
`to his son, J. Ingersoll Bowditch. Ingersoll Bowditch
`continued editing the Navigator until George Blunt sold the
`copyright to the government. He outlived all of the principals
`involved in publishing and editing the Navigator, dying in
`1889.
`The U.S. government has published some 52 editions
`since acquiring the copyright to the book that has come to
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`author’s name,
`be known simply by its original
`“Bowditch.” Since the government began production, the
`book has been known by its year of publishing, instead of
`by the edition number. During a revision in 1880 by
`Commander Phillip H. Cooper, USN,
`the name was
`changed to American Practical Navigator. Bowditch’s
`original method of taking “lunars” was finally dropped
`from the book just after the turn of the 20th century. After
`several more revisions and printings through World Wars I
`and II, Bowditch was extensively revised for the 1958
`edition and again in 1995.
`Recognizing the limitations of the printed word, and that
`computers and electronic media permit us to think about the
`processes of both navigation and publishing in completely
`newways,NIMAhas,forthe2002edition,producedthefirst
`official Compact Disk-Read Only Memory (CD-ROM)
`version of this work. This CD contains, in addition to the full
`text of the printed book, electronic enhancements and
`additions not possible in book form. Our goal is to put as
`much useful navigational information before the navigator as
`possible in the most understandable and readable format. We
`are only beginning to explore the possibilities of new
`technology in this area.
`As much as it is a part of history, Bowditch is not a
`history book. As in past editions, dated material has been
`droppedand newmethods,technologiesand techniquesadded
`to keep pace with the rapidly changing world of navigation.
`The changes to this edition are intended to ensure that it
`remains the premier reference work for modern, practical
`marine navigation. This edition replaces but does not cancel
`former editions, which may be retained and consulted as to
`historical navigation methods not discussed herein.
`
`PART 1, FUNDAMENTALS, includes an overview of
`the types and phases of marine navigation and the organi-
`zations which develop, support and regulate it. It includes
`chapters relating to the types, structure, use and limitations of
`nautical charts; a concise explanation of geodesy and chart
`datums; and a summary of various necessary navigational
`publications.
`PART 2, PILOTING, emphasizes the practical aspects
`of navigating a vessel in restricted waters, using both
`traditional and electronic methods.
`PART 3, ELECTRONIC NAVIGATION, explains the
`nature of radio waves and electronic navigation systems.
`Chapters deal with each of the several electronic methods
`of navigation--satellite, Loran C, and radar, with special
`emphasis on satellite navigation systems and electronic
`charts.
`PART 4, CELESTIAL NAVIGATION, updates the
`former edition with more modern terminology, and discusses
`
`the use of calculators and computers for the solution of celestial
`navigation problems.
`PART 5, NAVIGATIONAL MATHEMATICS,
`remains unchanged from the former edition.
`PART 6, NAVIGATIONAL SAFETY, discusses recent
`developments in management of navigational resources, the
`changing role of the navigator, distress and safety communi-
`cations, procedures for emergency navigation, and the
`increasingly complex web of navigation regulations.
`PART 7, OCEANOGRAPHY, has been updated to
`reflect the latest science and terminology.
`PART 8, MARINE WEATHER incorporates
`updated weather routing information and new cloud
`graphics.
`
`Thepronoun“he,”usedthroughoutthisbookasareference
`to the navigator, refers to both genders.
`The printed version of this volume may be corrected
`using the Notice to Mariners and Summary of Corrections.
`Suggestions and comments for changes and additions may
`be sent to:
`NATIONAL IMAGERY AND MAPPING AGENCY
`MARITIME SAFETY INFORMATION DIVISION
`MAIL STOP D-44
`4600 SANGAMORE RD.
`BETHESDA, MARYLAND, 20816-5003
`UNITED STATES OF AMERICA
`
`This book could not have been produced without the
`expertise of dedicated personnel from many government
`organizations, among them: U.S. Coast Guard, U.S. Naval
`Academy, U.S. Naval Oceanographic Office, US Navy
`Fleet Training Center, the U.S. Naval Observatory, Office
`of the Navigator of the Navy, U.S. Merchant Marine
`Academy, U.S. Coast and Geodetic Survey, the National
`Ocean Service, and the National Weather Service. In
`addition to official government expertise, we must note the
`contributions of private organizations and individuals far
`too numerous to mention. Mariners worldwide can be
`grateful for the experience, dedication, and professionalism
`of the many people who generously gave their time in this
`effort. A complete list of contributors can be found in the
`“Contributor’s Corner” of the CD-ROM version of this
`book.
`
`THE EDITORS
`
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`TABLE OF CONTENTS
`
`NATHANIEL BOWDITCH ........................................................................................................................................... iii
`PREFACE ................................................................................................................................................................... vii
`
`PART 1 — FUNDAMENTALS
`CHAPTER 1.
`INTRODUCTION TO MARINE NAVIGATION ...........................................................................1
`CHAPTER 2.
`GEODESY AND DATUMS IN NAVIGATION ...........................................................................15
`CHAPTER 3.
`NAUTICAL CHARTS ...................................................................................................................23
`CHAPTER 4.
`NAUTICAL PUBLICATIONS ......................................................................................................51
`
`PART 2 — PILOTING
`CHAPTER 5.
`SHORT RANGE AIDS TO NAVIGATION ..................................................................................63
`CHAPTER 6.
`COMPASSES .................................................................................................................................81
`CHAPTER 7.
`DEAD RECKONING .....................................................................................................................99
`CHAPTER 8.
`PILOTING ....................................................................................................................................105
`CHAPTER 9.
`TIDES AND TIDAL CURRENTS ...............................................................................................129
`
`PART 3 — ELECTRONIC NAVIGATION
`CHAPTER 10. RADIO WAVES ...........................................................................................................................151
`CHAPTER 11.
`SATELLITE NAVIGATION .......................................................................................................163
`CHAPTER 12. LORAN NAVIGATION ...............................................................................................................173
`CHAPTER 13. RADAR NAVIGATION ..............................................................................................................187
`CHAPTER 14. ELECTRONIC CHARTS .............................................................................................................199
`
`PART 4 — CELESTIAL NAVIGATION
`CHAPTER 15. NAVIGATIONAL ASTRONOMY ..............................................................................................217
`CHAPTER 16.
`INSTRUMENTS FOR CELESTIAL NAVIGATION .................................................................261
`CHAPTER 17. AZIMUTHS AND AMPLITUDES ..............................................................................................271
`CHAPTER 18. TIME .............................................................................................................................................275
`CHAPTER 19. THE ALMANACS .......................................................................................................................287
`CHAPTER 20.
`SIGHT REDUCTION ...................................................................................................................295
`
`PART 5 — NAVIGATIONAL MATHEMATICS
`CHAPTER 21. NAVIGATIONAL MATHEMATICS ..........................................................................................317
`CHAPTER 22. CALCULATIONS AND CONVERSIONS .................................................................................329
`CHAPTER 23. NAVIGATIONAL ERRORS .......................................................................................................341
`CHAPTER 24. THE SAILINGS ............................................................................................................................345
`
`PART 6 — NAVIGATIONAL SAFETY
`CHAPTER 25. NAVIGATION PROCESSES ......................................................................................................363
`CHAPTER 26. EMERGENCY NAVIGATION ...................................................................................................373
`CHAPTER 27. NAVIGATION REGULATIONS ................................................................................................383
`CHAPTER 28. MARITIME SAFETY SYSTEMS ...............................................................................................393
`CHAPTER 29. HYDROGRAPHY ........................................................................................................................409
`
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`PART 7 — OCEANOGRAPHY
`CHAPTER 30.
`THE OCEANS ........................................................................................................................... 425
`CHAPTER 31.
`OCEAN CURRENTS ................................................................................................................ 433
`CHAPTER 32. WAVES, BREAKERS AND SURF ..........................................................................................441
`CHAPTER 33.
`ICE NAVIGATION ................................................................................................................... 453
`
`PART 8 — MARINE METEOROLOGY
`CHAPTER 34. WEATHER ELEMENTS ..........................................................................................................481
`CHAPTER 35.
`TROPICAL CYCLONES ..........................................................................................................503
`CHAPTER 36. WEATHER OBSERVATIONS .................................................................................................519
`CHAPTER 37. WEATHER ROUTING .............................................................................................................545
`
`NAVIGATION TABLES
`
`EXPLANATION OF NAVIGATION TABLES .......................................................................................................557
`MATHEMATICAL TABLES
`TABLE 1.
`LOGARITHMS OF NUMBERS ...............................................................................................565
`TABLE 2.
`NATURAL TRIGONOMETRIC FUNCTIONS .......................................................................575
`TABLE 3.
`COMMON LOGARITHMS OF TRIGONOMETRIC FUNCTIONS ......................................598
`TABLE 4.
`TRAVERSE TABLES ...............................................................................................................621
`CARTOGRAPHIC TABLES
`TABLE 5.
`NATURAL AND NUMERICAL CHART SCALES ...............................................................666
`TABLE 6.
`MERIDIONAL PARTS .............................................................................................................667
`TABLE 7.
`LENGTH OF A DEGREE OF LATITUDE AND LONGITUDE ............................................672
`PILOTING TABLES
`TABLE 8.
`CONVERSION TABLE FOR METERS, FEET, AND FATHOMS ........................................673
`TABLE 9.
`CONVERSION TABLE FOR NAUTICAL AND STATUTE MILES .....................................674
`TABLE 10.
`SPEED TABLE FOR MEASURED MILE ...............................................................................675
`TABLE 11.
`SPEED, TIME, AND DISTANCE ............................................................................................676
`TABLE 12.
`DISTANCE OF THE HORIZON ..............................................................................................679
`TABLE 13.
`GEOGRAPHIC RANGE ...........................................................................................................680
`TABLE 14.
`DIP OF THE SEA SHORT OF THE HORIZON ......................................................................682
`TABLE 15.
`DISTANCE BY VERTICAL ANGLE MEASURED BETWEEN SEA HORIZON
`AND TOP OF OBJECT BEYOND SEA HORIZON ................................................................683
`TABLE 16.
`DISTANCE BY VERTICAL ANGLE MEASURED BETWEEN WATERLINE
`AT OBJECT AND TOP OF OBJECT .......................................................................................685
`TABLE 17.
`DISTANCE BY VERTICAL ANGLE MEASURED BETWEEN WATERLINE
`AT OBJECT AND SEA HORIZON BEYOND OBJECT ........................................................687
`TABLE 18.
`DISTANCE OF AN OBJECT BY TWO BEARINGS ..............................................................688
`x
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`IPR2017-00946
`Garmin EX2001 Page 10
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`
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`CELESTIAL NAVIGATION TABLES
`TABLE 19.
`TABLE OF OFFSETS ..................................................................................................................691
`TABLE 20.
`MERIDIAN ANGLE AND ALTITUDE OF A BODY ON THE PRIME
`VERTICAL CIRCLE ....................................................................................................................692
`TABLE 21.
`LATITUDE AND LONGITUDE FACTORS ..............................................................................694
`AMPLITUDES .............