the Dark Ages some
Moslem cartographers as well as astronomers took inspiration from
Ptolemy. However, they knew that Ptolemy had overestimated the length
of the Mediterranean by some 200. Charts of the Indian Ocean, bearing
horizontal lines indicating parallels of latitude, and
vertical lines dividing the seas according
to the direction of the wind, were drawn by Persian and
Arabian navigators. The prime meridian separated a
windward from a leeward region and other meridians were drawn at
indicating "three hours sail." This information, though far from exact,
was helpful to the sailing ship masters.
Figure 109c. Ortelius' atlas Theatrum
was published at Antwerp in 1570. One of the most magnificent ever
produced, it illustrates Europe, Africa, and Asia with com-parative
accuracy. North and South America are poorly depicted, but Magellan's
Strait is shown. All land to the south of it, as well as Australia, is
considered part of Terra Australis Nondum Cognita (fig. 109c).
Mercator projection (art. 305). For hundreds, perhaps' thousands, of
years cartographers drew their charts as "plane" projections, making no
use of the discoveries of Ptolemy and Hipparchus. As the area of the
known world increased, however, the attempt to depict that larger area
on the flat surface of the plane chart brought map makers to the
realization that allowance would have to be made for the curvature of
Gerardus Mercator (Latinized form of Gerhard
Kremer) was a brilliant Flemish geographer who recognized the need for
a better method of chart projection. In 1569 he published a world chart
which he had constructed on the principle since known b y his name. The
theory of his work was correct, but Mercator made errors in his
computation, and because he never published a complete description of
the mathematics involved, mariners were deprived of the full advantages
of the projection for another 30 years.
Then Edward Wright
published the results of his own independent study in the matter,
explaining the Mercator projection fully and providing the table of
meridional parts which enabled all cartographers to make use of the
Wright was a mathematician at Carus College who
developed the method and table and gave them totertain navigators for
testing. After these proved their usefulness, Wright decided upon
publication, and in 1599 Certaine
Errors in Navigation Detected and Corrected
The Lambert projections.
Johann Heinrich Lambert, 1728-1777, self-educated son of an Alsace
tailor, designed a number of map projections. Some of these are still
widely used, the most renowned being the Lambert conformal (art. 314).
110. Sailing directions.
— From earliest times there has been a demand for knowledge of what lay
ahead, and this gave rise to the early development of sailing
of Scylax, written sometime between
the sixth and fourth centuries BC, is the earliest known book of this
type. Surprisingly similar to modern sailing directions, it provided
the mariner with information on distances between ports, aids and
dangers, port facilities, and other pertinent matters. The following
excerpt is typical:
Libya begins beyond the
Canopic mouth of the Nile. . . . The first people in Libya are the
Adrymachidae. From Thonis the voyage to Pharos, a desert island (good
harbourage but no drinking water), is 150 stadia. In Pharos are many
harbors. But ships water at the Marian Mere, for it is drinkable. . . .
The mouth of the bay of Plinthine to Leuce Acte (the white beach) is a
day and night's sail; but sailing round by the head of the bay of
Plinthine is twice as long.
Parts Around the World
Pytheas' book of observations made during his epic voyage in the fourth
century BO, was another early volume of sailing directions. His rough
estimates of distances and descriptions of coast lines would be
considered crude today, but they served as an invaluable aid to
navigators who followed him into these otherwise unknown waters.
during the Renaissance.
No particularly noteworthy improvements were made in sailing directions
during the Middle Ages, but in 1490 the Portolano Rizo was published,
the first of a series of improved design. Other early volumes of this
kind appeared in France and were called "routiers" — the rutters of the
English sailor. In 1557 the Italian pilot Battista Testa Rossa
Compendio del Arte del Navigar
which was designed to serve the mariner on soundings and off. It
forecast the single, all-inclusive volume that was soon to come, the
About. 1584 the Dutch pilot Lucas Jans Loon
Waghenaer published a volume of navigational principles, tables,
charts, and sailing directions which served as a guide for such books
for the next 200 years. In Speighel
(The Mariner's Mirror), Waghenaer gave directions and charts for
sailing the waters of the Low Countries and later a second volume was
published covering waters of the North and Baltic seas.
met with great success and in 1588 an English translation of the
original book was made by Anthony Ashley. During the next 30 years, 24
editions of the book were published in Dutch, German, Latin, and
English. Other authors followed the profitable example set by
Waghenaer, and American, British, and French navigators soon had
"Waggoners" for most of the waters they sailed.
The success of
these books and the resulting competition among authors were
responsible for their eventual discontinuance. Each writer attempted to
make his work more inclusive than any other (the 1780 Atlantic Neptune
contained 257 charts of North : America alone) and the result was a
tremendous book difficult to handle. They were too bulky, the sailing
directions were unnecessarily detailed, and the charts too large. In
1795 the British Hydrographic Department was established, and charts
and sailing directions were issued separately. The latter, issued for
specific waters, were returned to the form of the original Periplus
The publication of modern sailing directions by the U.S. Navy
Hydrographic Office is one of the achievements properly attributed to
Matthew Fontaine Maury. During the two decades he headed the
institution, Maury gathered data that led directly to the publication
of eight volumes of sailing directions. Today there are more than 70
volumes providing the mariner with detailed information on almost all
foreign coasts, in addition to ten volumes of coast pilots of the
United States and its possessions, published by the U.S. Coast and
111. The compass.
— Early in the history of navigation man noted that the pole star (it
may have been a Draconis then) remained close to one point in the
northern sky. This served as his compass. When it was not visible, he
used other stars, the sun and moon, winds, clouds, and waves. The
development of the magnetic compass, perhaps a thousand years ago, and
the 20th century development of the gyro compass, offer today's
navigator a method of steering his course with an accuracy as great as
he is capable of using.
The magnetic compass (art. 623) is one
of the oldest of the navigator's instruments. Its origin is not known.
In 203 BC, when Hannibal set sail from Italy, his pilot was said to be
one Pelorus. Perhaps the compass was in use then; no one can
for certain that it was not. There is little to substantiate the story
that the Chinese invented it, and the legend that Marco Polo introduced
it into Italy in the 13th century is almost certainly false. It is
sometimes stated that the Arabs brought it to Europe, but this, too, is
unlikely. Probably it was known first in the west. The Norsemen of the
11th century were familiar with it, and about 1200 a compass used by
mariners when the pole star was hidden was described by a French poet,
Guyot de Provins.
A needle thrust through a straw and floated
in water in a container comprised the earliest compass known. A 1248
writer, Hugo de Bercy, spoke of a new compass construction, the needle
"now" being supported on two floats. Petrus Peregrinus de Maricourt, in
his Epistola de Magneto of 1269, wrote of a pivoted floating compass
with a lubber's line, and said that it was equipped with sights for
The reliability of the magnetic compass of
today is a comparatively recent achievement. As late as 1826 Peter
Barlow reported to the British Admiralty "half of the compasses in the
Royal Navy were mere lumber, and ought to be destroyed." Some 75 years
ago, Lord Kelvin developed the Admiralty type compass used today.
compass card, according to tradition, had its beginning when Flavin
Gioja, of Amalfi, attached a sliver of lodestone, or a magnetized
needle, to a card about the beginning of the 14th century. But, the
rose on the card is probably older than the needle. It is the wind rose
of the ancients. Primitive man naturall y named directions by the
winds. The prophet Jeremiah speaks of the winds from the four quarters
of heaven (Jer. 49:36) and Homer named four winds---Boreas, Eurus,
Notus, and Lephyrus. Aristotle is said to have suggested a circle of 12
winds, and Eratosthenes, who measured the world correctly, reduced the
number to eight about 200 BC. The "Tower of Winds" at Athens, built
about 100 BC, had eight sides. The Latin rose of 12 points was common
on most compasses used in the Middle Ages.
709) was well understood 200 years ago, and navigators made allowance
for it, but earliest recognition of its existence is not known.
Columbus and even the 11th century Chinese have been given credit for
its discovery, but little proof can be offered for either claim.
secular change in variation was determined by a series of magnetic
observations made at Limehouse, England. In 1580 William Borough fixed
the variation in that area at approximately 11°25' east. Thirty-two
years later Edmund Gunter, professor of astronomy at Gresham College,
determined it to be 6°13' east. At first it was believed that
had made an error in his work, but in 1633 a further decrease was
found, and the earth's changing magnetic field was established.
South Atlantic expedition was led by Edmond Halley at the close of the
17th century to gather data and to map, for the first time, lines of
variation. In 1724 George Graham published his observations in proof of
the diurnal change in variation. Canton determined that the change was
considerably less in winter than in summer, and about 1785 the strength
of the magnetic force was shown by Paul de Lamanon to vary in different
The existence of deviation (art. 709) was known to
John Smith in 1627 when he wrote of the "bittacle" as being a "square
box nailed together with wooden pinnes, because iron nails would
attract the Compasse." But no one knew how to correct a compass for
deviation until Captain Matthew Flinders, while on a voyage to
Australia in HMS
in 1801-02, discovered a method of doing
so. Flinders did not understand deviation completely, but the vertical
bar he erected to correct for it was part of the solution, and the
Flinders bar (art. 720) used toda y is a memorial to its discoverer.
Between 1839 and 1855 Sir George Airy, then Astronomer Royal, studied
the matter further and developed combinations of permanent magnets and
soft iron masses for adjusting the compass. The introduction, by Lord
Kelvin, of short needles as compass magnets made adjustment more
The gyro compass (art. 631). The age of iron ships
demanded a compass which could be relied upon to indicate true north at
all times, free from disturbing forces of variation and deviation.
1851, at the Pantheon in Paris, Leon Foucault performed his famous
pendulum experiment to demonstrate the rotation of the earth.
Foucault's realization that the swinging pendulum would maintain the
plane of its motion led him, the following year, to develop and name
the first gyroscope, using the principle of a common toy called a
"rotascope." Handicapped by the lack of a source of power to maintain
the spin of his gyroscope, Foucault used a microscope to observe the
indication of the earth's rotation during the short period in which his
manually-operated gyroscope remained in rotation. A gyro compass was
not practical until electric power became available, more than 50 years
later, to maintain the spin of the gyroscope.
Elmer A. Sperry,
an American, and Anschutz-Kampfe, a German, independently invented gyro
compasses during the first decade of the 20th century. Tested first in
1911 on a freighter operating off the East Coast of the United States
and then on American warships, Sperry's compass was found adequate, and
in the years following World War I gyro compasses became standard
equipment on all large naval and merchant ships.
auxiliaries commonly used today were added later. These include gyro
repeaters, to indicate the vessel's heading at various locations; gyro
pilots, to steer vessels automatically; course recorders, providing a
graphic record of courses steered; gyro-magnetic compasses, which
repeat headings of magnetic compasses so located as to be least
affected by deviation; and others in the fields of fire control,
aviation, and guided missiles.
112. The log.
the beginning of navigation, the mariner has attempted to determine his
speed in traveling from one point to another. The earliest method was
probably by estimate.
The oldest speed measuring device known
is the Dutchman's log. ()rally, any object which would float was thrown
overboard, on the lee side, from a point well forward, and the time
required for it to pass between two points on the deck was noted. The
time, as determined by sand glass, was compared with the known distance
along the deck between the two points to determine the speed.
the end of the 16th century a line was attached to the log, and as the
line was paid out a sailor recited certain sentences. The length of
line which was paid out during the recitation was used to determine the
speed. There is record of this method having been used as recently as
the early 17th century. In its final form this chip log, ship log, or
common log consisted of the log chip (or icy ship), log line, log reel,
and log glass. The chip was a quadrant-shaped piece of wood weighted
along its circumference to keep it upright in the water (fig. 112). The
log line was made fast to the log chip by means of a bridle, in such
manner that a sharp pull on the log line dislodged a wooden peg and
permitted the log chip to be towed horizontally through the water, and
hauled aboard. Sometimes a stray line was attached to the log to veer
it clear of the ship's wake. In determining speed, the observer counted
the knots in the log line which was paid out during a certain time. The
length of line between knots and the number of seconds required for the
sand to run out were changed from time to time as the accepted length
of the mile was altered.
The chip log has been superseded by
patent logs that register on dials. However, the common log has left
its mark on modern navigation, as the use of the term knot to indicate
a speed of one nautical mile per hour dates from this device. There is
evidence to support the opinion that the expression
"dead reckoning" had its origin in this same device, or
in the earlier Dutchman's log. There is logic in attributing "dead"
reckoning to a reckoning relative to an object "dead" in the water.
written by Nathaniel Bowditch and published in
FIGURE 120. A Babylonian map of about
500 BC. The Babylonians believed the earth
to be a flat disk encircled by a salt water river.
seafarers knew that the last to be seen of a ship as it disappeared
over the horizon was the masthead. They recognized the longer summer
days in England when they sailed to the tin mines of Cornwall, as early
as 900 BC. In that "north land" the Mediterranean sailors noticed that
the pole star was higher in the sky and the lower southern
constellations were no longer visible. When Thales invented the
projection, about 600 BC, he must have believed the earth to be a
sphere. Two centuries later Aristotle wrote that the earth's
shadow on the moon during an eclipse was always circular. Archimedes
(287-212 BC) used a glass celestial globe with a smaller terrestrial
globe inside it. Although the average man has understood the spherical
nature of the earth for only a comparatively short period, learned
astronomers have accepted the fact for more than 25 centuries.
121. Celestial mechanics.
— Among astronomers the principal question for 2,000 years was
the shape of the earth, but whether it or the sun was the center of the
universe. A stationary earth seemed logical to the early Greeks, who
calculated that daily rotation would produce a wind of several hundred
miles per hour at the equator.
Failing to realize that the
earth's atmosphere turns with it, they considered the absence of such a
wind proof that the earth was stationary.
The belief among the
ancients was that all celestial bodies moved in circles about the
earth. However, the planets — the "wanderers," as they were called —
contradicted this theory by their irregular motion. In the fourth
century BC Eudoxus of Cnidus attempted to account for this by
suggesting that planets were attached to concentric spheres which
rotated about the earth at, varying speeds. The plan of epicycles, the
theory of the universe which was commonly accepted for 2,000 years, was
first proposed by Apollonius of Perga in the third century BC. Ptolemy
accepted and amplified the plan, explaining it in his famous books, the
Ptolemy, the planets moved at uniform speeds in small circles, the
centers of which moved at, uniform speeds in circles about the earth
At first the Ptolemaic theory was accepted without
question, but as the years passed, forecasts based upon it proved to be
inaccurate. By the time the Alfonsine Tables were published in the 13th
century AD, a growing number of astronomers considered the Ptolemaic
doctrine unacceptable. However, Purbach, Regiomontanus, Bernhard
Walther of Kuremberg, and even Tycho Brahe in the latter part of the
century, were among those who tried to reconcile the earth-centered
epicyclic plan to the observed phenomena of the heavens.
early as the sixth centur y BC, a brotherhood founded by Pythagoras, a
Greek philosopher, proposed that the earth was round and self-supported
in space, and that it, the other planets, the sun, and the moon
revolved about, a central fire which they
the hearth of
the universe. The sun and the moon, they said, shone by reflected light
central fire was never located, however, and a few hundred years later
Aristarchus of Samos advanced a genuine heliocentric theory. He denied
the existence of Hestia and placed the sun at the center of the
universe, correctly considering it to be a star which shone by itself.
The Hebrews apparently understood the correct, relationship at least as
early as Abraham (about 2000 BC), and the early inhabitants of the
Western Hemisphere probably knew of it before the Europeans did.
Ptolemaic theory was generally accepted until its inability to predict
future positions of the planets could no longer be reconciled. Its
replacement by the heliocentric theory is credited principall y to
Nicolaus Copernicus (or Koppernigk). After studying mathematics at the
University of Cracow, Copernicus went to Bologna, where he attended the
astronomical lectures of Domenicao Maria Novara, an advocate of the
Pythagorean theory. Further study in Martianus Copella's Satyricori,
which includes a discussion of the heliocentric doctrine, convinced him
that the sun was truly the center of the universe.
the year of his death Copernicus tested his belief by continual
observations, and in that year, 1543, he published De Revolutiunibus
. In it he said that the earth rotated on
daily and revolved in a circle about the sun once each year. He placed
the other planets in circular orbits about the sun also, recoguizing
that Mercury and Venus were closer than the earth, and the others
farther out. He concluded that the stars were motionless in space and
that the moon moved circularly about the earth. His conclusions did not
become widely known until nearly a century later, when Galileo
publicized them. Today, "heliocentric" and "Copernican" are synonymous
terms used in describing the character of the solar system.
Other early discoveries.
— A knowledge of the principal
planets permitted reasonably accurate predictions of future positions.
Other, less spectacular data, however, were being established to help
round out the knowledge astronomers needed before they could produce
the highly accurate almanacs known today.
More than a century
before the birth of Christ, Hipparchus discovered the preceSWon of the
equinoxes (art. 1419) by comparing his own observations of the stars
with those recorded by Tirnocharis and Aristyllus about 300 BC.
Hipparchus cataloged more than a thousand stars, and compiled an
additional list of time-keeping stars Which differed in sidereal hour
angle by 15° (one hour), accurate to 15'. A spherical star map, or
planisphere, and a celestial globe were among the equipment he
designed. However, his instruments did not permit measurements of such
precision that stellar Parallax could be detected, and, consequently,
he advocated the geocentric theory of the universe.
Three centuries later Ptolemy examined and confirmed Hipparclius'
discovery of precession. He published a catalog in which lie arranged
the stars by constellations and gave the magnitude, declination, and
right ascension (art. 1426) of each. Following Hipparclius, Ptolemy
determmined longitudes by eclipses. In the Ailmagest
he included the plane and spherical trigonometry tables which
Hipparchus had developed, mathematical tables, and an explanation of
the circumstances upon which the equation of time (art. 1912) depends.
next thousand years saw little progress in the science of astronomy.
Alexandria continued as a center of learning for several hundred years
after Ptolemy, but succeeding astronomers at the observatory confined
their work to comments on his great books. The long twilight of the
Dark Ages had begun.
Alexandria was captured and destro yed by
the Arabs in AD 640, and for the next 500 years Moslems exerted the
primary influence in astronomy. Observatories were erected at Baghdad
and Damascus during the ninth century. Ibn Yunis' observatory near
Cairo gathered the data for the Tlakiniite tables in the 11th century.
Earlier, the Spanish, under Moorish tutelage, set up schools of
astronomy at Cordova and Toledo.
123. Modern astronomy
may be said to date from Copernicus, although it was not until the
invention of the telescope, about 1608, that precise measurement of the
positions and motions of celestial bodies was possible.
Galilei, an Italian, made outstanding contributions to the cause of
astronomy, and these served as a basis for the work of later men,
particularly Isaac Newton. He discovered Jupiter 's satellites,
providing additional opportunities for determining longitude on land.
He maintained that it is natural for motion to be uniform and
it straight line and that a force is required only when direction or
speed is changing. Galileo's support of the
theory, his use and improvement of the telescope, and particularly the
clarity and completeness of his records provided firm footing
Early in the 17th century , before
the invention of the telescope, Tycho Brahe found the planet Mars to be
in a position differing by as much as 8' from that required by the
geocentric theory . When the telescope became available, astronomers
learned that the apparent diameter of the sun varied during the year,
indicating that the earth's distance from the sun varies, and that its
orbit is not circular.
Johannes Kepler, a German who had
succeeded Brahe and who was attempting to account for his 8'
discrepancy , published in 1609 two of astronomy's most important
doctrines, the law of equal areas, and the law of elliptical orbits.
Nine years later he announced his third law, relating the
of revolution of any two planets to their respective distances from the
sun (art. 1407).
Kepler's discoveries provided it mathematical
basis by which more accurate tables of astronomical data were computed
for the maritime explorers of the age. His realization that the sun is
the controlling power of the system and that the orbital planes of the
planets pass through its center almost led film to the discover y of
the law of gravitation.
Sir Isaac Newton reduced Kepler's
conclusions to the universal law of gravitation (art. 1407) when he
published his three laws of motions in 1687. Because the planets exert
forces one upon the other, their orbits do not agree
Kepler's laws. Newton's work compensated for this and, as it
astronomer was able to forecast with greater accuracy the positions of
the celestial bodies. The navigator benefited through more
tables of astronomical data.
Between the years 1764 and 1784, the Frenchmen Lagrange and Laplace
conclusively proved the solar system's mechanical stability.
Nathaniel Bowditch translated and commented upon Laplace's Mécanique Céleste
bringing it up-to-date. Prior to their work this stability had been
questioned due to apparent inconsistencies in the motions of some of
the planets. After their demonstrations, men were convinced and could
turn to other important work necessary to refine and improve the
But there were real, as well as apparent,
irregularities of motion which could not be explained by the law of
gravitation alone. By this law the planets describe ellipses about the
sun, and these orbits are repeated indefinitely, except as the other
planets influence the orbits of each by their own gravitational pull.
Urbain Leverrier, one-time Director of the Paris Observatory, found
that the line of apsides of Mercury was
advancing 43" per century
faster than it should, according to the law of gravitation and the
positions of other known planets. In an attempt to compensate for the
resulting errors in the predicted positions of the planet, he suggested
that there must be a mass of circulating matter between the sun and
Mercury. No such circulating matter has been found, however, and
Leverrier's discovery is attributed to a shortcoming of
law, as explained by Albert Einstein.
In Einstein's hands,
Leverrier's 43" became a fact as powerful as Brahe's 8' had been in the
hands of Kepler. Early in the 20th century, Einstein announced the
theory of relativity (art. 1407). He stated that for the planets to
revolve about the sun is natural, and gravitational force is
unnecessary for this, and he asserted that there need be no circulating
matter to account for the motion of the perihelion of Mercury as this,
too, is in the natural order of things. Calculated from his theory, the
correction to the previously computed motion of the perihelion in 100
years is 42".9.
Prior to Einstein's work, other discoveries had helped round out man's
knowledge of the universe.
(art. 1417), discovered by James Bradley about 1726, accounted for the
apparent shifting of the stars throughout the year, due to the combined
orbital speed of the earth and the speed of light. Twenty years later
Bradley described the periodic wobbling of the earth's axis, called
nutation (art. 1417), and its effect upon precession of the equinoxes.
in 1718 Edmond Halley, England's second Astronomer Royal, detected a
motion of the stars, other than that caused by precession,
led him to conclude that they, too, were moving. By studying the works
of the Alexandrian astronomers, he found that some of the most
prominent stars had changed their positions by as much as 32'. Jacques
Cassini gave Halley's discovery further support when he found, a few
years later, that the declination of Arcturus had changed 5' in the 100
years since Brahe made his observations. This proper motion (art. 1414)
is motion in addition to that caused by precession, nutation, and
Sir John Herschel, the great astronomer who
discovered the planet Uranus, about 1800 proved that the solar system
is moving toward the constellation Hercules. As early as 1828 Herschel
advocated the establishment of a standard time system. Neptune was
discovered in 1826 after its position had been predicted by the
Frenchman Urbain Leverrier. Based upon the work of Percival Lowell, an
American, Pluto was identified in 1930. Uranus, Neptune, and Pluto are
of little concern to the navigator.
A more recent discovery may
well have greater navigational significance. This is the existence of
sources of electromagnetic energy in the sky in the form of radio stars
(art. 1414). The sun has been found to transmit energy of radio
frequency, and instruments have been built which are capable of
tracking it across the sky regardless of weather conditions.
Maryland State Archives
FIGURE 124a. — The ancient astrolabe, one of the earliest
altitude measuring instruments.
— Prior to
the development of the magnetic compas, the navigator used the heavenly
bodies chiefly as guides by which to steer. The compass,
led to more frequent long voyages on the open sea, and the need for a
vertical-angle measuring device which could be used for determining
altitude, so that
latitude could be found.
the first such device used at: sea was the common quadrant, the
form of all such instruments. Made of wood, it was a fourth part of it
circle, hold vertical by means of it plumb bob. An observation made
this instruruent at sea a two- or three-man job. This device was
probably used ashore for centuries before it went to sea, although its
earliest use by the mariner is unknown.
Invented perhaps by
Apollonius of Perga in the third century BC, the astrolabe (fig. 124a)
— from the Greek for star
and to take
been made portable by
the Arabs possibly as early as AD 700. It was in the hands of
pilots by the end the 13th century, often as an elaborate and beautiful
creation wrought of precious metals. Some astrolabes could be used as
finders (art. 2210) by fitting all engraved plate to one side. Large
astrolabes were among the chief instruntents of 15th and 16th century
observatories, but the value of this instrument at sea was limited.
principle of the astrolabe was similar to that of the common quadrant,
the astrolabe consisted of it metal disk, graduated in degrees, to
which a movable sight
was attached. In using the astrolabe, which may be likened to a pelorus
held on its side, the navigator adjusted the sight vane until it was in
line with the star, and then read the zenith distance from the scale.
As with the common quadrant, the vertical was established by plumb bob.
Three men were needed to make an observation with the astrolabe
(one held the instrument by a ring at its top, another aligned the
sight vane with the body, a third made the reading) and even then the
least rolling or pitching of a vessel caused large acceleration errors
in observations. Therefore, navigators were forced to abandon the plumb
bob and make the horizon their reference.
Figure 124b. — The
cross-staff, the first instrument to utilize the
visible horizon in making celestial observations.
(fig. 124b) was the first instrument which utilized the visible horizon
in making celestial observations. The instrument consisted of a long,
wooden shaft upon which one of several cross-pieces was mounted
The cross-pieces were of various lengths,
the one being used depending upon the angle to be measured. The
navigator fitted the appropriate cross-piece on the shaft and, holding
one end of the shaft beside his eye, adjusted the cross until its lower
end was in line with the horizon and its upper end with the body. The
shaft was calibrated to indicate the altitude of the body observed.
University of Southern Maine
FIGURE 124c.--The backstaff, or sea quadrant, a
favorite instrument of American colonial navigators.
using the cross-staff, the navigator was forced to look at the horizon
and the celestial body at the same time. In 1590 John Davis, author of
The Seaman's Secrets, invented the backstaff (fig. 124c) or sea
quadrant. He was one of the few practical seamen
(Davis Strait is named for him, in honor of his attempt to find the
Nort Passage} to invent a navigational device. The backstatf marked a
long advance and was particularly popular among American
In using this instrument, the navigator turned his back to the sun and
aligned its shadow with true horizon. The backstaff had two
arcs, and the sum of the values shown on each was the
altitude of the sun. Later, this instrument was fitted with a mirror
to permit observations of bodies other than the sun.
Figure 124A. The nocturnal, an instrument used to determine
latitude by an observation of Polaris.
instrument developed about the same time was the nocturnal.
purpose was to provide the mariner with the appropriate correctionl
to be made to the altitude of Polaris to determine latitude. By
Polaris through the hole in the center of the instrument and adjusting
movable arm so that it pointed at Kochab, the navigator could
read the correction from the instrument. Most nocturnals had
an additional outerdisk graduated for the months and days of the year
and by adjusting this the navigator could also determine solar time.
Tycho Brahe designed several instruments with arcs of 60°, having
fixed sigh another movable
one. He called the instruments sextants the name is now
to all alt itude-measureing devices used by the navigator (ch. XV). In
Newton sent to Edmond Haller, the Astronomer Royal, a description of a
device having double-reflecting mirros,
the principle of modern marine sextant. However,
was not made public until after somewhat similar instruments
had been made in 1730 by Englishman John Hadley, and the American
The original instrument constructed by Hadley was, in fact, an octant
, but due
to the double-reflection principle it measured angles up
to one-fourth of a circle, or 90°. Godfrey 's instrument is
have been a quadrant
so could measure a through 180°. The
men received equal awards from England's Royal Society, as their work
was considered to be a case of simultaneous invention, although Haldey
probably preceded Godfrey by a few months in
the actual construction of his sextant. In the next few years
instruments were successfully tested at sea, but 20 years or
before the navigator gave up his backstaff or sea quadrant for
the new device. In 1733 Hadley attached a spirit level to a
quadrant, and with it was abe to measure altitudes without reference
to the horizon. Some years late first bubble sextant (art.
Vernier, in 1631, had attached to the limb of a quadrant a second,
smaller graduated arc, thereby permitting angles to be measured more
accurately, and this device was incorporated in all later
The sextant has remained
practically unchanged since its invention more than two centuries ago.
The only notable improvements have been the addition of an endless
tangent screw and a micrometer drum, both having been added during the
125. Determining latitude.
The ability to
determine longitude at sea is comparatively modern, but latitude has
been available for thousands of years.
Meridian transit of the
. Long before the Christian era, astronomers had determined
sun's declination for each day of the year, and prepared tables listing
the ata. This was a comparatively simple matter, for the zenith
distance obtained by use of a shadow cast by the sun on the day of the
winter solstice could be subtracted from that obtained on the day of
the summer solstice to determine the range of the sun's declination,
about 47°. Half of this is the sun's maximum declination, which
then be applied to the zenith distance recorded on either day to
determine the latitude of the place. Daily observations thereafter
enabled the ancient astronomers too construct reasonably accurate
Such tables were available long before the
average navigator was ready to use team, but certainly by the 15th
century experienced seamen were determining their latitude at sea to
within one or two degrees. In his 1594 The Seaman's Secrets, Davis made
use of his experience in high latitudes to explain the method of
determining latitude by lower transit observations of the sun.
observation of the sun
. The possibility of overcast skies at the
time each day when the navigator could get a reliable observation for
latitude led to the development of the "ex-meridian" sight. Another
method, involving two sights taken with a considerable time interval
between, had previously been known, but the mathematics were so
involved that it is doubtful that many seamen made use of it.
There are two methods by which ex-meridian observations can be solved.
The direct process was the more accurate, although it required a
trigonometrical solution. By the latter part of the 19th century,
tables were introduced which made the method of reduction
to the meridian more practical and, when occasion demands such an
observation, this is the method generally used today. However, with the
development of line of position methods and the modern inspection
table, ex-meridian observations have lost much of their popularity.
First use of the pole star to determine latitude is
known, but many centuries ago seamen who used it as a guide by which to
steer were known tocomment upon its change of altitude as they sailed
north or south.
By Columbus' time some navigators were using
Polaris to determine latitude, and with the invention of the nocturnal
late in the 16th century, providing corrections to the observed
altitude, the method came into more general use. The
development of the chronometer in the 18th century permitted exact
this made determination of latitude by Polaris a common practice. Even
today, more than a century after discovery of the celestial line of
position, the method is still in use. The modern inspection table has
eliminated the need for meridian observations as a special method for
determining latitude. Perhaps when the almanacs and sight reduction
tables make the same provision for solution of Polaris sights as they
do for any other navigational star, this last of the special methods
will cease to be used for general navigation. But customs die slowly,
and one as well established as that of position finding in terms of
separate latitude and longitude observations — instead of lines of
position — is not likely to disappear completely for many years to
126. The search for a method of
"discovering" longitude at sea
— A statement once quite common was, "The navigator always
knows his latitude." A
more accurate statement would have been, "The navigator never knows his
longitude." In 1594 Davis wrote: "Now there be some that are very
inquisitive to have a way to get the longitude, but that is too
seamen, since it requireth the deep knowledge of astronomy, wherefore I
not have any man think that the longitude is to be at sea by any
instrument, so let no seamen trouble themselves with any such rule
but let them keep a perfect account and reckoning of the way of
ship." In speaking of conditions of his day, he was correct, for it was
until the 19th century that the average navigator was able to determine
longitude with accuracy.
knowledge of his
longitude, the navigator of old it necessary on an ocean crossing to
sail northward or southward to the latitude ` destination, and then to
follow that parallel of latitude until the destinatio reached, even
though this might take him far out of his way. Because of this pr
parallel sailing was an important part of the navigator's store of
knowledge. method was a crude one, however, and the time of landfall
was often in error matter of days, .and, in extreme cases, even weeks.
Almost as early as
the rotation of the earth was established,
astron recognized that longitude could be determined by comparing local
time with t. the reference meridian. The problem was the determination
of time at the. ref meridian. One of the first methods proposed was
that of observing the disappeara; Jupiter's satellites as they were
eclipsed by their planet. This method, ori^ proposed by Galileo for use
on land, required the ability to observe and identi satellites by using
a powerful telescope, knowledge of the times at which the e+ would take
place, and the skill to keep the instrument directed at the bodies
aboard a small vessel on the high seas. Although used in isolated cases
for years, the method was not satisfactory at sea, due largely to the
difficulty of oh tion (some authorities recommended use of a telescope
as long as 18 or 19 feet) ar lack of sufficiently accurate predictions.
Variation of the compass
seriously considered as a method
of detern longitude for 200 years or more. Faleiro, Magellan's advisor,
believed it could utilized, and, until the development of the
chronometer, work was carried on to p the theory. Although there is no
simple relationship between variation and long those who advocated the
method felt certain that research and investigation eventually provide
the answer. Many others were convinced that such a so! did not exist.
:In 1676 William Bond published The Longitude Found, in whi stated that
the latitude of a place and its variation could be referred to the
meridian to determine longitude. Two years later Peter Blackborrow
rebutted with The Longitude Not Found
Variation was put to
good use in determining the nearness to land by shipm familiar with the
waters they plied, but as the solution to the longitude problem i a
failure, and with the improvement of lunar distance methods and the
inventi the chronometer, interest in the method waned. If it had been
possible to provid mariner with an accurate chart of variation, and to
keep it up-to-date, a mea establishing an approximate line of position
in areas where the gradient is large v have resulted; in many cases
this would have established longitude if latitude known.
first method widely used at sea to determine long with
some accuracy was that of lunar distances (art.. 131), by which the
navigator determined GMT by noting the position of the relatively
fast-moving moon among the stars. Both Regiomontanus, in 1472, and John
Werner, in 1514, have been credited with being the first to propose the
use of the lunar distance method. At least one source states that
Amerigo Vespucci, in 1497, determined longitude using the moon's
to that of another body. One of the principal reasons for establishing
the Royal Observatory at Greenwich was to conduct the observations
necessary to provide more accurate predictions of the future positions
of the moon. Astronomers, including the Astronomers Royal, favored this
method, and half a century after the invention of the chronometer it
was still being perfected. In 1802 Nathaniel Bowditch simplified the
method and its explanation, thus eliminating much of the mystery
surrounding it and making it understandable to the average mariner.
Following Bowditch, the navigator was able to head more or less
directly toward his destination, rather than travel the many additional
miles often required in "running down the latitude" and then using
parallel sailing. An explanation of the lunar distance method, and
tables for its use, were carried in the American Practical Narigator
The Board of Longitude.
The lunar distance method, using the data and equipment available early
in the 18th century, was far from satisfactory. Ships, cargoes, and
lives were lost because of inaccurately-determined longitudes. During
the Age of
Discovery, Spain and Holland posted rewards for solution
to the problem, but in vain. When 2,000 men were lost as a squadron of
British men-of-war ran aground on a foggy night in 1707, officers of
the Royal Navy and Merchant Navy petitioned Parliament for action. As a
result, the Board of Longitude was established in 1714, empowered to
reward the person who could solve the problem of "discovering"
longitude at sea. A voyage to the West Indies and back was to be the
test of proposed methods which were deemed worthy. The discoverer of a
system which could determine the longitude within 1° by the end of
voyage was to receive £10,000; within 40', £15,000; and
£20,000. These would be handsome sums today. In the 18th century
127. Evolution of the chronometer.
the different methods were found unsatisfactory, it became
increasingly apparent that the problem was one of keeping the time of
the prime meridian. But the development of a device that would keep
accurate time during a long voyage seemed to most men to be beyond the
realm of possibility. Astronomers were flatly opposed to the idea and
felt that the problem was properly theirs. There is even some evidence
to indicate that the astronomers of the Board of Longitude made unfair
tests of chronometers submitted to them.
(1629-95), a Dutch scientist and mathematician, made a number of
contributions of great value in the field of astronom y, but his most
memorable work, to the navigator, was his attempt at constructing a
perfect timepiece. It was probably Galileo who first suggested using a
pendulum in keeping time. Huygens realized that an error would result
from the use of a simple pendulum, however, and he devised one in which
the bob hung from a double cord that passed between two plates in such
a way that it traced a cycloidal path.
1660 Huygens built his first chronometer. The instrument utilized his
cycloidal pendulum, actuated by a spring. To compensate for rolling and
pitching, Huygens mounted the clock in gimbals. Two years later the
instrument was tested at sea, with promising results. The loss of
tension in the spring as it ran down was the major weakness in this
clock. Huygens compensated for this by attaching oppositely-tapered
cones and a chain to the spring. A 1665 sea test of the new timepiece
showed greater accuracy, but still not enough for determination of
longitude. In 1674 he constructed a chronometer with a special balance
and long balance-spring, Although it was the best marine timepiece then
known, Huygens' last clock was also unsuited for use at sea due to the
error caused by temperature changes.
John Harrison was a
carpenter's son, horn in Yorkshire in 1693. He followed his father's
trade during his youth, but soon became interested in the repair and
construction of clocks. At the age of 20 lie completed his first
timekeeper, a pendulum-type clock with wooden wheels and pinions.
Harrison's gridiron pendulum, one which maintained its length despite
temperature changes, was designed about 1720, and contained alternate
iron and brass rods to eliminate distortion. Until the time that metal
having small coefficients of temperature expansion were developed,
Harrison's invention was the type of pendulum used by almost all
© Crown copyright, National Maritime Museum
Figure 127 Harrison's No. 1 chronometer. The first of four
time-keepers constructed by Harrison,
this clock weighs 65 pounds.
1728 Harrison felt ready to take his pendulum, an escapement he had
invented, and plans for his own marine timepiece before the Board of
Longitude. In London, however, George Graham, a famous clockmaker,
advised him to first construct the timekeeper. Harrison did, and
in (735 he submitted his No. 1 chronometer (fig. 127). The Board
authorized a sea trial aboard HMS Centurion
board, and upon her return, the error was found to he three
minutes of longitude, a performance which astounded members of the
Board. But the chronometer was awkward and heavy, being enclosed in
glass and weighing some 65 pounds, and the Board voted to give
£500, to be used in producing a more practical timepiece.
During the next few years he constructed two other chronometers, which
were stronger and less complicated, although there is no record of
being tested by the Board of Longitude. Harrison continued to devote
his life to the
construction of an accurate clock to be used in determining longitude,
and finally, as he
approached old age, he developed his No. 4. Again he went before the
Board, and again
a test was arranged. In November of 1761, HMS Deptford
sailed for Jamaica with
aboard, in the custody of Harrison's son, William. On arrival, after a
passage lasting two months, the watch was only nine seconds slow (23;
longitude). In January of 1762 it was placed aboard HMS Merlin
for the return voyage
to England. When the Merlin
anchored in English waters in April of that year, the
total error shown by the chronometer was 1 minute, 54.5 seconds. This
is equal to less
than a half degree of longitude, or less than the minimum error
prescribed by the
Board for the largest prize. Harrison applied for the full
£20,000, but the
led by the Astronomer Royal, allowed him only a fourth of that, and
insisted on another
Harrison sailed again with No. 4 for Barbados in March of 1764, and
throughout the almost four-months-long voyage the chronometer showed an
error of only 54 seconds, or 13.5 minutes of longitude. The astronomers
of the Board reluctantly joined in a unanimous declaration that
Harrison's timepiece had exceeded all expectations, but they still
would not pay him the full reward. An additional £5,000 were paid
the condition that plans be submitted for the construction of similar
chronometers. Even when this was done, the Board delayed payment
further by having one of its members construct a timepiece from the
plans. Not until 1773, Harrison's 80th year, was the rest of the reward
paid, and only then because of intervention by the king himself.
LeRoy, a great French clockmaker, constructed a chronometer in 1766
which has since been the basis for all such instruments. LeRoy's
several inventions made his chronometer a timepiece which has been
described as a "masterpiece of simplicity, combined with efficiency."
Others to contribute to the art of watchmaking included Ferdinand
Berthoud of France and Thomas Mudge of England, each of whom developed
new escapements. The balance wheel was improved by John Arnold, who
invented the escapement acting in one direction only, substantially
that used today. Acting independently, Thomas Earnshaw invented a
similar escapement. He built the first reliable chronometer at a
relatively low price. The chronometer the Board of Longitude had made
from Harrison's plans cost £450; Earnshaw's cost £45.
designed to provide the navigator with information other than time were
popular a century or more ago. One showed the times of high and low
water, the state of the tide at any time, and the phases of the moon;
another gave the equation of time and the apparent motions of the stars
and planets; a third offered the position of the sun and both mean and
sidereal times. But the chronometers produced by LeRoy and Earnshaw
were the ones of greatest value to the navigator; they gave him a
simple and reliable method of determining his longitude.
signals, which permit the mariner at sea to check the error in his
chronometer, are essentially a 20th century development. Telegraphic
time signals were inaugurated in the United States at the end of the
Civil War, and enabled ships to check their chronometers in port by
time ball signals. Previously, the Navy's "standard"chronometer had
been carried from port to port to allow such comparison. In their most
advanced form, time balls were dropped by telegraphic action. In 1904
the first official "wireless" transmission of time signals began from a
naval station at Navesink, N. J. These were low-power signals which
could be heard for a distance of about 50 miles. Five years later the
range had been doubled, and, as other nations began sending time
signals, the navigator was soon able to check his chronometer around
The search for longitude was ended.
128. Establishment of the prime
Until the beginning of the 19th century, there was little
uniformity among cartographers as to the meridian from which longitude
was measured. The navigator was not paricularly concerned, as he could
not determine his longitude, anyway.
in the second century AD, had measured longitude eastward from a
reference meridian two degrees west of the Canary Islands. In 1493 Pope
Alexander VI drew it line in the Atlantic west of the Azores to divide
the territories of Spain and Portugal and for many years this meridian
was used by chart makers the two countries. 1570 the Dutch
cartographer Ortelius used the easternmost of the Cape Verde Islands.
John Davis, in his 1594 The Seaman's
, said the Isle of Fez in the Canaries
was used because there the variation was zero. Mariners paid little
attention, however, and often reckoned their longitude from several
different capes and ports during a voyage, depending upon their last
The meridian of London was used as early as 1676,
and over the years its popularity grew as England's maritime interests
increased. The system of measuring longitude both east and west through
180° may have first appeared in the middle of the 18th century.
Toward the end of that century, as the Greenwich Observatory increased
in prominence, English map makers began using the meridian of that
observatory as a reference. The publication by the Observatory of the
first British Nautical Almanac in 1767 further entrenched Greenwich
as the prime meridian. A later and unsuccessful attempt was made in
1810 to establish Washington as the prime meridian for American
navigators and cartographers. At an international conference held in
in 1884 the meridian of Greenwich was officially established, by the 25
nations in attendance, as the prime meridian. Toda y all maritime
nations have designated the Greenwich meridian the prime meridian,
except in a few cases where local references are used for certain
129. Astronomical observatories.
— Thousands of years before the birth of Christ, crude observatories
existed, and astronomers constructed primitive tables which were the
forerunners of modern almanacs. The famous observatory at Alexandria,
the first "true" observatory , was constructed in the third century BC,
but the Egyptians, as well as the Babylonians and Chinese, had already
studied the heavens for many centuries. The armillary sphere (fig.
129a) was the principal instrument used by the early astronomers. It
consisted of a skeleton sphere with several movable rings which could
be adjusted to indicate the orbits of the various celestial bodies. One
source attributes the invention of the armillary sphere to Eratosthenes
in the third century BC; another says the Chinese knew it 2,000 veal's
earlier, as well as the water clock and a form of astrolabe. The
Alexandrian observator y was the seat of astronomical learning in the
western world for several centuries, and there Hipparchus discovered
the precession of the equinoxes, and Ptolemy did the work which led to
study did not cease entirely during the Dark Ages. The Arabians erected
observatories at Baghdad and Damascus in the nineth century AD,
and observatories in Cairo and northwestern Persia followed. The Moors
brought the astronomical knowledge of the Arabs into Spain, and the Toledan Tables
of 1080 resulted front awakening of scientific interest that brought
about the establishment of schools of astronomy at Cordova and Toledo
in the tenth century.
Encyclopedia Britannica, 1877
FIGURE 129a.—An armillary sphere, one of the most important
of the ancient astronomers.
great voyages of western discovery began early in the 15th century, and
chief among those who recognized the need for greater precision in
navigation was Prince Henry "The Navigator" of Portugal. About 1420 he
had an observatory constructed at Sagres, on the southern tip of
Portugal, so that more accurate information might be available to his
captains. Henry's hydrographic expeditions added to the geographical
knowledge of the mariner, and he was responsible for the simplification
of many navigational instruments.
The Sagres observatory was
rudimentary, however, and not until 1472 was the first complete
observatory built in Europe. In that year Bernard Walther, a wealthy
astronomer, constructed the Nuremberg Observatory, and placed
Regiomontanus in charge. Regiomontanus, born Johann MUller, contributed
a wealth of astronomical data of the greatest importance to the
The observatory at Cassel, built in 1561, had a revolving dome and
an instrument capable of measuring altitude and azimuth at, the same
time. Tycho Brahe's Uranihurgum Observatory, located on the Danish
island Hveen, was opened in 1576, and the results of his
observations contributed greatly to the navigator's knowledge.
Prior to the discovery of the telescope, the astronomer could
increase the accuracy of his observations only by using larger
instruments. Brahe used a quadrant with a radius of 19 feet, with
which lie could measure altitudes to 0'.6, an unprecedented degree of
precision at that time. He also had an instrument with which he could
determine altitude and azimuth simultaneously (fig. 129b). After
Brahe, Kepler made use of the observatory and his predecessor's records
in determining the laws which bear his name.
The telescope, the
modern astronomer's most important tool, was invented by Hans
Lippershey about 1608. Galileo heard of Lippershey's invention, and
soon improved upon it. In 1610 he discovered the four great moons
of Jupiter, which led to the "longitude by eclipse" method successfully
used ashore for many years and experimented with at sea.
With the 32 power telescope he eventually built, Galileo was able
to observe clearly the motions of sun spots, by which he proved that
the sun rotateson its axis. In Paris, in 1671, the French National
Observatorty was established.
Greenwich Royal Observatory.
for navigational advancement was ignored by
Henry VIII and Elizabeth I, but in 1675 Charles II, at the urging of
John Flamsteed, Jonas Moore, Le Sieur de Saint-Pierre, and Christopher
Wren, established the Greenwich Royal Observatory. Charles limited
construction costs to £500, and appointed Flamsteed the first
Astronomer Royal, at an annual salary of £100. The equipment
available in the early years of the observatory consisted of two
clocks, a "sextant" of seven-foot radius, a quadrant of three-foot
radius, two telescopes, and the star catiilog published almost a
century before by Tycho Brahe Thirteen years passed before Flamstead
had an instrument with which he could determine his latatude
accurately. In 1690 a transit instrument equipped with a
telescope and vernier was invented by Romer, and he later added a
verticle circle to the device. This enabled the astronomer to
determine declination and right ascension at the same time.
One of these instruments was added to the equipment at Greenwich in
1721, replacing the huge quadrant previously used. The development and
perfection of the chronometer in the next hundred years added further
to the accuracy of observations.
Other national observatories
were constructed in the years that followed; at Berlin in 1705, St.
Petersburg in 1725, Palermo in 1790, Cape of Good Hope in 1820,
Parrametta in New South Wales in 1822, and Sydney in 1855.
S. Naval Observatory
. The first observatory in the United
said to have been built in 1831-1832 at Chapel Hill, N.C. The Depot of
Charts and Instruments, established in 1830, was the agency from which
the U.S. Navy Hydrographic Office and the Naval Observatory evolved 36
years later. Under Lieutenant Charles Wilkes, the second
Officer-in-Charge, the Depot about 1835 installed a small transit
instrument for rating chronometers. The Mallory Act of 1842 provided
for the establishment of a permanent observatory, and the director was
authorized to purchase all such supplies as were necessary to continue
astronomical study. The observatory was completed in 1,844 and the
results of its first observations were published two years later.
Congress established the Naval Observatory as a separate agency in
1866. In 1872 a refracting telescope with a 26-inch aperture, then the
world's largest, was installed. The observatory, located at Washington,
D.C., has occupied its present site since 1893.
Wilson Observatory of the Carnegie Institution of Washington was built
in 1904-05. The observatory's 100-inch reflector telescope opened wider
the view of the heavens, and enabled astronomers to study the movements
of celestial bodies with greater accuracy than ever before. But a still
finer tool was needed, and in 1934 the 200-inch reflector for the
Palomar Mountain Observatory was cast. The six-million-dollar
observatory was built, by the Rockefeller General Education Board for
the California Institute of Technology, which also operates the Mount
Wilson Observatory. The 200-inch telescope makes it possible to see
individual stars 20,000,000 light-years away and galaxies at least
1,600,000,000 light-years away.
As with earlier instruments,
the telescope has about reached the limit of practical size. Present
efforts are being directed toward application of the electron
microscope to the telescope, to increase the range of present
— From the
have undoubtedly recorded the results of their observations. Tables
computed from such results have been known for centuries. The work of
Hipparchus, in the second century BC, and Ptolemy, in his famous
, are examples. Then
the Toledan Tables
in AD 1080,
and the Alfonsine Tables
1252. Even with these later tables,
however, few copies were made, for printing had not yet been invented,
and those that were available were kept in the hands of astronomers.
Not until the 15th century were the first almanacs printed and made
available to the navigator. In Vienna, in 1457, George Purbach issued
the first almanac. Fifteen years later the Nuremberg Observatory, under
Regiomontanus, issued the first of the ephemerides it published until
1506. These tables gave the great maritime explorers of the age the
most accurate information available. In 1474 Abraham Zacuto introduced
his Almanach Perpetuum
130a) which contained tables of the
sun's declination in the most useful form yet available to the mariner.
Tabulae Prutenicae, the first tables to be calculated on Copernican
principles, were published by Erasmus Reinhold in 1551 and gave the
mariner a clearer picture of celestial movements than anything
previously available. The work of Brahe and Kepler at the Uraniburgum
Observatory provided the basis for the publication of the Rudolphine
Figure 130a. An excerpt from the Portuguese Regimento do estrolabio ado quadrante
of about 1509,
giving the sun's declination and other data based
upon Zacuto's calculations for month of March.
The first day of spring,
the 11th by the Julian calendar then in use,
is marked by the
symbol of Aries, the ram (ϒ).
Still, the information contained in these
books was intended primarily for the use of the astronomer, and the
navigator carried the various tables only that he might make
use of the portions applicable to his work. The first official
almanac, Connaissance des Temps
director at the time. During
20 years he held the position, the French Observatory rose to its
In 1767 the British Nautical Almanac
published. Nevil Mask was then Astronomer Royal, and he provided the
navigator with the best inform available. The book contained tables of
the sun's declination, and corrections to the observed altitude of
Polaris. The moon's position relative to other celestial bodies
was included at 12-hour intervals, and lunar distance tables gave the
angular distance between the moon and certain other bodies at
For almost a hundred years the British Nautical Almanac
was the one used
American navigators, but in 1852 the Depot of Charts and Instruments
published the first American
Ephemeris and Nautical Almanac
for the year 1855. Early American almanacs were distinguished by
their excessive detail in some cases and shortage of data of
importance to the navigator in others. Declination was given
to the nearest 0".1 and the equation of time to the nearest 0".01. Most
figures were given only for noon at Greenwich, and a tedious
interpolation was involved in converting the information to that
at a given time at the longitude of the observer. Lunar distances were
given at three-hour intervals. Few star data were listed
Since 1858 the American
Nautical Almanac has been printed without the ephemeris section, that
part of value chiefly to astronomers. Until 1908 the positions of
the brighter stars were given only for January 1st, and in relation to
the meridian of Washington. Beginning in
that year, the apparent places of 55 major stars were given for the
each month. In 1913 the tables of distances were dropped. In 1919
sunrise and sunset tables were added.
One of the greatest
inconveniences involved in using the old almanacs wa astronomical day,
which began at noon of the civil day of the same date. This
abolished in 1925, and the United States adopted the expression "civil
time" to designate time by the new system. Greenwich hour angle was
published for the moon in the Lunar
Ephemeris for Aviators
for the last four
months of 1929. This publication became a supplement to the Nautical
in 1931, and for 1932 they were merged.
130b. Star data from the 1855 Nautical Almanac.
in declination and right ascension can be used
to obtain reasonably
correct values today.
, designed by Lieutenant Commander P. V. H. Weems,
1933, giving Greenwich hour angle for all bodies included. For 1934
this information was given in the Nautical
, and the Air Almanac
was discontinued. The first British air almanac was published for the
last quarter of 1937, and modified for 1939 with features followed
closely in the first American Air
, for 1941. In 1950 a revised Nautical Almanac
patterned after the popular American
Starting with the 1953 edition, the British and American air almanacs
were combined in a single publication. In that year the United States
reverted to the expression "mean time" in place of "civil time." The
British and American nautical almanacs have been combined
starting with the edition for 1958.
The navigational triangle. — It is customary for modern navigators to
reduce their celestial observations by solving the triangle whose
points are the elevated pole, the celestial body, and the zenith of the
observer. The sides of this triangle are the polar distance of the body
(codeclination), its zenith distance (coaltitude), and the polar
distance of the zenith (colatitude of the observer).
A spherical triangle was first used at sea in solving lunar distance
problems. Simultaneous or nearly simultaneous observations were made of
the altitudes of the moon and the sun or a star near the ecliptic, and
the angular distance between the moon and the other body. The
zenith of the observer and the two celestial bodies formed the vertices
of the triangle, whose sides were the two coaltitudes and the angular
distance between the bodies. By means of a mathematical calculation the
navigator "cleared" this distance of the effects of refraction
and parallax applicable to each altitude, and other errors.
The corrected value was then used as an argument for entering the
almanac, which gave the true lunar distance from the sun and several
stars at three-hour intervals.
the navigator had set his watch, which could be relied upon for short
periods, by a meridian transit observation to determine local apparent
time. The equation of time was obtained from the almanac to establish
local mean time; and this, applied to the Greenwich mean time of
thelunar distance observation,
gave the longitude.
The mathematics involved was tedious, and few mariners were capable of
solving the triangle until Nathaniel Bowditch published his simplified
method in 1802 in The New American
. Chronometers were reliable by that time,
but their high cost prevented their general use aboard the majority of
naval and merchant ships. Using Bowditch's method, however, most
navigators, for the first time, could determine their longitude, and so
eliminate the need for parallel sailing and the lost time associated
with it. The popularity of the lunar distance method is indicated by
the fact that tables for its solution were carried in the I until the
second decade of the 20th century.
The determination of latitude was considered a separate problem,
usually solved by means of a meridian altitude or an observation of
The time sight.
theory of the time sight (art. 2106) had been known to mathematicians
since the dawn of spherical trigonometry, but not until the chronometer
was developed could it be used by mariners.
The time sight made use of the modern navigational triangle. The
codeclination,or polar distance, of the body could be determined from
the almanac. The zenith distance (coaltitude) was determined by
observation. If the colatitude were known,
three sides of the triangle were available. From these the meridian
angle was computed. The comparison of this with the Greenwich
hour angle from the almanac yielded the longitude.
The time sight was mathematicall y sound, but the navigator was not
always aware that the longitude determined was only as accurate as the
latitude, and together they merely formed a point oil is known today as
a line of position. If the observed
body was on the prime vertical, the line of position ran north and
south and a small error in latitude generally had little effect oil
longitude. But when the body was close to the meridian, a small error
in latitude produced a large error in longitude.
Figure 131. The first celestial
line of position, obtained by
Captain Thomas Sumner in 1837.
The line of position
celestial observation (art. 1703) was unknown until discovered in 1837
by 30-year-old Captain Thomas H. Sumner, a Harvard graduate and son of
a United States Congressman from Massachusetts. The discovery of the
"Sumner line," as it is sometimes called, was considered by Maury ''the
commencement of a new era in navigation." In Sumner's own words, the
discovery took place in this manner:
Having sailed from Charleston, S.C., 25th November, 1837,
Greenock, a series of heavy gales from the Westward promised a quick
passage; after passing the Azores, the wind prevailed from the
Southward, with thick weather after passing Longitude 21°W., no
observation was had until near the land; but soundings were had not
far, as was supposed, from the edge of the Bank. The weather was now
more boisterous, and very thick; and the bid still Southerly; arriving
about midnight, 1701 December, within 40 miles, by dead reckoning, of
Tusker light; the wind hauled S.E., true, making the Irish coast a lee
shore; the ship was then kept close to the wind and several tacks made
to preserve her position as nearly as possible until daylight, when
nothing being in sight, she was kept on E.N.E. under short sail, with
heavy gales; at about 10 A.M. an altitude of the sun was observed, and
Chronometer time noted; but, having run so far without any observation,
it was plain the Latitude by dead reckoning was liable to error, and
could not be entirely relied on.
Using, however, this Latitude, in finding the Longitude by
Chronorneter, it was found to put the ship 15' of Longitude, E. from
her position by dead reckoning, which in Latitude 52°N. is 9
nautical miles; this seemed to agree tolerably well with the dead
reckonuig; but feeling doubtful of the Latitude, the observatiioonn as
tried with a Latitude 10' further N., finding this placed the ship
E.N.E. 27 nautical miles, of
the former position, it was tried again with a Latitude 20' N. of the
dead reckoning; this also
placed the ship still further E.N.E., and still 27 nautical miles
further; these three positions were then seen to lie in the direction
of Small's light. It then at once appeared, that the observed
altitude must have happened at all the three points, and at Small's
light, and at the ship, at the same instant of time; and it followed,
that Small's light must bear E.N.E., if the Chronometer was right.
Having been convinced of this truth, the ship was kept on her course,
E.N.E, the wind being still S.E., and in less than an hour, Small's
light was made bearing E.N.E.E., and close aboard.
Sumner published his book, A New and
Accurate Method of Finding a
Ship's Position at Sea by Projection on Mercator's Chart
with great acclaim. In it he proposed that a single time sight be
solved twice, as he had done (fig. 131), using latitudes somewhat
greater and somewhat less than that arrived at by dead reckoning, and
joining the two positions obtained to form the line of position. It is
significant that Sumner was able to introduce this revolutionary
principle without seriously upsetting the method by which mariners had
been navigating for years. Perhaps he realized that a better method
could be derived, but almost certainly navigators would not, have
accepted the line of position so readily had he recommended that they
abandon altogether the familiar time sight.
Sumner method required the solution of two time sights to obtain each
position. Many older navigators preferred not to draw the lines on
their charts but to fix their position mathematically by a method which
Sumner had also devised and included in his book. This was a tedious
procedure, but a popular one. Lecky recommended the method, and
it was still
in use early in the 20th century.
The alternative to working
two time sights in the Sumner method was to dot the azimuth of the body
and to draw a line perpendicular to it through the obtained by working
a single time sight. Several decades after the appears Sumner's book,
this method was made available to navigators through the publ of
accurate azimuth tables, and the system was widely used until
comparatively times. The 1943 edition of the American Practical
Navigator included example. use. The two-minute azimuth tables still
found on many ships were d+ principally for this purpose. The
mathematical solution for azimuth was not a part of the time sight.
St.-Hilaire altitude difference method
. Commander Adolphe-Li
Mareq de Blonde de Saint-Hilaire, of the French Navy, introduced the a
difference method of determining the line of position in 1875. This
method, long as the "new navigation," has become the basis of virtually
all celestial navigatigation.
132. Modern methods of celestial
— Sumner gave the mariner the line of position;
altitude difference or intercept method. Others who followed these men
applied their principles to provide the navigator with rapid for
determining his position. The new navigational methods developed by
men, although based upon work done earlier, are largely a product of
the 20th century.
Four hundred years ago Pedro Nunes used a globe
to obtain a fix by two altitudes of the sun, and the azimuth angles.
years later Robert Hues deterrmined latitude on a globe by using two
observations and the time interval between them. G. W. Littlehales,
of the U S. Navy Hydrographic Office, advocated using stereographic
projection to obtain computed altitude and azimuth in his Altitude, Azimuth
and Geographical Position
, published in 1906.
and mechanical methods have also been proposed. Of these, only the Star
of Captain P.V.H. Weems USN (Ret.), has had
and this almost entirely among aviators. During World War II some were
fitted with a device called an "astrograph," which projected star
altitude from film upon a special plotting sheet. The curves could be
moved to allow earth's rotation. When they were properly oriented, part
of the line of position could be traced on the plotting sheet. More
generally, however, the navigational has been solved mathematically or
by the use of tables.
Spherical trigonometry is the basis for
solving every navigational triangulation, and until about 80 years ago
navigator had no choice but to completely solve each triangle himself.
cosine formula is a fundamental spherical trigonometry formula by which
navigational triangle can be conveniently solved. This formula was
used in lunar distance solutions when they were first introduce because
ambiguous results are obtained when the azimuth is close to 90° or
mathematicians turned to the haversine, which has the advantage of
increasing numerically from 00° to 180°. The cosine-haversine
was by navigators until recent years.
Toward the end of the 19th
century the "short" methods began to appear. 1875, A. C. Johnson of the
British Royal Navy published his book On
. No plotting was involved in Johnson's method,
but he made use
of the principle that a single time sight be worked, rather than the
two that Sumner proposed, and the line of position drawn
through the point thus determined.
In 1879 Percy L. H. Davis, of the British Nautical
Almanac Office, and Captain J.E. Davis collaborated on it Sun's True
Bearing or Azimuth table, which
enabled the navigator to lay down a line of position using a computed
, published by Percy Davis 20 years later,
covered latitudes up to 50° and gave local hour angle values for
selected altitudes to one minute of arc. In 1905 his Requisite Tables
were issued, enabling the mariner to "solve spherical triangles with
three variable errors." These were the first of a large number
of "short" solutions which followed the work of Marcq
Generally, they consist of adaptations of the formulas of spherical
trigonometry, and tables of logarithms in a convenient arrangement. It
is customar y for such methods to divide the navigational triangle into
two right spherical triangles by dropping a perpendicular from one
vertex to the side opposite. In some methods, partial solutions are
made and the results tabulated. Aquino and Braga of Brazil; Ball,
Comrie, Davis, and Smart of England; Bertin, Hugon, and Souillagouet of
France; Fuss of Germany; Ogura and Yonemura of Japan; Blackburn$ of New
Zealand; Pinto of Portugal; Garcia of Spain; and Ageton, Driesonstok,
Gingrich, Rust, and Weems of the United States are but a few of those
providing such solutions. Although "inspection tables" have largely
superseded them, many of these "short" methods are still in use, kept
alive largely by the compactness of their tables and the universality
of their application. They are an intermediate step between the tedious
earlier solutions and the fast tabulated ones, and they encouraged the
navigator to work to a practical precision. The earlier custom of
working to a precision not justified by the accuracy of the information
used created a false sense of security in the mind of sonic navigators,
especially those of little experience.
A book of tabulated solutions,
from which an answer can be extracted by inspection, is not a new
idea. Lord Kelvin, generally considered the father of modern
navigational methods, expressed interest in such a method. However,
solution of the hundreds of thousands of triangles involved would have
made the project too costly if done by hand. Modern electronic
computers have provided a practical means of preparing the tables. In
1936 the first published volume of H.O. Pub. No. 214 was made
available, and later H.O. Pub. No. 249 was provided for air navigators.
British editions of both these sets of tables have been published, and
a Spanish edition of H.O. Pub. to. 214 is being published.
hundred years ago
Thales of Miletus commented upon basic electrical phenomena, but more
than two millenniums were to pass before men first approached a clear
understanding of electricity and the uses to which it could be put.
about 1682 the only known method of creating electricity was by rubbing
glass with silk or amber with wool. Then Otto von Guericke of Magdeburg
invented an "electric machine" and made possible the creation of
electricity for experimental work. The Leyden jar, the electrical
condenser (or machine) commonly used today, had its origin in 1745 when
its principle was accidentall y discovered independently by P. van
Mlusschenbroek, of the University of Leyden, and von Kleist.
Gray, about 1729, demonstrated the difference between conductors and
non-conductors, or insulators, and ten years later Hawkesbee and DuFay,
workingindependently, each discovered the positive and negative
qualities of electricity.
In the middle of the 18th century Sir William Watson of England,
developrt of the Leyden jar in essentially its present form, sent
than two miles by wire. Whether Watson was aware of the tremendous
possibilities his experiment demonstrated is not known. Twenty-five
years later, about 1774, Lesage devised what is believed to have been
the first method of electrical
communication. He had a separate wire for each letter of the
alphabet and momentarily charged
the apppropriate wire to send each letter.
A German scholar, Francis Aepinus (1728-1802), was the first to
recognize the reciprocal relationship of electricity and magnetism. In
Gauss and Wilhelm Weber collaborated in inventing a reflecting
galvanometer for use in
telegraphic work, which was the forerunner of the galvanometer at one
time employed in submarine signaling. Michael Faraday (1791-1867), in a
lifetime of experimental
work, contributed most of what is known today in the field of
inductiduction. In 1864 James Clerk Maxwell of Edinburgh made
public his electromagnetic
theory of light. Many consider it the greatest single advancement in
knowledge of electricity.
134. Electronics. — In
1887 Heinrich Hertz provided the proof of Maxwell's theory by producing
electromagnetic waves and showing that they could be reflected. A
later Joseph J. Thomson discovered the electron and so provided the
the development of the vacuum tube by Fleming and DeForest,. In 1899
R.A. Fessenders pointed out that directional reception of radio signals
possible if aingle coil or frame aerial was used as the receiving
1895 Guglielmo Marconi transmitted a "wireless" message a distance of
mile. By 1901 he was able to communicate between stations more than
apart. The following year Arthur Edwin Kennelly and Oliver Heaviside
introduced the theory of an ionizes layer in the atmosphere and its
reflect radio waves. Pulse ranging had its origin in 1925 when
and Merle A. Tuve used this principle to measure the height of the
135. Application of electronics to
— Perhaps the
first application of electronics to navigation was the transmission of
time signals (art. 1909) in 1903, thus permitting the mariner to check
chronometer at sea. Telegraphic time signals had been sent since 1865,
a means of checking the chronometer in various ports.
broadcasts providing navigational warnings, begun in 1907 by the U.S.
Hydrographic Office, helped increase the safety of navigation at sea.
the latter part of World War I the directional properties of a loop
were successfully utilized in the radio direction finder (art. 1202).
The first radiobeacon was installed in 1921.
Early 20th century
experiments by Behm and Lanngevin led to the development, by the U. S.
of the first practical echo sounder (art. 619) in 1922.
early as 1904, Christian I3ulsmeyer, a German engineer, obtained
several countries on a proposed method of utilizing the reflection of
radio waves as an obstacle detector and a navigational aid to ships.
Apparently, the device was never constructed. In 1922 Marconi said,
It seems to me that it should be possible to design
apparatus by means of which
a ship could radiate or project a divergent beam of these rays
(electromagnetic waves) in any desired direction, which rays if coming
across a metallic
object, such as another ship, would be reflected back to a treceiver
screened from the local transmitter on the sending ship, and thereby
reveal the presence and bearing of the other ship in fog or thick
In that same year of 1922 two scientists, Dr. A. Hoyt Taylor and Leo C
Young, testing a communication system at the Naval Aircraft Radio
Laboratory at Anacostia, D.C., noted fluctuations in the signals when
on opposite sides of the Potomac River. Although the potential value of
the discovery was recognized, work on its exploitation did not
begin until March
1934, when Young suggested to Dr. Robert M. Page, an assistant, that
this might bear
further investigation. By December, Page had constructed a pulse-signal
determined the positions of aircraft. This was the first radar
(art. 1208). In the
spring of 1935 the British, unaware of American efforts, began work in
this field, and
developed radar independently. In 1937 the USS Leary
tested the first seagoing
radar. In 1940 United States and British scientists combined their
in more rapid progress. Probably no scientific or industrial
development in history
expanded so rapidly
in all phases — research, development, design, production, trials, and
training — and on such a scale. In 1945, at the close of hostilities of
World War II, radar was made available for commercial use.
the pulse technique upon which radar is based was utilized for other
navigational aids. Work on loran (art. 1302) began at the Radiation
Laboratory at the 'Massachusetts Institute of Technology in 1941. By
the end of 1942 the first stations had been established, in the North
Atlantic. Installations in the Aleutians and the South Pacific soon
followed. With the termination of hostilities, loran, like radar, was
made available for public use. A somewhat similar system, gee (art.
1308), was developed simultaneously in Great Britain, Another pulse
system, shoran (art. 1213), was developed by the United States for
bombing through undereast. Following World War II this aid was further
perfected and used for measurement of distances in surveying. A
lower-frequency, longer-range system called electronic position
indicator (EPI) (art. 1213) was developed by the U.S. Coast and
Geodetic Survey for use in locating survey ships a considerable
distance offshore. Another American development, Raydist (arts. 1214,
1311), is used in accurate measurement of distance for surveying and
for ship speed trials. Raydist; Decca (art. 1309), a British hyperbolic
system of high accuracy used for navigation and surveying; and lorac
(art. 1310), a somewhat similar American system, use continuous waves,
rather than pulses. Not only are such devices improving the accuracy of
charted features, but they may well apply directly to geodesy,
permitting a more accurate determination of the size and shape of the
earth, for they make possible measurement of distances across
previously inaccessible terrain.
A rotating electronic beam
was utilized during World War II in the German navigation system called
sonne (art. 1206), later further perfected by the British under the
name tunsol (art. 1206).
In air navigation electronics was
used to develop an automatic direction finder. Four-course radio ranges
(art. 1207) and the more recent vortac (art. 1207) have been used to
mark the federal airways. Electronics has various applications to
traffic control in congested areas, and in low-visibility approach
systems permitting landings under conditions of reduced horizontal and
Electronics permits measurement of
weather conditions at various heights and distances from observing
stations, and the transmission of observations from isolated stations
to weather centrals. Radar is permitting study of the structure and
movement of thunderstorms.
High-speed electronic computers
make practicable the modern inspection table, and rapidly perform
lengthy computations which make it possible for loran tables and
chartsto become available to the navigator almost as soon as new
stations are operational.
The application of electronics to
navigation is almost limitless. Many systems not mentioned have been
suggested, and undoubtedly new ones will be operational in the future.
has come a long way, but thero-is no evidence that it is nearing the
end of its development. Progress will continue as long as man remains
unsatisfied with the means at his disposal.
Perhaps the best guides to the future are the desires of the present,
for a want usually precedes an acquisition. Pytheas and his
contemporaries undoubtedly dreamed of devices to indicate direction and
distance. The 16th century navigator had these, and wanted a method of
determining longitude at sea. The 18th century navigatorcould determine
longitude, but found the task a tedious one, and perhaps longed to be
freed from the drudgery of navigation. The modern navigator is still
seeking further release from the work of navigation, and now wants to
be freed from the limitations of weather. There is little probability
of further major development in the
simplification of tables for celestial navigation. Further release from
the work of navigation is more likely to come through another approach
— automation This process might
be said to have started with the application of electronics to
computation. The direct use of electronics in navigation is more
spectacular, but in this it is vulnerable to jamming by an unfriendly
power, intentional or accidental mechanical damage, natural failure,
propagation limitations in certain areas and at certain times, and
accuracy limitations at long ranges.
In the future, it is likely that electronics will be applied
increasingly as an additional source of energy to extend the range of
usefulness of other methods, rather than to replace them. To date
electronics has been related primarily to piloting, extending its range
far to sea, and permitting its use in periods of foul weather. In the
future it can be expected to play an increasingly important role in the
field of dead reckoning and celestial navigation. Inertial and Doppler
systems (art:. 809) are under development for use in guided
missiles and aircraft, and a geomagnetic electrokinetograph (GEK) (art.
611) has been developed to measure the cross component of a current by
means of two electrodes towed astern a vessel, utilizing the earth's
magnetic field. Radio astronomy (art. 1102) may provide a practical
means of determining position astronomically through overcast. Star
trackers and electronic recorders and computer, may further extend the
application of electronics to celestial navigation.
It is not inconceivable that a fix may some day be automatically and
continuously available, perhaps on latitude and longitude dials.
However, when this is accomplished, by one or a combination of systems,
it will be but a short additional step to feed this information
electronically to a pen which will automatically trace the path of the
vessel across a chart. Another An step would be to feed the information
electrically to a device to control the movements of the vessel, so
that it would automatically follow a predetermined track.
When this has been accomplished, new problems will undoubtedly arise,
for it is not likely that the time will ever come when there will be no
problems to be solved.
137. The navigator.
It might seem drat when complete automation has been achieved, all of
the work of the navigator will have been eliminated. However, advance
planning of route and schedule will undoubtedly require human
intelligence. So will the interpretation of results en route, and the
alteration of schedule when circumstances render this desirable. I
milers the automatic system can he made 100 percent reliable it remote
prospect for the foreseeable future it will need checking from time to
time, and provision will have to he made for other, perhaps cruder,
methods in the event of failure.
such time as mechanization may become complete and perfect, the prudent
navigator will not permit himself to become wholly dependent upon
"black boxes" which may fail at crucial moments, or ready-made
solutions that may not be available when most needed. Today and in the
future, as in the past, a knowledge of fundamental principles is
essential to adequate navigation. If the navigator contents himself
with the ability to read dials or look up answers in a book, he will be
of questionable value. His future, if he has one, will be in jeopardy.
beings who entrust their lives to the skill and knowledge of a
navigator are entitled to expect him to be capable of handling any
reasonable emergency. When his customary tools or methods are denied
him, they have a right to expect him to have the necessary ability to
take them safely to their destination, however elementary the knowledge
and means available to him.
The wise navigator uses all reliable aids available to him, and seeks
to understand their uses and limitations. He learns to evaluate his
various aids when
he has means for checking their accuracy and reliability, so that he
can adequately interpret their indications when his resources are
limited. He stores in his mind the fundamental knowledge that may be
needed in an emergency. Machines may reflect much of the science of
navigation, but only a competent human can practice the art of
Collinder, Per. A History of Marine
. Tr. Maurice Michael.
New York, St.
Rawson, J.B. A History of the
Practice of Navigation
Glasgow, Brown, 1951.
Petze, C.L., Jr. The Evolution of
. Vol. 26, Ideal Series. New York, Motor Boating,
Stewart, J.Q. and Pierce, N.L. "The History of Navigation,"
Marine and Air Navigation
(Boston, Ginn, 1944). Chap. 29.
Taylor, E.G.R. The Mathematical
Practitioners of Tudor and Stuart England
Cambridge University Press, 1955.
Wroth, L.C. Some American
Contributions to the Art of Navigation, 1519-1802
Carter Brown Library, 1947.
In addition, articles pertaining to the
history of navigation are frequently carried in certain periodicals,
"The American Neptune." (Salem)
"The Journal of the Institute of Navigation." (London)
"The Nautical Magazine." (Glasgow)
"Navigation, Journal of the Institute of Navigation." (Los Angeles)
"Navigation, Revue Technique de Navigation Maritime et Aerienne."
"United States Naval Institute Proceedings." (Annapolis)