MAPS AS MODELS
-Jack R. Holt
A STONE MAP
As one drives along secondary roads in the
rolling country in northeastern Oklahoma, in the
environs of the Delaware powwow grounds near
Copan, he will see here and there an isolated
cedar, the gnarled limbs of old peach and apple
trees, or the decaying logs that were once part of
the walls of a cabin. -C. A. Weslager (1972)
In the mid 1970's I went on a trek through
land that had been granted to the Delaware
Nation (also known as Lene Lenape) when they
were moved into Oklahoma. A reservoir then
under construction was to inundate some of their
important sites, not the least of which were the
remains of their last working long house.
Anyway, I recall that we were side tracked by
dinner and extended conversation with a colorful
local rancher whom I knew only as Uncle Joe.
He was a large man with flowing white hair and
deep creases in his weathered face. He was one
of the first settlers to move into Oklahoma
Territory and had become something of a legend
in the area. After our lunch and talk Joe
happened to mention a stone map on his land.
The archeologist could barely contain himself
and prevailed upon the old man to take us there.
He walked us up a clearing that had been cut for
a power line right of way and then led us into a
cross timber forest of mixed black jack and post
oak. We fought to keep up with him as he
guided us through the wooded hillside to an area
covered by oak leaves that for all the world
looked like the rest of the woods. He pulled out
a rake that he had stashed next to a rock. He
gave me the handle and told me where to remove
the leaves. Soon I had exposed what looked like
a small stone patio. Some of the features of the
stone had been enhanced by a chisel to illustrate
hills and streams. Joe said that the map had been
shown to him by an old Delaware who claimed
that it was at least as old as he was.
FIGURE 1.
A map of
Oklahoma
and
Indian
Territories from 1899 published
by the Philadelphia Inquirer.
The arrow indicates the location
of the stone map. By this time,
the Delawares Nation had
become part of the Cherokee
Nation
in
an
economic
confederation.
Note the
gridwork of latitude and
longitude in which the map is
framed. Note also that the
indicates the differences in time
between that of London and the
time in that zone. All of these
conventions were centuries in
the making and the story of
their development is the theme
of this essay.
From The Philadelphia Inquirer Co.
(1899)
2
Joe said that he had spent some time
studying that map and tried to correlate it with
local surface features, but no place seemed to fit.
The archeologist studied the map for some time
and then became very excited. He asked for a
boost up into a tree and studied the map some
time longer. Finally he announced that he
thought that we had been trying to interpret the
map at the wrong scale. He suggested that if the
carved hills represented the Appalachian
Mountains and the creek were the Mississippi
River, then the stone map might represent most
of the eastern half of the United States. I stood
in awe as the rock patio transformed itself before
my eyes.
The world transforms itself when it presents
itself in two dimensions as a map. The pictorial
representation of surface features of the earth or
part of it imparts knowledge and power over the
unknown. Consider your own use of maps in
navigating your car or perhaps even a boat. The
ability to know where you are demands that you
accept the lines on a sheet of paper as a
conceptual model of the reality of a place.
TO MEASURE THE EARTH
There was among them a man of genius but as he
was working in a new field they were too stupid
to recognize him. As usual in those cases they
proved not his second-rateness but only their
own.
-George Sarton (1964)
Similarly, the world transformed itself in the
minds of ancient philosophers as they accepted
the concept of the earth as a sphere. Pythagoras
first proposed it. Plato, Eudoxus, and Aristotle
conceptualized it and Eratosthenes demonstrated
it at the time of a summer solstice in ancient
Alexandria.
FIGURE 2. Eratosthenes of Cyrene Image
from: http://www-history.mcs.standrews.ac.uk/history/Mathematicians/Eratosthe
nes.html
Eratosthenes of Cyrene (c. 276-194 B.C.E.;
see Figure 2) was a versatile natural philosopher
of his time. He contributed to geography, and
mathematics, literature, etc. Because of his
versatility, the newly installed Greek rulers of
Egypt asked him to be the head of the Library at
Alexandria. This library, also known as the
Museum because it was dedicated to the Muses,
the deities of inspiration, was more than a
collection of books. It was a government
sponsored site for research and contemplation.
The site quickly attracted the great minds in
mathematics and natural philosophy throughout
the Mediterranean region. The setting seemed to
foster specialists rather than a generalist like
Eratosthenes. He bore the scorn often heaped
upon an administrator by members of an
institution and began to be called "Beta" or
second rate and "Pentatholos", one who excels in
many things but is master of none. Still, this
generalist made some contributions to science
that cannot be ignored even today.
FIGURE 3. The globe of the earth with the
relative positions of the Tropic of Cancer, Tropic
of Capricorn, the Arctic and Antarctic Circles,
and the Equator. Eratosthenes used a knowledge
of the Tropic of Cancer to determine the size and
shape of the earth.
It seems that Eratosthenes helped to
establish the apparent seasonal path of the sun
(and stars) across the sky. He and others at
Alexandria assumed that the paths of the sun and
planets (called the ecliptic) were inclined to the
equatorial plane of the earth by about 24O (Note
that today we say that the earth is inclined 23.5O
to the ecliptic of the solar system). Thus, the sun
seemed to be directly over the equator at the
times of the fall and spring equinoxes. It was
over a line about 24O north of the equator
(Tropic of Cancer) on the day of the summer
3
solstice before it began its trip south to a line
over 24O south of the equator (the Tropic of
Capricorn) at the time of the Winter Solstice (see
Figure 3).
Probably while contemplating this problem,
Eratosthenes heard that the town of Syene had a
well that was illuminated all the way to the
bottom around noon on the day of the summer
solstice. He reasoned that Syene must lie on the
Tropic of Cancer and that at noon on the
Summer Solstice, the sun shone from directly
overhead. Thus, a well could be illuminated and
vertical sticks cast no shadows. He did know
that on the same day, a large stone obelisk called
a gnomon did cast a shadow in Alexandria. That
was all that he needed to know to demonstrate
that the earth was a sphere and to determine its
diameter.
Eratosthenes knew the height of the gnomon
and measured the length of the shadow that it
cast at noon on the Summer Solstice. That
meant that he knew two sides of a right triangle
(a triangle in which one of the three angles is
90O) and could calculate the other side. More
importantly, he could calculate the angle that the
ray of the sun made with the top of the Gnomon
which is the same as the angle at the center of the
earth between Syene and Alexandria (See
Figures 4 and 5).
FIGURE 4. At noon on the day of the Summer
Solstice (the longest day of the year in the
northern hemisphere), an obelisk casts a shadow
in Alexandria while on the same day, the sun
shines to the bottom of a well in Syene.
He knew that a camel caravan took about 50
days to make the trip from Syene to Alexandria.
Furthermore, he knew that a caravan traveled at
about 100 stadia per day. Thus, the total
distance was about 5,000 stadia (or about 725
km). He knew from his measurements of the
angle of the shadow from the top of the Gnomon
(see Figures 4 and 5) in Alexandria that the arc
from Syene to Alexandria was just over 7O (or
1/50th of a circle). Thus, the circumference of
the earth must be about 50 times 5,000 stadia or
250,000 stadia (1 km approximately equaled 5.4
stadia) thus 46,300 km (actually it is about
40,000 km).
Remarkably, Eratosthenes
produced a number that was unsurpassed in
accuracy for the next 20 centuries.
FIGURE 5. The angle (a) at the top of the
gnomon is equal to the angle (a) between
Alexandria and Syene at the center of the earth.
This was a breathtaking example of the
ability of the human mind to create a conceptual
model of the earth and then use that model to
come to an answer. Sadly because Eratosthenes
was derided as second rate by the other natural
philosophers of the Library, his numbers were
not accepted and his conclusions were suspect.
Others confirmed the spherical nature of the
earth also by the use of celestial observations.
Thus, the technique of taking measurements of
stars, moon, and sun to determine geography had
been established.
PTOLEMY'S GEOGRAPHICA
The task of Geography is to survey the whole in
its just proportions, as one would the entire
head.
-Claudius Ptolemy (ca. 90-170)
One of the most celebrated members of the
Library (nearly five centuries after the time of
Eratosthenes) was Claudius Ptolemy (Figure 6).
He is most well known for the mathematical
model of the universe that he published in the
book that we know as The Almagest. He also
wrote a book that we know as Geographica or
Geography. This work was a major influence on
the way that those who followed in the Greek
philosophical tradition viewed the earth for the
next 1,000 years.
4
Geographica was a careful compilation of
Greek geographic speculation. In it he defined
the discipline of geography and the methods by
which maps should be drawn. In addition he
added a compendium of place names and their
descriptions. Most importantly he included a
collection of 26 maps, one of which was a map
of the known inhabited world.
Ptolemy accepted a revision of Eratosthenes'
estimate of the global circumference. This put it
at 25% smaller than the current globe.
Furthermore, he assumed that the known
inhabited lands occupied 1/2 or 180O of the
globe. So, he stretched the continents of Europe
and Asia over half of the earth.
Ptolemy used the known positions of major
cities as benchmarks in drawing his maps. These
positions had been determined by astronomical
observations and filled in the coast lines and
terrestrial features by using descriptions from
travelogues, mariners, etc.
Ptolemy also
indicated that his maps should be modified as
more accurate geographical information became
available.
FIGURE 6. Claudius Ptolemy.
http:// es.rice.edu/ES/humsoc/Galileo/
Images/Port/ptolemy.gif
He recognized that the spherical nature of
the earth required that any map of a large area
must be a projection that distorts the surface. He
chose to use a conic projection that showed the
known world from the Atlantic Ocean in the
west to Asia in the east. He showed most of the
known northern hemisphere and part of the
southern hemisphere including part of Africa.
He assumed that the earth must be balanced so
the southern hemisphere should have a land mass
at least comparable to that in the north. He
called the unknown continent Terra Australis
(the southern land).
In the tradition of Greek geography and
cartography, Ptolemy thought of the earth's
sphere as being covered by a regular grid of eastwest and north-south lines. The lines divided the
globe along 360o in the north-south plane and the
east-west plane. The equator made a natural line
from which to begin the designation of the east
west parallels of latitude. He designated the
equator as 0O and the poles as 90O.
Perpendicular to the parallels of latitude,
Ptolemy set up lines or meridians of longitude
(see Figure 3). These lines were not parallel.
Instead, they converged at the poles and
exhibited greatest divergence at the equator.
Unlike the lines of latitude, the starting point or
0O longitude was arbitrary. Ptolemy placed it in
the Atlantic Ocean just west of all land masses.
He numbered the longitudinal lines from that
point eastward. Thus, Ptolemy could designate
any point on earth by two sets of numbers in the
grid. Not only could he designate the position by
degrees, but each degree was divided into 60
minutes and each minute was divided into 60
seconds. Thus he could designate particular sites
on earth with great precision.
The grid as described was regular on the
globe of the earth, but it became distorted as it
was flattened out into two dimensions as a map.
If distortion was a natural result of projecting the
3 dimensions onto 2, why would anyone do it?
Well, globes are cumbersome and anything but
portable. Maps can be rolled, folded and are
very portable. Besides, to have a globe that is as
detailed as a typical road map would require a
sphere many stories in diameter. Thus, the
utility of maps is evident, despite the necessary
distortions.
Still, Ptolemy sought to minimize the level
of distortion in the world maps by producing a
projection that translated the globe of the earth
into a cone and then just unrolled the cone into a
flat sheet (see Figure 7). The parallels of latitude
were low, sweeping u's and the longitudinal lines
diverged from a parallel near the pole to the
equator where they began to converge again in
the southern hemisphere. His projections of the
world allowed for a distortion that retained the
relative sizes of the land masses. However, it did
distort directions and distances. Thus, it was
useful as a picture of the earth but not very
helpful as a navigational tool. However, he did
add other regional maps that had little distortion
and could be used to estimate direction and
distance.
5
.
FIGURE 7. Ptolemy's spherical projection of the known inhabited world. This was from a 10th century
manuscript of Ptolemy's Geography. http://www.henry-davis.com/MAPS/AncientWebPages/119G.html
Because
his
Geography
was
so
comprehensive and carefully written, it served as
the model for cartography from that point on.
With it began cartographic conventions such as
placing north on the top and east on the right of
maps, and the division of degrees by minutes and
seconds (rather than the old fractional method).
The successors of Greek learning in the Islamic
Empire augmented maps of Ptolemy but kept the
cartographic conventions in place.
They
followed Ptolemy's methods and added to his
maps by the methods that Ptolemy described.
Maps and collections of maps appeared all over
the Islamic Empire housed in great libraries that
were patterned after the library at Alexandria.
MERCATOR'S ATLAS
[Mercator] set out, for scholars, travelers, and
seafarers to see with their own eyes, a most
accurate description of the world in large
format, projecting the globe on to a flat surface
by a new and convenient device, which
corresponded so closely to the squaring of the
circle that nothing, as I have often heard from
his own mouth, seemed to be lacking except
formal proof.-Walter Ghim (1569, quoted in
Wilford, 2000)
Western Europe became introduced to
philosophy in the tradition of the Greeks when
one of the great Islamic libraries fell in 1089 to a
Christian army in Toledo. In this way, the
impoverished Europeans began to appreciate the
intellectual riches of the Greeks and Arabs.
Educated Europeans from this point on were
schooled in the tradition that the earth was a
sphere. Thus, Columbus never believed that he
might fall off of the edge of a flat earth.
However, he did accept the Ptomlemaic view
that the inhabited world stretched halfway across
the globe. Also, he seemed to have calculated
the remaining ocean between the Canary Islands
and Asia was only about 4,300 km (the actual
distance from Spain westward to Asia was
almost 20,000 km). Fortunately for Columbus,
the Americas happened to be about where he
expected to find Asia. The discovery of the New
World set off a flurry of exploration by
Europeans. In order to accomplish the discovery
in a successful and profitable way, however,
more accurate maps had to be generated.
6
FIGURE 8. A map produced by Geradus Mercator in 1538. This was a spherical projection similar to the
projection of Ptolemy. http://www.scg.ulaval.ca/gps-rs/Images/Mercator.gif
FIGURE 9. The modern outline map of the earth (left) illustrates the Mercator projection with gradual
elongation of the longitudinal lines toward the poles. In this projection, the latitudinal and longitudinal
lines are always perpendicular to each other. Also, the lines of longitude are always parallel. The poles
cannot be shown in this projection. The Greenland problem illustrates the distortion inherent to this kind of
projection. The surface area of South America is about nine times that of Greenland; however, because of
size distortion near the poles, Greenland appears to about the same size as South America on a Mercator
projection. The map on the left was published in the early 17th Century.
http://www.atm.ch.cam.ac.uk/acmsu/utf/mercator.gif
7
Flanders was one of the principle map
making areas during the 16th Century and one of
its most innovative map makers was Gerardus
Mercator (born Gerhard Kremer; 1512-1594).
He was the son of an impoverished German
immigrant to Flanders and was raised by a more
well to do uncle who determined the course of
the rest of his life. Mercator graduated from the
University of Louvain and then traveled Europe
before he returned to Louvain and studied
mathematics and its applications to astronomy
and geography. Later he learned methods of
engraving and making instruments. All of these
methods served him well as a successful map
maker. After 1535 Mercator began to make
globes and maps. In 1538 he produced a map
with a new projection. It was somewhat similar
to the map of Ptolemy but it showed the whole
earth (see Figure 8).
Mercator understood that projections such as
his 1538 map, although innovative, perpetuated
some of the problems that had been common to
maps of all projections up to that point. In
particular the distortion necessary to "flatten the
globe" made most world maps poorly suited for
navigation., something that the dawning Age of
Discovery required. Mercator realized that he
could do that but would have to introduce
distortions in distance and size, particularly for
land masses near the poles. Thus Mercator
created his most famous map projection (see
Figure 9). The great modification for which
Mercator is remembered allowed navigators to
plot straight line courses. So, the angles relative
to north (or any other cardinal direction) were
constant. However, distances varied as one
plotted courses farther from the equator. Still,
the advantages far outweighed the disadvantages.
Besides, smaller more local maps could be used
to judge distance.
He used this philosophy when he published
his collection of maps, much like that of Ptolemy
and other mapmakers. He published a Mercactor
projection of the earth with a collection of
regional maps and began his book with a
genealogy of the Titan named Atlas, the GrecoRoman God who had the task of supporting the
heavens on his shoulders. Ever since then such a
collection of maps has been called an atlas.
The synergy between maps and navigation
helped to improve the general understanding of
the earth, its oceans, and continental boundaries
at an accelerating rate. Exploration of the kind
fostered by better maps also supported colonial
expansion of the Western powers and helped to
reap fantastic wealth from trade and conquest.
Thus, colonial, economic, and military prowess
depended upon accurate maps and the means of
finding oneself on those maps. Those could be
achieved only by the careful use of precision
instruments that could measure both earth and
sky.
MAPMAKER'S TOOLS
In the seventeenth and eighteenth centuries,
surveying assumed a more integral role in
geodesy and cartography…. No longer were
mapmakers dependent almost solely on the
meager fare that came their way from traveler's
tales, explorer's crude sketches, and mariner's
random compass bearings.
-John Noble Wilford (2000)
The tools for making maps had changed
little from the time of Ptolemy. Specifically, the
mapmaker had to determine specific locations
and then plot them on a coordinate grid system.
He then had to fill in between the known points
with other kinds of measurements and
information. The most accurate positions could
be determined by standard astronomical
observations. For example, latitude in the
northern hemisphere could be determined quite
precisely by taking the angle of a place relative
to the north star. That angle was parallel of
latutude (see Figure 10).
FIGURE 10. The angle (θ) between the
horizontal and the North Star (the arrow points to
it) is the latitude.
A magnetic compass allowed the mapmaker
to orient relative to north even if the skies were
overcast. It was not long, however, before the
precision of measurements demonstrated that the
magnetic north was not quite the same as true
8
north, which even varied from one place to the
next on the earth.
Navigators and surveyors employed the
methods of both locating places on maps and
making maps. For both groups, maps and
measurements were the arts of the trade.
Surveyors needed to depict an area as accurately
as possible because they measured land and land
was money. They employed chains and wheels
to estimate overland distances. They developed
methods of triangulation to find distances and
angular positions relative to north from a known
point. They employed similar means to measure
elevation in relation to known points. Thus,
more accurate and detailed depictions of place
could be made. Tools of the surveyor resembled
those of the astronomer in which precise
determinations of angles became the allimportant task.
A
B
FIGURE 11. A shows three known positions
(squares) and distances between them. The
circles represent features hat need to be mapped.
B shows the result of triangulation in which the
circles can be accurately determined according to
distance and direction.
ground. Consider Figure 11A. Suppose that the
squares are known points; then the interesting
features (the circles) can be determined by
triangulation. As the positions of the circles
become known, then their baselines can be used
in turn to determine the positions of the other
circles (see Figure 11B). If the baseline is of a
measured distance, then all lines on the map are
drawn proportional to that line and true to the
compass directions. Thus, triangulation and
instruments designed for that task allowed
surveyors to map local areas with great
precision.
The determination of longitude proved to be
a more difficult problem. Longitude has no
astronomical object against which to measure
because the earth turns on an axis where the lines
of longitude converge at the poles. The most
obvious way of telling longitude would be to
consider what happens as the earth turns on its
axis. In a 24 hour period the sun appears to
travel across the sky and then to disappear during
the night. Thus, the earth turns a full 360O in 24
hours or 15O per hour. Suppose that you know
that local time is noon when it is 1pm at the
Royal Observatory at Greenwich, then you know
that you are 15O east of Greenwich. However, in
the seventeenth and eighteenth centuries clocks
just were not accurate enough to determine time
at another place. So, astronomical methods were
used. For example, Galileo had suggested that
the transit of the moons of Jupiter and their
relative positions might be used as a great clock
in the heavens.
Giovanni Domenico Cassini (1625-1712),
astronomer to the Pope, began the task of
mapping France. First, he worked out the
appropriate tables for Jupiter's moons so that he
could read the time in Paris. He then compared
that time (determined at night) against local time
(determined during the day). Pendulum clocks
could be trusted to keep the time from the night
observations to the daytime determination. The
difference in time could be interpreted as
longitude. The mapping project became the
work for the rest of his life. He did not finish it
and its completion fell to his son and then to his
grandson. The map of France finally was
completed in 1745 in the first great precision
surveying effort.
Simple triangulation could be done using a
flat or plane table. The surveyor lined up the
table relative to north and mounted an arbitrary
point on the table over a known point on the
9
THE LONGITUDE PRIZE
I have treated about matters pertaining to the
strictness of measuring time…; and I have also
treated of the improper, troublesome, erroneous
- tedious method, which the professors at
Cambridge and Oxford would have to be for the
longitude at sea.
-John Harrison (1775)
Astronomical methods like those employed
by the Cassinis were very useful in surveying
and cartographic projects on land. However,
they did not work well at sea. Trying to make
sightings of Jupiter's moons on the rolling decks
of ships was nearly impossible. Another method
had to be established for the accurate
determination of longitude. For states such as
Great Britain this problem was a very serious
one. By the 18th Century Great Britain had
emerged as the most powerful and wealthy seafaring nation on earth. Its position as an island
nation and colonial power depended on a strong
and effective navy whose capability depended on
good navigation. The nautical charts had been
much improved over those of Mercator and his
contemporary mapmakers. The instruments for
navigation also had been improved and
developed to allow the determination of accurate
positions, particularly with regard to latitude.
However, precise methods for the determination
of longitude still eluded navigators with many
mishaps at sea as a consequence.
Dead
reckoning remained the standard method, a
method by which ships could be off by as much
as 10O or more even with the most experienced
navigators. For example, Magellan's pilot with
his experience and all of the scientific equipment
available to him at that time placed the
Philippines correctly with respect to latitude, but
was off by 53O (or 1/7 of the distance around the
earth) in his determination of longitude.
In recognition of the problem and the
importance of its solution, the British Parliament
passed the Longitude Act of 1714 in the wake of
several navigation-related naval disasters. The
rules of the prize stipulated that Parliament
would award £10,000 for a method by which the
determination of longitude would be accurate to
within 1O ; £15,000 for a method accurate to
within 2/3O , and £20,000 for a method that was
accurate to within 1/2O of longitude. These were
princely sums (£20,000 then would be more than
one million dollars in today's money). This just
showed how important, some said insoluble, the
problem was.
The Longitude Act called for the creation of
a Board of Longitude. This was stacked with
astronomers, naval officers, and members of
Parliament. In general, the scientific-minded of
the day favored an astronomical solution. The
moons of Jupiter were too small, but some, like
Edmond Halley (1656-1742), believed that the
time at the Greenwich Observatory could be
determined by observing the position of the
moon and its proximity to major stars because
the moon moves about 13O with respect to the
"fixed stars" each day. This method held
promise, but it required much work to construct
tables for its implementation.
Meanwhile, other methods were explored,
but few believed that the answer would be the
production of a clock that could hold its time and
not be affected by the rolling motion of a ship,
the changes in humidity and temperature, or the
corrosive sea salt while under sail. Indeed, the
mechanical solution was seen as impossible and
likened to our response to the possibility of
constructing a perpetual motion machine. Still,
the prize attracted many hopeful incompetents
and the records attest to a plethora of hairbrained schemes.
In this atmosphere of incredulity John
Harrison (1693-1776; see Figure 12), a selftaught clockmaker and instrument maker began
to see the possibility of achieving the prize. He
had a particular genius with clockworks and
managed early on to make clocks that required
no lubrication nor were they affected by changes
in temperature. In 1835, Harrison produced a
large clock whose moving parts were balanced
such that the motion of a rolling ship did not
alter its regular action. Harrison presented this to
the Board of Longitude, which although it
wanted an astronomical solution, saw that
Harrison's clock, which was called H-1, might
work. It was subjected to a short sea trial in
which it performed very well.
However,
Harrison, ever the perfectionist, saw that his
clock could be improved and withdrew it from
competition. He worked to make the clock
smaller (H-1 stood nearly 1 meter high). He
improved its design through H-2, and H-3.
Unsatisfied, Harrison withdrew H-3 right after he
submitted it to the Board of Longitude.
Harrison began a different approach to the
clock and completed H-4 in 1761 (see Figure
13). This was a departure from the earlier
timepieces in that H-4 was made as a large
pocket watch about 15cm across. Its reliability
and accuracy during a sea trial to the West Indies
and back was well within the 1/2O of longitude
specified by the Longitude Act. The Board,
however, refused to give the full amount and
required Harrison to make two duplicates of H-4
10
without the plans or the original clock to use as a
guide. Then, Parliament changed the rules and
required a whole battery of sea trials. In the
mean time, the astronomers were working hard
to complete their lunar tables.
FIGURE 12. John Harrison near the end of his
life.
H-4 sits in the background.
http://www.rog.nmm.ac.uk/museum/harrison/har
rison.html
by Harrison's treatment and performed his own
trials of the newest timepiece called H-5. This
one performed beautifully and the king
demanded that Harrison be acknowledged as the
winner. Finally, Harrison was given the full
amount that he sought. Although his award did
equal about £20,000 in its various increments,
Parliament had changed the rules of the
longitude prize so that technically the award was
never claimed.
Captain James Cook took a copy of H-4
with him on his second (1772-1775) and unlucky
third (1776-1779) voyages around the world.
Although he tried both the chronometer and
lunar methods of longitude, Cook certainly
preferred the chronometer. He referred to the H4 copy as "our faithful guide through all the
vicissitudes of climates." John Harrison, finally
vindicated, died within the year of Cook's return
from his second voyage.
A single chronometer might cost £200 or
more while a sextant and a book of lunar tables
could cost a tenth of that. Still, the advantages of
the clock method were obvious. The navigator
could determine longitude independently of
clouds and the times of the month when the
moon was close to the sun (periods of the new
moon). The glaring disadvantage was what
would happen if the clock stopped or
malfunctioned.
FIGURE 13.
John Harrison's crowning
achievement, the chronometer known as H-4.
http://www.rog.nmm.ac.uk/museum/harrison/h4.
html
Harrison struggled to make the duplicate
clocks (now called chronometers) while the
original H-4 had been taken by his chief rival to
the Royal Observatory at Greenwich for
extended accuracy trials which, of course, it
failed. Fed up with the manipulation of his
father by the Board of Longitude, Harrison's son
petitioned King George III for an audience and
related the entire affair. The king was incensed
FIGURE 14. The centerpiece of James Cook's
coat of arms is a globe with prominent lines of
latitude and longitude.
http://home.earthlink.net/~donmiguel1/
name_files/cook_coat_arms.html
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The chronometer method became the
standard for the British Navy. To counteract the
prospect that a chronometer might malfunction,
British exploration and mapping vessels often
had multiple chronometers aboard, each serving
as a check for the others. Captain Fitzroy of The
Beagle, had the charge of mapping the coastline
of South America. To support this, he had more
than 40 chronometers on ship. Usually such
mapping expeditions also engaged in geological
and biological surveys to coordinate with the
maps that they produced. Fitzroy's second
expedition (1831-1836) to map the coastline of
South America introduced a young naturalist
named Charles Darwin to the diversity of life.
Even though little of the earth's surface had
been surveyed in a scientific way, the methods
available by the early 19th Century assured that it
could be. The only remaining problem was the
matter of standardizing aspects of cartography.
In particular, there was no standard of
international measurement and there was no
agreement on the location of the Prime Meridian,
the line of longitude against which all others
would be determined.
MODERN MAP MAKERS
That the Conference proposes to the
Governments here represented the adoption of
the meridian passing through the centre of the
transit instrument at the Observatory of
Greenwich as the initial meridian for longitude.
-Resolution of the International Meridian
Conference, Washington D.C. (1884).
Prior to 1875 maps and measurements were
reported in a cacophony of units. In many cases,
standard measurements changed from one region
of a country to another. No country suffered
more from this than France in the latter part of
the 18th Century. After the French Revolution,
sweeping reforms of almost all of the old
systems caused the new government to look at a
scientific standard for the unit of length. After
much debate, 1 ten-millionth of the distance
from the pole to the equator was adopted as the
meter, the foundation of the whole metric
system.
Gradually, science and commerce
adopted France's system. Finally, the Meter
System Treaty of 1875 established the metric
system as the standard means of measurement
for international transactions and a common unit
of distance for international charts and maps.
The problem of the Prime Meridian was a
significant issue in the mid 19th Century.
Because of rising nationalism throughout Europe
and the Americas, there were at least 14 different
Prime meridians in use. Because of their
accuracy and pervasive use, the British sea charts
with their reference to the longitude at
Greenwich Royal Observatory as 0 longitude
were well-known internationally. Thus, when
the United States called for a standardization of
longitude and hosted a meeting (International
Meridian Conference Washington, D.C.) on the
issue in 1884, Greenwich was adopted as the
International Prime Meridian with longitude
numbered to 180o both east and west from that
line.
With the establishment of a Prime
Meridian, International Time Zones could be
created, a move that fostered commerce,
particularly by rail.
The next major step in cartography was the
use of aerial photography to support on the
ground surveys. This method was first used in
mapping parts of the Pocono region in
Pennsylvania. Since then it proved to very
valuable, particularly when mapping rugged
terrain and when updating existing maps. The
photographs also suffered from lateral
distortions.
One solution to the distortion
problem was to get very far away and take the
photos straight down. With the advent of the
space age, the problem of distance and the
computer power to make maximum use of the
information came together.
Now, satellite
images of the earth can be downloaded routinely.
For example, satellites in the Landsat series
(1972-present under the authority of NASA and
the USGS) can view the earth with a variety of
sensors (see Figure 15) and provide valuable
information for "global change research and
applications in agriculture, geology, forestry,
regional planning, education and national
security."
FIGURE 15. An image depicting Landsat 7,
launched in 1999.
http://www.csc.noaa.gov/products/sccoasts/html/
pdecript.htm
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Similarly, the U.S. military put aloft a series
of 24 satellites (called Space Vehicles or SVs).
They orbit the earth at 20,200 km in a particular
pattern of 6 orbital planes, 4 satellites in each
plane. They form the ideal technology for
navigation and survey.
With a Global
Positioning System (GPS) receiver, anyone
could know latitude, longitude, and elevation
that the Cassinis and Harrisons could not dream
possible. With the GPS system, we once again
look to the heavens to find where we are.
FIGURE 16. Part of the GPS satellite system
that allows for precise triangulation in the
determination of place (latitude, longitude, and
elevation).
MAPS AS MODELS
Watcher was chief; he looked toward the sea.
At this time, from north and south, the whites
came.
They are peaceful; they have great things; who
are they?
-End of the Walam Olum (these lines accompany
the pictographs of Figure 17).
Our ability to know and map the earth has
increased in leaps and bounds. The methods that
we can employ have been used to map the moon
and Mars so that we know them better than we
knew the earth only a century ago. Maps are
useful because they obey the rules of Ptolemy
and conform to the standardized conventions that
have developed over the centuries.
Such
conceptual models as maps are powerful tools
because they tell of where we have been and
There are other kinds of conceptual models
that portray the earth, too. The predecessor of
the stone map on Delaware land in Oklahoma
was a much older mythology, an oral text that
accompanied a series of pictographs often
written in red ochre on bark called the Walam
Olum (or Red Scribe). The pictures depict
Delaware history from the mythic times of the
origin of the world to their ancestors' travels
across a land from the west to the eastern ocean.
Liberal interpretations of the stories suggest that
the Delaware describe their life in Asia and the
crossing of the frozen waters of the Bearing
Straits.
Curiously, the Walam Olum ends with a
bittersweet statement about the coming of the
whites and closes with the question, " They are
peaceful; they have great things; who are they?"
The last pictograph of the Walam Olum
illustrates a ship on the eastern ocean, a ship that
arrived by means of charts and instruments,
which allowed its inhabitants to find their way
across the sea. After that the Delaware added no
further pictographs to the Walam Olum. The
U.S. government moved them out of
Pennsylvania to Ohio, then Indiana, Kansas, and
finally into Northeastern Oklahoma (then called
Indian Territory; see Figure 1). In one of life's
ironies, I now live in a house that sits on land
inhabited by the Delaware when they created that
last pictograph. Maps were one of those "great
things" that those who came from the north and
south brought with them. Perhaps the stone map
was an attempt to tell a new story with a new
model of the earth, a western-style pictograph,
the map.
FIGURE 17. The last pictographs of the Walam
Olum. Note the bottom figure illustrates a ship
on the sea. From Brinton (1999).
13
Sources that I used to write this essay
Brinton, Daniel G. 1999 (originally published
1885). The Lenape and their Legends; With
the Complete Text and Symbols of the
Walam Olum. Wennawoods Publishing.
Lewisburg, PA.
Holt, Jack R. and Patricia Nelson. 2001. Paths of
Science.
Kendall/Hunt Publishing Co.
Dubuque, IW.
Philadelphia Inquirer. 1899. Pictoral Atlas of the
Greater United States and the World. The
Philadelphia Inquirer Co. Philadelphia.
Ptolemy, Claudius. 1991 (from a 2nd Century
text). The Geography. Trans & ed. Edward
Luther Stevenson. Dover Publications, Inc.
New York.
School of Mathematics and Statistics, University
of St Andrews, Scotland. 1996. Gerardus
http://www-history.mcs.stMercator.
andrews.ac.uk/history/Mathematicians/Merc
ator_Gerardus.html date accessed: March
11, 2002.
School of Mathematics and Statistics, University
of St Andrews, Scotland. 1999. Eratosthenes
http://www-history.mcs.stof Cyrene.
andrews.ac.uk/history/Mathematicians/Erato
sthenes.html date accessed: March 13, 2002.
Sheffner, Ed. 1999. Welcome to the Landsat
Program.
http://geo.arc.nasa.gov/sge/landsat/landsat.ht
ml date accessed: March 29, 2002.
Sobel, Dava. 1995. Longitude. TheTrue Story of
a Lone Genius Who Solved the Greatest
Scientific Problem of His Time. Penguin
Books. New York.
Weslager, Clinton A. 1972. The Delaware
Indians, A History. Rutgers University
Press. New Brunswick, NJ.
Wilford, John Noble. 2000. The Mapmakers.
Revised Edition. Alfred A. Knopf. New
York.
Questions to Think About
1. Other than you think of a conceptual model other than a map?
2. Why was Eratosthenes considered by his peers to be mediocre? How did he
calculate the circumference of the earth?
3. What underlying belief (other than the earth is a sphere) did Ptolemy use in
creating his map of the world?
4. What is the advantage of the Mercator projection? What is at least one
disadvantage?
5. How does triangulation work to produce a map?
6. Why was determination of latitude relatively easy compared to longitude?
7. How did John Harrison win the longitude prize? Why were the authorities
reluctant to award him the prize?
8. Why was the concept of the prime meridian so important to map mapmakers
as well as to the railroads?
9. How does the GPS system work?
10. How were the pictographs of the Walam Olum conceptual models?
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