Chapter 1: Introduction
Chapter 1: Introduction
Introduction
Maps are so much a part of our everyday lives that most people give them no more thought than
they give to writing. Yet both are profoundly important means of communication that have changed the
course of human history and continue to exert a powerful influence on our affairs today. Maps have
caused wars and sometimes have determined the outcome of wars. They document the history of world
exploration and have in turn been both the cause and the means of exploration and settlement. Today
maps in hard-copy and electronic formats guide a driver to an address in Vancouver or a pilot to a safe
landing on the other side of the globe and they document the vast array of spatial activity on our planet
and beyond.
Yet, also like writing, mapping is a skill that few do well and many are unable to do at all.
Similarly, as the illiterate are denied the meaning of words, many lack the means to read the message of
maps. Just as a written passage can be superficially skipped over, or intensely searched for deeper and
perhaps more subtle layers of meaning, a map has a superficial layer accessed by many, but more subtle
layers of meaning await those with the skills to probe further.
Map reading is a basic skill of the geographer. Indeed, it is an essential tool for anyone who
communicates through spatial images. Perhaps because we do take maps for granted, many or even
most people, do not possess the skill of 'reading' a map; learning this language is the subject of this
manual.
This book constitutes a course manual for Geography 250 (Cartography) at Simon Fraser
University and is designed to introduce students to the basic theory and practice of surveying, map
construction, and map interpretation. Although the course is concerned with the wide range of maps and
mapping techniques used by geographers, emphasis is on topographic mapping. Understanding the
construction and use of topographic maps, however, involves many concepts that are directly transferable
to other kinds of maps.
For example, there is no fundamental difference between the problems
encountered in describing the three-dimensional surface form of the ground (landform) on a map and
those to be solved by the geographer wishing to map a statistical surface.
A map can be defined broadly as a representation to scale of features on a real surface. Thus it
is a medium for measuring the property of location, a concept at the very heart of geography. The
features may be visible and tangible things such as rivers and mountains or they may be abstractions
such as administrative and political boundaries and regional incomes and prices, for example. Although
we will not consider aerial photographs until much later in this discussion, we should note that they also
fall within our broad definition of a map.
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Chapter 1: Introduction
A great advantage of building our mapping skills on an understanding of topographic maps is that
the transfer of information between the real world and its map is very direct. We can construct an image
of reality from our map and readily check its validity by looking at the landscape of which we are a part.
Nevertheless, the skill of 'seeing' or picturing a real three-dimensional landscape from an abstract twodimensional map involves the use of some very complex 'transfer functions'. No one quite knows how our
brain accomplishes this task but experience has shown clearly enough that most people who practise relating a map to the ground and vice versa can become quite expert in the art of map reading. Like so
many other skills, the key to accomplishment is practice. For this reason much of our time will be spent
on developing these skills by undertaking 'practical' exercises on a variety of maps, some of which will be
constructed by you from your own field surveys; more about that later. Meanwhile, it will be instructive to
remind ourselves that most of our ideas, including those about maps, are gifts from the past.
A brief history of mapping
The history of mapping is a scholarly discipline in itself and is supported by a very substantial
literature. Indeed, documented map-making is an ancient craft spanning some 4 000 years of human
curiosity; all we can do here is to touch a few mileposts along the way. If you are interested in finding out
more about the history of maps and map-makers I have listed some references at the end of the book
which will help you find your way into this material.
It is not possible to know, of course, when humans first produced maps but it would be fair to
guess that the first map dates almost from the very beginning of our species. Perhaps it was a rough
sketch scratched in the sand to show a fellow hunter the site of an animal kill. It is entirely possible that
some prehistoric maps may have been quite sophisticated.
After all, we seem to be egocentrically
disposed to think of our early ancestors as being far more primitive than the 12 000 - 34 000 year old CroMagnons who created the beautiful cave paintings of Lascaux and Altamira. Nevertheless, the beginning
of map-making is a speculative matter and we must leave it at that.
Perhaps the oldest known map is a 4 500 year-old Babylonian clay tablet depicting the location of
a man's estate on the Euphrates River in the ancient kingdom of Babylonia (Figure 1.1A). This and other
ancient maps usually depict simple details and presumably many were also route maps for travelers.
Although such ancient maps appear in several parts of the world, the era of scientific cartography,
certainly within the western or European tradition, had its origins in the classical world of ancient Greece.
As early as the fourth century B.C. Greek philosophers and scholars had deduced from observations of
various kinds that the Earth might be spherical in shape. A century or so later the Head of the Great
Library of Alexandria, Eratosthenes of Cyrene, was to make the first theoretically sound attempt to
measure the planet's circumference. By noting the time of day when the sun was directly overhead (from
the bottom of a well!) in two places a known distance apart, he computed Earth's circumference to be
2
Chapter 1: Introduction
250 000 stadia or about 45,000 km. Given the crude measuring instruments available to Eratosthenes,
his result (within 14% of its true size), obtained some 250 years before the birth of Christ, is quite
remarkable.
It seems that another quite remarkable cartographic contribution made by Eratosthenes was a
map of the classical 'world', that we now know as the Mediterranean region.
Although the original map
has never been found, detailed descriptions of it by his contemporaries and later scholars, have allowed
its reconstruction (Figure 1.1B). Apparently, it recognized the spherical nature of Earth's surface by
making use of spherical coordinates - an irregular grid of seven meridians and seven parallels - including
the equator and northern tropic. Considering its antiquity, Eratosthenes' map of the Mediterranean
coastline is surprisingly accurate. Indeed, it compares favourably with many drawn a thousand years
later!
Although Eratosthenes' cartography represents a very significant contribution to the science of
mapping, his work was largely overshadowed three hundred years later by another quite remarkable
Alexandrian Greek scholar, Claudius Ptolemy (A.D. 90-168). Ptolemy's eight-volume Geographia, a sort
of natural history encyclopedia, included a discussion of the theory and practice of making a world map,
the estimated latitude and longitude of some eight thousand locations, and instructions for constructing
twenty-six regional maps and two map projections!
Whether or not Ptolemy ever followed his own
instructions in actually drawing these maps is not known for no original has survived. But we do know
from medieval copies that someone made use of his insights and that these reconstructions exerted a
profound influence on cartography for more than a thousand years. In the late fifteenth century Ptolemy's
world map was to re-emerge as an important foundation of modern cartography. Ptolemy's world map is
distinctly modern in appearance with the locations of coastlines, mountains and rivers around the
Mediterranean and adjacent areas shown accurately on a system of converging meridians and curved
parallels. As we might expect, further afield errors increase in the marginal less well-known regions
where, for example, the Indian Ocean is shown enclosed and Sri Lanka is oversized. A less obvious error
in his map is the scale: Ptolemy's map of the earth is only about three quarters of the actual size. He
adopted Posidonius' estimate of the earth's circumference (1
o
o
= 500 stadia = 90 km) instead of
Eratosthenes' more accurate estimate (1 = 700 stadia =125 km).
o
It is interesting that, because
o
Ptolemy's combined length of Europe and Asia is 180 , instead of the actual 130 , the implied sea gap
between the Orient and western Europe is narrower than it is in fact. It often has been argued that this
mistake is one of the factors that encouraged Columbus and other explorers to seek a westerly route from
western Europe to the spices of the Orient.
The existence of a great southern land providing a balance to the known land masses in the north
was also an idea which originated with the Classical Greeks, as shown by the Mela map of 43 A.D.
(Figure 1.1D). A revival of this notion appears in the Ortelius map of 1570 in which a supposed Terra
3
Chapter 1: Introduction
4
Chapter 1: Introduction
Australis Incognito balances the mass of the northern hemisphere continents. This idea of an enormous
1.1: Maps through the ages
A:
B:
C:
D:
E:
F:
G:
H:
I :
A sketch of a 4 500-year-old Babylonian clay-tablet map discovered in the ruins of Nuzi in
northern Mesopotamia, now in the Semitic Museum, Harvard University (from Raisz, 1962).
Reconstruction of Eratosthenes' map of 200 B.C. (from Dickinson, 1969).
Reconstruction (Rome, 1490) of Ptolemy's map of150 A. D. (from Dickinson, 1969).
The Mela map, 43 A.D. (sketch based on a photograph in Harley and Woodward, 1987).
The Turin 'T in O' map, 800 A.D.(?) in a manuscript in Turin Library (sketch based on Brown, 1949).
The Roman 'Orbis Terrarum' (from Raisz, 1962).
Map in Hereford Cathedral, 13th century (a sketch of the original document from Dickinson, 1969).
A Portolan chart (after Wolfenbuttel in Imago Mundi, from Raisz, 1962).
A world map by Ortelius,1570 (from Dickinson, 1969).
5
Chapter 1: Introduction
southern continent persisted on navigational charts until Captain James Cook's exploration of the
southern seas in the eighteenth century revealed much of the details of southern hemisphere geography.
With the fall of the Greek civilization and the later dissolution of the Roman Empire, Ptolemy's
cartography, along with the great bulk of classical knowledge, was lost to the western world.
This
tragic setback to growth of the human mind and spirit marks the start of the so-called Dark Ages of the
Early Medieval Period. For about 1500 long years, science and letters languished in the intellectual
doldrums that saw classical logic and critical thought to a large extent displaced by the teaching and
philosophy of the early Christian Church.
Maps now became fanciful rather than factual, often with more attention being given to illustrating
the divine scheme of creation than to depicting geographic facts.
Often maps were centred on
Jerusalem, of which the scriptures declared, God had 'set in the midst of nations and countries'. Pride of
place also was given to Paradise and the Garden of Eden (usually in the east and at the top of the map)
along with Noah's Ark aground on Mount Ararat. The lesser known 'outer areas' were depicted as evil
places, perhaps the domain of the devil where monsters of unimaginable horror and terror lurked in wait
for the unwary traveler!
Maps of the early Middle Ages commonly were in the form of a flat disk in a surrounding ocean, a
general concept likely based on the Roman Orbis Terrarum style of map (Figure 1.1F). Particularly
common were 'T in O' type maps portraying the world divided among the three sons of Noah. Seldom did
these maps show meridians and parallels or bear a scale.
Although a few maps from this period depict the earth as a sphere or hemisphere, they are rare.
In general, it is fair to conclude that the science of map making at this time lapsed into an amazing decline
from Ptolemaic cartography to a low from which it was not to show signs of recovery until the fourteenth
and early fifteenth centuries.
The Renaissance, that revival of art and letters which flourished in Europe in the 14th to 16th
centuries, was based on the rediscovery of long-forgotten classical models.
Cartography made
tremendous progress during the Renaissance, in large part because of the new enlightenment that led to
the rediscovery of the works of Ptolemy. The stimulus for change must also be attributed, however, to the
needs of mariners. The great period of world exploration, which reached its climax between 1500 and
1800, was just beginning and practical mariners demanded realistic and useful charts, not imaginative
maps drawn to praise God.
The practical demands of fourteenth century sailors were met by a remarkable group of maps
known as the Portolan Charts or simply as Portolanos . These mainly Italian maps date from the early
fourteenth century although their origin is obscure and they may have been copies of still older charts.
Some of the earliest charts may have been constructed from detailed and clearly quite accurate logs of
sailing times and compass directions accumulated by Genoese sailors and other sea captains. In later
versions the exceptionally detailed coastline might have actually been surveyed using the magnetic
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Chapter 1: Introduction
compass, an instrument which became widely used by navigators after about 1100. Oddly enough, these
Portolanos show neither latitude nor longitude; instead they are criss-crossed by a network of intersecting
rhumb lines (lines indicating compass direction) originating from numerous compass roses (Figure 1.1H).
The main contribution of the Portolanos to the revival of cartography was to focus attention on the
essentially practical nature of maps. The rediscovery of Ptolemy by the thirteenth and fourteenth century
Arabian world and later in the fifteenth-century by western Europe had a much greater impact on mapmakers because he spoke to both practical and theoretical cartography. For the next several centuries
large numbers of world and regional maps based on Ptolemy's descriptions, including the errors, were
produced. Correction and elaboration followed as the pace of world exploration quickened during the
Great Age of Discovery.
World maps of the sixteenth and seventeenth centuries are far more accurate than their
predecessors although they too contain many errors. Lesser known parts of the world, such as the
Americas and 'Terra Australis', were mapped with great generalization and vagueness and positioning
often is inaccurate. Although latitude of the known world was measured and depicted with relative
accuracy on maps of this period, navigators had much more difficulty with longitude. Indeed, it was not
until the widespread use of Harrison's chronometer, invented in 1735, that errors in the longitude of
positions were sensibly eliminated.
But these early maps also exhibit such innovative advances as the use of mathematically derived
map projections (developed far beyond the suggestions of Ptolemy) and a graticule of latitude and
longitude. As if not to completely break with the traditions of the 'ecclesiastical' maps, from the sixteenth
century onward most world maps also displayed very elaborate titles, compass roses, and scales.
Oceans often were embellished with ships, whales, or even mermaids and sea serpents, while mountains
and towns appeared in semi-pictorial form.
The mapping of the vast tract of land that is Canada largely was accomplished, at first by
explorers searching on land and sea for a route to China and a North West Passage, and later by others
seeking to open up this new northern land for commerce and trade. Indeed, the story of the European
discovery and exploration of North America can be told through the maps of the period. Although the
Indians and Innuit had mental pictures of the lakes and rivers and coastlines of their particular homelands,
the broader continent-scale outline of this immense northern part of North America did not become
apparent until European navigators, explorers, surveyors and map-makers had accumulated several
centuries of information about Canada's geography.
Although the Vikings had visited North America about a thousand years ago (Leif Eriksson
probably reached the Labrador coast in 1001 A.D.), no authenticated charts date from these early
European contacts. It was not until much later, in the decades following Columbus' discovery of the New
World, that the observations of the North American coastline by fisherman, and navigators such as John
Cabot, began to appear in maps drawn by European cartographers. Perhaps the first European depiction
7
Chapter 1: Introduction
of the coast of North America is on a world map drawn by Juan de la Cosa in 1500 (Figure 1.2). This early
imaginative geography of Atlantic Canada was refined quickly following the more systematic charting by
early explorers such as Jacques Cartier, who reached the St Lawrence in 1534-35, and the various British
seekers of the North West Passage, such as Martin Frobisher (1576-78), John Davis (1585-1587), Henry
Hudson (1610-1611), and Thomas James (1631-1632).
The 17th century maps of New France
shown in Figures 1.3 reveal the wealth of
geographic data accumulated to this time although
clearly the surveyor's accuracy in places continued
to be less impressive than the cartographer's
artistic embellishment!
By the 18th century,
however, coastal mapping in Canada was being
conducted by highly professional navigators,
perhaps the greatest of the period being Captain
James Cook, an officer in the British Navy. He
charted Gaspé and helped prepare the map that
enabled James Wolfe's armada to navigate the St
Lawrence River in 1759.
In 1763-67 he also
charted the intricate and treacherous coast of
Newfoundland (Figure 1.4).
Following his epic
explorations of the South Pacific between 1768
and 1775, he explored the Canadian west coast,
anchoring in Nootka Sound on Vancouver Island
in April - March, 1778, and subsequently adding
considerable detail to the existing charts of the
1.2: Part of a world map drawn by Juan de la
Cosa in 1500. Clearly shown are the islands of
the Caribbean in the top half of the chart and the
coast of Atlantic Canada in the lower right (west is
at the top of the map). This map is thought to be
the first European depiction of the coast of North
America.
region during his northward voyage in search of
the elusive North West Passage. His surveys were
followed in 1792-94 by the more comprehensive
surveys of another British naval officer, Captain
George Vancouver (Figure 1.5)
After the Hudson's Bay Company was established in 1670, information about the geography of
the western and northern interior of Canada rapidly accumulated as trader/explorers such as Alexander
Mackenzie, David Thompson, and Simon Fraser, among others, explored the inland waterways.
Mackenzie's treks to the uncharted lands of the Arctic and Pacific are recorded on a map in hisVoyages,
published in 1801 (Figure 1.6). In 1814 David Thompson's thousands of kilometres of reconnaissance
8
Chapter 1: Introduction
A
B
1.3: 17th century maps of New France (From prints in the Public Archives of Canada, Ottawa).
A. according to Samuel de Champlain, 1632
B. according to Jean-Baptiste Franquelin, 1678
9
Chapter 1: Introduction
1.4: Captain James Cook's map of
Newfoundland, 1793 (From a print in
the Public Archives of Canada, Ottawa).
1.5: A section of Captain George
Vancouver's 1798 map showing
Vancouver Island and the Strait
of Georgia (From a print of a French
edition of the map in the Public Archives
of Canada, Ottawa).
10
Chapter 1: Introduction
1.6: Alexander Mackenzie's 1801 map of his Arctic and Pacific
expeditions (From a print in the Public Archives of Canada, Ottawa).
11
Chapter 1: Introduction
1.7: Part of David Thompson's remarkable 1814 map of Western Canada (From the
original in the Public Archives of Ontario, Toronto).
1.8: Part of John Franklin's 1823 map of the Canadian Arctic (From a print
in the Public Archives of Canada, Ottawa).
12
Chapter 1: Introduction
1.9: The 1854 Arrowsmith map of North America (From a map in the
Public Archives of Canada, Ottawa)
surveys were compiled in a remarkable map of a vast area from Sault Ste Marie to the Pacific coast.
This compilation was a working trail map for use by fur traders and here for the first time all major lakes,
rivers, and trading posts are accurately located (Figure 1.7). Simon Fraser's explorations on behalf of the
North West Company between 1805 and 1808 did much to elucidate the geography of central British
Columbia and at the same time establishing Fort McLeod in1805, Forts St James and Fraser in1806 and
Fort George (now Prince George) in 1807. In 1808 he followed Mackenzie's 1793 trail down what he
thought was the Columbia River and as a result was the first white man to explore the perilous Fraser
River Canyon.
As one might expect, the Canadian Arctic presented the greatest mapping challenge of the
nineteenth century and consequently it was the last area of North America to be accurately surveyed and
mapped. After the Napoleonic wars Britain's interest in finding and mapping the North West Passage was
renewed and a number of expeditions were mounted. These included overland journeys to the north by
Captain John Franklin in 1819-22 and 1825-27 and maritime expeditions by William Parry,1819-25, and
Sir John Ross, 1818 and 1829-33, among many others. John Franklin's 1823 map (Figure 1.8) clearly
shows the rudimentary state of mapping in the western Arctic at that time. The rapid progress made in
13
Chapter 1: Introduction
correcting the situation is recorded in the Arrowsmith maps, a series regularly revised in London,
England, on the basis of information supplied by the Hudson's Bay Company and by British explorers. By
the middle of the nineteenth century the general outline of Arctic Canada was known accurately although
some islands remained unknown or poorly delineated (Figure 1.9).
Modern maps are the logical extension of the mapping developments of the last few
centuries although they contrast in their relative directness and simplicity of presentation. Maps have
become very specialized as well as standardized and of course accuracy has improved tremendously.
The use of extremely accurate optical, electronic and laser-based survey instruments on the ground and
aerial photography and satellite and other remote sensing technology, has wrought a revolution in
cartography. An integral part of twentieth century developments in cartography has been the incredible
advances in computers.
Computers not only have relieved surveyors of the computational tasks in
surveying but they are now responsible for the production of automated contour maps and for the
statistical processing necessary for the production of thematic maps (see Chapter 9).
In general
computers have shortened enormously the time required to produce maps and they have so reduced map
costs that maps virtually are available to everyone. Most countries of the world have state mapping
agencies and few places do not have map coverage at several different scales.
Yet for all our advances, any map is only as useful as the user finds it. It remains necessary to
learn how to read a modern map before its store of information becomes fully accessible. A good place to
start any such complex business is at the beginning.
The basic elements of a map
Although maps may differ, one from the other, in purpose and style of presentation, they should
also be similar with respect to certain other basic properties. Essential elements common to all maps are:
(1) title or description
(2) scale
(3) data and legend
(4) locational grid
(5) direction indicator
The title of a map should indicate the area represented by the map and the nature of the data
displayed, as in Canada: Population, or Geology of British Columbia. In the case of data that may change
over time, it also is important to specify the date of compilation, as in Energy Consumption in France,
1978 -1982 or World Gross National Product, 1987. The most prominent lettering on a map should be
reserved for the title which should be concise yet informative and well separated from the rest of the map
data.
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Chapter 1: Introduction
The scale of a map should clearly specify the relationship between distances represented on the
map and the corresponding real distances on the ground. Scales may be shown on a map in one or more
of the following ways.
A statement in words relating the map distance to the ground distance; for example,
One centimetre represents five hundred metres;
Ten centimetres represent one kilometre;
One centimetre represents ten kilometres;
Or in the old Imperial system of units, for example,
One inch represents ten yards;
One inch represents one mile;
Six inches represents one mile;
Conventionally, one of the
measurements in a statement of scale should always be a unit
distance (1 cm, 1 inch, 1 km, 1 mile etc).
A representative fraction (R.F.) is an alternative expression of scale in which the numerator and
denominator of the fraction are in the same units. The numerator represents the distance on the map and
the denominator represents the corresponding distance on the ground. Conventionally, the numerator of a
representative fraction always is unity.
For example, an R.F. of 1/100 000 specifies that one unit on the map represents 100 000 units
on the ground and one of 1/10 specifies that one unit on the map represents ten units on the ground, and
so on. Sometimes an R.F. is expressed as a scale ratio, so that 1/10 is written 1:10 and an R.F. of 1/100
000 would be written as 1: 100 000. Conceptually, these two conventions are identical.
A statement of scale may be converted to a representative fraction by converting the ground
distance to the same units as the corresponding distance on the map:
For example, one map centimetre represents five kilometres
or, one map centimetre represents five hundred thousand centimetres
or, 1/500 000
Again, if five map centimetres represent one kilometre,
then five map centimetres represent one hundred thousand centimetres
or, 5/100 000 = 1/20 000
Operations such as these are relatively simple for metric scales but they become rather more
clumsy for scales expressed in Imperial units. Nevertheless, the same simple principles are involved.
For example, to convert the scale statement, 'one inch represents five miles', to an R.F., the following
steps are involved:
Since there are 63 360 inches in one mile,
1 inch represents five miles = 5 x 63 360 inches = 316 800
Thus the corresponding R.F. is 1/316 800
By way of another example we can similarly convert an R.F. of 1/7 200 to the corresponding
15
Chapter 1: Introduction
Imperial scale statement by reversing the steps shown above:
1/7 200 specifies that
one inch represents 7 200 inches = 7 200/12 = 600 feet = 600/3 = 200 yards.
Therefore, 1/7 200 also means that one inch represents 200 yards. Note that this R.F. of 1/7 200,
or any other, could also have been converted to a metric scale statement. In this case, 1/7 200 specifies
that one centimetre represents 7 200 cm = 7 200/100 = 72 metres.
Expressing scales in the form of a representative fraction has the obvious advantage that the R.F.
is dimensionless. That is, the R.F. in the form 1/x states the ratio of one unit of map distance to x units of
ground distance and remains constant regardless of the units chosen for the scale. If the R.F. is a small
fraction, say 1/100 000, then we refer to a small-scale map; if the fraction is large, say 1/100, then we
refer to a large-scale map. Small-scale maps therefore represent large areas on a sheet of given size
and large-scale maps represent small areas, but presumably showing greater detail.
A line scale is simply the graphical representation of the map scale. A line scale appears on all
topographic maps and it allows direct measurement of distances on the map using a compass or dividers.
Construction of a line scale is straightforward in the case of most common scales and examples
are shown in Figure 1.10B. Sometimes scales may be quite arbitrary, however, and the line scale may
not follow so readily.
For example, a map produced directly from an aerial photograph might have an
R.F. of 1/18 657, or 1 cm represents 0.18657 kilometres. In this case a 10 cm-long line scale would
represent 1.8657 kilometres, a clumsy reference length which is awkward to use. A far more sensible line
scale would be one representing a round number, say 3.0 kilometres. We determine the length of a line
scale representing 3.0 kilometres as follows:
If 1 cm represents 0.18657 km,
then 1/0.18657 cm = 5.36 cm represents 1 km, and 3.0 km would be represented on the map
by 3.0 x 5.36 = 16.08 cm.
Subdivision of this line into three smaller equal-interval units of 1.0 km and further subdivision of the lefthand 1.0 km unit into ten 100 m sub-units can be achieved by the method illustrated in Figure 1.10.
In
this case an 11.2 cm line AB is drawn with another line AC, constructed at some arbitrary angle, is divided
into any three equal divisions. Join BC and draw two parallels through the divisions on AC to intersect AB
forming three equal-interval divisions on the scale. This procedure is repeated to yield the 100 m subunits on the left-hand side of the line scale.
The distance between two points on a map is determined by measuring the length with dividers or
marking the interval on a straight edge of paper and referring this interval to the line scale. The length of
a non-linear feature such as a river or road can be determined by setting the dividers at some small
known interval and stepping off the distance along the curved line. Alternatively, a piece of cotton can be
laid along the line in question and then stretched out against the line scale. Several types of measuring
16
Chapter 1: Introduction
1.10: Line scales
A A line scale showing the graphical technique for dividing a line
into a given number of equal internal divisions.
B Examples of several styles of line scale commonly used on maps.
wheels also are available for the measurement of distances on maps. These are pen-like instruments with
a rotating ball or wheel linked to a counter to read actual distance or scaled distance as required.
An important additional advantage of having a line scale on a map, is that, unlike a scale
statement or representative fraction, a line scale automatically adjusts to photographic enlargement or
reduction of the original. Such photographically produced scale changes in maps are commonly utilized in
geographic research.
The data and legend of a map are necessary because the map abstracts reality and we need a
directory to decode this process for interpretation. Very often the need to abstract is simply the result of
scaling problems. It is only on very large-scale maps that features can be shown pictorially and true to
the scale of the map. For example, on a large scale (1/1 000) town plan a 10 m-wide road can be drawn
to scale (1 cm wide on the plan) but on a 1/50 000 topographic map the same road would be represented
by a line just 1/5 mm thick if it were drawn to scale. Such a line would be hard to see against the
background of other data and so a compromise is made by increasing the width of the line until it is
clearly visible. Thus the symbols for roads on 1/50 000 topographic maps are not scaled versions of
reality but simply symbols. Similarly, railroads, houses, trees, small rivers, and so on, are all represented
by 'larger than life' symbols. In recent years many of these symbols have become standardized on the
maps of Canada's National Topographic System (NTS) and are similar to those used in the national
17
Chapter 1: Introduction
surveys of many other countries.
In many cases a symbol used on a map will have an obvious meaning but others may be more
obscure. For this reason it is necessary that all symbols appearing on the map be listed and explained in
a legend. The legend often appears around the border of NTS maps or on the back of more recent
editions.
In the case of thematic maps the statistical data represented should be acknowledged by
source and the symbol scaling should be clearly stated in the legend. We will return to these matters in a
later chapter.
On coloured topographic maps certain colour conventions should be noted. Brown is used to
represent relief features, blue for water bodies (oceans, lakes and rivers), and green for vegetation. The
colours black and red are reserved for cultural features such as roads, towns, administrative boundaries,
and so on.
Locational Grids on maps primarily are used as a reference framework or address for finding
and specifying locations. But they also provide a graphical expression of the scale and shape distortion
introduced to the map by the projection used in constructing it. This latter topic is very important and we
will look more closely at it in a later chapter; for now we largely will concern ourselves with the former
matter of positioning.
All of us are familiar with a commonly used device employed in street directories whereby
locations are given by a combination of letters and numbers referring to a grid formed by columns and
rows on a page. For example we may be referred to Royal Columbia Hospital at B3 on a page divided
into A through H columns and 1 through 8 rows. This type of positioning is ideal in applications where
location to the nearest square of the grid is adequate. It works poorly or not at all if point rather than
square locations need to be specified and clearly it is not possible to relate a location reference on one
page to that on another. Positioning on topographic maps must be more precise and flexible than this
method although the general principle used in topographic map referencing is the same.
An ideal global map reference system should have the following attributes:
(a) It must be applicable to all points on the planet. That is, a map reference for any given point
specifies its position with respect to all other points.
(b) It must be applicable to all map scales. The level of precision may vary with map scale but
the basic reference system must be common to all to all scales.
(c) It must give a point's location to any required level of accuracy. In other words, the system
must be flexible enough to allow specification of general addresses appropriate to small-scale maps as
well as the high-level precision possible on large-scale maps.
and
(d) It must be easy to understand and use.
18
Chapter 1: Introduction
The map reference scheme used on Canadian and most other topographic maps is one of two
types: the geographic coordinate system or the rectangular grid system.
The geographic coordinate system of latitude and longitude is one of the oldest methods of point location
and is the most universally adopted. In this system the position of any point on the globe is specified by
its spherical coordinates (Figure 1.11). The first coordinate, latitude, is given by the angle (measured in
1.11: The geographic grid
A The angular measurement of latitude
B Lines of latitude and longitude on the globe.
degrees, minutes, and seconds) north or south of the equator subtended from the centre of the globe; the
equator is 0
o
o
and the poles are 90 north or south of the equator. The second coordinate, longitude, is
given by the angle (also measured in degrees, minutes, and seconds) east and west of the Prime
Meridian subtended from the centre of the globe.
The Prime Meridian is defined arbitrarily as the
o
meridian passing through Greenwich, a suburb of London, England. Thus, the highest longitude is 180 ,
a meridian which passes through the eastern extremity of the Soviet Union just west of the Bering Strait in
the northern hemisphere and through the Fijian Islands in the southern hemisphere. Conventionally,
latitude is given before longitude when specifying the geographic coordinates of a location. Thus the
o
o
geographic coordinates of Vancouver, British Columbia are 49 20'N 123 10'W.
The length of a degree of latitude on the ground is sensibly constant at 111 km (69 miles)
regardless of location on the globe. One minute of latitude, therefore, is about 1.85 km (1.15 miles or one
19
Chapter 1: Introduction
nautical mile) and one second of latitude is approximately 30 m (100 feet).
Determining the latitude of a location in the field involves the use of angular sun or star
measurements obtained with a sextant and related to latitude by standard navigation tables. Longitude
measurements are based on the difference between local time and Greenwich time, since one complete
360o rotation of the earth, by definition, corresponds to 24 hours in time.
Determining the geographic coordinates of a location from a map is very simple because the
latitude and longitude appears on all standard topographic maps.
On Canada's NTS sheets the four
borders that enclose the body of the map (the neatlines) are lines of latitude and longitude. These are
subdivided into minutes and/or seconds depending on the scale of the map. On maps at scales of
1/50 000 or larger the position of a point in question can be projected horizontally and vertically to these
bordering scales and the geographic coordinates read directly.
Parts of one minute or second, as
appropriate, can be determined as a simple proportion of the smallest units shown. On maps of the
1/250 000 series the area covered is sufficiently large that the borders display some curvature because of
the Transverse Mercator Projection used.
In this case positions must be referred to geographic
coordinate markers (small crosses) printed on the face of the map and then they can be related to the
marginal scale as before.
The rectangular grid system, as the term implies, is a network of vertical and horizontal lines
forming a regular grid on the map that allows the full application of coordinate geometry and trigonometry
to specify locations, distances and directions. In Canada the Transverse Mercator Projection is used for
most topographic mapping and on such maps it is normal to print a grid with the following spacing:
1/5 000 and larger scales:
100 m squares
Between 1/5000 and 1/100 000 scales: 1 km squares
Smaller than 1/100 000 scales:
10 km squares
The Universal Transverse Mercator grid (UTM grid) is the basis of the rectangular grid shown on
all Canadian NTS maps. In order to keep to a minimum the distortion implicit in mapping a spherical
surface on flat maps, the ground features are projected on to a planar reference surface in sixty northo
o
south strips called zones, each 6 of longitude wide and about 84 of latitude long. The UTM grid is then
superimposed independently on each zone so that in the northern hemisphere the basal origin or
abscissa is the equator; in the southern hemisphere the origin is a base ten million metres south of the
equator. Each UTM zone, therefore, is a giant ten million-metre long rectangular grid, one million metres
wide with its centre (500 000 metres from the western edge) coinciding with the central meridian of the
zone (Figure 1.12A). The UTM zones and central meridians for Canada are shown in Figure 1.12B).
The UTM grid can be used to specify a unique locational coordinate for any point on Earth. Grid
references are based on the numbered grid lines; those running north-south or vertically are known as
20
Chapter 1: Introduction
eastings (because they specify distance east of the grid origin) and those running east-west or
A
1.12: The Universal Transverse Mercator Grid
A A UTM grid zone
B UTM zones and central meridians for Canada
horizontally are known as northings (because they indicate distance north of the grid origin on the
equator). Eastings are always given before northings when specifying a grid reference (first the 'X' axis
value, then the 'Y' axis value; the phrase 'read right up' may help you to remember this convention - that
is, read the coordinates to the right, then upwards).
In Figure 1.13 is an extract of the Abbotsford 1/25 000 topographic sheet on which is located a
target at the centre of the runways of the Abbotsford Airport. The grid numbers on the map tell us that the
grid line to the west of the target is 546 000 metres east of the zone origin. Since these are 1 000-metre
grid squares, the target is a further 300 metres to the east (one third of a grid square). The easting of the
grid reference for the centre of Abbotsford Airport, therefore, is 546 300. Similarly, we can see that the
target is about one tenth of a grid square or 100 metres above the nearest northing of 5 430 000 metres
(north of the equator). Therefore, the northing of the grid reference for the target is 5 430 100. So now
we can specify the location of the centre of the Abbotsford Airport on the UTM grid as Zone 10, 546 300 5
430 100. Note that, in North America the first two digits specify the zone number, the next six digits are
the easting, and the next seven are the northing.
coordinate as 105463005430100.
21
Thus we can unambiguously rewrite this UTM
Chapter 1: Introduction
Although there are many advantages to having a unique numerical address for any point in
Canada, the digit string is unnecessarily long and clumsy for most purposes and a shortened version
called a map reference is commonly used in the field or for tasks involving local positioning. A map
reference may be a six or eight figure coordinate depending on the accuracy required. Thus, for the
Abbotsford Airport target we can simply specify the Abbotsford sheet and eliminate the need for the zone
number and the first digit of the easting and the first two digits of the northing, giving a map reference,
Abbotsford 463301. Note that the two coordinates conventionally are run together; it is understood that
the digit string is symmetrical, with the left half specifying the easting and the right half specifying the
northing. If the accuracy of the coordinates can be increased to specify the nearest one hundredth of a
grid square (10 metres) then an eight figure map reference is appropriate; for example, Abbotsford
46283013. On a 1/50 000 topographic map, references are commonly given to six figures. If the map
references are used in calculations it is important to remember that such a level of accuracy specifies
hundreds of metres. In our example, Abbotsford 463301 means 46 300 metres east of local origin and
30 100 metres north of local origin.
It also is important to remember that, because map references refer to a local origin (a particular
map sheet), a given map reference is only locally unique. That is, another point 100 km away can have
the same map reference. If this duplication is likely to cause confusion a full grid reference should be used
instead.
In order to accurately determine the tenths, and especially the hundredths, of a grid square,
careful measurements of both the grid width and the distance of the point east and north of the grid line
must be made. If numerous map references are required it may be more efficient to construct a 'roamer',
a scale set at the width of the grid interval and subdivided into tenths or even finer intervals. The roamer
can be a simple scale carefully drawn along the edge of a small piece of paper or more elaborate scales
on transparent plastic are available commercially. On metric scale maps the grid interval will be evenly
divisible into centimetres or millimetres and so a ruler can be used to interpolate the subdivisions.
Direction indicators are shown on all topographic maps. Conventionally maps are arranged
with north at the top of the sheet but this may not necessarily be the case. Many marine charts and
small-scale atlas maps, for example, are oriented differently.
If a numbered geographic grid is
superimposed on the map, however, the direction of true north clearly is evident. On small-scale atlas
maps north may be in the same direction over the entire map or it may vary from place to place,
depending on the map projection used. On such maps it should be remembered that the north-south
direction at any point is always the direction of the meridian at that location.
Most topographic maps, and certainly those of the Canadian NTS, show several 'norths' in a
marginal 'declination diagram' such as that illustrated in Figure 1.13.
True north refers to the earth's north pole on the planet's axis of rotation. It is a constant or fixed
location from which directions are measured in a clockwise direction as angles referred to as true
22
Chapter 1: Introduction
1.13: An extract from the Abbotsford 1/25 000 topographic map (courtesy of the Governments of
British Columbia and Canada).
23
Chapter 1: Introduction
bearings.
o
o
All bearing angles are measured in degrees, minutes, and seconds with north at both 0 and
o
o
o
360 , east at 90 , south at 180 , and west at 270 . On Canadian NTS topographic maps true north is
indicated by the two meridians that form the east and west neat-lines of the map and by the true-north
prong on the declination diagram (always topped with a star: the North Star).
Grid north refers to the north-south lines (eastings) of the UTM grid which are parallel to one
another and to those on adjoining sheets in the same grid zone. Their strictly linear geometry means that
the direction of these grid lines must diverge from that of a local meridian to some degree. The divergence
o
is never very great (always less than 3 in Canada) and true north and grid north can be regarded as the
same thing for many practical purposes. But in others where considerable precision is required the
difference between true north and grid north must be taken into account. On Canadian topographic maps
the grid north prong of the declination diagram is always topped by a small square.
Magnetic north refers to the point towards which a compass needle will point in response to the
earth's magnetic field. Magnetic north is marked by an arrow in the declination diagram and the angle
between true north and magnetic north is known as the magnetic declination. Magnetic declination varies
from one map to another and may even vary over the area covered by a given map; it is specified for the
centre of the sheet for Canadian topographic maps; in the Vancouver area magnetic declination is about
o
22 . Unfortunately, magnetic declination also varies over time and it also may be necessary to adjust for
this magnetic variation.
Annual magnetic changes are printed with the declination diagram on most
topographic maps. In order to update the magnetic declination angle, the total magnetic variation (the
annual magnetic change x years since map publication) must be added to or subtracted from it, as
appropriate.
Converting from true to grid to magnetic bearings is quite straightforward provided you refer to the
declination diagram (construct one yourself if there is not one on the map). From the relations among the
three 'norths' on such a diagram it will be obvious whether you should be adding or subtracting
differences when converting bearings from one frame of reference to another.
This chapter provides a brief introduction to the basic elements of maps. In subsequent chapters
some of these basic elements will be developed to a much greater degree, but for the moment we must
concentrate on laying and consolidating a firm foundation of basic concepts and skills.
24