from the portolan chart of the mediterranean to the latitude

Transcription

FROM THE PORTOLAN CHART
OF THE MEDITERRANEAN TO THE
LATITUDE CHART OF THE ATLANTIC
CARTOMETRIC ANALYSIS AND MODELING
Joaquim Filipe Figueiredo Alves Gaspar
Dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy in Information Management:
Geographic Information Systems
Doutor em Gestão da Informação:
Sistemas de Informação Geográfica
Advisors
Marco Painho
Francisco Contente Domingues
Instituto Superior de Estatística e Gestão de Informação
Universidade Nova de Lisboa
2010
Copyright ® 2010 by
Joaquim Alves Gaspar
All rights reserved
Pluralitas non est ponenda sine necessitate
(Plurality should not be posited without necessity)
Apocryphally attributed to William of Occam
(ca. 1285–1349)
ABSTRACT
In this thesis a methodology for the systematic geometric analysis and modeling of
pre-Mercator nautical charts is proposed and tested, aiming at contributing to better
understand their geometric properties and methods of construction. The suggested
approach involves the application of a series of cartometric techniques: georeferencing, on the basis of a sample of control points of known geographic coordinates; the
interpolation of the geographical graticules implicit to the representations; the assessment of scales of distance and latitude; the assessment of the navigational accuracy,
by comparing the latitudes, directions and distances measured on the charts with the
corresponding exact values, affected by magnetic declination; and the identification of
the routes underlying the charts’ construction. A numerical model was developed
using the concept of ‘multimensional scaling’, here generalized to distances and directions measured on a spherical Earth, to simulate the main geometric features of the
charts. To estimate the spatial distribution of the magnetic declination in various times
two sources were used: the historical observations made by D. João de Castro in 1538
and 1541, and a recent geomagnetic model.
The methodology of cartometric analysis proposed in the thesis proved to be effective
and accurate. Five Portuguese charts from circa 1471 to 1504 were analyzed using the
full set of techniques mentioned above. The analysis revealed the coexistence of two
distinct cartographic models in the nautical cartography of the time: the ‘portolanchart’ model, based on magnetic directions and estimated distances, used to represent
the Mediterranean, the Black Sea and Western Europe; and the ‘latitude chart’ model,
based on astronomically-observed latitudes, used to represent Brazil and Africa. Historically relevant conclusions about the construction details and the sources used in the
compilation of the charts were drawn. Some of the most interesting refer to the Cantino planisphere, whose cartographic information was found to be compiled from several sources of distinct origins, times and accuracies. Certain peculiarities of its geometry, especially the location of Greenland, the distorted shape of Africa and the orientation of the Mediterranean, are shown to be the result of the navigational and charting
methods of the time, under the influence of magnetic declination. Concerning the
standards adopted in the Iberian pre-Mercator nautical cartography, important conclusions were drawn on the type of distance scales and the length of the degree of
latitude, some of them contradicting the results of previous studies. One of the most
© Joaquim Alves Gaspar
iv
interesting is that the various lengths of the degree adopted in the charts of the time
had little navigational impact, being only an echo of the traditional models of the Earth
and of the political disputes between Portugal and Spain.
The numerical model developed for the purpose of simulating the main geometric features of the charts proved to be a valuable research tool and was used, not only for
producing the simulations presented in the thesis, but also for quickly assessing the
influence of the various factors affecting the geometry of the charts.
The variety and richness of the conclusions drawn in the present research eloquently
confirm the utility and effectiveness of the proposed methodology. Hopefully they will
arouse the interest of others and help recognizing the need for a multidisciplinary
approach in the study of old nautical charts.
v
RESUMO
Nesta tese, é proposta e testada uma metodologia para a análise geométrica sistemática e a modelação numérica das cartas náuticas que antecederam a projecção de
Mercator, com o objectivo de contribuir para uma melhor compreensão das suas características geométricas e métodos de construção. Tal metodologia envolve a aplicação de uma série de técnicas cartométricas: a georreferenciação, com base numa
amostra de pontos de controlo de coordenadas geográficas conhecidas; a interpolação
das redes de meridianos e paralelos implícitas às representações; a análise das escalas
de distância e de latitude das cartas; a estimação da exactidão das cartas para a navegação através da comparação das latitudes, direcções e distâncias medidas sobre elas
com os correspondentes valores exactos, afectados pela declinação magnética; e a
identificação das rotas subjacentes à construção de cada carta. Foi desenvolvido um
modelo numérico, utilizando o conceito de multidimensional scaling generalizado a
distâncias e direcções medidas sobre a superfície esférica da Terra, com o objectivo de
simular as características geométricas mais importantes das cartas. Para estimar a distribuição espacial da declinação magnética em várias épocas, foram utilizadas duas
fontes: as observações realizadas por D. João de Castro em 1538 e 1541, e um modelo
geomagnético recente.
A metodologia de análise cartométrica proposta na tese provou ser eficaz e exacta.
Cinco cartas portuguesas entre cerca de 1471 e 1504 foram analisadas, utilizando as
técnicas cartométricas referidas. Os resultados revelaram a coexistência de dois modelos cartográficos distintos: o da ‘carta-portulano’, baseado em direcções magnéticas e
distâncias estimadas, usado na representação do Mediterrâneo, Mar Negro e Europa
ocidental; e o da ‘carta de latitudes’, baseado em observações astronómicas, utilizado
para representar o Brasil e África. Conclusões historicamente relevantes sobre a construção das cartas e as fontes utilizadas na sua compilação foram retiradas. Algumas
das mais interessantes dizem respeito ao planisfério de Cantino, cuja informação cartográfica se concluiu ter sido compilada de múltiplas fontes de diferentes origens, idades e exactidões. Certas peculiaridades da sua geometria, designadamente a localização da Gronelândia, a forma distorcida de África e a orientação do Mediterrâneo são
explicadas pelos métodos de navegação e cartografia da época, sob a influência da
declinação magnética. Relativamente aos padrões adoptados pela cartografia ibérica
pré-Mercator, foram retiradas importantes conclusões sobre o tipo de escalas de dis-
vi
tância e o comprimento do grau de latitude, algumas delas contradizendo o resultado
de estudos anteriores. Um dos mais interessantes diz respeito aos vários comprimentos do grau de latitude adoptados nas cartas da época, os quais, sendo meramente um
eco dos modelos tradicionais da Terra e das disputas políticas entre Portugal e Espanha, tinham reduzido impacto na navegação.
O modelo numérico desenvolvido com o objectivo de simular as características geométricas das cartas revelou-se uma ferramenta valiosa e foi utilizado, não só para produzir as simulações apresentadas nesta tese, mas também para avaliar, de forma expedita, a influência dos vários factores que afectam a geometria das cartas.
A variedade e riqueza das conclusões obtidas nesta investigação confirmam de forma
eloquente a utilidade e eficácia da metodologia proposta. Espera-se que possam despertar o interesse de outros e ajudar a reconhecer a necessidade de uma abordagem
multidisciplinar ao estudo das cartas náuticas antigas.
vii
To the memory of António Barbosa (1892-1946)
who said it all more than seventy years ago
To my son and daughters
Romeu, Sara, Leonor and Inês
viii
ACKNOWLEDGEMENTS
I want to acknowledge the support of a number of persons who have contributed in
diverse ways to the completion of this project: to Captain Jorge Semedo de Matos,
professor of History in the Portuguese Naval Academy, for our long discussions about
the geometry of the old charts and the navigation in the sixteenth century, from which
I have learned so much; to professor Marco Painho, scientific advisor of this PhD project, for his initial offer and continuing support; to Francico Contente Domingues, professor of History in the Faculty of Letters of the University of Lisbon, for kindly accepting to be my expert counselor in the historical matters; to Waldo Tobler, for his initial
encouragement and discrete suggestions, to which I have listened carefully and almost
always accepted, with obvious benefit to the quality of the study; to my family, for the
obvious reasons.
This PhD project received the financial support of the Fundação para a Ciência e Tecnologia (SFRH/BD/27297/2006).
This thesis was defended September 21st, 2010, in the Instituto Superior de Estatística
e Gestão da Informação (ISEGI) – Universidade Nova de Lisboa. The grade was Approved with Distinction and Praise, by unanimity. The thesis jury was:
Manuel José Vilares, ISEGI – Universidade Nova de Lisboa (President)
John Hessler, Library of Congress, USA
Waldo Tobler, University of California, Santa Barbara, USA
Marco Painho, ISEGI – Universidade Nova de Lisboa
Francisco Contente Domingues, Faculdade de Letras – Universidade de Lisboa
João Carlos Garcia, Faculdade de Letras – Universidade do Porto
João Catalão Fernandes, Faculdade de Ciências – Universidade de Lisboa
ix
CONTENTS
List of Figures
List of Tables
Symbols
1. Introduction
Objectives and study hypotheses
Study hypotheses
Organization
2. Navigation and charting
xiv
xvii
xix
1
5
5
8
11
Navigational methods
The magnetic declination
The Mediterranean portolan chart
The latitude chart
How charts were made
Geometric inconsistency
The myth of the square chart
Cartographic evolution
Miles, leagues and degrees
Early Portuguese charts
13
17
21
26
27
32
33
34
38
43
3. Cartometric and modeling tools
45
Cartometric analysis
Control points
Map comparison and georeferencing
Scale measurements
Latitude measurements
Estimating the magnetic declination
Assessing courses and distances
Numerical modeling
The EMP model
4. Charts of the Atlantic and the Mediterranean
Overview
x
46
47
48
54
58
61
66
73
76
85
86
90
Meridians and parallels
Scale measurements
Assessing the latitudes
Modeling the North Atlantic and the Mediterranean
Synthesis and conclusions
91
99
108
112
120
124
5. The Cantino planisphere
129
130
134
134
135
136
138
139
141
142
147
151
157
166
174
179
Overview and sources
Mediterranean and Black Sea
Northern Europe
North Atlantic islands
Africa
America
Brazil
Scale measurements
The enormous isthmus
Modeling the Cantino planisphere
6. Conclusion
183
184
188
190
190
192
193
195
195
197
Discussion of the thesis hypotheses
Cartometric analysis and modeling
Conclusions with historical relevance
Leagues and degrees
The advent of the latitude chart
The Cantino planisphere
The chart of Pedro Reinel, ca. 1504
Future research
Concluding remarks
Bibliography and references
199
Annex A – Control points
211
Annex B – Latitude errors
223
Annex C – Distribution of magnetic declination
227
xi
Annex D – The EMP model
General description and use
Options
Formulae
Rhumb-line distances and directions
Coordinate adjustments
Tissot ellipses and angular distortion
229
229
229
232
232
233
235
Annex E – Scales and modules
237
Annex F – Miles and meters
240
Annex G – Courses and distances in charts
241
Annex H – Chart reproductions
243
Author index
249
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LIST OF FIGURES
Chapter 2
Figure 2.1 – Point of fantasy and set point
15
Figure 2.2 – The amendments to the set point according to Manuel Pimentel
16
Figure 2.3 – The amendments to the set point according to Fontoura da Costa
17
Figure 2.4 – Manipulating the compass rose to correct for magnetic declination
18
Figure 2.5 – Influence of the magnetic declination on the charted position
19
Figure 2.6 – Longitudinal error of the set point due to magnetic declination
20
Figure 2.7 – Spatial distribution of magnetic declination in 1400 and 1500
21
Figure 2.8 – Geometric inconsistency of the charting process
32
Figure 2.9 – Detail of the Catalan Chart with an overlaid scale of latitudes
36
Chapter 3
Figure 3.1 – Control points used in the study
48
Figure 3.2 – Comparing two images with displacement vectors and a warped grid
49
Figure 3.3 – Using MapAnalyst for georeferencing the Cantino planisphere
52
Figure 3.4 – Scale of leagues and scale of latitudes in a chart of Pedro Reinel
55
Figure 3.5 – Measuring latitudes by extending the parallels from the graphical scale
58
Figure 3.6 – Measuring latitudes with a digital scale
59
Figure 3.7 – Types of latitude errors
60
Figure 3.8 – Reconstruction of the route followed by D. João de Castro in 1538
62
Figure 3.9 – Estimating the magnetic declination in Lisbon and Cape Palmas
64
Figure 3.10 – Estimating the magnetic declination in São Nicolau
64
Figure 3.11 – Imprecision in the measurement of courses and distances
66
Figure 3.12 – Positions determined using the point of fantasy and set point methods
69
Figure 3.13 – Rhumb-line tracks used in the analysis
70
Figure 3.14 – Some sequences of rhumb-line tracks with origin in Lisbon
72
Figure 3.15 – Empirical projections by Waldo Tobler
74
Figure 3.16 – Influence of the choice of tracks in the charting process
75
Figure 3.17 – Interface of the EMP model application
77
Figure 3.18 – Adjustment process in the method of the point of fantasy
79
Figure 3.19 – Adjustment process in the set point method
80
Figure 3.20 – Sample model outputs I: loximuthal and Mercator projections
81
xiii
Figure 3.21 – Sample model outputs II: point of fantasy and set point methods
82
Figure 3.22 – Sample model outputs III: simulating the Mediterranean
83
Figure 3.23 – Sample model outputs IV: world map with minimal distortion
83
Chapter 4
Figure 4.1 – Anonymous Portuguese chart of ca. 1471 with geographic grid
th
92
Figure 4.2 – Pedro Reinel’s chart of the 15 century with geographic grid
93
Figure 4.3 – Jorge de Aguiar’s chart of 1492 with geographic grid
94
Figure 4.4 – Excerpt of the Cantino planisphere with geographic grid
95
Figure 4.5 – Pedro Reinel’s chart of ca. 1504 with geographic grid
96
Figure 4.6 – Magnetic declination in the Atlantic between 1250 and 1550
97
Figure 4.7 – Variation of the magnetic declination in Lisbon between 1300 and 1700
97
Figure 4.8 – Variation of the magnetic declination in the Mediterranean and Black Sea
98
Figure 4.9 – Distribution of the latitude errors in the Atlantic for charts before 1500
109
Figure 4.10 – Distribution of the latitude errors in the Atlantic for charts after 1500
110
Figure 4.11 – Distribution of the latitude errors for latitudes larger than 40º N
111
Figure 4.12 – Greenland and Newfoundland in the Cantino planisphere
117
Figure 4.13 – Greenland and Newfoundland in Reinel’s chart of ca. 1504
118
Figure 4.14 – Output of simulation A
121
Figure 4.15 – Outputs of simulations B and C
122
Chapter 5
Figure 5.1 – The sheets of parchment in the Cantino planisphere
131
Figure 5.2 – Greenland and Scandinavia in the Cantino planisphere
135
Figure 5.3 – Scale of leagues in the Cantino planisphere
143
Figure 5.4 – Line of Tordesillas and Cape Verde archipelago in the Cantino planisphere
143
Figure 5.5 – Interpolated geographic grid of the Cantino planisphere
148
Figure 5.6 – Interpolated geographic grid for a corrected set of control points
150
Figure 5.7 – Distribution of the latitude errors in the Atlantic
151
Figure 5.8 – Distribution of the latitude errors in the North Atlantic (Europe and Azores)
153
Figure 5.9 – Distribution of the latitude errors in the North Atlantic (Africa)
153
Figure 5.10 – Distribution of the latitude errors in the coast of Africa
154
Figure 5.11 – The southern African coast in the Cantino planisphere
155
Figure 5.12 – Distribution of the latitude errors in the coast of Africa and Hindustan
156
Figure 5.13 – Distribution of the latitude errors in the coast of Brazil and Caribbean Sea
157
Figure 5.14 – Charted tracks versus theoretical routes
162
Figure 5.15 – Charted tracks versus theoretical routes in the eastern coast of Africa
165
Figure 5.16 – The Red Sea and the Isthmus of Suez in the Cantino planisphere
167
xiv
Figure 5.17 – Red Sea and Mediterranean in two map projections and Cantino
169
Figure 5.18 – Tracks along the eastern coast of Africa
172
Figure 5.19 – Output of simulation A with tracks
176
Figure 5.20 – Comparison between the Cantino graticule and simulation A
177
Figure 5.21 – Displacement vectors between the Cantino graticule and simulation A
177
Figure 5.22 – Displacement vectors between the Cantino graticule and simulation B
178
Figure 5.23 – Displacement vectors between the Cantino graticule and simulation C
179
Annex C
Figure C.1 – Spatial distribution of magnetic declination in 1200 and 1300
227
227
228
228
Annex D
Figure D.1 – Interface of the EMP model application
230
Figure D.2 – Coordinate adjustment for the method of the point of fantasy
234
Figure D.3 – Coordinate adjustment for the set point method
234
Figure D.4 – Projected ellipse of distortion
236
Annex H
Figure H.1 – Anonymous Portuguese chart, ca. 1471
244
Figure H.2 – Chart by Jorge de Aguiar, 1492
245
th
Figure H.3 – Chart by Pedro Reinel, 15 century.
246
Figure H.4 – Anonymous Portuguese chart, 1502 (Cantino planisphere)
247
Figure H.5 – Chart by Pedro Reinel, ca. 1504
248
xv
LIST OF TABLES
Chapter 2
Table 2.1 – Iberian references to the length of the degree of latitude
40
Chapter 3
Table 3.1 – Historical observations of the magnetic declination
63
Table 3.2 –Magnetic declination at some control points
65
Table 3.3 – Courses and distances along tracks from Lisbon
67
Table 3.4 – Courses and distances along tracks from the Canary Islands and Cape Verde
68
Chapter 4
Table 4.1 – Joint distribution of modules and types of scales
100
Table 4.2 – Dimensions and geographic limits
102
Table 4.3 – Scales I
103
Table 4.4 – Scales II
104
Table 4.5 – Metric length of the league
107
Table 4.6 – Latitude errors in Newfoundland
112
Table 4.7 – Courses along tracks for fifteenth century charts
113
Table 4.8 – Distances along tracks for fifteenth century charts
113
Table 4.9 – Courses along tracks for sixteenth century charts
114
Table 4.10 – Distances along tracks for sixteenth century charts
115
Table 4.11 – Ratios between the lengths of parallels and meridians
123
Chapter 5
Table 5.1 – Spacing between the Equator, tropics and Arctic Circle
142
Table 5.2 – Distances measured on the Cantino and other charts
144
Table 5.3 – Courses and distances from Lisbon
158
Table 5.4 – Courses and distances from the Canary Islands and Cape Verde
163
Table 5.5 – Comparison between the model outputs and the Cantino graticule
179
xvi
Annex E
Table E.1 – Estimated lengths of the degree of latitude according to Franco (1957)
237
Table E.2 – Estimated lengths of the degree of latitude
238
Annex G
Table G.1 – Courses and distances in fifteenth century charts (Atlantic)
241
Table G.2 – Courses and distances in sixteenth century charts (Atlantic an Mediterranean) 241
Table G.3 – Courses and distances in southern Atlantic and Indian Ocean
242
xvii
SYMBOLS
a ......................... major semi axis of the ellipse of distortion
b ......................... minor semi axis of the ellipse of distortion
C, C0, C1 .............. rhumb-line course
Cm ....................... magnetic course
D, D0, D1 ............. rhumb-line distance
Dm....................... equivalent rhumb-line distance
d ......................... distance measured on a chart, in leagues or miles
g ......................... metric length of one degree of latitude, on the surface of the Earth
L ......................... length of one degree of latitude, in leagues
N......................... number of leagues per section, in a distance scale of a chart
R ......................... length of one degree of latitude, measured on a chart
S ......................... length of one section of a distance scale, measured on a chart
s.......................... metric length of one league; root-mean-square positional error
x ......................... abscissa
y ......................... ordinate
w ........................ weighting parameter in the EMP model application
δ ......................... magnetic declination
ϕ ......................... latitude
∆ϕ ...................... latitude difference
λ ......................... longitude
∆λ....................... longitude difference
Ψ ........................ meridional part
∆Ψ...................... meridional part difference
µ ......................... average positional error
ω ........................ maximum angular distortion
xviii
xix
1. INTRODUCTION
More than three hundred years separate the development of the portolan chart of
the Mediterranean, in the beginning of the thirteenth century, from the presentation
of the Mercator projection, in 1569. But only two hundreds later, following the invention of the maritime chronometer and the development of methods for finding
the longitude at sea, it became possible to abandon the old cartographic models and
full adopt the Mercator chart in maritime navigation. For five centuries an apparently
naïve method of representation, in which magnetic directions and estimated distances were transferred directly to a plane with a constant scale, ignoring the spherical shape of the Earth, served marine navigation and played a fundamental role in
European discovery and maritime expansion. This was made possible by the introduction of astronomical navigation, in the second half of the fifteenth century, and
its reflection upon the nautical charts of the time. Being able to determine the latitude on board was a major advancement for marine navigation, as the pilots were no
longer dependent on the proximity of land for determining the ship’s position. By
reflecting the knowledge of the latitude on the construction of the nautical charts, a
hybrid type of representation was created, making the transition between the portolan chart of the Mediterranean, based on routes, and the Mercator chart, based on
geographic coordinates. This new cartographic model was developed some time after the introduction of navigational astronomy and became known as the ‘plane
chart’, or ‘latitude chart’1. Because the observed latitude always prevailed over the
two other elements of navigational information (the course and the distance), the
geometry of the latitude chart is clearly distinct from the geometry of the portolan
chart, from which it evolved. Parallels are approximately straight, east-west oriented
and equally-spaced, and meridians are curved, making variable angles with the parallels. Like the portolan chart, if suffers from an intrinsic geometric inconsistency
caused by ignoring the sphericity of the Earth, which makes each chart a unique representation, dependant on the particular set of routes used in its construction. Although this type of inconsistency causes significant distortion, which cannot be ignored when representing large areas, it did not affect much the effectiveness of the
1
Throughout this thesis the two designations are considered to be equivalent but preference is generally given to the second.
1
CHAPTER 1 - INTRODUCTION
latitude chart as a navigational tool because pilots were usually aware of its limitations. Magnetic declination was also an important element affecting navigation and
the geometry of the charts. Surprisingly it could be disregarded by pilots in most navigational situations and its existence was even ignored until the end of the fifteenth
century. The reason is all nautical charts up to, at least, the end of the sixteenth century were drawn on the basis of uncorrected magnetic directions.
What methods did the chart makers use in the construction of the nautical charts of
the Middle Ages and Renaissance? How is the geometry of the charts related to the
contemporary navigational methods? What errors affected those charts and how did
the pilots account for them? How did the geometry of the portolan chart of the Mediterranean evolve in order to accommodate astronomical navigation? These are
some of the issues addressed in this thesis, using the modern tools of digital cartometry and numerical modeling, in the light of the historical evidence given by the
extant charts and written documentation.
The Portuguese nautical charts of the fifteenth and sixteenth centuries were studied
by prominent researchers: Luciano Pereira da Silva (1846-1926), Armando Cortesão
(1891-1977), Avelino Teixeira da Mota (1920-1982) and Luís de Albuquerque (19171992), just to mention some of the best known names of the last century. However,
their analyses were usually focused on the historical, geographical and cultural aspects, and no systematic study was ever published on the geometric nature of the
cartographic representations and its relation with the navigational methods of the
time. Luís de Albuquerque recognized this omission and specifically referred to the
necessity of assessing the distortions of the sixteenth century’s charts, after the introduction of the latitude scale, as well as of clarifying the nature of its cartographic
projection (Albuquerque, 1989a, p. 97-99). To my knowledge no significant advancement has yet been made on this subject. As for the more general scope of the
geometry of pre-Mercator charts, very few quantitative studies were published, the
most relevant being those by Lanman (1987) and Loomer (1987) on the portolan
charts of the Mediterranean. There is a simple explanation for the scarcity of such
studies, which is the difficulty posed by the multidisciplinary nature of the subject,
comprising history, mathematical cartography and marine navigation. Quite often,
the failure to recognize the relevance or properly deal with these two last components led to incorrect and sometimes ridiculous interpretations of the geometry of
the early charts, such as the idea that they were based on some exotic map projection or those of the fifteenth and sixteenth centuries were drawn according to the
principles of the cylindrical projection. This particular misinterpretation, to which I
have called the ‘myth of the square chart’, has caused considerable damage to our
present knowledge on the geometry, methods of construction and use of pre2
Mercator charts. Although the theory is inconsistent with what we known about the
navigational and charting methods of the time, and not supported by any quantitative analysis, as António Barbosa (1938b) has emphatically shown a long time ago, it
was accepted by most researchers of the last century and is still repeated by leading
specialists in important international publications.
There exists a vast and complex bibliography on the genesis and geometric nature of
the medieval portolan chart. Of the various conflicting theories, the one asserting
that no system of projection was explicitly used in its construction, which was based
on directions given by the magnetic compass and distances estimated by pilots,
clearly prevails today. The hypothesis is compatible with the geometry of the extant
charts and corroborated by the counterclockwise tilt of their north-south axes, which
was caused by the magnetic declination in the Mediterranean, when the cartographic information was collected. It is consensually accepted that the earliest charts used
by the Portuguese pilots of the fifteenth century in the Atlantic were geometrically
identical to the portolan charts of the Mediterranean. However the introduction of
astronomical navigation, necessary to conduct ships in the open sea, made things
change. When a scale of latitudes was for the first time added to the old charts,
probably in the last quarter of the fifteenth century, it eventually became obvious
that their geometry had to be adapted to the new navigational methods, in which
the latitude has become the preponderant element of navigational information. The
resulting cartographic model is clearly distinct from the portolan chart (from which it
evolved) and represented a major breakthrough in the nautical cartography of the
Renaissance, marking the beginning of the evolution between the ‘route-enhancing’
maps, based on routes (Woodward, 1990, p. 119-20), to Ptolemy’s model, based on
geographical coordinates. Due to the impossibility of determining longitude with the
required accuracy, to the lack of knowledge of the spatial distribution of magnetic
declination and to some resistance from the pilots, this hybrid model would last for
more than two centuries, well beyond the appearance of the Mercator chart (in
1569), despite of its errors and limitations.
Simple cartometric techniques, consisting in the measurement of distances and directions, are not new in the study of old charts. These techniques were used in the
first detailed study of the Cantino planisphere, made in 1923 by Duarte Leite, for
determining the standard length of the degree of latitude and estimating the linear
scale of the representation and, very recently, by Ramón Pujades (2007), for assessing the approximate scale of a number of portolan charts. Digital techniques applied to the quantitative study of old maps are only now becoming known among
historians. Although the main ideas and fundamental principles have been intro-
3
duced more than forty years ago, through the pioneering work of Tobler (1966)2, and
later used in some studies, computers were not powerful or friendly enough at the
time to make those techniques effective for routine cartometric analysis. In our time,
not only high quality digital reproductions of many old maps and charts are easily
available for research at a reasonable price, but also sophisticated applications have
been developed, capable to perform complex cartometric operations in a routine
basis and present the results in expressive graphical ways. Still some suspicion remains in the community of traditional historians on the reliability of digital cartometric techniques for other purposes than the most simple or trivial. It is significant, for
example, that few articles making use of such tools for the purpose of suggesting or
supporting new historical interpretations have appeared in the most influential journals specialized in the history of Cartography. I believe that part of this resistance (or
indifference) can be explained by the innumeracy of many historians, as well as the
lack of a well-established group of recognized researchers making an effective use of
the techniques. Another common reaction among historians of Cartography, especially those familiarized with the early navigational methods, is the belief that old
nautical charts are not accurate enough for consistent conclusions to be drawn from
the analysis of their geometry. The present thesis shows that it is often possible, not
only to identify the source of the various errors affecting the old charts, but also to
relate them with specific charting solutions.
A suitable numerical approach for simulating the construction of pre-Mercator charts
is offered by ‘multidimensional scaling’ (mds), a multivariate statistical technique
used for exploring similarities and dissimilarities between objects in social sciences.
Starting with some given distances among a sample of points in an n-dimensional
space, the process consists in re-arranging their positions in a lower dimension space,
so that the differences between the initial (given) and the final (calculated) distances
are minimized. This is conceptually equivalent to the method used in geodetic surveying for adjusting measurements in trilateration, in which a series of distances between points in a triangular network are used for determining their planimetric locations. The application of this principle to cartographic purposes, using distances
measured on the spherical surface of the Earth as input, was first suggested by Tobler (1977), who introduced the expression ‘Empirical Map Projections’ to designate
the resulting representations. The same concept was here generalized to spherical
directions and distances, and used to simulate the geometry of old charts.
2
The method proposed by Tobler was based on a sample of control points of known geographical
coordinates, positively identified in the old map and in a modern representation, from which the grid
of meridians and parallels implicit in the first was numerically estimated. The comparison of this grid
with the characteristic graticules of various map projections would eventually permit to identify the
system used or, at least, the one closer.
4
Objectives and study hypotheses
The main objectives of the present research are:
− To propose and test a methodology for the systematic cartometric analysis and
modeling of early nautical charts, aiming at a better understanding of their geometry and methods of construction;
− To characterize the main geometric features of the earliest nautical charts of Portuguese origin and clarify their relations with the contemporary navigational and
charting methods.
The proposed methodology consists of a series of cartometric techniques which includes georeferencing, the assessment of scales and distance units, the assessment
of latitudes, and the comparison between directions and distances measured on the
charts with the corresponding theoretical values. These techniques are systematically applied to a series of five charts of Portuguese origin, from the late fifteenth and
early sixteenth centuries3, aiming at characterizing their geometric features and clarifying particular aspects related to their construction. The analysis takes into account
the navigational methods of the time as well as the spatial distribution of the magnetic declination, as estimated using the extant historical sources and a modern geomagnetic model. The grids of meridians and parallels implicit to each representation, obtained through georeferencing, are used to quickly assess the gross geometric features of the charts, to make preliminary assessments of their cartographic accuracy and to help identifying the areas where distinct sources or charting methods
may have been used. By applying the concept of multidimensional scaling, here generalized to rhumb-line directions and distances measured on the spherical surface of
the Earth, the geometry of the charts is simulated. The comparison of the model’s
results with the interpolated grids of the originals is used to validate the a-priori assumptions and to clarify the details of the construction methods.
Study hypotheses
The following study hypotheses are assumed in this study, concerning the geometry
and use of the old nautical charts, and the possibility of simulating its main features:
3
The five Portuguese charts analyzed in this study are: an anonymous chart of the Atlantic, ca. 1471
(Biblioteca Estense Universitaria, Modena); Jorge de Aguiar chart of the Atlantic and Mediterranean,
1492 (Beinecke Library, University of Yale); Pedro Reinel chart of the Atlantic, ca. 1492 (Archives
Départementales de la Gironde, Bordeaux); anonymous chart of 1502 (Cantino planisphere) (Biblioteca Estense Universitaria, Modena); and Pedro Reinel chart of the Atlantic, ca. 1504 (Bayerisch Staatsbibliotek, Munich). Page-size reproductions of the charts are in Annex H.
5
Hypothesis 1: pre-Mercator nautical charts were constructed to be used at sea and
reflect the needs of marine navigation and the navigational methods of the time.
This is a central a-priori assumption of the whole research and applies both to the
portolan chart of the Mediterranean and to the latitude chart. The hypothesis is now
consensually accepted by most researchers though some authors still insist on the
old theory that the first portolan charts may have been drawn for other purposes
than supporting marine navigation4. However this interpretation can no longer be
taken seriously, especially after the detailed documentary evidence presented by
Pujades (2007) on the use of sea charts in the Mediterranean during the High Middle
Ages.
Hypothesis 2: pre-Mercator nautical charts were constructed by transferring directly
to the plane the directions and distances measured on the spherical surface of the
Earth, with a constant scale, as if it were flat. This method made the resulting representations geometrically inconsistent, in the sense that they were dependent on the
particular set of routes used for constructing each chart, and caused certain distortions that can be identified through cartometric analysis.
In our days it is generally accepted that pre-Mercator charts are projection-less, in
the sense that no explicit map projection was used in their construction. The construction and copying methods are documented in various well-known Portuguese
and Spanish historical sources. What this study seeks to show is that the geometry of
those charts clearly reflects the charting methods of the time, in the form of certain
distinctive features and distortions that are dependent on the particular set of routes
on which each chart was based. This principle applies both to the portolan charts,
based on magnetic directions and estimated distances, and to the latitude chart,
based on observed latitudes. The hypothesis is expected to be confirmed on the basis of comparisons made between sets of routes measured on the charts, assumed to
have been used to construct them, and the corresponding tracks defined on the
spherical surface of the Earth.
Hypothesis 3: most pre-Mercator nautical charts were drawn on the basis of uncorrected magnetic directions and their geometry reflects the spatial distribution of the
magnetic declination at the time the navigational information was collected.
This is consensually recognized in the case of the portolan charts up to the eighteenth century, in which the axis of the Mediterranean appears rotated counter4
That is the case of Fernández-Armesto (2007, p. 749), who suggests that the sea chart ‘may have
been a visual aid to illustrate – for the enlightenment of passengers, landlubbers, and such interested
parties as merchants – the data pilots preferred to carry in their head or rutters. ‘
6
clockwise by an angle close to the average value of the magnetic declination in the
region, at the time the information was collected. In the case of the latitude chart it
is uncertain when the magnetic declination started to be corrected for but that was
certainly not before the beginning of the eighteenth century. The hypothesis is to be
tested by comparing sets of routes measured on the charts with the corresponding
theoretical values affected by magnetic declination. The spatial distribution of the
magnetic declination is to be estimated from the extant historical sources, especially
the observations made by D. João de Castro in 1538 and the outputs of a modern
geomagnetic model.
Hypothesis 4: the equidistant cylindrical projection was not, implicit or explicitly, used
in the construction of the nautical charts of the fifteenth and sixteenth centuries.
This can be regarded as a corollary of the last two hypotheses concerning the methods of chart making and the influence of the magnetic declination. It is known, from
the extant written documentation of the sixteenth and seventeenth centuries, how
charts were drawn and that no explicit use was made of the geometric principle of
the equidistant cylindrical projection. This study is also to show, contradicting the
myth of the square chart, that the geometry of the resulting representations is clearly distinct from the geometry of such projection.
Hypothesis 5: the geometry of pre-Mercator charts can be numerically replicated by
simulating the charting methods of the time, taking into account the routes supposedly used to construct them and the spatial distribution of the magnetic declination.
As explained above, the simulation of the charts’ geometry is accomplished using a
numerical modeling technique similar to multidimensional scaling. The input of the
model is a set of distances and directions between places, assumed to be representative of the maritime routes used for constructing the real charts, and the spatial distribution of the magnetic declination at the time the information is supposed to have
been collected. The output is a grid of meridians and parallels interpolated through
the final adjusted positions of the places. The hypothesis is considered to be confirmed if the most significant geometric characteristics of the original charts, revealed through their implicit grids of meridians and parallels, can be replicated by the
model. By ‘significant geometric characteristics’ it is here understood the general
orientation and spacing of meridians and parallels, and the distortions caused by the
uncorrected magnetic declination and by the inconsistencies inherent to the charting
process. This is a non-trivial hypothesis since the possibility of the main geometric
features of the charts being masked by spurious errors, due to their intrinsic lack of
accuracy, cannot be ignored.
7
No explicit goals or study hypotheses are established for detailed matters pertaining
to the origin of each chart, such as its authorship or date, or even for relevant historical subjects as is the transition between the portolan chart and the latitude chart or
the standard length of the degree in the Iberian cartography. However, and since
most of the cartometric and modeling techniques used here are for the first time
applied in a systematic way, it is expected some interesting historical conclusions on
those matters to be drawn.
Organization
The thesis is organized in six chapters and eight annexes, to where some detailed
information, not essential to the understanding of the text, was relegated. Due to the
multidisciplinary nature of the theme it was found appropriate, in order to facilitate
reading, to depart from the usual thesis organization in which the revision of literature is clearly separate from the original contributions, and from the presentation
and discussion of the results. This applies particularly to the discussion of historical
matters with strong technical components in the fields of navigation and Cartography (Chapter 2), where a general overview of the sources and literature is tempered with personal interpretations. In general, the revision of the literature is in
Chapters 2 (History) and 3 (Cartometry and modeling), though some studies are introduced or further discussed in Chapters 4 and 5. The methodology of the cartometric analysis and modeling is described in Chapter 3. All results and conclusions derived from the cartometric analysis and modeling are in Chapters 4 and 5.
Chapter 1 – Introduction
The chapter contains a brief overview of the historical context in which the latitude
chart was developed, an introduction to the cartometric techniques used in the research, the definition of the objectives and study hypotheses of the dissertation, and
a description of the organization of the text.
Chapter 2 – Navigation and charting
A general overview is made of the present knowledge on the medieval and Renaissance nautical cartography and navigational methods, in the aspects directly or indirectly related to the geometry, conception, construction and use of nautical charts.
Important historical sources documenting the construction and geometric features of
the charts are introduced and discussed. A critical revision of some relevant studies is
made.
8
Chapter 3 – Cartometric and modeling tools
The chapter contains a detailed description of the cartometric and numerical modeling techniques used in the research, and briefly introduces and discusses some relevant works of the literature. The computer application EMP (‘Empirical Map Projections’), which was developed for the simulation of the geometry of early nautical
charts, is introduced with some application examples.
Chapter 4 – Charts of the Atlantic and Mediterranean
In this chapter the application of the cartometric methods and modeling techniques
described in Chapter 3 to four charts of Portuguese origin is presented and discussed
(some results relative to the Cantino planisphere, addressed in Chapter 5, are also
presented for comparison purposes). The chapter starts with a revision of some important information and literature relative to each of the charts, focusing on the historical aspects considered to be more relevant for the present research. The description and discussion of a detailed cartometric analysis, which included the application
of the techniques mentioned above, follows. In some specific matters, like the assessment of the length of the degree of latitude, the analysis is extended to a larger
group of Portuguese and non-Portuguese charts. The chapter also presents and discusses a simulation of the cartographic representation of the North Atlantic, using
the EMP model application, taking into account the results obtained in the cartometric analysis.
Chapter 5 – The Cantino planisphere
Due to its particular historical relevance and geometric complexity, this whole chapter is dedicated to the Cantino planisphere. The chapter starts with an overview of its
main geometric features and a description of the sources from which its information
might have been compiled, including the exploration missions and previous cartography. A complete cartometric analysis of the chart is then presented and discussed.
A detailed analysis of a notorious feature of the chart, the eastward distention of the
African continent and the exaggerated size of the Isthmus of Suez, follows. The chapter also presents and discusses a simulation of the geometry of the chart, using the
modeling techniques introduced before and the results obtained in the cartometric
analysis.
Chapter 6 – Conclusion
In this chapter the most relevant results and partial conclusions obtained in the previous chapters are integrated and discussed, in the light of the objectives of the present research, and some suggestions for future research are made. The chapter in-
9
cludes a detailed discussion of the five study hypothesis presented above and ends
with some considerations about the contribution of this thesis for the multidisciplinary study of old nautical charts.
10
2. NAVIGATION AND CHARTING
Terrestrial maps and nautical charts have distinct geneses and evolutions in Europe.
When scientific cartography was reborn in the beginning of the fifteenth century,
following the translation and dissemination of Ptolemy’s Geography, the portolan
chart was already established, for more than a century, as an effective navigational
tool. And while terrestrial maps were being constructed by the erudite, using the
geographic coordinates and instructions given by Ptolemy, portolan charts were
made with the sole purpose of supporting navigation, on the basis of magnetic directions and estimated directions observed by the pilots at sea. Three centuries separate the earliest known portolan charts, developed during the thirteenth century,
from the Mercator chart, presented in 1569. Another 200 years had still to pass until
the old plane chart was definitely abandoned and the new model was fully adopted
by marine navigation. It may seem paradoxical how such an apparently naïve method
of representation, as was the pre-Mercator nautical chart, could survive for half a
millennium and be used throughout the whole discoveries and maritime expansion
period. The explanation lays in the fact that navigation was not prepared to take full
profit of the Mercator projection, at the time it was presented, due to the impossibility of finding the longitude at sea and the lack of knowledge on the spatial distribution of magnetic declination. While the Mercator chart was based on geographic coordinates and true rhumb-line directions between places, portolan charts were constructed on the basis of observed magnetic directions and estimated distances. Even
after the incorporation of observed latitudes in the charting process the incompatibility persisted, as the improved model was still based on magnetic directions and
the available astronomical methods could not address the longitude problem. In an
article with the significant title From the Mediterranean portulan chart to the marine
world chart of the Great Discoveries: the crisis in cartography in the sixteenth century,
Randles (1988a, p. 118) refers to the inadequacies of the plane chart, ‘only palliated
with the aid of ad-hoc correctives’, but concludes that it ‘seems to have served mariners for better or for worse enabling them to navigate on known routes across the
whole globe’. The term ‘crisis’ in the title appears somehow excessive or even displaced. If there was indeed a crisis it lasted well beyond the presentation of the Mercator chart, as its causes were of navigational rather than cartographic nature. Even
after the longitude problem was solved, in the middle of the eighteenth century, it
11
CHAPTER 2 – NAVIGATION AND CHARTING
took some time for the old plane chart to be abandoned and replaced by the Mercator projection. In his Tratado em defensam da carta de marear (‘Treatise in defense
of the navigational chart’), of 1537, the mathematician Pedro Nunes addresses the
geometric properties and inconsistencies of the nautical chart of his time and comments:
‘And in all this I don’t criticize the chart but complain that it is poorly understood, being the best instrument one can find for the navigation and the discovery of new lands, and our navigating art [is] the most founded on mathematical
sciences than any other one might use’ (Nunes, 2002, p. 137)1.
History has emphatically proved the rightness of Nunes’ judgment, as the latitude
chart has served marine navigation for about three hundred years, including the discoveries and maritime expansion periods, notwithstanding its limitations and inconsistencies.
The purpose of this chapter is to provide a general overview of the medieval and Renaissance nautical cartography and navigational methods in the aspects related to
the geometry, construction and use of charts. The chapter is organized in the following sections:
− Navigational methods: an introduction to the methods used for fixing the position of the ship at sea in the Renaissance focusing on the period of transition,
when astronomical navigation was introduced in the Atlantic, and on the reflexes
of the innovation upon the nautical cartography of the time. The effect of the
magnetic declination on the practice of navigation and the geometry of the
charts is discussed;
− The Mediterranean portolan chart: a brief critical review of some important
studies on the geometric features, origin and method of construction of the Mediterranean portolan chart;
− The latitude chart: the section begins with a review of some relevant literature
and historical sources on the new cartographic model that evolved from the portolan chart, following the introduction of astronomical navigation. Emphasis is
put on the methods of construction and geometric properties of the charts;
1
The original reads: e em tudo isto eu nam digo mal da carta mas aqueyxome de ser mal entendida:
sendo ella ho melhor estromento que se podera achar: pera a navegaçam: e descubrimeto de terras e
a nossa arte de nauegar a mais fundada em sciencias mathematicas: que nenhua outra de que se
poderá usar. This excerpt is taken from the part of Nunes’s treatise where the distortion of the Mediterranean in the charts of his time is addressed. Once again the mathematician criticizes the incapacity of the pilots to understand the geometry of the charts, as he had already done in the beginning,
when stating the objective of the treatise (see p. 27 and Note 20, in this chapter).
12
− Miles, leagues and degrees: a discussion about the cartographic standards
adopted in the charts of the Middle Ages and Renaissance, concerning the type of
distance scales and units, and the length of the degree of latitude. A brief review
of some historical sources and relevant studies is made;
− Early Portuguese charts: a listing and short description of the earliest extant
charts of Portuguese origin, from ca. 1471 to ca. 1506.
Navigational methods
When the exploration of the western coast of Africa began, during the first half of
the fifteenth century, the method for fixing the ship’s position at sea was still based,
as in the Mediterranean, on magnetic directions and estimated distances. After 1434,
when the Cape Bojador (present Cap Boujdour) was first crossed, it soon became
obvious that a better way to make the return trip would be to first withdraw from
the coast, to avoid the contrary winds and southerly Canary current, and then make
profit of the prevailing clockwise wind circulation by sailing north to the latitude of
the Azores and, from there, to Lagos or Lisbon. However, with much larger periods
without seeing land, the usual navigational method was no longer adequate. As time
elapsed, the accuracy of the new estimated positions quickly degraded to the point
of becoming almost useless, becoming quite easy for a ship to be lost at sea after a
few days sailing. The introduction of astronomical navigation proved to be an adequate and durable solution to the problem. In the earliest phase, altitudes of the Pole
Star were used to estimate the north-south displacement of the ship relatively to
some reference position. Later, in the last quarter of the fifteenth century, with the
introduction of simple ephemerid tables and the simplification of the astronomical
quadrant and astrolabe, it became possible to determine the latitude at sea by
measuring the height of the Pole Star and the Sun above the horizon2. The earliest
unmistakable mention to the use of astronomical methods in navigation is in a report
attributed to Diogo Gomes and written by Martin Behaim, ca. 1460 (Albuquerque,
2001, p. 199-200). According to it, the pilot used a quadrant to measure and to record the height of the Pole Star near the Island of Santiago, Cape Verde3. Other im2
Good summaries of the development of astronomical methods during the fifteenth century are in
Albuquerque (1971a; 1971b; 2001, p. 185-293) and Barbosa (1938b).
3
In my opinion these methods might have been introduced at least two decades before, during the
second quarter of the century, when the colonization of the Azores started. It is hard to believe that
routine trips to the archipelago, involving several ships, could have been organized without some
rudimentary form of astronomical navigation. With the east-most islands laying about one thousand
nautical miles from the western coast of Portugal, a relatively small error in the course steered could
make a ship to sail beyond the archipelago without seeing it. The problem could be easily solved by
knowing the approximate latitude at the point of destination (the height of the Pole Star above the
horizon), and then using the quadrant or astrolabe to sail along the corresponding parallel. This meth-
13
portant dates related to the development of astronomical methods of navigation are,
according to Albuquerque (1965, p. 59-67):
− 1481-82: in the ships that departed from Lisbon to the Gulf of Guinea under the
command of Diogo de Azambuja, to start the construction of the Mina fortress,
astronomical instruments may have been used;4
− ca. 1485: according to Columbus, master José Vizinho, physician and astrologist
of King João II of Portugal, was sent to ‘Guinea’ (Africa) to measure the height of
the Sun;5
− 1485-95: in the Esmeraldo de Situ Orbis, published around 1505-8, Duarte
Pacheco Pereira writes about the astronomical observations of the Sun he made
in Africa some time before (Pereira, 1954). Though the dates of the observations
are uncertain, at least some of them were certainly made before the death of
King João II, in 1495 ;
− 1488: according to Columbus, Bartolomeu Dias measured the latitude of the
southern tip of Africa, the Cape of Good Hope6;
− 1494: the determination of the latitude by the Sun is referred to in the text of the
Treaty of Tordesillas, as one of the methods used in the demarcation of the Portuguese and Spanish areas;
− 1497-98: according to João de Barros (1932, Vol. 1, Livro IV, Cap. 2, p. 280), several astrolabes were taken in the voyage of Vasco da Gama to India, and observations of the Sun were made in the bay of St. Helen, using a large instrument;
− 1500: in a letter written to King Manuel I, from Brazil, master João reports the
observation of the Sun’s height, made on land.
Before the introduction of astronomical methods, the nautical charts used by the
European pilots in the Atlantic were identical to the portolan charts of the Mediterranean. The ship’s position was determined, on the chart, as the intersection between a segment with origin in the last known (or estimated) position, in the direc-
od, known as ‘parallel sailing’, was commonly used by the pilots from the end of the fifteenth century
on. Gago Coutinho goes even further when he asserts that observations of the Sun were already made
in 1431, during the trips to the Azores, when D. Henrique (Prince Henry) was still alive (Coutinho,
1969, Vol. I, p. 127-32).
4
Ravenstein (1908, p. 16), as cited by Albuquerque (1965, p. 59).
5
This is known from a handwritten note attributed to Columbus, or to his brother Bartolomeo, on the
margin of a copy of Historia Papae Pii (Venetiis, 1447). A facsimile of the note is in Raccolta di Documenti e Studi publicati della Comissioni Colombiana. Autografi di Cristoforo Colombo, Parte I, Vol. III.
Roma, 1892.
6
This is known from a handwritten note by Columbus, on the margin of Pierre d’Ailly’s Imago Mundi.
A facsimile of the note is in Raccolta di Documenti e Studi publicati della Comissioni Colombiana. Autografi di Cristoforo Colombo, Parte I, Vol. III., Tav. LXX, n.° 23, Roma, 1892.
14
tion of the course steered, and an arc of circumference whose radius was the distance estimated by the pilot (Figure 2.1)7. This method of fixing was known by the
Portuguese pilots as the ponto de estimativa (‘estimated point’) 8 or ponto de fantasia (‘point of fantasy’)9.
N
N
point of
departure
point of
departure
Course
Course
d
ϕ
PF
SP
Figure 2.1 – Point of fantasy (left) and set point (right) (ϕ is the latitude). Due to the
error introduced in the course by magnetic declination and the uncertainty in the
estimated distances, the point of fantasy and the set point didn’t usually coincide.
When astronomical observations started to be made for navigational purposes, both
at sea and on land, the method had to be modified to accommodate the new element of information: the latitude. To the resulting position, in which the observed
latitude always prevailed over the course and the distance, was given the name of
ponto de esquadria (‘square point’ or ‘set point’). In the absence of any errors, both
in the estimated distance and the compass direction, the set point and the point of
fantasy were theoretically coincident. However, and due to the effect of magnetic
declination and the uncertainty in the estimated distance, that was not usually the
case. In most situations the three available elements (course, distance and latitude)
were not in perfect agreement, i.e., the observed latitude did not necessarily confirm
the point of fantasy. In those cases, a set of rules, whose function was to harmonize
the point of fantasy with the information of latitude, was applied. These rules,
named emendas do ponto de fantasia (‘amendments to the point of fantasy’), were
7
No traces were usually made on the chart. The positions were determined with the help of two dividers: one opened in the distance sailed (as measured in the scale of leagues), and the other, in the
distance between the old position and the closest rhumb line indicating the course steered.
8
This is the name used by Francisco da Costa in his Arte de Navegar, of the end of the sixteenth century (Albuquerque, 1970a, p. 187), and also in the Livro de Marinharia, in a section considered to have
been written in the fifteenth century (Rebelo, 1903, p. 7-8). In this same text the alternative designation of ponto de marinharia is also used (no satisfactory English translation) (Ibidem, p. 8).
9
This name was used by the cosmographer Manuel Pimentel, in his Arte de Navegar, of 1712 (Cortesão et al., 1969, p. 144).
15
described by the cosmographer major Manuel Pimentel, in his Arte de Navegar of
1712 (Cortesão, 1969, p. 145-149) (see Figure 2.2). A slightly different description,
which have been accepted as the standard version in all studies that I know of, was
made by Fontoura da Costa (1983, p. 395-97) (see Figure 2.3)10. In both versions, the
observed latitude always prevails over the course and distance though the criteria
are different in the relative weight given to the distance. In the examples of the Livro
de Marinharia de João de Lisboa (Rebelo, 1903, p. 6-8), supposed to have been written in the fifteenth century, the latitude and the distance are always used to determine the position but it is uncertain whether this coincidence is significant or not.
Gonçalves (2006, p. 98-105), where these examples are analyzed, doesn’t clarify the
issue. Figures 2.2 and 2.3 illustrate the procedures described by Manuel Pimentel
and by Fontoura da Costa.
N
PF
N
SP
Case 2
N
SP
PF
PF
SP
Case 1
1/2
1/2
Case 3
Figure 2.2 – The amendments to the set point according to Manuel Pimentel (1712). Case 1: courses from NNW to NNE and from SSE to SSW;
Case 2: courses from ENE to ESE and from WSW and WNW; Case 3: all
other intermediate courses. The horizontal dashed lines represent the
parallel of the observed latitude.
Due to the fact that the magnetic declination affected differently the point of fantasy
and the set point, the traditional charts were not usually compatible with the new
navigational method. The problem may have become obvious when astronomical
navigation started to be used together with those charts, to which scales of latitudes
were eventually overlaid, resulting in some incompatibility between the information
shown and the observations of the pilots. The practical harmonization of the set
point method with the nautical cartography of the fifteenth century would still have
10
The author does not identify its historical origin, which is the reason why preference is given here to
the rules described by Manuel Pimentel.
16
to go through a transition phase, as extensive astronomical surveys were necessary
to its full implementation in the areas of interest11. Eventually the difficulties were
solved and a hybrid cartographic model was developed. The transition process between the portolan chart and the latitude chart is discussed in more detail later in
this chapter (see ‘Cartographic evolution’, p. 34).
N
N
PF
SP
Case 2
N
SP
PF
PF
Case 1
SP
Case 3
Figure 2.3 – The amendments to the set point according to Fontoura da Costa
(1983). Case 1: courses from NNW to NNE and from SSE to SSW; Case 2: courses
from ENE to ESE and from WSW and WNW; Case 3: all other intermediate courses.
The horizontal dashed lines represent the parallel of the observed latitude.
The magnetic declination
The magnetic declination is the angle, in a certain time and place, between the geographic north, i.e. the direction of the meridian, and the magnetic north, indicated by
the magnetic compass. The phenomenon was unknown up to the end of the fifteenth century, and the differences between the geographic and the magnetic north
were generally attributed to poorly magnetized needles or faulty compasses. According to the pilot João de Lisboa, it was a common practice among compass makers to
rotate the compass rose on top of the magnetized needles so that it pointed to true
north at the place of its construction (Albuquerque, 1982, p. 140) (Figure 2.4).
11
At about 1485, an astronomical survey of the coast of Guinea was ordered by King João II of Portugal (see p.14 and Note 5, in this chapter). In 1514 the pilot João de Lisboa, in the Tratado da Agulha de
Marear, still complained about the discrepancies between the charts of his time and the practice of
astronomical navigation (Albuquerque, 1982, p. 14).
17
Figure 2.4 – At left, a compass rose aligned with the magnetized needle, both
pointing to magnetic North (Nm); at right, a compass rose rotated clockwise to
point to true North (N). In both cases, the magnetic declination is 15° west.
The earliest known reference to the existence and influence of magnetic declination
on navigation is generally attributed to Columbus, during his first voyage to the West
Indies, in 1492, who reported having observed a ‘true meridian’ (meridiano vero),
where the magnetic declination was zero, near the Azores archipelago12. Also, the
name given to Cape Agulhas in the Cantino planisphere – Cabo das Agulhas (‘Cape of
the Needles’) – is an indication that the magnetic declination in the area was close to
zero at the time and that the phenomenon was observed and registered during some
exploratory mission that preceded the making of the chart13. The Portuguese pilots
used the verbs nordestear (to point ‘eastward’) and noroestar (to point ‘westward’)
to express the tendency of the magnetic needles to point to the east or to the west
of the geographic North.
The influence of the uncorrected magnetic declination in the position of the ship depended on the navigational method. For the method of the point of fantasy, both the
latitude and longitude were affected (Figure 2.5, left); for the set point method, only
the longitude was affected because the observed latitude always prevailed over the
12
For a discussion of the discovery of the magnetic declination and the role of Columbus, see Mitchell
(1937).
13
This was confirmed by D. João de Castro (1500-1548), who made the earliest known systematic
measurements of the magnetic declination during his trip from Lisbon to India, in 1538. In the Roteiro
de Lisboa a Goa (‘Rutter from Lisbon to Goa’), on 5 July 1538, he writes: ‘this Cabo das Agulhas is the
place where the pilots have the precept that their needles don’t show any variation’ (este Cabo das
Agulhas é o lugar onde os pilotos têm por maxima que as suas agulhas não variam coisa alguma). See
Castro (1538).
18
estimated distance (Figure 2.5, right). Only if the magnetic declination were zero (or
corrected for), and supposing that no errors were made in the estimation of the distance, did the point of fantasy and the set point coincide.
d
δ
δ
d
PF 2
SP 2
PF 1
SP 1
ϕ
Figure 2.5 – The influence of the magnetic declination on the point of fantasy
(left) and on the set point (right). PF 1 and SP 1 are, respectively, the point of
fantasy and the set point, unaffected by the magnetic declination; PF 2 and SP 2
are, respectively, the point of fantasy and the set point, as affected by the magnetic declination. The horizontal line connecting SP 1 and SP 2 represents the
parallel of the observed latitude, ϕ.
The adoption of one or the other method for cartographic purposes leads to different geometries. While in the first case (point of fantasy), the spatial variation of the
magnetic declination is reflected upon a variable orientation of both meridians and
parallels, that is not the case with the second (set point), where the parallels are always shown straight, east-west oriented and equally spaced (assuming that no errors
were committed in the determination of the latitudes). For this reason, it becomes
relatively easy to identify the charting methods used in an old nautical chart, once
the grid of meridians and parallels implicit to the representation is revealed through
georeferencing. This is a central point to understand the geometry of the preMercator nautical charts. While the development of the set point method represented a breakthrough in the navigation and cartography of the sixteenth century, its
accuracy was strongly affected by the magnetic declination, especially for courses
close to east and west. The resulting errors, which affected the relative longitudinal
position between places (see Figure 2.6), could be corrected for, or at least palliated,
by replacing the magnetic course with the estimated distance in the determination of
the ship’s position, as considered in the ‘amendments to the set point’ (Figures 2.2
and 2.3). However it is unlikely that such correction was ever extended to chart making as it could insert significant errors into the magnetic courses shown between
19
places on the charts, which was a much more important element of navigational information than the distances.
point of
fantasy
d
δ
ϕ
set point
true position
Figure 2.6 – The longitudinal error of the set point with courses close to
east or west, due to magnetic declination. By using the estimated distance (d) instead of the magnetic course to calculate the ship’s position
this error could be avoided or palliated.
D. João de Castro, in his Roteiro de Lisboa a Goa, is aware of the longitudinal distortions introduced in the charts by the magnetic declination. After describing its spatial
variation along the route from Lisbon to Brazil and to the Cape of Good Hope (where
the compasses pointed to the east of the geographic north), and from there to India
(where the compassed pointed to the west of the geographic north), he comments:
‘From these things it follows that the island of Madeira, Canarias, Cape Verde,
as well as the beaches of Brazil, which are opposed to the easterly wind, are
more distant from the meridian of Lisbon to the western side than they are situated in the marine charts […]; and the islands of Tristão da Cunha, Cape of Good
Hope, with all land and sea […] up to the coast of India […] are closer to the meridian of Lisbon by many degrees than shown in the charts and globes.’ 14
Because the magnetic declination varies both in space and time, its influence on the
geometry of the old nautical charts can only be assessed with reliable information on
its distribution in different times. A good source for the period covered in this research can be found in the observations made by D. João de Castro in the Atlantic,
Indian Ocean and the Red Sea, in 1538 and 1541, and registered in the Roteiro de
Lisboa a Goa and Roteiro do Mar Roxo (‘Rutter of the Red Sea’) (Castro, 1538; 1541).
14
The original reads: Destas cousas se segue que a Ilha da madeira, Canareas, Ilhas do cabo verde, e
assi mesmo as prayas do Brasil que se opoem ao vento leste, estão maes apartados do merediano de
Lisboa pêra a banda do occidente do que jazem situadas nas cartas de marear […]; e também que as
Ilhas de Tristão da cunha, cabo de boa esperança, com toda a terra e mar que se contem ate a costa
da India […] jazem maes chegados ao merediano de Lisboa por muitos graos do que nas cartas e pomas se mostra. See Castro (1538), p. 200-207.
20
Magnetic declination as of 1500
3
4
2
-6
1
3
-4
-5
4
1
-7
3
1
-2
-3
-6
0
-11
-8
-1
-7
-9
1
-1
-5
3
-1
-2
2
-5
2
20
4
0
2
-40
3
1
-4
0
5
4
3
-40
-7
-20
0
-7
3
5
-20
-4
-60
-6
-5
-6
-8
2
-1
-1
0
4
-1 0
-3
2
5
4
-4
-6
0
1
2
-2
-2
-40
-3
1
3
6
-3
-5
2
-1
4
5
3
0
-2 - 1
-2
-4
-6
20
-2
5
3
2
-1
-20
-2
-3
-34
2
6
2
-6
-4
1
1
0
4
-2
4
0
1
-2
3
-3
4
-2
-1
1
40
-3
0
2
3
4
2
0
0
-7
-1
5
-9
20
-7 -8
1
0
1
-1 0
-4
-1 1
60
3
2
-1
-1 6
3
-1 5 4 -1
-1
2
-1 0
1
9
-1 1 - -
6
4
-3
-8
-1
2
-1
- 90
-4
3
-5
2
5
40
1
-6
-5
60
-1
-5
-1 89
-1
-1 7
-1 6
-1 5
-1 4
-1 3
40
60
80
-60
-40
-20
0
20
40
60
80
Figure 2.7 – Spatial distribution of the magnetic declination in 1400 (left) and 1500 (right),
according to the geomagnetic model of Korte and Constable (2005).
To my knowledge, these are the earliest known systematic measurements of the
magnetic declination. D. João de Castro was a competent and careful observer: most
determinations were made by measuring the azimuth of the Sun before and after the
meridian passage, with the 'shadow instrument' invented by the mathematician Pedro Nunes. Many of the results were double checked and, whenever possible, observations were made on land. A complementary source is given by the geomagnetic
model of Korte and Constable (2005), developed on the basis of a series of archeomagnetic and paleomagnetic data15. The use of this model in the present research is
discussed in Chapter 3. Annex C contains graphical illustrations of the spatial distribution of the magnetic declination in the Atlantic, Mediterranean and Indian Oceans,
between 1200 and 1600, as estimated by the model. Figure 2.7 illustrates two of
those outputs, for the years 1400 and 1500.
The Mediterranean portolan chart
The medieval portolan chart has been considered as a unique achievement in the
history of maps and marine navigation, and its advent one of the most important
turning points in the whole history of Cartography (Cortesão, 1969, p. 215-6). It took
place in a time when the cartographic representation of the known world, in general,
and terrestrial cartography, in particular, were still in a pre-scientific era. The oldest
known portolan chart, the Carta Pisana (‘Pisan chart’), was drawn around 1285 and
its accuracy and detail are so striking, when compared with the symbolic representa-
15
Directional data (magnetic declination) was obtained from the analysis of lake sediments, archeomagnetic artifacts and lava flows. See Korte and Genevey (2005) for the detailed spatial and temporal
distribution of the data.
21
tions of the world made at the time, that it is fair to assume that the techniques used
in its construction were already known for at least some decades.
Much has been written in the last two hundred years on the origin and method of
construction of the portolan charts. Still, these matters continued to be the object of
some controversy until very recently, as no one theory was able to gather unanimous
agreement. Important references to the subject are the works of Nordenskiold,
Periplus (1897), and of Tony Campbell, Portolan Charts from the Late Thirteenth Century to 1500 (1987). In this last study, a review is made of the various theories addressing the origin of the nautical chart of the Mediterranean, which are grouped in
two classes, whether they consider an ancient or a medieval origin (Campbell, p. 38084). To the first belong those asserting an old cartographic tradition (Greek, Roman
or Egyptian), from which the medieval portolan chart evolved. The most popular
theory in this class is the one attributing to Marinus of Tyre the authorship of the
first nautical charts; to the second belong those considering the portolan chart to
have been developed during the Middle Ages. As for the nature of the projection,
several theories coexisted at the time Campell’s study was made, including the cylindrical equidistant and the Mercator projection. However, and as pointed out by the
author, the majority opinion at the time had already rejected the possibility of an
explicit map projection having been used in the conception of the charts, any resulting geometric properties being accidental (Ibidem, p. 385-86). As for the possibility of
the portolan charts having been compiled from magnetic directions given by the marine compass, Campbell is very cautious, calling for more detailed cartometric analyses from which a solid correlation between the distortions of the charts and the
pattern of magnetic variation could be established (Ibidem, p. 385).
An important turning point in the present knowledge about the origin of the portolan
chart was the recent publication of Les Cartes Portolanes (Pujades, 2007). This is a
detailed and authoritative study addressing the historical context in which the medieval nautical cartography was born, as well as the main questions concerning the
when, where, who and how portolan charts were developed. As for the when, it is
shown that the first nautical charts could not have appeared before the beginning of
the thirteenth century, when some specific developments in the field of Mathematics, including the introduction of the decimal system, took place (Ibidem, p. 515). A
rediscovered manuscript portolan from ca. 1200, the Liber de existencia riveriarum,
referring to a nautical chart which once accompanied the text, constitutes a strong
confirmation of the relationship between the ‘portolans’ (the rutters) and the charts,
as well as of the involvement of the pilots in the compilation process. The prologue
of the manuscript reads:
22
‘We propose to write about our Mediterranean sea, about the form of the sea
itself and its shores, in accordance with how its places are located in terms of
the winds on the globe of the Earth. In order to represent it on a mappamundi
chart, I drew up this brief text on the number of miles that separate its places
[…]. Reasonably represented are the length, width and the short distances between its two shoreline sides, those of Libya [Africa] and Europe, in accordance
with what I managed to discover and calculate from information provided by
ship’s officers and their portolans […]’ 16
As for the where and who, the same text points to a specific coastal stretch between
Pisa and Genoa and to a milieu of scholars in contact with the world of maritime
trade, where the first portolan charts might have been constructed, during the first
quarter of the thirteenth century (Ibidem, p. 515). Concerning the how those charts
were made, Pujades clearly supports the thesis defended by many authors before
him that the magnetic compass played a fundamental role in their conception, a
clear confirmation being the strong correlation between the northwestern tilt of the
Mediterranean axis and the average value of the magnetic declination at the time.
Based on several inventories of skippers and pilots, it is also shown that the only navigational instruments used at sea were the magnetic compass, to determine the direction, and the hourglass, to measure the passage of time. No inventories mention
instruments for astronomical navigation (Ibidem, p. 510).
The possibility of a precise match between the sailing directions written in the portolans and the nautical charts that were hypothetically based on them is clearly an
oversimplification, one the reasons being that the charts contain much more information. An attempt to establish such connection was made by Lanman (1987), who
used the shoreline information registered in two portolans (one of them is Lo Compasso da navigare, ca. 1300, the oldest known) to construct two representations of
the Mediterranean basin which were later compared to, respectively, the Carta Pisana (ca. 1285) and a chart by Matteo Prunes (1559). Though a recognizable outline of
the Mediterranean is obtained in both cases the accuracy and detail of the representations are a far cry of the charts they are supposed to reproduce. However the work
of Lanman is a first and important step in the right direction. Instead of using only
the directions and distances between adjacent places, as a transverse in a topographic survey, it would have been better to also include the offshore routes, as a
way to minimize cumulative errors and preserve the overall shape of the basin. The
author’s implicit conclusion that a cylindrical equidistant projection centered on the
Equator (i.e. a plate carrée) was used in the construction of portolan charts, based on
the square-gridded areas shown in a few of them, is not supported by any cartomet16
Translation from the Latin, partially reproduced from Pujades (2007, p. 513).
23
ric analysis and seems incompatible with the main results of the article. Either the
portolan charts were drawn on the basis of observed directions and distances between coastal places, as the article attempts to show, or the known geographic coordinates of those points were plotted in a square grid of meridians and parallels.
The two processes are obviously incompatible with each other. In Lanman’s work,
the angle of rotation of 25 portolan charts, from about 1300 to the second half of the
seventeenth century, are compared with the available paleomagnetic data for the
Mediterranean area. There is a good agreement between both values up to the middle sixteenth century, when the charts began to be corrected for the magnetic declination. The conclusion that the counterclockwise rotation of the axis of portolan
charts is due to the effect of magnetic declination is correct, though the way to assess its value, based on a single line connecting Gibraltar to Antioch, seems too
coarse and doesn’t allow for its spatial variation. The last conclusion contains a
wrong interpretation on the way the Portuguese latitude charts were constructed.
Because the parallels are east-west oriented on those charts, the author concludes
that the magnetic declination was corrected for, which is not true, as shown earlier
in the present chapter.
Another important work dealing with the geometric properties, accuracy and method of construction of portolan charts is a dissertation by Loomer (1987), where an
extensive cartometric analysis of 26 charts, from 1339 to 1508, is presented. The
author starts by taking a sample of about 360 control points, positively identified
both in the old and in a modern chart, whose geographic (in the modern chart) and
Cartesian (in the old charts) coordinates are to be used for cartometric purposes.
With the rhumb circles of the charts as a geometric reference, a projective transformation was then applied to each set of Cartesian coordinates, with the purpose of
correcting them for possible post-drafting distortions caused by time and other factors (Ibidem, p. 115)17. Several composite charts, consisting of the average positions
of the control points in various chosen groupings (time, origin and geographic location) of the available charts, were computed, with the purpose to check for trends in
their geometric properties. A comparison of each individual and composite chart
with various map projections was then made, with the objective of finding the best
fit. The author emphatically stresses that it is not his conjecture that the medieval
cartographers had consciously employed any formal map projection, but rather, that
the construction method might have preserved characteristics of the underlying data
which could be inferred from the properties of the best fitting projection (Ibidem, p.
107). In all cases, it was found a high degree of correlation with the Mercator and
17
The adjustment process consisted in forcing the distorted circles defined by the lines of the wind
roses into true circles.
24
equirectangular projections, the results for the Mercator’s being slightly better
(Ibidem, p. 133, 166). From this result the author concludes that the charts were likely based on loxodromic course bearings, rather than distances, and suggests a method of construction analogous to triangulation (Ibidem, p. 146). A rotation of the axis
of the portolan charts with respect to true North was observed in all charts, ranging
from about -9.1° to -10.5°. When the representation of individual sub-basins was
further analyzed, a clear west-east trend in the value of the average rotation was
found, varying from about -4°, in the western part of the Mediterranean, to about -9°
to -10°, in the eastern Mediterranean and Black Sea. Based on a paleomagnetic study
in the central Mediterranean (which indicates a value of -13° at Mount Etna, in 1300,
increasing to -18.5°, in 1400), the author concludes that there is no indication that
the rotation of the charts is related to the magnetic declination at the time they were
drafted (Ibidem, p. 151, 167). Instead, the rotation is suggested to be the result, according to an unpublished article by James Kelley, of an overall compensation for the
sphericity of the Earth when constructing a frame of reference based on a triangulation (Ibidem, p.160, 161). In my opinion the use of a triangulation scheme to plot the
places on the chart, using the internal angles measured at each vertex, rather than
doing it directly with the observed bearings, is an unnecessary complication. Theoretically it could be a way to compensate for the unknown value of the magnetic declination affecting the observed bearings, but the hypothesis seems too unrealistic to
be true, as there is no indication that the phenomenon was even known at the time
or that such techniques were used. The principle of parsimony is clearly applicable to
this situation: a much simpler interpretation is that directions observed by pilots at
sea were directly used to plot the places on the chart, thus causing spatially varying
distortions in the orientation of the cartographic North, according to the distribution
of the magnetic declination. Furthermore the distribution of the magnetic declination in the area, as estimated by the model of Korte and Constable (2005), reasonably agrees with the east-west trend indicated in Loomer’s work. Two other important
results were reached by Loomer in his study: first, there is no evidence of any improvement or degradation in the accuracy of the charts with time. The author concludes that the methodology for the chart construction was fixed early in their history and was followed afterwards without alterations (Ibidem, p. 168); second, the
analysis of the charts by individual basins shows distinctly regional characteristics,
which is taken as evidence that they were developed from a series of regional charts
tied together (Ibidem, p. 169).
In a recent study (Gaspar, 2008a) I have applied some of the cartometric and modeling techniques presented in this thesis to the analysis of two portolan charts of different periods and origins: Angelino Dulcetto (1339) and Jorge de Aguiar (1492).
25
First, the geographic grids of meridian and parallels implicit in the old charts were
interpolated, on the basis of a sample of control points. Next, the geometry of the
charts was simulated numerically, using a sample of rhumb-line directions and distances as input. For the simulation of the spatial distribution of the magnetic declination, the geomagnetic model of Korte and Constable (2005) was used. It is concluded
in the study that the geometry of the portolan charts is well explained by the use of
uncorrected magnetic courses and estimated distances, plotted in a plane with a
constant scale. No significant differences in the main geometric features of the two
charts were found, including the tilt of the Mediterranean axis, the proportion between the lengths of meridians and parallels and the convergence of meridians. This
result, coupled with the available information on the skewing of some other portolan
charts, from ca. 1300 to 1600, is an indication that the construction methods did not
evolve during this period, and that the orientation of the Mediterranean was copied
from older prototypes and remained more or less constant until 1600, notwithstanding the significant variation of the magnetic declination.
The latitude chart
The beginning of the sixteenth century marks the transition between the portolanchart model, based on magnetic directions and estimated distances, and the latitude
chart model (or ‘plane chart’), based on astronomical methods. The Cantino planisphere, made by an anonymous cartographer in 1502, is the oldest known Portuguese nautical chart clearly incorporating observed latitudes18.
The scientific literature on the Portuguese nautical cartography is dominated by the
exhaustive work of Armando Cortesão and Teixeira da Mota, Portugaliae Monumenta Cartographica (1960) in which all known Portuguese charts from the fifteenth to
the seventeenth century, at the time of the publication, are presented and discussed.
A facsimiled edition was published in 1987, including some newly discovered specimens and a supplement about the genesis of the Portuguese cartography, written by
Alfredo Pinheiro Marques (Marques, 1987). Some of the interpretations of the first
edition concerning the earliest charts have been revised in later works, like the study
of Marques (1989), about the dating of the oldest Portuguese charts, of Guerreiro
(1997), about the charts of the fifteenth century, and the general introduction to the
Portuguese cartography in the Renaissance by Alegria et al. (2007), which includes a
section on the first Portuguese charts (p. 983-987). Detailed studies on individual
charts were made by Guerreiro (1992), on Jorge de Aguiar’s chart of 1492, and by
18
The planisphere of Juan de la Cosa, dated 1500, is the earliest known nautical chart showing the
Equator and the tropical lines. However their positions on the chart are only approximate.
26
Amaral (1995), on Pedro Reinel’s chart of ca. 1492. This later work, reviewed in
Chapter 4, presents a fresher and well documented view on some difficult themes
related to the dating of the charts and to the transition between the old and the new
cartographic models.
How charts were made
No text prior to 1500 is known describing how nautical charts were constructed during the Renaissance. The earliest known source where the geometry of the latitude
chart is discussed is the Tratado en defensam da carta de marear (‘Treatise in defense of the navigational chart’) published in 1537 by the Portuguese mathematician
Pedro Nunes (2002)19, who was cosmographer major of the kingdom from 1547 to
his death, in 1578. This is a long text illustrated with practical examples, in which
Pedro Nunes addresses the apparent inconsistencies of the nautical charts of the
time and discusses the best way to plot the places on them, according to their latitudes and courses from other places. The intent of the work, according to the words
of the author, was ‘to excuse the chart from the faults and errors of which everybody
accuses it, and not the ignorance, faults, perfidy and contumacy of the pilots’
(Ibidem, p. 127)20. The treatise of Pedro Nunes shows some contradictions in which
the geometry of the plane chart is concerned. At first, he asserts that the routes are
there represented by straight lines, making true angles with the meridians, which are
equidistant and parallel to each other, forming a square graticule with the parallels
(Ibidem, p. 121-22). However, and after considerable reasoning on how the longitudinal displacement between places should be represented on the chart, according to
the distances observed at sea, Pedro Nunes finally admits that the meridians cannot
be straight and that the spacing between them must decrease with the latitude21. He
closes the subject with an unexpected conclusion that seems to contradict his initial
purpose of excusing the chart ‘from the faults and errors of which everybody accuses
it’:
‘But the best would be: to avoid all these troubles: to make the chart in many
parts [or sheets]: with a good large scale: in which we keep the proportion of
the meridian to the middle parallel: like Ptolemy does in the province tables:
because all longitudes, latitudes and courses would be correct, at least there
wouldn’t be a notable error: and carry the chart as a book [...]. And in the parts
19
Nunes (2002). The whole title of the treatise reads: Tratado que ho doutor Pero nunez Cosmographo
del Rey nosso Senhor fez em defensam da carta de marear: cõ regimento da altura.
20
The full text, in Portuguese, reads: Mas porque meu intento nesta pequena obra he desculpar a
carta das culpas e erros: de que todos a acusam: e nam as ignorâncias: enganos: perfias: e contumácias dos mareantes.
21
Ibidem, p. 127-134, 138-41. See, in particular, figures in p. 131 and 140 illustrating Pedro Nunes’
proof that, in the chart, meridians cannot be straight and parallel to each other.
27
[or sheets] that do not contain land: going beyond eighteen degrees of latitude
we can make all degrees equal to those of the meridian since the difference is
small: and beyond [the eighteen degrees of latitude]: we will make the degrees
of longitude equal to those of the middle parallel [...]’ 22
Pedro Nunes suggests here that the use of an atlas composed of several large scale
sheets drawn in the cylindrical equidistant projection, each of them centered on the
respective middle parallel, was a better solution for navigation. This text has been
considered by some authors as an important contribution for the development of the
cylindrical conformal projection, which was presented 22 years later (the Mercator
projection). However, it is doubtful that this suggestion had any practical purpose, as
Pedro Nunes was certainly aware of the impossibility of determining the longitude at
sea, which was absolutely necessary for the use of the cylindrical projection as a navigational tool, and of the difficulties caused by the uncorrected magnetic declination.
Only a little step separated the suggestion of Pedro Nunes from the Mercator projection, but that step was never taken by him, though a new version of his text was published almost thirty years later, in Basel. Also, Pedro Nunes never made the connection between the representation of the loxodromic curve, first described by him in
1537, and the desired properties of the nautical chart.23 We know, from the words of
the cartographer Lopo Homem, a contemporary of Pedro Nunes, that he was responsible for the establishment of a new official pattern chart, based on astronomicallyobserved longitudes. But the judgment of Lopo Homem on this new pattern is extremely harsh, as he reports that many ships were lost on their way to India and the
pilots forced to look for adequate charts in Castile (Matos, Luís de, p. 318-322, as
cited by Albuquerque, 1989a, p. 153). According to his words, ‘all charts made from
this pattern […] are very distracted from the truth and navigation science […]’24. This
means, of course, that courses and distances taken from the new charts did not
match those observed by the pilots and represented on the old charts. The new official pattern, as well as any charts supposedly copied from it, did not survive. However the possibility of this initiative being a serious attempt of Pedro Nunes to concretize his previous suggestion seems unlikely, as it would have necessarily involved an
22
Ibidem, p. 141. The Portuguese text reads: Mas ho milhor seria pera escusarmos todos estes trabalhos: que fizessemos a carta de muitos quarteyrões: de bom compasso grande: nos qaues guardemos
ha proporção do meridiano ao paralello do meo: como faz Ptolomeu nas tauoas das prouincias: por
que assi ficariam todas as longuras alturas e rotas no certo ao menos nam auera erro notauel: e trazesea a carta em liuro […] E nos quarteyrões em que nam ouuer terra: que passe de dezoyto graos de
altura poderemos fazer todolos graos iguais aos do meridiano polla deferença ser pouca: e como daqui
passar: faremos os graos da longura: iguaes aos do peralello do meo […]
23
For a more detailed discussion of Pedro Nunes’ suggestion and its relation with the Mercator projection the see Gaspar, 2005, p. 336-41.
24
The original text, as transcribed from Albuquerque (1989a, p. 153), reads: Todas as cartas que por
este padrão se fizeram […] são mui desvairadas de toda a verdade e ciência de navegar.
28
enormous surveying effort. On the other hand, even if the longitude measurements
were sufficiently detailed and exact, the resulting representation would be almost
useless for the normal practice of navigation, which was based on uncorrected magnetic courses. About thirty years after the publication of the ‘Treatise’, Pedro Nunes
reaffirms his conviction that the equidistant cylindrical projection is the best suited
for marine navigation but admonishes that ‘few or almost no places should be transported from the usual navigational chart to this new tables due to the uncertainty in
their longitudes‘.25
Concerning the practical production of nautical cartography, a description of the various steps for making a copy of an existing chart is given in Martin Cortés de Albacar’s
Breve compendio de la esfera y del arte de navegar, published for the first time in
1551. First, a sheet of vellum or paper is prepared with a pattern of rhumb-lines; next
the coastline is traced from an existing prototype and the toponyms are written; finally, the distance scales, graduations of latitude and decorative motives are added.
The method described for tracing the coastline makes use of two different kinds of
paper: one transparent, for copying from the model, and the other smoked, to transfer the image to the new chart26. Regarding the Spanish cartography, and according
to the navigation textbooks of the time (see Sandman, 2007, p. 1099-1100), there
were two distinct processes for making a chart: from an existing pattern or from a
report, this last method being only used to construct new patterns. A detailed description on how to draw a section of a coastline using the second process is given by
the cosmographer Alonso de Chaves, in his unpublished navigation book (Chaves,
1983, p. 110 -12). After drawing the web of rhumb lines and the scales of latitude
and longitude,
‘one should pick a well-known place, such as a promontory or cape or river, and
draw it in its appropriate latitude on the chart. Then, picking another wellknown close place close by, one should put the two in the correct relation to
one another, checking the latitude first, then the distance and compass bearing
between them, and finally drawing the second feature. The last step in the process was to draw the coastline between the two points, with all its particularities’. (Sandman, 2007, p. 1100)
25
Nunes, 2008, p. 47. The original Latin text reads: Hoc tamen admonemus, pauca aut nulla propemodum loca transferri debere ex consueta marina charta ad has tabulas, ob incertitudinem longitudinis
locorum in ea positorum, multo autem minus x tabulis Ptolemaei. The Portuguese translation reads:
poucos ou quase nenhuns lugares devem ser transportados da carta de marear usual para estas tábuas, devido à incerteza das longitudes dos lugares nela colocados (Ibidem, p. 299).
26
Martín Cortés de Albacar (1551) – Breve compendio de la esfera y del arte de navegar, as referred to
by Ramón Pujades (2007), p. 472.
29
Another description of the construction of a nautical chart in the sixteenth century is
given by Francisco da Costa, who was a professor of the Class of the Sphere in the
College of Santo Antão, in Lisbon, at the end of the sixteenth century. His Tratado da
Hidrografia reads:
‘For representing the sea and show the land that confines with it in the hydrographic charts, [...] two things are presupposed, whose knowledge is absolutely
necessary: the first [is] that [...] the heights of all ports, capes, inlets, [...], etc.,
are known [...]; the second thing to be known by the hydrographer are the sailings of the coasts, ports, etc., both between each other and in respect to the
same coast; we call sailing to a straight line or course that goes from one place
to another, because these are the ways used to sail in the sea, [...] By means of
these heights and sailings describe the hydrographers all sea and any of its places like the geographers do by means of heights and longitudes.’ 27
A little further in the text, Francisco da Costa explains what to do when one place is
to be represented relative to another, if they have the same latitude. Finally, he
makes clear that these methods are only used to register newly discovered features
on the charts, not for producing them:
‘However if one needs to situate places which are east-west at the same height
[…] it is necessary to know the distance there is between one place and the other and, once it is known, it will be taken in the scale of leagues how many there
are between them, and they will be placed at that distance one from the other,
at the height they have. […] These are the two methods used to draw all sea,
with islands, shoals, rocks, etc. in the hydrographic charts; but to avoid the work
and boredom […] the hydrographers have other [charts] with different sizes, to
which they call patterns, from which with great ease they do all charts we see,
and only use the above methods to plot some land, island or shoal newly found
[…]’.28
27
Albuquerque (1970a, p. 111). The original reads: Para nas cartas hidrográficas se representar o mar
e dar mostra da terra que com ela confina [...], se pressupõem duas coisas, cujo conhecimento é totalmente necessário: a primeira que se saibam [...] as alturas de todos os portos, cabos, enseadas, [...],
etc.; [...]; a segunda coisa que há-de saber o hidrógrafo são as derrotas por que correm as costas,
portos, etc., tanto entre si como em respeito da mesma costa; derrota chamamos a uma linha direita
ou rumo que vai de um lugar a outro, que estes são os caminhos por onde o mar se navega [...] Por
meio, pois, destas alturas e derrotas descrevem os hidrógrafos todo o marítimo e quaisquer seus lugares como os geógrafos o fazem por meio das alturas e lonjuras […].
28
Ibidem, p. 113. The original reads: Porém, havendo de situar lugares que jazem de leste a oeste na
mesma altura, […] é necessário que se saiba a distância que há de um lugar ao outro, o qual sabido se
tomará no tronco de léguas as que entre eles houver, e tanto se porá um afastado do outro na altura
em que estiverem. […] Estes são os dois modos por que se lança todo o marítimo, com ilhas, baixos,
penedos, etc. nas cartas hidrográficas; mas para evitar trabalho e enfadamento […] têm os hidrógrafos outras de diferentes grandezas, a que chamam padrões, pelos quais com muita facilidade fazem
tantas cartas como vemos, e somente se servem dos sobreditos modos para situarem alguma terra,
ilha ou baixos de novo achados […]
30
The construction of the distance scales of the charts is also explained by Francisco da
Costa in this same text. In the first modality, a segment with the length of 4 degrees
of latitude, as measured in the chart’s scale of latitudes, is divided into seven equal
parts, each one containing ten leagues29. Then each of these divisions is further subdivided in five (of two leagues each) or ten parts (of one league each). In the second
modality, a segment measuring 24 degrees of latitude (420 leagues) is divided in 35
parts, each one with 12.5 leagues.
Manuel Pimentel (1650-1719), who was a student at the College of S. Antão and
cosmographer major of the kingdom, writes in his Arte de Navegar about the three
different cartographic models used at his time, the portolan chart, the latitude chart
and the Mercator chart:
‘There are three species of nautical charts. The first, from which the other derived, is of those charts that are described by courses and distances, disregarding the latitudes or heights of the lands, or the longitudes. […] The second species is of those charts that are named common, or plane or of equal degrees, in
which the meridians and parallels are represented by equidistant lines, which
make equal squares […] These charts are made by sailings and heights, putting
the lands in their pole heights and courses relative to other lands […] . The third
species if of those charts [in which] the meridian […] is divided into unequal
parts’ 30
Notice how the cosmographer misinterprets the geometry of the latitude chart, as
others have done before and after him. However, the method to ‘put the lands on
the chart’, according to their latitudes and courses relative to other lands, is quite
clear and agrees with what Pedro Nunes and Francisco da Costa have written before.
One important point should be retained from the interpretation of the historical
sources on the navigational and charting methods of the Renaissance: as navigational
tools, nautical charts were constructed in close agreement with the methods for finding the ship’s position at sea. The suggestion that their making was based on any
29
The author considers the standard of 17.5 leagues per degree of latitude.
Cortesão (1969, p. 137, 138, 141. The original reads: Três espécies há de cartas de marear. A primeira, donde as outras tiveram princípio, é daquelas cartas que se descrevem por rumos e distâncias, sem
se atender às latitudes, ou alturas das terras, nem às longitudes […]. A segunda espécie é daquelas
cartas que se chamam comuns ou planas ou de graus iguais, nas quais os meridianos e paralelos se
representam em linhas equidistantes que fazem quadrados iguais […]. Estas cartas se fazem por derrotas e alturas, pondo-se as terras nas suas alturas do pólo e nos rumos que se correm com outras terras
[…]. A terceira espécie é daquelas cartas [em que] o meridiano […] se reparte em partes desiguais. The
description of the three types of charts is made in Chapter XV, De diversas espécies de cartas de
marear (‘Of the different species of navigational charts’), p. 137-142. Chapter XVI, Do uso da carta
plana ou comum (‘Of the use of the common or plane chart’), p. 142-3, describes the use of the plane
chart.
30
31
theoretical map projection concept, such as the cylindrical equidistant projection
centered at the Equator (plate carrée), ignores the fact that they were intended to
support marine navigation, which was constrained by the use of the magnetic directions and the impossibility of determining the longitude at sea. These were also the
main reasons causing the full adoption of the Mercator chart by marine navigation to
only occur well into the eighteenth century, after the longitude problem was solved.
Geometric inconsistency
An important issue concerning all pre-Mercator nautical cartography is the geometric
inconsistency inherent to the charting process, which consisted in the position of a
place being dependent on the particular set of routes used for plotting it on the
chart.
C
A
C’1
A’
803’
59
4’
B
C’2
59
4’
59
59
4’
803’
4’
B’
Figure 2.8 - The inconsistency of the charting process. At left, the relative positions and rhumb-line
distances between Lisbon (A), Madeira (B) and Terceira (C), as measured on the surface of the Earth.
At right, the position of point C (Terceira) was determined using two different tracks (AC and ABC ),
plotting directly on a plane the angles and distances measured on the curved surface of the Earth
(reproduced from Gaspar, 2007, p. 74).
For example, the longitudinal position of the Terceira Island relative to Lisbon will be
different whether it is plotted using a single rhumb-line track connecting the two
places or two consecutive rhumb-line tracks: one from Lisbon to Madeira and the
other from Madeira to Terceira, all referred to the same linear scale (Figure 2.8). This
is due to the fact that it is not possible to represent a spherical triangle on a plane
without distorting sides and angles. While the north-south component of a spherical
rhumb-line track is conserved when the track is plotted on a plane surface, the same
doesn’t happen with its east-west component, due to the convergence of meridians.
In the example above, the combined east-west component of the two consecutive
tracks (Lisbon-Madeira-Terceira) is larger than the east-west component of the first
(Lisbon-Terceira), due to the fact that the spacing of the meridians increases towards
the equator, making the two final positions to dist about forty nautical miles from
each other.
32
If the area represented is relatively small, the inconsistencies can be ignored and the
angles and distances measured on the plane are approximately equal to the corresponding spherical ones. This so-called ‘planimetric method’ is used in our days for
topographic purposes when the area being surveyed is small and the expected errors
are not larger than the uncertainty of the observations. In a larger scale, that is also
the case of the cartographic representation of the Mediterranean and Black Sea in
the traditional portolan charts, where the errors originated by the crude navigational
methods of the time and the influence of the spatially-varying magnetic declination
masked the inconsistencies resulting from the charting process. Additionally, those
inconsistencies tended to be minimized by a natural optimization process through
which the relative positions of the places on the charts were progressively adjusted
over time. When the exploration of the Atlantic began and the area represented in
the nautical charts became significantly larger, first only to the south, along the
western coast of Africa, and after, also to the Americas and Indian Ocean, the weaknesses of the charting process could no longer be ignored. The introduction of astronomical navigation and its reflection on the nautical cartography, which led to the
latitude chart model, did not solve the inconsistency problem. While in some more
or less restricted areas, like the one comprising the Atlantic islands, from Cape Verde
to the Azores, and the western coasts of Africa and southern Europe, the errors resulting from ignoring the curvature of the Earth could still be minimized by a similar
adjustment process, the same could not be done with the whole Atlantic. First, because the area was too large, and second, because it was not covered by a similar
dense network of maritime routes, from which such adjustment could be done.
The myth of the square chart
Another important point to be noted concerning the way the latitude chart was used
for reading and plotting latitudes and directions is the implicit assumption that North
was always oriented upward, and that all rhumb lines, including meridians and parallels, were represented by straight segments making true angles with the meridians.
This assumption is false due to the following reasons: first, directions were not corrected for the magnetic declination, which affected the orientation of all rhumb lines
but the parallels; second, a single linear scale was used for the whole chart, making
the meridians to converge; and third, the inconsistencies caused by the assumption
of a flat Earth caused variable geometric distortions, which were dependent on the
particular set of routes used to make each chart. The wrong idea that, in the latitude
chart, meridians and parallels are approximately straight, equidistant and perpendicular to each other, originated in the sixteenth century and managed to propagate to
the twenty-first through the words of many authors of different times. To its acceptance and dissemination certainly contributed Pedro Nunes’ ‘Treatise in defense
33
of the navigational chart’, whose careless or incomplete reading may have passed
the wrong idea that such was the interpretation of the great mathematician.
The first author to contest the theory of the so-called ‘square chart’, as it became
known, was Barbosa (1938b) 31, much later seconded by Mota (1973, p. 5, 6) and
Albuquerque (1991, p. 37, 38). However, and due to the fact that Barbosa’s studies
were written in Portuguese and generally unknown by the international scientific
community, the myth managed to survive to our days, being still repeated in important international publications by leading specialists like Snyder (1993, p. 6-8;
2007, p. 374-378) and Monmonier (2004, p. 28-29). In a more recent work (Gaspar,
2007), I have shown that the cylindrical equidistant projection is not suited for marine navigation and that the geometry which results from the charting methods of
the sixteenth century in clearly different from such representation. A preliminary
cartometric analysis of the Cantino planisphere is presented in that study and a simple numerical model simulating its geometry is suggested. It is there concluded that
the main geometric features of the chart are well reproduced by plotting directly on
the plane the observed latitudes, courses and distances, as if the Earth were flat.
Cartographic evolution
Little is known on how the latitude chart evolved from the portolan chart, following
the introduction of astronomical navigation in the Atlantic. Also, it is not possible to
establish a well-defined line separating the charts based on the method of the point
of fantasy from those based on astronomical observations. Not only the traditional
method of navigation never stopped being used (especially when the sky was cloud31
António Barbosa (1892-1946) was a Portuguese mathematician and historian who specialized in the
study of the nautical science of the discoveries. His most important work, Novos subsídios para a história da ciência náutica portuguesa da época dos descobrimentos (‘New contributions to the history of
the Portuguese nautical science at the time of the discoveries’), first published in 1938 and re-printed
in 1948 with some improvements, represented a significant advance in the understanding of the geometry of the old charts. Barbosa carefully reviews what has been written about the nautical charts
used during the period of the Portuguese discoveries, describes the evolution between the portolan
chart and the latitude chart and explains the close connection between the navigational and the
charting methods of the time. The contributions of Barbosa to the study of the nautical science of the
discoveries are, in general, relevant, accurate and original. Still, they are seldom referred to in Portugal and completely unknown abroad. Three main reasons explain why: first of all, the early death of
the author, in 1946; second, the fact that he only wrote in Portuguese (with a single exception of an
article written in French and published in Paris, 1939); and third, his conclusions about the geometry
of the plane chart refuted the prevailing theory at the time, which was supported by prominent Portuguese researchers of the twentieth century, like Duarte Leite (1864-1950), Luciano Pereira da Silva
(1864-1926), Fontoura da Costa (1869-1940), Gago Coutinho (1869-1958) and Armando Cortesão
(1891-1977). His conclusions were violently opposed by Cortesão (1969, p. 138-140), whose authority
clearly prevailed over the scientific soundness of Barbosa’s arguments. Only more than 50 years later,
did Luís de Albuquerque (who was also a mathematician) fully recognized that Barbosa was right and
told us about his own disagreement with Cortesão (Albuquerque, 1991, Part 1, p. 34-38). For a summary of Barbosa’s works, see Gaspar, 2008b.
34
ed, not allowing astronomical observations to be made), but also both cartographic
models – the portolan and the latitude chart models – coexist in the charts from the
sixteenth century on. Earlier in this chapter it was noted that, in the absence of any
errors, the point of fantasy and the set point were identical. This can be visually confirmed by the examination of Figure 2.1, which shows that the two navigational triangles coincide if no errors affect the distance, the course and the latitude. Since
charts were drawn on the basis of the same elements of information, using the same
geometric constructions, the coincidence of those points implies the corresponding
cartographic representations to be identical. The only reason for the geometries of
the charts adopting one or the other models to be different is the influence of the
magnetic declination. As already explained in this chapter, while the effect of the
magnetic declination in the charts based on the point of fantasy is a variable orientation of meridians and parallels, the latitude chart always represents the parallels as
straight, east-west oriented and equally-spaced lines. Because of this it is usually
easy to identify the methods used to represent different areas on a chart, provided
the magnetic declination was sufficiently large at the time the information was collected. Mutatis mutandis, such identification may become difficult, or even impossible, if the magnetic declination was small.
In an excellent article on the origin and evolution of the Portuguese nautical cartography, Barbosa (1938a) suggests that charts of the portolan-type, constructed in a
time when the declination was small, may have been used together with the new
astronomical methods of navigation without much error, thus mitigating the difficulties of the transition. According to this author the cartographic representations of
the Atlantic coastlines of Iberia and northern Africa, as well as of Madeira and Porto
Santo, were already stabilized at the time the Portuguese cartography was born
(Ibidem, p. 187-88)32. All the cartographers had to do, in order to prepare the charts
for being used with the astronomical methods was to overlay a scale of latitudes.
Barbosa’s point is eloquently illustrated by a reproduction of a chart of ca. 1375,
from the Catalan Atlas, to which a scale of latitudes was added (Figure 2.4), as to
match the exact latitudes of Cape Fisterra and Gibraltar. With few exceptions, the
latitudes of 22 places on the coastline between Cape Boujdour and Cape Fisterra, as
read in the overlaid scale, show errors smaller than ½ degree (Ibidem, p. 191-93).
32
The first Portuguese contributions for those representations were probably made still in the time of
Prince Henry, who ordered a stretch of 450 leagues of coastline beyond the Cabo Bojador to be added
to the charts (Azurara, 1989, p. 209).
35
~
Figure 2.9 – Detail of the Catalan Chart of ca. 1373, from the Atlas of the Viscount of Santarém, to which a scale of latitude was overlaid (reproduced from
Barbosa, 1938a, Fig. 4, p. 192).
This is not an exceptional case, as in most (if not all) portolan charts from the fourteenth century on, the western coast of the Iberian Peninsula appears correctly oriented in the south-north direction, contrarily to the axis of the Mediterranean, which
is always represented with a counterclockwise tilt of eight to ten degrees. According
to Barbosa (Ibidem, p. 196), the development of a new cartographic model did not
worry the pilots and cartographers of the time of Prince Henry, who were much
more concerned with the problem of developing a more accurate method for determining the ship’s position during the long oceanic passages. The thesis of Barbosa is
convincing and his inference that the magnetic declination was small along the Atlantic coasts of Portugal and Africa, at the time the cartographic information was collected (Ibidem, p. 180, 184), is correct (see Figure 2.7). This subject is further dis-
36
cussed in Chapter 4, where the cartometric analysis of four early Portuguese charts is
presented.
A different issue, discussed by the same author in another study, concerns the alleged effect of the manipulation of the marine compasses, during the fifteenth and
sixteenth centuries, on the information registered in rutters and charts. According to
Barbosa (1937, p. 251-53; 264-65), who based his interpretation in some Portuguese
and Spanish rutters, the nautical charts of that period should be organized in four
groups:
− First group (15th century): charts made on the basis of directions measured with
magnetic compasses whose needles were rotated clockwise one or two points
(i.e., by 11 ¼ or 22 ½ degrees), relative to the compass rose33;
− Second group (last quarter of 15th and first years of 16th century): charts made on
the basis of directions measured with magnetic compasses whose needles were
rotated clockwise by one or half a point relative to the compass rose34;
− Third group (16th century): charts made on the basis of directions measured with
magnetic compasses whose needles were rotated clockwise by 2/3 of a point relative to the compass rose35;
− Fourth group (from last quarter of 16th century on): charts made on the basis of
directions measured with magnetic compasses whose needles pointed to magnetic North36.
Barbosa bases his reasoning on the courses between Lisbon and Madeira, registered
in rutters and charts, and cites some historical texts where the manipulation of the
compasses is mentioned, as a mean to compensate for the magnetic declination in
Lisbon. Only from the last quarter of the sixteenth on this procedure would have
33
This is justified by an excerpt taken from the Tratado da Agulha de Marear de João de Lisboa (Albuquerque, 1982, p. 14), where the pilot complains: ‘and because the ancients didn’t feel this variation
[of the compasses] they were moving the irons away from the fleur-de-lis [the North direction, in the
compass rose] so that on those meridians where they had been magnetized they were fixed on the
poles of the world; and for this reason we find all coasts on the charts false by one point and by two’.
The original, in modern Portuguese, reads: e porque os antigos não sentiram esta variação, andavam
mudando os ferros das agulhas fora da flor de lis, para que naqueles meridianos onde as cevavam
fossem fixas nos pólos do mundo; e por esta razão achamos nas cartas todas as costas falsas por uma
quarta e por duas.
34
This is justified by other excerpts taken from the Tratado da Agulha de Marear (Ibidem, p. 20 ), the
Livro de Marinharia of Alonso de Santa Cruz (p. 28) and De magnete, magneticisque, etc., by Guilherme Gilberto (as cited by Barbosa, 1937, p. 252-53). See also Albuquerque (1982, p. 15), where an alternative reading of the text in the Tratado is given.
35
This is justified the Regimento dos Pilotos, by Mariz Carneiro (1655), as cited by Barbosa (1937, p.
253).
36
This is justified by the title of various rutters of the sixteenth and seventeenth centuries, in which
the use of non-manipulated compasses is explicitly referred to (Ibidem, p. 248-49).
37
been completely abandoned. In his ‘Treatise in defense of the navigational chart’,
Pedro Nunes (2002, p. 132) writes: ‘one cannot deny that the island of Madeira is
northeast southwest relative to this city [Lisbon] […] a thing that is experienced every
day’37. This is also the course registered in the Portuguese nautical charts of the first
half of the sixteenth century. Still, it is known from various historical sources of the
time, including D. João de Castro, that the magnetic declination in Lisbon was about
7° E in 1538. The explanation given by Barbosa is that the compasses were manipulated to point to the geographic North at Lisbon, thus making the compass course to
Madeira to be close to its true value. While the mismatch between the courses registered in rutters and charts and the historical observations of the magnetic declination seem to confirm Barbosa’s idea, it is unlikely that such practice was ever extended beyond the Atlantic Islands, where the magnetic declination was very different
from the one observed in Lisbon, making the compensation useless or detrimental.
That was certainly recognized by the pilots of the beginning of the sixteenth century,
who were already aware of its spatial variation. Also, the information of the Livro de
Marinharia that the compasses were compensated for one or two points (11 ¼ or 22
½ degrees), during the fifteenth century, is hard to accept, as there is no evidence
that such high values of the magnetic declination ever occurred during that period.
On the contrary, and as noted earlier in this section, the magnetic declination was
small during the fifteenth century along the coast of Portugal, when a local absolute
minimum probably occurred (see Figure 4.7, in Chapter 4)38.
It is not in the scope of the present research to make a detailed investigation of this
complex subject, as it would imply a large number of charts from the sixteenth century to be studied. However the possibility is considered in Chapter 4, after the cartometric analysis made to the charts is presented.
Miles, leagues and degrees
All pre-Mercator nautical charts show, at least, one graphical scale of distances,
placed either along the margins or in any other location where they don’t affect the
use of the charts. As pointed out by Pujades (2007, p. 481), they would have been
practically useless without one. Very early a standardized form of scale became
common in the portolan charts from the fourteenth century on, consisting of rectangular sections of 50 miles, subdivided into five parts of 10 miles each, alternate with
37
The original reads: nam se pode negar estar a ylha da Madeira com esta cidade nordeste sudueste
[…] cousa que cada dia se experimenta.
38
Small values of the magnetic declination during the fifteenth century can also be extrapolated from
the observations made by Portuguese pilots and cosmographers from 1500 on, and compiled by Barbosa in the same study (1937, Fig. 1, p. 251).
38
blank sections of the same size. The distance unit used in most of the portolan charts
was the Italian mile, though there is a considerable uncertainty on its exact metric
value. When a scale of latitudes started to be added to the charts during the fifteenth century, whether they were based on astronomically observed latitudes or
not, a standard value had to be chosen for the length of one degree of latitude, expressed in the distance units of the charts. Three different standards are known to
have been used in the Portuguese and Spanish nautical cartography: 16 2/3, 17 ½
and 18 leagues per degree39. It was considered by Costa (1983, p. 210-6) and others
that these were Portuguese maritime leagues though many sources also refer to the
use of Spanish or Castilian leagues. However the units were probably identical or
very similar, which might explain the apparent indifference in their use by pilots and
cartographers of the time40.
It is generally considered that the first module to be adopted in Portugal was 16 2/3
leagues per degree. This standard is mentioned in the Livro de Marinharia de João
de Lisboa (Rebelo, 1903), part of which was written in the fifteenth century, and was
probably used by Bartolomeu Dias in his voyage of 1487-88 (Mota, 1961a). The module of 17 ½ would have followed, as a result of more accurate measurements made
by the Portuguese at sea (Costa, 1983, p. 214). The module of 18 leagues per degree
was first suggested by Duarte Pacheco Pereira, in the Esmeraldo de situ orbis (ca.
1505-8), and later referred to by other sources. Table 2.1 identifies some Iberian
sources of the sixteenth century where those standards are mentioned.
Casaca (2005, p. 55-6) associates a different unit of distance to each of the modules
and considers that the corresponding perimeter of the Earth and, with it, the length
of one degree of latitude, was identical in all cases41. Although it is probably true that
some modules (if not all) were based on traditional models of the Earth, each of
them using its own unit of distance42, the idea that they were associated, for the
purpose of navigation, with leagues of different lengths cannot be accepted. Not only
no written documental evidence of that association has come to us, but the adoption
39
These were called módulos (‘modules’) by Franco (1955, p. 70) and by Albuquerque (1989b, p. 106).
For the equivalence between the Portuguese league and other distance units during the fifteenth
and sixteenth centuries, see Fontoura da Costa (1983, p. 210-16). According to this author, the Portuguese league contained four Roman miles and measured about 5920 m. According to Casaca (2005, p.
55) the Spanish league, adopted by Spanish and Portuguese from the sixteenth century on, measured
5572 m. In his Arte de Navegar, of 1712, the cosmographer Manuel Pimentel considers the Spanish
and Portuguese leagues to be identical (see Cortesão , 1969, p. 52, 54).
41
According to this author, the standard of 16 2/3 leagues per degree was based on French nautical
leagues of 5846 m; the standard of 17 ½ leagues per degree, on Spanish leagues of 5572 m; and the
standard of 18 leagues per degree, on a short league of 5413 m. To these standards he associates
almost identical lengths of the degree of latitude, of about 97 500 m.
42
A detailed description of the various types of nautical leagues used in the Iberian Peninsula in the
Middle Ages is given by Franco (1955, p. 42-86).
40
39
of such system would have caused an unacceptable confusion in the practise of navigation.
Table 2.1
Iberian texts of the sixteenth century with references to the length of the degree of latitude
(adapted from Mota, 1961a, p. 2; Casaca, 2005, p. 46)
Source
Author
Modules
Date
16 2/3
Esmeraldo de Situ Orbis
1
Duarte Pacheco Pereira
17 ½
ca. 1505
18
X
Regimento de Munique
ca. 1509
X
Regimento de Évora
ca. 1517
X
Reportório dos Tempos
Valentim Fernandes
1518
X
X
Suma de Geografia
Martin de Enciso
1519
X
X
Tratado da Esfera
Francisco Faleiro
1535
X
X
Tratado da Esfera
Pedro Nunes
1538
X
Arte de Navegar
Pedro de Medina
1545
X
Tratado da Esfera
João de Castro
1545
X
Livro de Marinharia
Bernardo Fernandes
ca. 1548
X
X
Livro de Marinharia
João de Lisboa
ca. 1550
X
X
1
ca. 1550
X
X
Livro de Marinharia
André Pires
Breve Compendio de la Sphera
Martin Cortés deAlbacar
1551
X
X
De Regulis Instrumentis
Pedro Nunes
1566
X
X
X
Probable date of compilation. Most texts are from 1500-1520 (Albuquerque, 1989b, p. 25).
A different possibility is that the diversity and evolution of the adopted length of the
degree in cartography, between the fifteenth and the eighteenth centuries, reflected
a continuing attempt to improve the accuracy of the charts and navigation. That was
suggested by Costa (1983, p. 214), who asserts that the adoption of the 17 ½ module,
in the beginning of the sixteenth century, might have been driven by the realization
of the exiguity of the 16 2/3 one, during the voyages made the Portuguese in the
north-south direction. Although this theory seems tempting, it is contradicted by the
long and apparently pacific coexistence of the three different modules in the extant
historical sources and charts throughout the sixteenth and seventeenth centuries.
Also, it is very doubtful that accurate enough values could be obtained on the basis
of distances estimated at sea. As noted by Randles (1998, p. 48), the earliest known
attempt, in Iberia, to determine experimentally the length of the degree on land was
made by Antonio de Nebrija, ca. 1510, who found it to be 20 Spanish leagues (a value
very close to the correct one, if a league of 5572 m is considered). However, there is
no evidence that this result was ever taken into account by the pilots or cartographers of the time, or that similar initiatives were taken with the purpose of improv40
ing the cartographic and navigational standards. Mota (1961a, p. 3) suggests that the
module of 18 leagues per degree, introduced by Duarte Pacheco Pereira in the Esmeraldo de Situ Orbis (ca. 1505-8) is of Portuguese origin and was probably determined during the astronomical survey of the African coast, ordered by King João II ca.
1485. But why make those measurements so far from home when the western coast
of Portugal, with its north-south orientation, was perfectly suited for the purpose? In
my opinion, such type of survey was not even necessary for making the transition
between the old and the new cartographic models, for the simple reason that the
distances along the Atlantic coasts of Europe and Africa were already known with
sufficient accuracy. All the cartographers had to do was to compile the latitudes of
the places represented in the existing charts and, from the corresponding northsouth distances, deduce the desired ratio. As pointed out by Barbosa (1938a) and
already mentioned above (p. 35-36), the transition between the two models was
much facilitated by the fortunate circumstance that the magnetic declination was
small in the region, during the fourteenth and fifteenth centuries, allowing a latitude
scale to be overlaid to the old charts without much error.
On the other hand the adoption of a specific module was not critical for the routine
practise of navigation during the fifteenth and sixteenth centuries. First, because
observed latitudes and courses, rather than estimated distances, were used whenever possible; and second, because the estimation techniques, based on the experience
of the pilots and their knowledge of the characteristics of the ships, where probably
not accurate enough to discriminate a difference of less than 10% in the length of the
degree. The knowledge of the physical size of the Earth started to have a relevant
practical importance with the proposal of Columbus to reach India by sailing west
and became crucial for the commercial and political ambitions of Portugal and Spain
after the Treaty of Tordesillas. In particular, the problem of finding the exact longitude of the Moluccas Islands, which were claimed by both countries, was directly
related to the adopted length of the degree of latitude (Costa, 1983, p. 215). Considering some accepted distance between Lisbon and the Moluccas, expressed in Spanish leagues, longer equatorial degrees (which are equal to latitude degrees) would
favour Portuguese interests because they would eventually place the archipelago
inside the Eastern hemisphere; shorter equatorial degrees would place the archipelago inside the western (Spanish) hemisphere. We know that the module of 17 ½
leagues per degree was already in use in Portugal and Spain by the time the two
parts met at the Junta de Elvas-Badajoz, in 1524. And that this standard continued to
be used thereafter notwithstanding the opinion of Hernando Colón, of the Spanish
delegation, who defended a shorter degree of 14 2/3 leagues (Franco, 1957, p. 44).
Contradicting the theory defended by Casaca (2005, p. 51-53), it was not the length
41
of the league that was relevant in this dispute, but the length of the degree and, with
it, the overall size of the Earth and the longitude of the spice islands.
In theory, it is possible to identify the module used in each chart, provided that both
a scale of leagues and a scale of latitudes are shown43. The method consists in expressing the length of the degree of latitude in units of the scale of leagues. For example, if the average length of a section of 10 degrees of latitude in the chart is
8.4 cm and each section of 12.5 leagues measures 0.6 cm, then each centimetre has
0.6/12.5 leagues and each degree of latitude has (8.4/10)/(0.6/12.5)= 17.5 leagues44.
All Portuguese charts up to end of the sixteenth century adopt the traditional scale of
the portolan charts, consisting of rectangular sections subdivided in five parts, alternating with blank sections of the same size. To each of these sections the Portuguese
called troncos (‘logs’). Two different types of scales are documented, depending on
the number of leagues per section: sections of 12.5 leagues, further subdivided in
five parts of 2.5 leagues each, and sections of 10 leagues45. The first type (12.5
leagues) is the oldest known and probably derived from the traditional graduation of
the portolan charts, in which each section represented 50 miles. But while in the portolan charts those were Italian miles, in the Portuguese and Spanish charts of the
Atlantic they were Spanish miles, each league containing 4 miles. As noted by Franco
(1957, p. 130), this type of scale very seldom shows an explicit graduation46. The second type (10 leagues) was introduced probably during the sixteenth century47, being
used in the charts attributed to Bartolomeu Velho of 1560-6148, and is usually graduated explicitly. A different standard, of 12 leagues per section, might have been used
in the Cantino planisphere, the earliest known Portuguese chart graduated in latitude. A detailed cartometric analysis is presented in Chapter 5, where the possibility
of this value being the result of a mistake made by the cartographer is discussed.
Whatever the historical truth is, it should be noted that this type of scale is not referred to in any known source of the time (see Franco, 1958, p. 156) and no other
chart has yet been found to use it. Assuming for now that it was indeed adopted in
43
A detailed study on the medieval nautical league is due to Salvador Franco (1957), who analyzed a
number of charts of different origins, from the fourteenth to the seventeenth centuries, with the
purpose of identifying the adopted modules. The results of Franco are presented and discussed in
Chapter 4.
44
A detailed explanation of the methods used in this research to estimate the values of the modules
in the charts is in Chapter 3 (‘Scale Measurements’).
45
The first type is documented in the Livro de Marinharia de João de Lisboa (Rebelo, 1903, p. 29). Both
are described by Francisco da Costa, in his Tratado de Hidrografia of the end of the sixteenth century
(Albuquerque, 1970a, p. 110)
46
An anonymous Portuguese chart of ca. 1506, usually known as ‘Kunstmann III’, is an exception to
this rule. See reproduction in Cortesão and Mota (1987), Vol. I, Plate 6.
47
Franco (1957, p. 132) is of the opinion that this modality was introduced still in the fifteenth century, but presents no examples of earlier uses.
48
See Portugaliae Monumenta Cartographica (Cortesão and Mota, 1987), plates 201-204 and 227.
42
this case, the choice should be considered as exceptional in the cartography of the
sixteenth century and was not probably repeated in later charts.
Early Portuguese charts
Very few Portuguese charts of the fifteenth century are extant. Though it is certain
that nautical cartography was produced in Portugal already in the time of Prince
Henry, probably introduced by Master Jacme of Majorca49, most of the charts were
lost. The earliest written mention to such charts is in Zurara’s ‘Chronicle of Guinea’
(Azurara, 1989), where references are made to the representation of the African
coast near (Ibidem, p. 204) and to the south of Cap Boujdour (Ibidem, p. 209). In this
last case the date of 1446 is mentioned as the time Prince Henry ordered a coastal
stretch of 450 leagues to be added to the existing charts. Various reasons have been
suggested for the disappearance of the earliest Portuguese charts, from which the
earthquake of 1755, which severely damaged the Armazéns da Casa da Índia, and
the policy of secrecy concerning the exploratory missions, are the most popular. According to Marques (1987, p. 44-45), these are acceptable but not sufficient reasons
to explain the situation. A simpler explanation is proposed by this author. We know
that almost all extant charts, dating from the sixteenth and seventeenth centuries,
were not intended for navigation because of their luxurious decoration and lack of
marks of use. Those were preserved by princes, diplomats and other important people, mainly outside Portugal, because of their value and beauty. The same would not
have happened with the charts intended to be used at sea, which were probably the
majority during the fifteenth century, because of their natural decay and the absence
of any relevant reason to preserve them.
All known charts of Portuguese origin up to ca. 1506 are listed below, with a reference to the plate number where they are reproduced in Portugaliae Monumenta
Cartographica (Cortesão and Mota, 1987). Only a brief description is given here. For
the convenience of the reader, more detailed information, including a discussion on
their dating and geometric properties have been moved to Chapters 4 and 5. Reproductions of the five charts analyzed in this study are shown in Annex H.
− Anonymous, ca. 1471 (Biblioteca Estense Universitaria, Modena). Usually accepted as the earliest known Portuguese chart, it is drawn on a sheet of parchment
measuring 617 x 732 mm and depicts the western coasts of Europe and Africa,
49
According to Duarte Pacheco Pereira, in the Esmeraldo de Situ Orbis (Pereira, 1954, Book 1, Chapter
33), a Majorcan cartographer named Master Jacme was called to the service of Prince Henry at the
beginning of the fifteenth century. Though it is now recognized that this cartographer could not have
been the son of Abraham Cresques, as it was supposed for many years, the important point to retain
is that this man was the representative of one of the best cartographic schools of the time.
43
from about the Island of Ouessant, in France, to Lagos, in the Gulf of Guinea.
(PMC: Plate 2)
− Pedro Reinel, ca. 1492 (Archives Départementales de la Gironde, Bordeaux). The
earliest known signed chart of Portuguese origin. It is drawn on a sheet of parchment measuring 711 x 948 mm and represents the eastern Atlantic Ocean, the
oriental and central Mediterranean, and the coastlines of Africa and Europe, from
the British Islands to the mouth of Congo River. (PMC: Plate 521 )
− Jorge de Aguiar, 1492 (Beinecke Library, University of Yale). The earliest known
signed and dated nautical chart of Portuguese origin, drawn on a sheet of parchment measuring 770 x 1030 mm. It is a typical portolan chart, both in style and
geographic coverage, depicting the Mediterranean and Black Sea, the western
coast of Europe, including the British Islands, and part of the northwestern coast
of Africa, up to Elmina, in the Gulf of Guinea. (PMC: Plate I )
− Anonymous, end of fifteenth century (Arquivo Nacional da Torre do Tombo, Lisboa). Two fragments of a chart showing part of the Mediterranean and western
coast of Europe. (PMC: Plate 3)
− Anonymous, 1502 (Cantino planisphere) (Biblioteca Estense Universitaria, Modena). The earliest known chart based on astronomically-observed latitudes. Represents the world, as it was known at the beginning of the sixteenth century, including the West Indies, Brazil and the Indian Ocean. It is drawn on six sheets of
parchment mounted side by side on a cloth, measuring the total 1050
x 2200 mm. (PMC: Plates 4, 5)
− Pedro Reinel, ca. 1504 (Bayerisch Staatsbibliotek, Munique). The earliest known
nautical chart with a scale of latitudes. It is drawn on a sheet of parchment measuring 620 x 893 mm and depicts the western and central Mediterranean, and the
North Atlantic, from the British Islands to Cape Verde, including Greenland and
Newfoundland. (PMC: Plate 8)
− Anonymous, ca. 1506 (Kunstmann III) (Formerly in the Hauptconservatorium der
Armee, Munique, but lost after World War II). The chart was drawn on a sheet of
parchment measuring 870 x 1170 mm and depicts the Atlantic Ocean, including
the western coast of Africa and part of the coasts of Brazil and North America,
and the Mediterranean. This is the second earliest known chart to show a scale of
latitudes. (PMC: Plate 6)
44
3. CARTOMETRIC AND
MODELING TOOLS
Cartometry is the field of Cartography which deals with measurements and calculations of numerical values from maps (ICA, 1973). These measurements and calculations traditionally include the evaluation of distances, areas, directions and number
of objects, as well as various other derived quantities54. One of the most important
cartometric operations used in the present research is georeferencing, through
which an Earth-based coordinate system (latitude and longitude) is assigned to an
old map with the objective of better retrieving its geographic information, determining and interpreting its geometric properties, assessing its accuracy and comparing it
with other maps. This is a preliminary step necessary for most cartometric operations
and applies both to maps with and without an explicit system of reference. To the
first group belong the oldest mappae mundi, which do not show latitude or longitude
lines, as well as the portolan charts of the Mediterranean. To the second, belong
those maps and charts depicting some form of Earth-based reference, like meridians,
parallels or scales of latitude, to which georeferencing can be applied to assess the
accuracy of the representations in their own reference systems. That is the case of
some of the latitude measurements presented in this study, in which the exact latitudes of a sample of control points are compared with the corresponding values
measured on the charts’ scales of latitudes. Another type of cartometric analysis
used here is the assessment of the graphic scales of distance and latitude, aiming at
determining the standard length of the degree of latitude adopted in each chart and
estimating the metric value of the distance units. Courses and distances measured
between chosen control points are also compared with the corresponding values on
the surface of the Earth, with the purpose of assessing their accuracy, identifying the
tracks used for the construction of each chart and relate them with the navigational
methods of the time.
The use of numerical modeling for simulating the geometry of the old charts is an
original contribution of this research. Starting with a sample of rhumb-line distances
and directions, defined on a spherical surface, it is possible to simulate the carto54
Maling (1989) describes and analyses the accuracy of various measurement techniques.
45
CHAPTER 3 – CARTOMETRIC AND MODELING TOOLS
graphic representation that would result from plotting those tracks on a plane, with a
constant scale, as if the Earth were flat. The output of the model, consisting of a geographic graticule, is then compared with the interpolated grid of the original charts,
in order to calibrate its parameters and validate the assumptions made on the charting methods and construction details.
This chapter contains two sections (Cartometric analysis and Numerical modeling),
where the cartometric and modeling techniques and methodologies used in the present research are presented and discussed, and some relevant works from the literature are introduced. Annex D contains a detailed explanation of the structure, mathematics and use of the computer application EMP (‘Empirical Map Projection’), which
was developed for the simulation of the geometry the nautical charts.
In this section the cartometric techniques and methodology used in the present research are presented and discussed. The section is organized in the following parts:
−
Control points: the sample of control points used in the various cartometric operations is presented, and the difficulties and criteria associated with its definition are explained;
−
Map comparison and georeferencing: the theoretical concepts of map comparison and georeferencing, as well as the basic techniques utilized in their implementation, are introduced. The application MapAnalyst, used in this research, is
briefly reviewed;
−
Scale measurements: the techniques used for assessing various types of linear
scales explicitly or implicitly contained in the old charts are introduced. These include the scales of latitude, the graphical scales of distance, the length of the degree of latitude and the metric length of the league;
−
Latitude measurements: the methods used to measure the latitudes on the
charts and to assess their accuracy, on the basis of a sample of control points,
are introduced. Various types of latitude errors, associated with the observations, the construction of the charts and the cartometric operations are identified;
−
Estimating the magnetic declination: the two sources of the magnetic declination used in this research are introduced: the available historical observations
and the output of a modern geomagnetic model. A table of values is estimated
for the period and areas covered by the charts;
46
−
Assessing courses and distances: the techniques used to compare the courses
and distances measured on the charts with the theoretical values, aiming at assessing their navigational accuracy and identifying the charting methods used in
the construction, are presented and discussed.
Control points
Most cartometric techniques used in this research require that an accurate correspondence between the old chart under analysis and the modern world is established. This is assured by compiling a sample of control points of known geographic
coordinates, which have been identified both in the old and in a modern representation. Preferably, the identification of all points in the chart should be done by name
and also by geographic context (location). That is not always possible, either because
no name is shown, the name is not legible or the relation between the archaic and
the modern toponyms is unknown. Also, the identification by geographic context is
often made difficult by the small scale and inaccuracies of the old charts, as well as
by the exaggeration of certain features, aiming at making them more conspicuous for
navigational purposes. That is the case of the representation of some islands and
capes, whose scale is often much larger than the average scale of the chart.
For the present study, a sample of 242 points was chosen, covering in a more or less
regular way the North and South Atlantic, the Mediterranean, the Black Sea and the
western part of the Indian Ocean (Figure 3.1). For the Mediterranean and Black Sea,
part of the list published by Scott Loomer, which includes old and modern names,
was used (Loomer, 1987, p. 195-208). Only the regions known to have been visited
by the European pilots up to the beginning of the sixteenth century are covered by
the sample. These regions do not include, for example, the southern part of South
America, most of the North American coast, Madagascar, the northern coasts of the
Arabian Sea and the Red Sea. To identify the points and determine the modern geographical coordinates, Google Earth proved to be a practical and effective tool, complemented with the Times Concise Atlas of the World55. The list of all control points,
including their modern names, the corresponding toponyms in the five charts analyzed in the study and the geographic coordinates is in Annex A. All values of latitude
and longitude are in decimal degrees, rounded to the second decimal place, to which
corresponds a precision of about 18 seconds of arc (560 m). Although this precision is
clearly excessive for the type of analysis presented here, it was considered that a
single decimal place wouldn’t be sufficient for referencing adequately small features,
like some islands and coastline details.
55
The Times Concise Atlas of the World, Eight Edition. London: Times Books, 2000.
47
Figure 3.1 – The control points used in the study. Only the regions known to have been visited by the Europeans up to the beginning of the sixteenth century are covered, which explains the scarcity of points in the Americas and Indian Ocean.
Map comparison and georeferencing
Map comparison and georeferencing are closely related operations 56 . In georeferencing one seeks to assign a geographic coordinate system to a non-metric map.
This is done by first taking a sample of positions from the map, determine their latitudes and longitudes (or other geo-referenced coordinates) with the help of a modern representation of the same area, and then construct a model by interpolating
through the given values, which will allow attributing a pair of coordinates to any
point of the map. This model usually consists of some regular or irregular grid of coordinated points, from which a graticule of meridians and parallels can be determined and overlaid to the map. In map comparison, two maps are compared with
the assistance of an intermediate model, which is constructed on the basis of the
coordinates of two samples of corresponding control points, one for each map. First,
the position, size and orientation of one of the maps are adjusted as to bring as nearly as possible to coincidence the two sets of control points. This transformation is
usually rigid, consisting of a translation, a rotation and a scale adjustment, and does
56
Simple introductions to the modeling concepts used in georeferencing and map comparison are,
respectively, in Balletti (2006), and Boutoura and Livieratos (2006).
48
not affect the shapes in the map. From the result it is then possible to determine a
quantitative representation of the difference between the two maps, expressed by
the residual vectors connecting corresponding control points (Figure 3.2, top left).
Another common way of representing the differences is through a warped grid, consisting in some regular mesh, first associated with one of the maps, and then deformed as to force the perfect coincidence between the two sets of control points
(Figure 3.1, bottom left). In this case, a more complicated model is constructed by
locally interpolating new coordinate values on the basis of the coordinates of the
control points. Conceptually, the grid of meridians and parallels which results from
georeferencing a map can be regarded as a warped grid obtained from the comparison between that map and a cylindrical equidistant projection of the same area, centered at the Equator (plate carrée). That would be the case of Figure 3.2 (bottom) if
the grid at right were a regular graticule of equidistant meridians ad parallels.
Figure 3.2 – The comparison between two images (left and right) using displacement vectors (up) and a warped grid (bottom). The displacement vectors and grid were determined after the two figures were brought to the best possible coincidence applying a rigid
Euclidean transformation to one of them. The small circles represent the control points.
The subject of quantitative map comparison has shown a remarkable evolution in the
last decades as a result of the growing power and availability of computers and digi-
49
tal techniques. An important article by Tobler (1994) has brought to the attention of
geographers and map historians the bidimensional regression techniques used in
Geodesy and Cartography and their potential use in many other fields. Tobler starts
by formalizing the general bidimensional case, in which one has an independent variable Z and a dependent variable W, each consisting of N pairs of numbers, respectively (xi, yi) and (ui, vi), and wishes to relate W to Z by a function W* so that the
mapping Z → W* is as close as possible to the original association Z → W. For example, suppose that the latitudes and longitudes (λi, ϕi) of a sample of N places in an old
map, with plane coordinates (xi, yi), have been determined and one wishes to estimate new values at some intermediate locations, with the purpose of interpolating a
geographic grid. In that case, W = (λi, ϕi) represents the longitudes and latitudes of
the sample, taken at positions Z = (xi, yi), and W* = f(Z) is a transformation permitting
to find new values of λ and ϕ at some intermediate locations in the map.
The bidimensional function W* is usually written as two separate functions u = f(x, y)
and v = g(x, y), whose parameters are found by the usual regression techniques,
which minimize the quantities:
∑ − (
, )
[3.1]
∑ − (
, )
[3.2]
The three linear models presented by Tobler (Ibidem, p. 193) are the Euclidean or
conformal, the affine and the projective transformations. The Euclidean transformation consists of a translation, a scale adjustment and a rotation,
= + cos − sin [3.3]
= + sin + cos ,
[3.4]
where u0 and v0 account for the translations along the x and y directions, m is the
scale factor and α is a counterclockwise rotation. The affine transformation consists
of a translation, a rotation for each coordinate axis and different scale adjustments in
the x and y directions,
= + cos − sin [3.5]
= + sin + cos ,
[3.6]
where u0 and v0 account for the translations in the x and y directions, mx and my are
the scale factors along the x and y directions, and α and β are counterclockwise rotations of the xx’ and yy’ axes. In the projective transformation, the result is a perspec-
50
tive image of the original, obtained from non-uniform rotations and scale adjustments,
=
!"!#
$!%!%
=
&!'!(
$!%!%
[3.7]
.
[3.8]
All the above transformations are linear, meaning that straight lines are always transformed into straight lines. The Euclidean transformation is rigid, in the sense that no
distortions in shape result from the translation, the scale adjustment and the rotation. This is the type of transformation used for bringing two different maps to the
best possible coincidence, with the purpose of comparing them. On the contrary, the
affine and projective transformations affect the geometry of the maps, as they introduce shear and spatially varying rotation and scale factors.
The transformations can be used in two different ways: as global transformations, in
which the parameters are calculated for the whole area of the map and the resulting
equations apply everywhere; and as local transformations, which are calculated and
applied to small areas in the vicinity of the locations where values are to be interpolated. The main practical difference between these two methods is that global transformations are usually not exact, meaning that the values of u and v of the control
points are not matched by the model W*. On the contrary, in the case of local methods there is usually an exact (or approximate) coincidence between the output of W*
and the values at the control points57. An example of a local transformation is the
finite-element method, in which a triangular grid is first created using the control
points as vertices, and then the facets of each triangle are used for interpolating the
values. A modern alternative is morphing, in which a smooth surface with an almost
elastic behavior is locally adjusted to some control points and then used for interpolating the values at intermediate locations (Boutoura and Livieratos, 2006, p. 65).
Besides the linear type explained above, a large variety of non-linear solutions are
also possible, mostly used in local transformations. These include splines, triangulation methods, weighted polynomials and many others. A critical introduction to
some of them, for the purpose of interpolation in local methods, is in Tobler (1994, p.
197).
In the earliest phase of the present research, a computer program based on twodimensional splines, developed in MatLab environment, was used for georeferencing
57
This depends on the method used in the interpolation. The coincidence is exact in the finiteelement and morphing methods and only approximate when a regular rectangular grid of values is
calculated.
51
the old charts. This program was later replaced by MapAnalyst, a freeware application developed by Bernhard Jenny and Adrian Webster (2005-2009)58. Some simple
comparison tests between the outputs of both applications permitted to conclude
that the results were similar.
Figure 3.3 – Using MapAnalyst for georeferencing the Cantino planisphere. The red circles
represent the two samples of corresponding control points. At right a plate carrée representation is shown with a regular geographic graticule; at left, this graticule is distorted, as to
bring into coincidence the two sets of control points, and overlaid on the Cantino planisphere.
MapAnalyst was designed for map comparison and takes the images of two maps as
inputs: an ‘old map’, which is shown at left in the user interface, and a ‘modern reference map’, shown at right (Figure 3.3). For a comparison to be made, it is first necessary to create two sets of control points, chosen at appropriate corresponding positions in the two maps, and then linked together. This can be done interactively,
using a pointer to identify the places in both maps or, alternatively, by loading a file
containing a list of coordinates. The control points are graphically represented by
small circles or diamonds and can be used to determine displacement vectors, distortion (warped) grids and other comparison information. Four different types of linear
functions are available for using as global models: Helmert 4-parameters (the same
as Euclidean see above), affine 5-parameters, affine 6-parameters and robust
Helmert transformation. The difference between the two affine transformations is
58
MapAnalyst is freely available in: http://mapanalyst.cartography.ch/ .
52
that the first only considers an overall angle of rotation while the second allows for a
different angle of rotation for each coordinate axis. The robust Helmert transformation assigns different weights to each pair of control points and is used when a
large number of outliers are expected. The Helmert transformation is expected to be
used in the generality of the situations, when no significant shear due to aging or
other factors is expected to affect the old map59. In those cases, an affine transformation can be used to minimize the distortions, before any further local transformation is applied. After the linear transformation is made, a summary report becomes available containing the values of the computed parameters. For the case of
the Euclidean transformation, these are (see Equations 3.3 and 3.4) the horizontal
and vertical translations (u0 and v0), the scale factor (m), the rotation angle (α), the
mean displacement error (µ) and the standard deviation of the displacements (σ).
In MapAnalyst, the most important graphical representations of the difference between the two maps are the displacement vectors and the distortion grids: the displacement vectors are immediately determined after the two maps are brought to
the best possible coincidence, using the global transformation, by connecting the
final positions of the control points, in each pair, with a straight segment (Jenny ,
2007, p. 90) ; the distortion grid is estimated on the basis of a non-linear model, in
which the two sets of control points are forced to exact coincidence, and a regular
grid of interpolated values of coordinates is constructed, from which isolines are
drawn (Ibidem, p. 90, 92). The interpolation scheme used in this process was developed by Dieter Beineke (as referred to by Jenny, 2007, p. 90) and involves the summation of equations of conic surfaces centered at each control point, according to
the concept of Hardy (1971). Two other forms of representing the differences between the maps are possible: isolines of scale and isolines of rotation. Both are based
on the construction of regular grids of values, which are interpolated locally using
one of the available linear transformations. Only the control points contained in a
circle of pre-determined radius, chosen by the user, are considered in each interpolation. The value of each control point is individually weighted, according to its distance from the center, using a Gaussian distribution. Because the shapes of the isolines thus obtained are strongly dependent on the radius of the circles, these representations should be used with care, especially when comparing results of different
maps (Ibidem, p. 92).
59
A shear can be introduced artificially when reproducing maps in less than optimal conditions. There
are other special cases, occurring in old paintings and engravings, where maps may be represented
with an altered perspective, as ’birds-eye views’. A simple example of this case is illustrated in Balletti
(2006, p. 37-939).
53
In the present research MapAnalyst was used both for georeferencing and for comparison purposes. Although the application was not designed for the purpose of
georeferencing and its documentation doesn’t mention the possibility60, the process
is straightforward, only requiring that a cylindrical equidistant projection centered at
the Equator (plate carrée) is used as ‘modern reference map’. Then, the horizontal
and vertical lines of the square grid defined by the application coincide with the
equally spaced parallels and meridians of the projection. Figure 3.3 (right) shows a
section of the plate carrée map used for georeferencing.
Scale measurements
Three types of scale measurements are made in this study: (i) those made to estimate a linear scale of latitudes when such scale is not shown explicitly on the chart,
with the objective of assessing the latitude accuracy; (ii) those made to determine
the length of the degree of latitude, in leagues, adopted in each chart; (iii) and those
made to estimate the metric length of the units used in the distance scales: the mile
or the league. In the first type of assessment, two cases are considered:
− The chart doesn’t have a graphical latitude scale but the Equator and other lines
of known latitude (e.g. the tropics and the Arctic Circle) are shown. In this case, a
conversion factor representing the length of one degree of latitude, in millimeters (R), is determined by diving the spacing between two of those lines by the
corresponding latitude difference. This is the method used in the Cantino planisphere;
− The chart doesn’t have a graphical scale of latitudes or any graduated parallels. In
this case, the geographic graticule implicit to the representation is first interpolated, using the georeferencing method explained in the previous section, thus
reducing the situation to the first case. As discussed below, the latitude scale obtained in this way is to be interpreted differently from the one defined by a
graphical scale.
60
Strangely the possibility of georeferencing is excluded from the available documentation (see
http://mapanalyst.cartography.ch/faq.html), the application being presented as a tool for the visualization and study of the planimetric accuracy of old maps (Jenny, 2006; Jenny et al. , 2007, p. 89). From
a personal communication with the first author it was possible to clarify this issue as a misunderstanding, because georeferencing a map is understood, in some circles, as distorting its geometry to bring it
to the best possible coincidence with a modern representation. In its last edition (as of May, 2009)
MapAnalyst comes with a built-in ‘modern reference map’ in the Mercator projection (OpenStreetMap). According to its documentation, the coordinates of all control points are re-projected
from the Mercator projection into a transverse cylindrical equal-area projection centered at the area
of interest, before any transformation is made, and the results are converted back to the Mercator
projection, for visualization. This is not a suitable solution for georeferencing because the square graticule which is superimposed on the reference map, and later distorted to match the control points on
the old map, is not a regular grid of meridians and parallels.
54
Figure 3.4 – Reproduction of a scale of leagues and a fraction of the scale of latitudes of the
chart of Pedro Reinel (ca. 1504). The latitude scale has been rotated 90° counterclockwise.
The assessment of the standard length of one degree of latitude is only possible
when a distance scale is shown on the chart, which is the case of most (if not all) extant charts. Two distinct possibilities have to be considered, whether a scale of latitudes exists (either explicitly shown as a graphical scale or through the existence of
graduated parallels) or not. In the first case the length L of a degree of latitude, expressed in the units of the distance scale (leagues or miles), is determined using the
expression:
L=
R× N
,
S
[3.9]
where R is the length, in millimeters, of a degree of latitude, S is the length of one
section of the distance scales and N is the number of units (leagues or miles) contained in each section61. To explain the use of the formula, consider the example of
Figure 3.4, taken from Pedro Reinel’s Atlantic chart of ca. 1504, where a scale of leagues and a fraction of the scale of latitudes are shown. In the figure, the length of 10°
of latitude measured on the scale is about 94 mm, from which R = 94/10 = 9.4 mm/°;
and the eight rightmost sections of the scale of leagues (the less distorted) measure
53 mm, from which S = 53/8 = 6.6 mm per section. Considering each section of the
scales of leagues to contain 12.5 leagues, one gets L = 9.4 x 12.5/6.6 = 17.8 leagues.
If a scale of latitudes is not shown on the chart (either explicitly or implicitly), the
question of what length of the degree was adopted in its construction cannot be taken literally, because the chart was most probably not drawn on the basis of observed
latitudes. Still, an estimate can be made by first determining the geographic grid im61
As explained in Chapter 2 (p. 42), the graphical scales of leagues are divided in sections (‘logs’) each
one containing either 12.5 or 10 leagues. Scales of the second type are usually graduated numerically.
55
plicit in the representation, using the georeferencing method introduced before, and
then taking the average spacing between the parallels to estimate the value of R,
provided these are approximately horizontal and equally-spaced62. This approach
seems appropriate when one needs to make comparisons between charts with and
without a scale of latitudes.
There is a subtle yet very relevant difference between the values obtained in one and
the other case: when a scale of latitudes is not shown, the value of L reflects directly
the ratio between the latitude differences between the places and the corresponding
north-south displacements estimated by the pilots. This means that, if no systematic
errors were made in the measurement and representation of those distances, the
resulting value of L would be exact. When a graphical scale of latitudes is shown, either it was added to an old representation not based on observed latitudes, in which
case the situation reduces to the previous one, or the distance scales were drawn as
to conform to a specific standard, for example, 17 ½ leagues per degree. Paradoxically, and because the adoption of those standards was likely driven by traditional or
political reasons (see discussion in Chapter 2, p. 38-42), it may well be that the older
charts, not depicting a scale of latitudes, are more accurate than the more recent
ones in what the distances between places are concerned. However, and as noted
before (Ibidem), the importance of those differences for the routine practice of navigation was probably minor.
A third type of assessment that can be made through measurements on the charts is
the estimation of the metric length of the distance units represented in the graphical
scales (miles or leagues). This is done by comparing a number of distances between
chosen places, expressed in the units of the chart, with the corresponding exact distances, in meters, as measured on the surface of the Earth. However the results of
such process must be taken as only relatively crude approximations because there
are several factors contributing to their uncertainty:
− Accurate distance standards didn’t exist before the eighteenth century and each
country or region used their own units, very often with the same names;
− The estimation of the distance sailed at sea, based on the experience of pilots
and their knowledge of the behavior of the ships, was very crude when compared
with our present standards or with equivalent estimates made on land;
− The distances represented on the charts of the time are affected by the distortions inherent to any plane representation of the Earth’s surface. Whilst these
62
Non-horizontal parallels typically result from uncorrected magnetic directions. In those cases the
vertical distances between adjacent parallels shouldn’t be used for assessing the degree of latitude.
56
distortions may be neglected when the area represented is relatively small, as is
the Mediterranean, that is not the case of the charts representing the Atlantic or
larger areas. In the case of the latitude charts, which were constructed on the basis of a series of tracks connecting chosen places, large errors may occur when
measuring distances between any other places;
− The distances represented on the charts are affected by magnetic declination
whenever the set point method was used (see Chapter 2, p. 17-20). The errors
depend on the magnitude of the magnetic declination and may have large values
when the course is close to east or west;
− Most medieval and Renaissance charts are compilations of different sources, often with different scales. This may cause a significant variability in the estimates
made for a single chart, depending on the area, the length and the orientation of
the tracks;
− The adoption of some conventional length for the degree of latitude, which took
place probably from the last decade of the fifteenth century on, affects directly
any estimation based on measurements made on the charts. For example, to a
module of 17.5 leagues per degree always corresponds a league of 111135/17.5 =
6350 m, where 111135 m is the average metric length of a degree. Because the
adoption of those modules was driven by traditional or political reasons, rather
than by scientific considerations or careful measurements, the resulting metric
length of the league is meaningless in which the standards of the time are concerned. That is why this parameter should only be evaluated on the charts where
the historical modules of 16 2/3, 17 ½ and 18 leagues for degree where not used,
that is, charts still based on the older non-astronomical methods.
The process used to estimate the metric length of a distance unit is straightforward.
If d is the distance between two places on the chart, measured in leagues (or some
other unit), and D is the corresponding rhumb-line distance, in meters, measured on
the spherical surface of the Earth, then the length s of a league in meters is given by:
s=
D
.
d
[3.10]
An alternative way of estimating the same parameter is through the length L, in
leagues, of one degree of latitude:
s=
g
,
L
[3.11]
where g = 111135 m is the average metric length of one degree of latitude.
57
Latitude measurements
The assessment of the latitude accuracy of a chart is made using a sample of control
points of known geographic coordinates, positively identified in the old and in a
modern representation. Two cases are considered, whether the chart shows a latitude scale or not (the scale may be implicit, as in the case of the Cantino planisphere.
In the first case, the latitude values read from the scale of the chart are compared
with the known latitudes of the places. In the second, the geographic grid implicit to
the chart is first interpolated, using the technique explained in a previous section,
and a linear scale of latitudes is deduced from the average spacing between adjacent
parallels.
Figure 3.5 – Measuring latitudes by extending the parallels from the graphical latitude scale
(chart by Pedro Reinel, ca. 1504).
Different methods are used to measure the latitudes of the control points in the
charts. When a graphical scale of latitudes is shown, parallel lines are extended horizontally to reach the area of interest and the values are read by visual interpolation.
That is the case, for example, of Pedro Reinel’s chart of ca. 1504 (Figure 3.5). In the
case of the Cantino planisphere, where no explicit latitude scale is shown, the first
step is to determine the average length of one degree of latitude, R, as explained in
the previous section. This is done by first measuring the spacing between two or
more parallels and then dividing the result by the corresponding latitude difference.
58
It may happen that parallels are not exactly equidistant due to distortions of the media. In those cases it may be necessary to determine various values of R in different
areas of the chart. Once the value of R has been estimated, the latitude of a point
can be determined either by measuring its north-south distance from the Equator,
and dividing the result by R, or by overlapping a digital ruler graduated in degrees, as
shown in Figure 3.6. To make a measurement, the ruler is first positioned on the vertical line containing the point of interest, and its origin is aligned with the Equator, a
tropical line or both. Then, the latitude is read directly on the ruler. This procedure
proved to be accurate enough and the most convenient in the majority of the situations. To compensate for some visible distortions, as in the case of the Cantino planisphere, it may become convenient to rotate the ruler, as to make it approximately
normal to the parallels, and to adjust locally the length of the degree.
Figure 3.6 – Measuring latitudes with a digital scale (Cantino planisphere, 1502).
A useful way of presenting the latitude errors measured in a chart is to graphically
display their variation with latitude. This kind of representation allows some of the
various possible sources to be identified, especially those causing systematic errors.
The following types of errors are considered to affect the accuracy of the latitudes of
old charts:
59
− Errors originated in the astronomical observations and related calculations. These
are expected to be normally distributed, to have an average value of zero and to
be generally less than one degree63. Figure 3.7a illustrates a hypothetical variation of this type of error with latitude, assuming that no other errors are present;
b. Random + constant error
1,5
1,5
1,0
1,0
Errors (degrees)
Errors (degrees)
a. Random errors
0,5
0,0
-0,5
0,5
0,0
-0,5
-1,0
-1,0
-5
0
5
10
15
-5
20
0
c. Random + scaling error
10
15
20
d. Random + constant + scaling error
1,5
1,5
1,0
1,0
Errors (degrees)
Errors (degrees)
5
Latitude
Latitude
0,5
0,0
-0,5
0,5
0,0
-0,5
-1,0
-1,0
-5
0
5
10
Latitude
15
20
-5
0
5
10
15
20
Latitude
Figure 3.7 – Types of latitude errors. Constant errors may originate in the imprecision of the
tracing process, making a certain section of the coastline to be transferred to an incorrect
position. Scaling errors may originate when copying parts of a model whose scale is different
from the scale of the chart being made.
− Errors originated in the making of the chart. They include the errors made in the
construction of the pattern from which the chart was copied and those resulting
from the copying process. Two types are considered: the accidental errors, associated with the imprecision inherent to the drawing and copying processes, which
are expected to be randomly distributed and centered at zero, their magnitude
being dependent on the scale of the chart; and the systematic errors, which may
be the result of some bias or miscalculation in transferring the latitudes of the
63
It is here assumed that most of the latitude information in the charts originated in observations of
the Sun made on land, using large astrolabes mounted on tripods. Under these conditions the expected accuracy of the observed heights is of the order of one third of a degree. Observations made
on board were less accurate, due to the smaller size of the instruments and the difficulty in handling
them with precision under the rolling of the ship. To the observation errors we should add those originate in the tables of declination of the Sun, usually much smaller.
60
places to the pattern chart or from the pattern chart to the chart being constructed. These errors are expected to affect the latitudes in a regular way,
through the addition of, or the product by, some constant factor. The result
would be a constant shift of all latitudes in a given area, in the first case (Figure
3.6b), and a latitude error proportional to the latitude, in the second (Figure
3.6c). Both effects are to be observed simultaneously if a certain fraction of the
coastline were copied from a model with a different scale or adopting a different
module (Figure 3.6d). This type of error is referred to in this thesis as a scaling error64;
− Errors resulting from the deformations of the parchment. These are difficult to
quantify, though their effects are often clearly visible in the charts, for example,
in the discontinuity between adjacent sheets and in the waving of scales and
lines. Whenever possible and adequate, they are minimized during the measurement phase, by avoiding the use of the distorted parts of the graphical scales
and making local adjustments to the digital rulers, as explained above. Special
care is to be taken with anisotropic deformations along the vertical and horizontal dimensions of the charts, as they may affect angles, distances and scales65.
To those errors we should add the mistakes made both in the drawing of the model,
or models, from which the chart was copied or in the tracing process itself. Except in
the cases where the latitude of a well-known and positively identified place is obviously wrong, it is not possible to distinguish these mistakes from the accidental errors. Finally, the errors resulting from the uncertainty inherent to the cartometric
measures should also be considered. These may originate in the incorrect identification of control points as well as in the imprecision with which their coordinates are
determined66.
Estimating the magnetic declination
The spatial distribution of the magnetic declination is used in this study to replicate
the navigational conditions during the time the information depicted in the old
charts was collected. All nautical charts of Portuguese origin analyzed here were constructed near the end of the fifteenth or the beginning of the sixteenth centuries.
64
A scaling error ε resulting from adopting a different length L’ for the degree of latitude (instead of L)
is given by ) = *(+′ − +)/+, where ϕ is the latitude.
65
See Loomer (1987, p. 98-104) for a practical method of determining and correcting for the deformations of the parchment through the analysis of the effect caused in the shape of the wind-rose
circles.
66
As noticed before, it was a common practice at the time to exaggerate the size of certain features,
like capes and islands, with the purpose of making them more conspicuous. The influence of these
errors in the accuracy of the measurements is minimized, whenever possible and adequate, by avoiding choosing those features as control points. In the case of islands, the position of the control points
was normally chosen at their geometric centers, rather than the extremities.
61
However it is certain that the representations of the Mediterranean and Red Sea,
and probably also those of the western European coast, were copied from older prototypes. This implies that any comparisons made between the theoretical magnetic
courses and the corresponding tracks measured on a chart should consider, not its
nominal or estimated date of construction, but the origin of each of its sources. The
same principle applies to the simulation of the geometry of the charts using numerical modeling.
50N
40N
6/4 (7.5)
10/4
30N
13/4 (6.5)
19/4
20N
23/4 (5.5)
11/9
2/9 (-9.8)
5/9
10N
26/4
26/8 (-8.2)
1/9 (-10.0)
29/8 (-9.6)
11/5 (6.0)
24/8 (-7.6)
0
15/5
21/8 (-7.2)
17/5
20/5 (11.0)
18/8
24/5
28/7
11/8
27/5 (11.0)
10S
(-6.7)
24/7
29/5
2/6
20S
22/7
6/6 (16.2)
5/6
17/7 (-5.0)
10/6 (19.6)
30S
12/7 (-5.0)
24/6 (10.0)
17/6 (15.6)
26/6
3/7 (0.0)
29/6
30/6 (1.3)
40S
50W
40W
30W
20W
10W
0
10E
20E
30E
40E
50E
60E
70E
80E
Figure 3.8 – Reconstruction of the route followed by D. João de Castro in his trip from Lisbon
to Goa, from April 6 to September 9, 1538 (Mercator projection). The numbers between
parentheses are the values of the magnetic declination.
Two sources were used for estimating the spatial distribution of the magnetic declination: the available historical observations, made during the sixteenth century, and
the geomagnetic model of Korte and Constable (2005). The first are scarce and localized in time and space, the most reliable and detailed being those made by D. João
de Castro in his voyages from Lisbon to India (1538) and from India to the Red Sea
(1541), registered in the Roteiro de Lisboa a Goa and Roteiro do Mar Roxo. Most observations were made by measuring the azimuth of the Sun before and after the meridian passage, with the 'shadow instrument' designed by the mathematician Pedro
62
Nunes. Castro was a competent and careful observer: many of the results were double checked and, whenever possible, extensive measurements were made on land.
Because of their reliability Castro’s values were preferred over the other few available historical observations. However some of the areas of interest are not covered by
them, including northern Europe and the western coast of Africa. A compilation of
the observations of latitude and magnetic declination registered by Castro in his voyages is in Cortesão and Albuquerque (1968, Vol. IV, p. 180-200). Based on these elements, the route followed by the vessel Grypho from Lisbon to India (1538) was estimated and represented in Figure 3.8, together with the observed values of the
magnetic declination67.
Table 3.1
Historical observations of the magnetic declination (degrees)
Location/source
Lisbon
João de Lisboa
(ca. 1514)
Diogo Afonso
(ca. 1530)
João de Castro
(1538)
2.8
7.5
7.5
Terceira (Azores)
Cape Verde
2.8
0.0
5.5
Two complementary historical sources were used in this study: the Tratado da Agulha de Marear de João de Lisboa, compiled in 1514 (Albuquerque, 1982, p. 148-49),
and the rutter of Diogo Afonso, published ca. 1530. Still these data don’t have the
reliability of Castro’s observations and there is a considerable uncertainty about the
dates to which they really refer to. From the first source two values were considered:
those measured at Lisbon and S. Vicente (Cape Verde); from the second, two values
were considered: Lisbon and Terceira (Azores). The observations of Diogo Afonso and
João de Lisboa used in the study are shown in Table 3.1, together with the corresponding values observed by D. João de Castro.
The second source of values of the magnetic declination is the geomagnetic model of
Korte and Constable (2005), which was constructed on the basis of archeomagnetic
and paleomagnetic observations covering the world68. Annex C contains graphical
illustrations of the spatial distribution of the magnetic declination in the Atlantic,
Mediterranean and Indian Oceans, between 1200 and 1600, as estimated by the
model. The comparison between the observations of D. João de Castro and the output of the model for the year 1538 shows relatively small differences in the northern
67
For a study of the Atlantic route followed by Castro’s ship see Coutinho, 1969, Vol. II, p. 268-296.
The route suggested by Coutinho (p. 280) is slightly different from the one presented here.
68
Directional data (magnetic declination) was obtained from the analysis of lake sediments, archeomagnetic artifacts and lava flows. See Korte and Genevey (2005) for the detailed spatial and temporal
distribution of the observations.
63
hemisphere, of the order of 3°, growing to more than 10° in the southern Atlantic
and southeastern coast of Africa. It is worth noticing, in Castro’s observations, the
value of 19.6° at about 30° S and the sharp spatial variation when passing from the
Atlantic to the Indian Oceans, none of them reproduced by the model.
8
10
8
Declination (deg)
Declination (deg)
6
6
4
2
4
2
0
0
-2
-2
-4
1450
CALS7K2
1500
1550
1600
Historical sources
1450
1650
Extralopated
1475
CALS7K2
1500
Extrapolated
1525
1550
Estimated
Figure 3.9 – Estimating the value of the magnetic declination in Lisbon (left) and Cape Palmas
(right), in 1500. The estimated value in Lisbon (1.5°) is an average of two extrapolations, using the trends of the historical sources and of the geomagnetic model. In Cape Palmas, the
value of 5.6° in 1538 is spatially extrapolated from the observation made in May 11 by D.
João de Castro (see Figure 3.8). The estimated value in 1500 (4.0°) is the average between
the output of the model and the extrapolated value.
8
Declination (deg)
6
4
2
0
-2
1450
CALS7K2
1475
1500
Historical sources
1525
1550
Extrapolated
Figure 3.10 – Estimating the value of the magnetic declination
in São Nicolau (Cape Verde), in 1500. The value (-1.5°) is the
average of two extrapolations, using the trends of the historical sources and of the geomagnetic model.
Considering that the charts being analyzed were constructed near the beginning of
the sixteenth century, the year of 1500 was chosen as a common reference for the
purpose of the cartometric and modeling operations. All historical observations were
64
extrapolated to 1500 taking into account the other available data and the variation
shown by the geomagnetic model. In some cases, spatial interpolation was found
necessary, when the places where the observations were made did not coincide with
the control points. In Figures 3.9 and 3.10 the extrapolation processes for Lisbon,
Cape Palmas (Gulf of Guinea) and São Nicolau (Cape Verde) are illustrated. Notice
how the extrapolations in time are made, whenever possible, using an average of the
trends indicated by the historical sources and by the model.
Table 3.2
Magnetic declination at some control points
Place
Lat
(deg)
Long
(deg)
CALC7K2
1500
1538
J. Lisboa
D. Afonso
J. Castro
δ
ca. 1515
ca. 1530
1538/1541
1500
C. Farvel
59.8
-43.9
-13.3
-11.4
-13.3
Slea Head
C. Race
Terceira
52.1
46.7
38.7
-10.5
-53.1
-27.2
1.1
-11.2
-1.7
2.6
-9.6
-0.3
1.1
-11.2
-2.2
C. Espichel
Madeira
38.4
32.8
-9.2
-17.3
3.7
2.3
4.3
3.1
Gran Canaria
São Nicolau
C. Palmas
27.7
16.6
4.4
-15.6
-24.3
-7.7
3.0
1.9
2.4
3.5
2.7
2.2
Ilhéu Rolas
C. Negro
0.0
-15.7
6.5
11.9
2.5
3.6
1.9
3.3
Porto Seguro
C. Good Hope
C. Agulhas
-16.4
-34.4
-34.8
-39.0
18.5
20.0
3.2
5.2
5.2
4.3
5.0
5.1
11.0
1
6.2
1
5.0
C. Padrone
G. Fish River
-33.8
-32.7
26.5
28.4
5.4
5.3
4.9
4.7
1.3
1
1.2
1
1.8
1.8
C. Correntes
I. Moçambique
Malindi
-24.1
-15.0
-3.2
35.5
40.7
40.2
4.5
2.7
1.4
3.5
1.5
0.0
-5.5
-6.7
1
-7.0
-4.5
-5.5
-5.6
Muqdisho
C. Guardafui
Bad al Mandab
2.0
11.8
12.4
45.3
51.3
43.3
-0.9
-4.2
-2.1
-2.4
-5.6
-3.6
-7.5
6
-8.3
6
-5.3
-6.0
-6.8
-3.7
Calecute
Cuba
11.3
20.2
75.8
-74.1
-8.2
-3.9
-9.0
-2.1
-10.0
-9.2
-3.9
Trinidade
10.9
-60.9
-1.6
0.2
-0.5
2.8
0.0
1
2.8
7.5
2
7.5
1
6.3
1.5
5.5
6.0
5.5
1
5.6
5.5
3
-1.5
4
4.0
5
4.1
3.6
1
10.1
6.4
5.1
-1.6
Notes: 1 – Spatially extrapolated; 2 – See Figure 3.9; 3 – See Figure 3.11; 4 – See Figure 3.10; 5 –
Spatially extrapolated from the value at C. Palmas; 6 – Values observed in 1541.
Table 3.2 contains the values of the magnetic declination for a chosen set of control
points in the Atlantic and Indian Oceans, as estimated using the methods explained
above. There is a considerable variability in the quality of the estimated values: the
best are probably those determined from the observations of D. João de Castro,
when no spatial extrapolation was needed. That is the case of the southern and east-
65
ern coasts of Africa; the worst are those yielded by the geomagnetic model CALC7K2
for the areas where no historical observations are available and the differences to
the real values are expected to be large, as in the western coast of Africa, to the
south of Cape Verde (especially in the Gulf of Guinea). The extrapolations in time
may also be a considerable source of error even when a trend can be estimated from
the historical observations. In general, it is expected the values in the last column of
Table 3.2 to be accurate to within two or three degrees, but the errors may be significantly larger in some cases.
By comparing the theoretical courses and distances between pairs of control points
with the corresponding values measured on the charts it is often possible to identify
the charting method, assess the navigational accuracy and contribute to determining
which individual tracks were used in the construction. Also, these tracks can be later
used for simulating the geometry of the charts using numerical modeling, as explained in the next section.
Figure 3.11 – Imprecision in the measurement of courses and distances between control
points in the Cantino planisphere.
For the present research, courses and distances were usually measured on high resolution digital copies of the charts, using computer techniques. All course measure66
ments were made relative to the chart’s vertical axis, from 0° to 360°, with a precision of 0.1 degrees. Distances were measured in millimeters and converted into
leagues or degrees, using the ratios R (length of a degree, in mm) and S (length of a
scale’s section, in mm) previously estimated for each chart. Annex G contains the
courses and distances measured on the five charts analyzed in this study. Comparisons between distances measured on the charts and the corresponding theoretical
values were usually made in degrees. In some cases, and due to the exaggerated size
of features like islands and capes, the position of the control points could not be defined with precision, affecting the accuracy of the measurements. An example of
such situation is illustrated in Figure 3.11, with the courses and distances between
Cape Espichel and Madeira, and between Cape Espichel and Terceira, measured on
the Cantino planisphere. Though the position of the control point over C. Espichel is
precisely defined, that is not the case of the control points in Madeira and Terceira
because the sizes of the islands sizes are exaggerated. The result is an uncertainty of
about 2.5° in the courses and of about 12% (Madeira) and 5% (Terceira) in the distances.
Table 3.3
Courses and distances along tracks from Lisbon to
the Atlantic and Mediterranean
Track
C0
D0
δ
Cm
Dm
C. Espichel – Madeira
C. Espichel – Terceira
C. Espichel – Slea Head
229.3
271.3
356.3
8.6
14.1
13.7
3.5
-0.4
2.4
225.8
271.7
353.9
8.1
-13.8
C. Espichel – C. Farvel
Terceira - Madeira
Terceira – São Nicolau
313.8
126.3
173.5
30.8
10.0
22.3
-5.9
0.4
-1.9
319.7
125.9
175.3
28.0
10.1
22.2
Terceira – C. Farvel
Terceira – C. Race
333.1
292.7
23.6
20.6
-7.8
-6.7
340.8
299.4
22.3
16.2
Madeira – Gran Canaria
Madeira – São Nicolau
Madeira – Punta Tarifa
163.9
201.5
71.5
5.3
17.4
10.1
2.8
2.0
3.4
161.1
199.5
68.1
5.4
17.2
8.6
Punta Tarifa – C. Carbonara
C. Carbonara - Alexandria
75.6
114.9
12.4
18.5
6.4
2.4
69.2
108.0
8.7
25.2
Gran Canaria – Cuba
Gran Canaria – São Nicolau
Slea Head – C. Farvel
261.7
216.0
292.3
54.0
13.8
20.2
0.8
2.5
-6.1
260.9
213.5
298.4
49.3
13.3
16.1
Slea Head – Iceland (south)
Iceland (south) – C. Farvel
340.2
253.1
12.1
12.8
-2.1
-9.3
342.3
262.4
12.0
28.1
During the fifteenth and sixteenth centuries the geographic directions were indicated
in the charts and marine compasses by means of wind roses divided in 32 parts, or
‘points’ (quartas, in Portuguese), each one measuring 11 ¼ degrees. In the old rutters
67
courses were expressed relative to the nearest inter-cardinal point, usually with the
precision of one point, though it is not rare the use of half-points. If a quarter of a
point is taken as a standard of chart precision then one may optimistically consider
the directions measured between places on the charts to be precise to about 3 degrees. These numbers should remain present when comparing courses measured on
the charts with the exact values. In Portugal and Spain distances at sea were usually
measured in maritime leagues, each league containing four Italian miles. As explained in Chapter 2, all charts have at least one scale of leagues divided in a variable
number of sections (or ‘logs’), each one containing 12.5 (the older charts) or 10
leagues. Typically the distances between places registered in the rutters are expressed in whole leagues.
Table 3.4
Courses and distances along tracks from the Canary Islands and
Cape Verde to the Americas, Africa and India
Track
São Nicolau – Porto Seguro
São Nicolau – Trinidad
São Nicolau – C. Palmas
C. Palmas – Ilhéu Rolas
Ilhéu Rolas – C. Negro
C. Negro – C. Good Hope
C. Good Hope – C. Agulhas
C. Agulhas – C. Padrone
C. Padrone – Great Fish River
Great Fish River – C. Correntes
C. Correntes - Moçambique
Moçambique - Malindi
Melinde – Mogadishu
Mogadishu – C. Guardafui
C. Guardafui – Bab-el-Mandeb
Malindi - Calecute
Porto Seguro – C. Good Hope
C0
D0
δ
Cm
Dm
203.7
260.8
126.9
107.1
161.2
162.4
111.2
78.7
56.1
36.0
28.5
357.2
44.7
31.0
274.4
67.8
109.2
36.0
36.0
20.4
14.9
16.6
19.6
1.3
5.4
1.9
10.6
10.3
11.8
7.4
11.4
7.8
38.3
54.7
4.3
0.2
1.2
4.1
3.9
5.0
5.8
3.4
1.8
-1.4
-5.0
-2.8
-5.8
-6.4
-5.3
-7.4
8.2
199.4
260.6
125.7
103.0
157.3
157.4
105.4
75.2
54.3
37.4
33.5
2.8
50.5
37.4
279.7
75.2
101.1
34.9
35.2
21.0
19.4
17.0
20.2
1.8
4.2
1.9
10.8
10.9
11.8
8.2
12.3
3.6
56.6
93.8
Starting with some typical maritime routes used during the fifteenth and sixteenth
centuries, including the exploration missions to the Americas, Africa and India documented in the historical sources, a series of idealized rhumb-line tracks connecting
pairs of control points were defined, supposedly representative of those used to construct the charts (Tables 3.3 and 3.4). The corresponding courses and distances, as
measured on a spherical surface of the Earth, were determined analytically and
compared with the corresponding routes measured on the charts. The following
quantities were calculated for each track:
68
− The theoretical rhumb-line course and distance, C0 and D0, between the point of
departure and the point of arrival, as determined using expressions [D.1] through
[D.6] in Annex D;
− The course and distance, Cm and Dm, which result from affecting C0 by the magnetic declination, δ. The magnetic declination is considered to be positive (eastward) or negative (westward) whether the direction of the magnetic North is, respectively, to the east or to the west of the geographic North. Dm only coincides
with the true rhumb-line distance, D0, when the magnetic declination is zero.
N
SP0
SPm
ϕ
PF
C0
m
0
D
Cm
D
δ
∆ϕ
P0
Figure 3.12 – Positions determined using the point of fantasy (PF)
and the set point methods (SP0 and SPm) in the theoretical tracks. N
represents the North of the chart, from which all courses are reckoned.
These values can be used for plotting the corresponding rhumb-line tracks on a
plane, as straight segments of length D0 (or Dm) making an angle C0 (or Cm) with a
conventional north-south direction. Depending on the quantities used, the procedure simulates the determination of the ship’s position on the chart using the point
of fantasy or the set point method. In Figure 3.12 the following situations are illustrated:
− For δ≠0 (the general case), the ‘point of fantasy’ (PF) is found at the intersection
between the segment representing the track, steered at course Cm, and an arc of
circumference with radius D0, centered at P0. The ‘set point’ (SPm) is found at the
intersection between the segment representing the track, steered at course Cm,
and the parallel of latitude ϕ. The resulting distance, Dm, between P0 and SPm can
be larger or smaller than the true rhumb-line distance, D0, depending on the
course and the sign of the magnetic declination. In the case illustrated in Figure
69
3.12, δ is westward (negative) because the magnetic North is to the west of the
geographic North, and Cm is larger than C069;
− For δ=0, the set point coincides with the point of fantasy and Dm=D0. This case
also covers the situations where the course information was not used (for being
too close to east or west) and the set point was determined on the basis of the
observed latitude and estimated distance.
In Figure 3.13 the tracks of Tables 3.3 and 3.4 are represented, using a cylindrical
equidistant projection centered at the Equator (plate carrée). Notice that neither the
courses nor the distances are conserved in the representation, which was made on
the basis of the latitudes and longitudes of the control points.
70
Iceland (south)
Cape Farvel
60
Slea Head
50
C. Race
C. Espichel
40
Terceira
Alexandria
Madeira
Latitude (degrees)
30
Gran Canaria
Cuba
20
São Nicolau
Bab-el-Mandeb
C. Guardafui
Calecute
10
Trinidad
C. Palmas
Ilhéu Rolas
0
Malindi
-10
C. Negro
Porto Seguro
I. Moçambique
-20
C. Correntes
-30
Great Fish River
C. Good Hope
-40
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
Longitude (degrees)
Figure 3.13 – Rhumb-lines tracks used in the analysis, represented in a cylindrical equidistant
projection centered at the Equator (plate carrée), according to the coordinates of the control
points. Compare with Figure 3.14.
In the analysis of the differences between the theoretical tracks and those measured
on the charts, the following typical cases were considered:
69
In the figure the vectors representing the geographic and the magnetic North are coincident with
the North of the chart.
70
− C0=C1 and D0=D1 (Figure 3.12: the end point of the track coincides with both SP0
and PF). This is the case where the route measured on the chart coincides with
the ‘true’ theoretical track. It corresponds to the trivial situation where the magnetic declination is zero and the point of fantasy coincides with the set point or,
alternatively, the set point was determined using the estimated distance instead
of the magnetic course. An alternative possibility is that the courses were corrected for the known value of the magnetic declination before represented on
the charts 70;
− Cm=C1 and Dm=D1 (Figure 3.12: the end point coincides with SPm). This is the case
where the track measured on the chart coincides with the magnetic theoretical
track, using the ‘equivalent distance’ Dm, instead of D0. It corresponds to the set
point method based on the latitude and magnetic course;
− Cm=C1 and D0=D1 (Figure 3.12: the end point coincides with PF). This is the case
where the route measured on the chart coincides with the magnetic theoretical
track, using the true distance D0. It corresponds to the method of the point of
fantasy.
Though the typical situations just described are useful in the characterization of most
tracks measured on the charts, some will have to be analyzed more carefully, such as
those affected by a significant latitude error. On the other hand, and due the inconsistencies associated with the charting methods, the final geometry of a chart depends on the particular set of routes used in its construction. For example, the position of Newfoundland will be different whether it is drawn relative to the British Islands or to the island of Terceira, in the Azores. Another example is the relative positions of Lisbon, Madeira and Terceira: the correct course between Madeira and Terceira will not be conserved if both islands are represented on the chart according to
their positions relative to Lisbon. If the geometry of each chart depends on the particular sequences of tracks used in its drawing, then the comparison between the
theoretical tracks and those measured on the chart in not enough to determine the
details of the construction. The process must be complemented with the comparison
between sets of tracks. For example, it is known that the Cape of Good Hope was
first reached by Bartolomeu Dias in an exploration mission along the western coast
of Africa, in 1487-88. So, it is reasonable to assume that at least the earliest representations of the area were made on the basis of this route, notwithstanding the fact
70
It is necessary to introduce this complexity to allow for the cases where the representations were
based on courses measured with manipulated compasses. That was a common practice up to, at least,
the middle of the sixteenth century as a way to force the needles to point to true North in the places
where the compasses were made or utilized. For a more detailed explanation of this practice and its
reflex on the charts see Chapter 2 (p. 37-38).
71
that, from 1497 on, the ships usually made a large westward detour in the south Atlantic, to make profit of the prevailing wind circulation. To confirm or infirm this assumption, the two alternative routes, as represented in the Cantino planisphere (the
earliest extant chart to depict the Cape of Good Hope), should be compared with the
corresponding theoretical tracks.
70
C. Farvel
60
Slea Head
50
40
C. Espichel
North-south distances (degrees)
Terceira
30
Madeira
20
São Nicolau
10
I. Rolas
0
C. Palmas
-10
-20
P. Seguro
-30
C. Good Hope
-40
-50
-50
-40
-30
-20
-10
0
10
20
30
East-west distances (degrees)
Figure 3.14 – Some sequences of rhumb-line tracks plotted with a constant
scale, with origin in a place near Lisbon (C. Espichel). Only the rhumb-line directions and distances along the represented tracks are conserved, as well as all
relative north-south distances. Notice how the positions of C. Farvel, Madeira
and C. Good Hope vary with the routes used to plot them.
In Figure 3.14 some sequences of rhumb-line tracks are plotted with a constant scale
on an isometric system of plane coordinates, according to their theoretical lengths
(in degrees of latitude) and directions, as measured on the spherical surface of the
Earth. Because no magnetic declination is considered, the process simulates both the
method of the point of fantasy (portolan-chart model) and the set point method (latitude chart model). It is important to emphasize that this representation cannot be
72
confused with the one in Figure 3.13 (a plate carrée representation), where the
tracks are plotted according to the latitudes and longitudes of the points. In Figure
3.14, while the graduation on the north-south direction can be confused with the
latitude, the same does not happen with the graduation in the east-west direction:
compare, for example, the longitudinal positions of C. Farvel and C. Good Hope in the
two representations.
Numerical modeling
The concept of ‘empirical map projection’, to designate those representations of the
Earth’s surface where numerical techniques are used to obtain useful properties, not
taking into account latitudes and longitudes, was introduced by Tobler (1977). Some
common map projections can be easily reproduced using this approach. For example,
by transferring to a plane the positions of a sample of places defined by their distances and directions measured from some chosen position along great circles, one
obtains an azimuthal equidistant projection. If, instead of great circles, loxodromes
are used, a loximuthal projection will be obtained71. Such representations have two
important points in common: first, they are exact solutions, meaning that if no errors
were made in the measurement and plotting of distances and directions, then the
desired geometric properties would be exactly fulfilled; and second, they can be constructed without knowing the geographical coordinates of the places or even the
shape of the Earth. Another good example of this kind is the Mercator projection,
which can be simulated by plotting on a plane a sample of rhumb lines making true
angles with straight and parallel meridians. One convenient question is whether it is
possible to make a representation, using this same empirical approach, where all
rhumb line distances and directions – and not only those that radiate from some
chosen point – are conserved. If such a projection existed, then the relative positions
of all places on the spherical surface of the Earth would be conserved, which is impossible. However, if some distortion is allowed and the representation is restricted
to a limited area, approximate solutions can be obtained. That was, after all, a method adopted by nautical cartography from the thirteenth century on, according to a
hypothesis of this research.
Suppose that one wants to estimate the relative positions of a sample of places
knowing only, with uncertain accuracy, some distances between them. There is a
numerical method to solve this problem which is known, in multivariate statistics, as
‘multidimensional scaling’ (mds). Starting with some arbitrary initial distribution of a
71
The loximuthal projection was first presented by Karl Siemon, in 1935, and independently formalized by Tobler, in 1966 (as referred to by Snyder, 1993, p. 208).
73
sample of points in some n-dimensional space, the process consists in re-arranging
their positions (in a lower dimensional space, if required), using a least squares approach, so that the differences between the initial (given) and the final (calculated)
distances are minimized. The process is equivalent to the method used in geodetical
surveying to adjust measurements obtained in trilateration and triangulation. The
application of this principle to the spherical surface of the Earth, for cartographic
purposes, was first suggested by Tobler (1977). Tobler started with a sample of
spherical distances (arcs of great circle) between a set of regularly spaced latitude
and longitude intersections, covering the United States, and then proceeded to determine the plane coordinates of the points, so that the sum of the squares of the
differences between the original spherical distances and the adjusted planar distances were minimized (Ibidem, p. 3-4). In the same article, Tobler replaced the great
circle distances with rhumb-line distances and applied the same optimization process
to the mapping of the Mediterranean and Black Sea, suggesting that the procedure
might be a reasonable analogy to the construction of the portolan charts of the thirteenth century (Ibidem, p. 6). The results of both experiments are shown in Figure
3.15.
Figure 3.15 – Cartographic representations obtained by using a set of spherical distances
along great circles (left) and loxodromes (right) between regularly spaced latitude and longitude intersections (reproduced from Tobler, 1977, p. 12, 13).
In the scope of the present research, the process presented by Tobler was generalized to both distances and directions, and applied to two types of spherical lines used
in marine navigation: great circles (or ‘orthodromes’), which define the shortest distance between two points on the surface of the Earth, and rhumb-lines (or ‘loxodromes’), which make constant angles with all meridians72. The approach for solving
the problem was based on geometrical considerations and implemented numerically
using an iterative process. No attempt was made to mathematically formalize the
method or to prove the convergence of the numerical algorithm. The results were
72
But only the rhumb-line option was used in the case studies presented in this thesis.
74
validated using some typical cases with known exact solutions, such as the loximuthal and the Mercator projections. In the following section, the computer application
which was developed to implement the process is presented.
7
1
30ºW
0º
6
5
8
4
2
3
60ºN
30ºN
30ºE
30ºW
0º
30ºE
Figure 3.16 – Influence of the choice of tracks in the charting process. At left, only the tracks
connecting points 1 to 8, in sequence, were used; at right, all possible connections between
the grid intersections were used. The relative north-south positions of all points are conserved in both cases. The points forming the coastlines were interpolated linearly.
With the application of this kind of modeling to the study of the old charts it is expected to better understand how they were constructed and used, and how the various factors associated with the acquisition and representation of the cartographic
information affected their geometry. According to one of the hypothesis of this thesis, pre-Mercator nautical charts were drawn by plotting directly on the plane the
courses and distances observed on the curved surface of the Earth, as if it were flat.
As explained in Chapter 2 (p. 32-33) geometric inconsistency resulted from this procedure and the geometry of each chart became dependent on the particular set of
routes used in its construction. Furthermore only the courses and distances which
were used to make a particular chart were, in principle, faithfully reproduced on that
chart. As for the tracks connecting all the other places, the distortions depended
mainly on the directions and distances between them. In limited areas crossed by
numerous maritime routes, like the Mediterranean, an optimization process conceptually identical to the one described above may have occurred in nautical cartography, making the relative positions of the places to gradually adjust to some optimal
configuration, in which the inconsistencies have become residual. The same could
not happen in the representation of large oceanic basins like the Atlantic and the
Indian Oceans, not only due their larger size but also because no similar network of
75
maritime routes existed. In these cases the geometry of the charts became determined by a particular set of more or less well-defined tracks, like the one connecting
Europe to the Cape of Good Hope and to the entrance of the Red Sea, along the African coast.
Figure 3.16 illustrates a hypothetical situation in which the region delimited by parallels 0° and 60° N and by meridians 30° W and 30° E is to be represented on a plane,
using the two methods described above. At left, only the tracks connecting points 1
to 8, in sequence, are used as input. Notice the gross distortion of the segment connecting point 1 to point 8, which results from the geometric inconsistency of the
method. This is the typical case of a region being represented on the basis of some
set of non-conflicting tracks, in which only the ones that have been used to construct
the chart are, in principle, faithfully reproduced. The representations may vary significantly depending on the input. At right, all possible courses and distances connecting the grid intersections were used as input. The final representation is the result of
an optimization process during which the position of the points were adjusted as to
minimize the differences between the theoretical courses and distances and those
represented on the plane. The influence of the set of points used as input in the final
result is minimal, provided that a sufficient number is provided. This is the typical
case of a relatively small region, like the Mediterranean, being represented on the
basis of a dense mesh of maritime routes.
The EMP model
Figure 3.17 shows the visual interface of a computer application, the EMP model
(‘Empirical Map Projection’), which was developed to simulate the construction of
old nautical charts using the empirical approach introduced in the previous section.
The input of the EMP model is a set of points defined by their geographic coordinates, from which spherical distances and directions are calculated; the output is a
cartographic representation where the coastlines and the grid of meridians and parallels, interpolated from the final positions of the points, are shown. The input of the
model (‘Input points’, in Figure 3.17) is defined either as a regular grid of meridians
and parallels, with a given spacing, from which the latitude and longitude intersections are used (‘Use geographic grid’), or given as an external file containing a set of
points and tracks between them (‘Use track’). The limits and spacing of the geographic graticule can be specified (‘Geographic grid’, in the figure).
Two types of spherical lines connecting pair of points can be chosen (‘Method’, in
Figure 3.17): ‘Orthodromes’ and ‘Loxodromes’. For the loxodrome (rhumb-line) case,
two types of charting methods, plus a mixed one, are considered: the ‘point of fanta-
76
sy’ method (to which corresponds the ‘portolan-chart model’), in which positions are
plotted on the plane according to the rhumb-line course and distance between the
two points on the sphere; and the ‘set point’ method (‘latitude chart model’), in
which the positions are plotted according to the latitudes and course (or distance)
between points. A ‘mixed model’ is also considered, for simulating those representations where both the point of fantasy and the set point methods are known to have
been used. In this case, it is possible to attach to each individual track a specific
charting method and modality73. All courses can be affected by magnetic declination,
given in the form of a matrix of values containing its spatial distribution for a given
time (‘Magnetic declination’, in the figure’), or as punctual values attached to each
geographic position of the input, when external tracks are used.
Figure 3.17 - Interface of the EMP model application.
73
In the set point method either the course or the distance can be used, with the latitude, to determine the position. However the second modality (distance and latitude) was probably only used for
cartographic purposes when the course was very close to east or west, making small errors in its value
to cause large differences in the resulting distances. For a more detailed discussion on this subject see
Chapter 2, p. 18-20.
77
Figure 3.12, in the previous section, illustrates how the spherical tracks are defined in
the two types of charting methods. P0 is the point of departure of a generic track,
and PF and SPm are, respectively, the point of arrival calculated using the point of
fantasy and the set point methods, under the effect of the magnetic declination. For
a null magnetic declination, the point of arrival coincides, in both methods, with position SP0. The general expressions used for calculating the rhumb-line courses and
distances between points are in Annex D.
At the bottom of the ‘Method’ box in the application interface a sliding scale is
shown. This is used to adjust the relative weight (w) given to distances and directions
in the optimization process, when the method of the point of fantasy is chosen74. For
w=0, only distances are considered, and the output is identical to the results obtained by Tobler (1977), shown in Figure 3.15; for w=1, only directions are considered; for a value of w between 0 and 1, both distances and directions are considered.
It is also possible to impose certain restrictions on the pairs of points to be used as
input (‘Constraints’, in Figure 3.17), for example, to consider only the tracks with
origin in a given point (‘Only from position…’) or to restrict the domain to distances
less than a certain value (‘Distances less than…’). The only restrictions relevant for
the present study are those limiting the maximum distance allowed. The ‘Distortion
info’ box in the visual interface allows distortion information to be represented in the
output: ‘Tissot ellipses’ and isolines of constant maximum angular distortion (‘Max
angular distortion’). The first are used for depicting qualitative information on the
various types of distortion present in a map especially angular and area distortions;
the second, for depicting quantitative information on the maximum values of the
angular distortion. The mathematical expressions used in the numerical assessment
of these quantities are in Annex D. The ‘Show lines’ box is used for showing arcs of
rhumb lines or great circles radiating from a chosen position (‘Origin’) and, also, the
corresponding lines of constant distance (‘Distance lines’), as measured from the
same point. This is useful for having a qualitative idea of the distortions affecting the
representation of those lines, when projected.
Once the limits of the area to be depicted have been set and all the other options
regarding the method, magnetic declination, tracks, etc. have been chosen, the ‘Plot’
button is used for launching the optimization process and present the results in the
form of a map. The initial plane coordinates, x and y, of the points are defined by the
application as, respectively, their longitudes (λ) and latitudes (ϕ), measured in degrees. An iteration routine will then start with the purpose of gradually adjust these
74
The optimization process only applies to the cases where the tracks form closed loops. In all other
cases an exact solution exists and the weighting has no effect on the final result.
78
coordinates until some pre-defined condition is met or the number of iterations
reaches a pre-defined maximum value. In Figures 3.18 and 3.19 graphic illustrations
of the numerical iterative process are shown, for the cases of the point of fantasy
and set point methods. The mathematical expressions used for calculating the various quantities are in Annex D (point of fantasy: equations D.9 to D.12; set point:
equations D.13 and D.14).
B’1
B’0.5
B
θ
A’0
B’0
θ
A
A’0.5
A’1
Figure 3.18 – Graphical illustration of the adjustment process for the case of the
method of the point of fantasy. A and B are the positions of the points before
the adjustment; A’w and B’w (with 0 ≤ w ≤ 1) are the adjusted positions.
For the method of the point of fantasy (Figure 3.18): A and B are the initial positions
of some pair of points in the plane, before iteration i, and AB is the present distance
between them. A’w and B’w are the final positions of the points, after the adjustment
is made, depending on the value w of the weighting parameter. θ is the present angle between the given direction between the places (as measured on the sphere) and
the orientation of segment AB in the plane. For w=0, only distances are considered
and points A and B are moved to A’0 and B’0, so that A’0 B’0 becomes equal the known
spherical distance between the places; for w=1, only directions are considered and
points A and B are moved to A’1 and B’1, so that θ becomes zero and the segment
A’1B’1 is oriented as the corresponding rhumb-line; for w=0.5, the points are moved
to positions A’0.5 and B’0.5, so that the new distance and direction become, respectively, the average between the present and the theoretical distances and directions.
For other values of w, A’ and B’ are moved to intermediate positions, on the arcs
79
connecting A’0 to A’1 and B’0 to B’1. Once these calculations are made, the algorithm
stores the corresponding displacements and moves to the next pair of points, without actually adjusting the position of the previous one.
B’2
B’1
θ2
A
θ1
θ1
B
θ2
A’1
A’2
Figure 3.19 – Graphical illustration of the adjustment process for the case of the
set point method. A and B are the positions of the points before the adjustment;
A’1 and B’1, or A’2 and B’2 are the adjusted positions, depending on the modality.
For the set point method (Figure 3.19): A and B are the initial positions of some pair
of points in the plane, before iteration i, and AB is the present distance between
them. In all cases, the ordinate y of both points remains constant and the displacements of A and B are only made in the x-direction75. Two modalities are considered,
whether the course or the distance between the points are used to determine the
set point. In the first case, A and B are to be displaced to positions A’1 and B’1, so that
the angle θ1 between the given and the present direction of the line connecting the
two points becomes zero; and in the second, to positions A’2 and B’2, so that the planar distance between the points becomes equal to the given rhumb-line distance.
At the end of iteration i, when all pairs have been considered, the positions of the
points are adjusted using the average of the displacement values obtained in all
steps. At this point, the root mean square errors of the distances (Sdist) and directions
(Sdir) are calculated, using expressions D.7 and D.8 in Annex D. The iteration process
ends when the values of Sdist and Sdir cease to show significant variations or a given
number of iterations is reached. The result of the process is then shown as a map,
where the meridians and parallels, as well as the coastlines and other lines, are interpolated from the final coordinates of the points.
A series of four example outputs are next presented to illustrate the use of the model and the influence of the various parameters on the geometry of the resulting
75
This is justified by the fact that, in the implementation of the model, the initial ordinates of the
input points coincide with the respective latitudes.
80
maps. Emphasis is put on the use of the rhumb-line methods, the only relevant for
the present research. Figures 3.20 through 3.23 show the outputs.
Rhumb-line directions and distances from a point (Figure 3.20, left)
•
Method = Loxodromes, Point of fantasy
•
w = 0.5
•
Input points = Use geographic grid
•
Constraints = Only from position lat=60; long=0
•
Show lines = Loxodromes, Distance lines (origin: lat=60; long=0)
This is an exact solution corresponding to a loximuthal projection, in which rhumb
line distances and directions measured from a chosen position.
Figure 3.20 - Sample model outputs I. At left: rhumb-line distances and directions measured
from a point (loximuthal projection); at right: rhumb-line directions only, with Tissot ellipses
(Mercator projection).
Rhumb line directions only (Figure 3.20, right)
•
•
w=1
•
•
Distortion info = Tissot ellipses
•
Constraints = No constraints
This is an exact solution corresponding to the Mercator projection, in which
rhumb-lines are straight and make constant angles with all meridians.
Portolan chart model (Figure 3.21, left).
•
•
w = 0.8
•
•
81
•
Constraints = Distances less than 50 degrees
•
Magnetic declination = 1500.
This is a hypothetic result of the application of the portolan chart model, based on
the point of fantasy, to the representation of the Atlantic, considering the effect
of magnetic declination as of 1500 and using only distances less than 50 degrees.
Figure 3.21 - Sample model outputs II. At left: method of the point of fantasy; at right: set
point method (latitude model). In both cases, magnetic declination as of 1500 and distances
less than 50 degrees.
Latitude model (Figure 3.21, right)
•
Method = Loxodromes, Set point
•
•
•
Restrictions = distances less than 50 degrees
•
Magnetic declination = 1500
This is a hypothetic result of the application of the latitude model, based on the
set point method, to the representation of the Atlantic, considering the effect of
magnetic declination as of 1500 and using only distances less than 50 degrees.
Portolan chart model (Figure 3.22)
•
•
w = 0.8
•
Restrictions = distances less than 15 degrees
•
Magnetic declination = 1300
This is a hypothetic result of the application of the portolan chart model to the
representation of the Mediterranean and Black Sea. Only distances less than 15°
were considered. Magnetic declination as of 1300.
82
Figure 3.22 – Sample model output III. Method of the point of fantasy, simulating the geometry of a portolan chart of the Mediterranean. Magnetic declination
as of 1300 and distances less than 15 degrees.
70
40
80
60
50
20
30
10
5
5
40
6050
30
80
70
60
50
40
20
34
2
20
10
20
30
10
10
20
2
40
30
20
50
60
30
20
40
80 70
10
10
5
20
5 43
40
30
50
60
80
50 0
6
70
Figure 3.23 – Sample model output IV. A world map showing lines of maximum angular distortion. Method of the point of fantasy, no constraints. The output would be identical if the
set point method were used because magnetic declination is considered to be zero.
World map (Figure 3.23)
•
•
w = 0.5
•
Distortion info = Max angular distortion
83
This is a representation of the world where the distortion of rhumb-line directions
and distances are minimal. Because magnetic declination is zero everywhere, the
solution is identical to considering the set point method.
The two outputs in Figure 3.20 illustrate exact solutions and are presented as test
results. In the loximuthal projection notice the distance circles and the loxodromes
radiating from the centre, not perfectly circular or straight. In the Mercator projection, notice the non-circular shape of the ellipses over the south-most and northmost parallels. These imperfections are due to the fact that a limited number of
points were used to calculate the graticules. In Figure 3.21 notice how the same spatial distribution of the magnetic declination is reflected differently on the geometries
of the two types of representations: curved meridians in the first case (portolan
model), straight and equally spaced meridians in the second (latitude model). In Figure 3.22 the geometry of a portolan chart of the Mediterranean is simulated. Notice
the maximum allowed distance (about 900 km), which is less than half the longitudinal length of the Mediterranean and the reference date of the magnetic declination
(all portolan charts up to about 1600 share a similar counterclockwise tilt, which is
close to the average magnetic declination in 1300). Figure 3.23 illustrates a hypothetical use of the model to construct a projection where the distortion of rhumb-line
directions and distances is minimized. Notice the small values of the maximum angular distortion around two symmetrical positions in the central meridian.
84
4. CHARTS OF THE ATLANTIC
AND MEDITERRANEAN
In this chapter the application of the cartometric and modeling techniques described
in Chapter 3 to four Portuguese charts of the end of the fifteenth and beginning of
the sixteenth centuries is presented and discussed. Page-size reproductions of all
charts are in Annex H. In the following list, the expressions between parentheses are
used to identify the charts in the text:
− Anonymous Portuguese, ca. 1471 (‘Modena ca. 1471);
− Pedro Reinel, fifteenth century (‘Reinel 15th century’);
− Jorge de Aguiar, 1492 (‘Aguiar 1492’);
− Pedro Reinel, ca. 1504 (‘Reinel ca. 1504’).
Together with the Cantino planisphere of 1502, addressed in Chapter 5, these are the
earliest known charts of Portuguese origin, covering a period during which the astronomical methods of navigation were being reflected on nautical cartography, making
the transition between the portolan chart of the Mediterranean and the latitude
chart of the Atlantic1. It is not possible to establish a clear divisor line separating the
cartography adopting the old and the new models, as they coexisted in the same
charts throughout the sixteenth and seventeenth centuries. On the other hand, as
suggested in Chapter 2 (p. 6-8), the transition between the two models was facilitated by the occurrence of small values of the magnetic declination during the fourteenth and fifteenth centuries, permitting a scale of latitudes to be added to the existing charts with little error and making more difficult to determine which areas
were charted according to observed latitudes and which were not. Only one of the
1
There is an anonymous Portuguese chart depicting a scale of latitudes, now kept in the Bayerisch
Staatsbibliotek, in Munich, Germany, which was first studied by Winter (1940) in a paper presented to
the Congresso do Mundo Português, in Lisbon. Winter referred to the chart as an ‘anonymous ca.
1500’, and suggested the name of Pedro Reinel as the possible maker. The chart was also studied by
Cortesão and Mota (1987, Vol. I, p. 23-24), who agreed with the interpretation of Winter though raising some doubts about the authorship. In a later work, these same authors rejected the idea that the
chart may have been made by Reinel (Ibidem, Vol. V, p. 3). The date of ca. 1500 has been later corrected to after 1510, by Campbell (1987, p. 386), on the basis of a more careful examination of the
flags depicted on the chart.
85
CHAPTER 4 – CHARTS OF THE ATLANTIC AND MEDITERRANEAN
four charts depicts a scale of latitudes, Pedro Reinel’s chart of ca. 1504. However the
possibility of observed latitudes having been also used in the other three should be
investigated, as it is usually accepted that some rudimentary forms of astronomical
navigation preceded the systematic and accurate measurement of latitudes2.
The chapter is organized in four sections. In the first (Overview), a short introduction
to each chart is made, referring to previous studies and focusing on the aspects considered to be more relevant for the present research. In the second (Cartometric
analysis), the results of a systematic cartometric analysis is presented and discussed.
Due to its particular historical relevance and geometric complexity, the analysis of
the Cantino planisphere is presented and discussed in Chapter 5. When appropriate,
some of the results presented there are compared with those of the other four
charts, in this chapter. In some specific matters, like the assessment of the length of
the degree, it was found necessary to extend the analysis to a number of Portuguese
and non-Portuguese charts from the fourteenth to the seventeenth centuries, and to
discuss the results obtained by other authors. In the third section (Modeling the
North Atlantic and the Mediterranean) a simulation of the cartographic representation of the area covered by the charts, making use of the results obtained in the previous section, is presented and discussed. In the fourth and last section (Synthesis
and conclusions) the most important results and conclusions reached in the previous
sections are synthesized.
Overview
The anonymous chart of ca. 1471 (‘Modena chart’), now kept in the Biblioteca Estense Universitaria, in Modena, Italy, is usually considered the earliest known Portuguese chart (see Figure H1, in Annex H). It is drawn on a sheet of parchment mounted on cloth, which folds over the edges, and measures 617×732 mm. It depicts the
western coasts of Europe and Africa, from about the Island of Ouessant, in France, to
Lagos, in the Gulf of Guinea. According to Costa (1940), to whom the first thorough
analysis is owned, the chart was probably copied from the royal pattern by an anonymous cartographer, immediately after Rio do Lago (present Lagos) was reached by
João de Santarém and Pero Escobar, in 1471. The toponym Rio de Santarém (‘Santarém’s river’), appearing for the first time in a chart, is a clear reference to the name
of the explorer (Peres, 1923, p. 167). Cortesão and Mota (1987, Vol. I, p. 3-4) argue
2
In the earliest period, observations of the Pole Star may have been used to estimate the north-south
displacement of the ships, by comparing the heights of the body above the horizon in two different
occasions and converting the difference to leagues. Also, the use of the quadrant or astrolabe to sail
along the parallel of the destination point, known as ‘parallel sailing’, was commonly used by the pilots from the end of the fifteenth century on.
86
that nothing proves the synchronicity of the chart with the Portuguese discoveries
and suggest that it may have been made much later, during the three last decades of
the fifteenth century. The exam of the general outline of the coastline in the region
of the Gulf of Guinea (which doesn’t show any evidence of the use of astronomical
observations) and a more careful analysis of the toponomy drove Marques (1989, p.
87-90) to conclude that the chart was certainly made before the astronomical survey
ordered by King João II ca. 1485 (for the origin of this information see Note 5, on
Chapter 2). Also significant is the fact that the spot where the castle of S. Jorge da
Mina were to be built, from 1482 onward, only appears as amina do ouro (‘the golden mine’)3. The Modena chart is very sober in terms of decoration and represents
only the Atlantic, with exclusion of the Mediterranean and northern Europe, which
suggests that it was constructed with the purpose of supporting navigation along the
coast of Africa, particularly in the newly discovered regions.
Pedro Reinel’s chart of the fifteenth century (‘Reinel 15th century’), now kept in the
Archives Départementales de la Gironde, France, is the earliest known signed chart
of Portuguese origin4. It represents the eastern Atlantic Ocean, from the British Islands to the mouth of the Congo River, and the oriental and central Mediterranean.
Part of the African coastline, to the east and south of Cape Coast (Cabo Corço), is
shown as an inset drawn over the Sara and Sahel, in Africa. The chart became first
known during the Fifth International Colloquium on Maritime History (Lisbon, 1960)
and a study was published by Cortesão (1960, p. 99-101), in a work separate from
Portugaliae Monumenta Cartographica, whose first four volumes were already completed at the time. The date suggested by Cortesão for the making of the chart was
ca. 1485, later amended to the period 1484-87 (Cortesão and Mota, 1987, Vol. V, p.
3-4) and, finally, to 1483 (Cortesão and Albuquerque, 1971, p. 207-11). Of the various
studies later published by other authors, the most relevant are probably those by
Marques (1987; 1989) and by Ferreira do Amaral (1995), this last containing original
elements and interpretations related to its construction. Concerning the part of the
African coastline drawn as an inset, various explanations have been suggested for
this uncommon and ingenious, though not rare, expedient. The one given by Cortesão and Mota (1987, Vol. V, p. 4) is that the chart was nearly ready, and most of
the area of the parchment was already used, when Diogo Cão arrived from his mission to the southwestern coast of Africa, in 1484. The cartographer then decided to
draw an additional fraction of the coastline, from Cape Coast to Congo River, in the
available space. The reason for not depicting the rest of the coast discovered by Di3
In all later Portuguese cartography, the castle is always represented in an ostentatious way (Alegria
et al., 2007, p. 984).
4
The period 1484-92 for the likely construction of the chart was proposed by Marques (1989, p. 93),
replacing the one first suggested by Cortesão and Mota (1960), 1483-85.
87
ogo Cão in the same mission, as far as Cape Santa Maria, is explained by a hypothetic
interdiction of King João II to represent the region beyond the Congo River. Based on
the examination of the flags, the depiction of the island of Pagalu (Ano Bom) and the
results of some latitude measurements, Amaral (1995, p. 173-84) contests the dating
of Cortesão and Mota, suggesting that the two sections of the chart were completed
in two different times: one between 1492 and 1497; and the other in 1504, or shortly
after5. According to the same author, the reason why the original coastline of Africa
was interrupted before Elmina (Mina) would have been a prohibition of King João II
to represent the newly discovered lands; and the reason why the added coastline
was interrupted at the mouth of the Congo River would have been the charter of
1504, by King Manuel I, forbidding the coast of Guinea to be shown beyond the Congo River6. A further sign that the inset was drawn in a posterior date, already incorporating astronomical observations is, according to Amaral, the small latitude errors
in the area, which do not occur in the rest of the chart (Ibidem, p. 138-41)7. In my
opinion, there is a simpler explanation for the curious graphical solution adopted in
this chart. Knowing that most charts were constructed by copying the coastlines from
the available patterns, as explained by Francisco da Costa at the end of the sixteenth
century8, the cartographer was probably forced to draw the newly discovered parts
inland, due to the limited size of the animal skin and the fact that no adequate pattern had yet been prepared covering the whole region9. With the discovery of new
lands to the south, during the last decades of the fifteenth century, those models had
certainly to be remade in different scales, since the size of the available skins didn’t
vary much. A similar interpretation is given by Marques (1989, p. 90-93), who states
that the point at which the coast ends and the overlapping section begins is not related to the date of the chart or to the recent advancements of the discoveries, but
to the model used by each cartographer, who were reluctant to abandon the old
patterns. Still Alegria et al. (2007, p. 984-86) reject this interpretation as based in a
‘rather obscure hypothesis that Reinel used preexisting maps to which he merely
added new stretches of coastline’ (Ibidem, p. 985). In the opinion of these authors,
5
Amaral (1995, p. 175-76) considers the red banner over Granada not to be Islamic. Knowing that the
city was conquered by the Spanish Catholic Monarchs in 1492, the construction of the chart could not
have been initiated before this date. On the other hand, the chart could not have been finished before
1504 because of the Aragonese-Catalan flag depicted over Naples, which was conquered by the same
monarchs only in that year. Alegria et al. (2007, p. 985) do not consider Amaral’s arguments about the
flags sound enough to be conclusive.
6
See Leite, p. 227-9. A transcription of D. Manuel’s charter to modern Portuguese is in Amaral (1995,
p. 180-81).
7
The measurements and conclusions of Amaral on this matter are commented in the next sections.
8
As well as by Martin Cortés de Albacar, in his Breve compendio de la esfera y del arte de navegar, of
1551. See Chapter 2, p. 29-30, on the routine production of nautical charts.
9
It is interesting to notice how similar are the linear scales of the three extant Portuguese charts of
the fifteenth century (see last column of Table 4.3).
88
the only thing that we can be sure about the dating of the chart is that it was produced after 1483. Like ‘Modena ca. 1471’, Reinel’s chart was certainly constructed to
be carried aboard due to its sober decoration and signs of use, particularly the compass marks on the distances scales. The designation here adopted, ‘Reinel 15th century’, reflects the uncertainty of the dating and my conviction, based on the results of
the cartometric analysis present below, that it was completed before the end of the
century.
Jorge de Aguiar’s chart of 1492 (‘Aguiar 1492’) is the earliest known signed and dated
nautical chart of Portuguese origin. It was brought to the attention of the international community in 1968, during the First International Reunion for the History of
Nautical Science, and it is now kept in the Beinecke Library, University of Yale, USA. A
first study, published by Vietor in 1968 (re-edited in 1970), was followed by the
works of Cortesão (1968), Marques (1987, p. 75-79; 1989, p. 93-95) and Guerreiro
(1992). It is a typical portolan chart, in style and geographic coverage, depicting the
Mediterranean and Black Sea, the western coast of Europe, including the British Islands, and part of the Atlantic coast of Africa, up to Elmina, in the Gulf of Guinea.
Because of its Catalan-Majorcan type of decoration, Marques (1989, p. 95) is of the
opinion that the chart’s model belongs to the earliest period of the Portuguese cartography, which preceded Pedro Reinel’s and was named by Cortesão (1935, p. 2830) as the ‘school of the Infant’ (escola do Infante). Like in ‘Reinel’s 15th century’, an
inset was drawn over the African continent, showing the continuation of the African
coast from Sierra Leone to Elmina, in the Gulf of Guinea. Once again, it is my conviction that the reason for this expedient is the use of an outdated pattern from which
most of the information was traced. Still, and knowing that at the time the chart was
made, all the Atlantic coast of Africa had already been discovered, it is difficult to
explain why the stretch represented in the inset is interrupted at Elmina. As noted by
Amaral (1995, p. 176-77), if the date of the chart were not explicitly given we would
probably consider it to be from a decade before. Nothing extraordinary has yet been
noted about Aguiar’s chart, other than being the only extant example of the earliest
period of Portuguese cartography. Marques (1989, p. 95) refers to the accuracy of
the charted latitudes, in the Atlantic coasts, but concludes that nothing can be decided about the possible inclusion of astronomical data in its making.
The Atlantic chart of Pedro Reinel, of ca. 1504 (‘Reinel ca. 1504’), now kept in the
Bayerisch Staatsbibliotek, in Munich, is probably the oldest known nautical chart
with a scale of latitudes10. It depicts the western and central Mediterranean, and the
10
The Cantino planisphere, though certainly based on astronomical data and depicting the Equator,
the tropical lines and the Arctic Circle, does not have a graphical scale of latitudes. About the anonymous chart with a latitude scale, first dated as ca. 1500, see Note 1 on this chapter.
89
North Atlantic, from the British Islands to Cap Verde, including Greenland and Newfoundland. Due to the fact that it is one of the earliest nautical charts representing
Newfoundland11, as well as the first to depict an oblique scale of latitudes, it has
been studied by several authors, including Cortesão and Mota (1987, Vol. I, p. 25-27).
The date of ca. 1504 has been suggested by these authors (p. 27) because geographic
information only known in 1503 is represented. Several features make this chart historically important, the most relevant for the present study being the depiction of
two scales of latitude, one of them oblique, and the representation of Greenland and
Newfoundland. One of the first authors to discuss the oblique scale of latitudes was
Winter (1937)12, who explained the expedient as a correction made to the wrong
orientation of the Newfoundland coastline, which was affected by magnetic declination. A different interpretation was given by Gernez (1952)13, who suggested that the
position of Newfoundland was plotted on the chart according to the magnetic course
and estimated distance from Lisbon; the latitude scale was added later, as a way to
register the latitudes observed by the pilots in the region.
In the present section a detailed cartometric analysis of the four charts introduced
above (as well as of the Cantino planisphere, when appropriate) is presented and
discussed. The text is organized in the following subsections each of them dealing
with a specific type of analysis:
− Meridians and parallels: in this subsection the grids of meridians and parallels
implicit in each chart, interpolated using MapAnalyst, are presented and interpreted. The results are discussed in the light of the navigational methods of the
time and the influence of magnetic declination;
− Scale measurements: in this subsection the analyses made to some geometric
properties of the charts related to their cartographic standards, including the assessment of distance scales, latitude scales and the length of the degree, are presented and discussed. The results are compared with similar assessments made
on other charts of different origins, when found necessary for a better interpretation;
− Assessing the latitudes: in this subsection the latitudes of a sample of control
points measured on the charts are compared with the exact values. The results
are presented in the form of distributions of the errors with latitude, aiming at
11
The earliest are Juan de la Cosa planisphere, of 1500, and the Cantino planisphere, of 1502.
As referred to by Cortesão and Mota (1987, Vol. I, p. 25-26).
13
As cited by Cortesão and Mota (1987, Vol. I, p. 26-27).
12
90
identifying the sources of information and the charting methods used in the different sections of the charts;
− Assessing courses and distances: in this subsection a sample of routes measured
on the charts are compared with the corresponding theoretical rhumb-line
tracks. The results may contribute to identify some of the tracks used in the construction of each chart, to determine the corresponding charting methods and to
know when the cartographic information was collected.
Figures 4.1 to 4.5 show the implicit geographic graticules of the five charts as determined on the basis of a set of control points, using MapAnalyst (see explanation
about the georeferencing and interpolation processes in Chapter 3, p. 52-54)14. In
two of the charts, ‘Aguiar 1492’ and ‘Reinel 15th century’, the parts of the African
coastline represented as insets were pasted in their correct geographic positions before the interpolation. In the first part of this analysis, only the Atlantic areas of each
chart are addressed. The representations of the Mediterranean are analyzed separately, as it is known that they were compiled from non-Portuguese sources and constructed according to the portolan-chart model.
In the interpolated grids depicted in the figures parallels are shown approximately
straight, east-west oriented and equally spaced. Two types of exceptions occur:
clearly tilted parallels, especially in the Mediterranean and part of the Atlantic coast
of Africa, to the south of Cape Verde; and irregularities in their orientation, especially
in the vicinity of the Atlantic islands. These irregularities are caused by positional
errors of each island relative to the others in the same group and by the exaggeration of their sizes when compared with the average scale of the charts15. The fluctuations are larger in ‘Modena ca. 1471’ and much less noticeable in the other charts,
suggesting an evolution in the cartographic quality. Distorted parallels and meridians
also occur in ‘Cantino’, in the vicinity of Iceland, and in ‘Reinel ca. 1504’, in the vicinity of the British Islands and Newfoundland. While straight and equally spaced parallels are to be expected in the charts graduated in latitude, such as ‘Cantino’ and ‘Reinel ca. 1504’, the result is somehow surprising in the charts of the fifteenth century,
suggesting some form of astronomical information. However, that is not necessarily
the case, as a similar result would have been obtained if no large errors were made
14
Only the representation of the northern Atlantic is shown for the Cantino planisphere. A complete
analysis of the entire grid is presented in Chapter 5.
15
As explained before this type of exaggeration was a common practice in the nautical cartography of
the time and causes some uncertainty in the location of the control points (see Chapter 3, p.61, 66).
91
in the observation of courses and distances and the magnetic declination in the area
were sufficiently small.
Figure 4.1 – The geographic grid implicit in the anonymous chart of ca. 1471 (‘Modena ca.
1471’). The red diamonds represent the control points. Notice the distortion of meridians
and parallels near the Canary Islands and the Azores.
This same issue was addressed in Chapter 2 (‘Cartographic evolution’, p. 34-36),
where the thesis of Barbosa (1938a) that small values of the magnetic declination,
during the fourteenth and fifteenth centuries, would have facilitate the transition
between the portolan and the latitude chart, was discussed.
92
Figure 4.2 – The geographic grid implicit in Reinel’s chart of the fifteenth century (‘Reinel 15th
century’). The red diamonds represent the control points. The part of the African coastline
representing the Gulf of Guinea was overlapped in its correct geographic position. Notice
that parallels are approximately straight and east-west oriented to the north of Cape Verde.
Figures C.1 through C.4, in Annex C, illustrate the spatial distribution of the magnetic
declination in the area, between 1200 and 1600, as yielded by the geomagnetic
model of Korte and Constable (2005). Figure 4.6 shows its variation, between 1250
and 1550, for eight places in the Atlantic, from Gran Canaria, in the south, to Slea
Head (Ireland), in the north. Two interesting features are to be noticed in the figure:
the occurrence of an absolute minimum in all places, but the island of Terceira, dur© Joaquim Alves Gaspar
93
ing the period 1300-1450; and the relatively small spatial and temporal variation between 1300 and 1550. With the exception of Terceira, all values in 1400 are between
-1.5° and 2.0°; and in 1450, between -0.5° and 2.8°. The small spatial variation is also
apparent in the distributions shown in Figures C.2 to C.4, to the west of the European
and African coastlines, where the spacing between the isogonics is relatively large.
Figure 4.3 – The geographic grid implicit in Jorge de Aguiar’s chart of 1492 (‘Aguiar 1492’).
The part of the coastline drawn as an inset was overlapped in its correct geographic position.
The red diamonds represent the control points. Notice the counterclockwise tilt of the Mediterranean axis, indicating that the area was not charted using observed latitudes.
In Fig. 4.7 a comparison is made between the variation of the magnetic declination in
Lisbon between 1300 and 1700, as estimated by the model, and some historical values observed by Portuguese pilots and cosmographers (as compiled by Barbosa,
1937, p. 251, Fig. 1). No historical data are known prior to 1500. Still the available
values confirm that the magnetic declination was relatively small in Lisbon in the beginning of the sixteenth century and that a sharp variation occurred from about 1575
on, after a local maximum of 7.5° E was reached (about 4.2° E, in the model). Given
the little precision of the marine compasses of the time, which was certainly reflected in the accuracy of the directions represented on the charts, the differences be-
94
tween the historical values and the output of the model are not considered critical
for the purpose of the present discussion.
Figure 4.4 – The geographic grid implicit in the representation of the North Atlantic and
Mediterranean, in the Cantino planisphere. The red diamonds represent the control points.
From the above results, one may then conclude that conditions were favorable during the fourteenth and fifteenth centuries for a cartographic representation of the
Atlantic coasts of Europe and northern Africa, between the British Islands and the
Canary Islands, to consolidate. Because the average value of the magnetic declination affecting such representations was relatively small, the resulting charts could
easily accommodate a scale of latitudes and be used for supporting astronomical
navigation, as soon as it was introduced. The use of manipulated compasses to compensate for the magnetic declination in specific areas (for example, in the area comprising the coast of Portugal and the archipelagoes of Madeira, Canary Islands and
Azores) would have facilitated the navigational use of such charts (see Chapter 2, p.
37-38, for an explanation of this practice)16.
16
In another study (Gaspar, 2008a), I considered this practice to have been used in the Mediterranean
during the fifteenth and sixteenth centuries, to compensate for the differences between the 8 to 10
degrees’ tilt of the north-south direction in most portolan charts and the average value of magnetic
declination at the time they were used.
95
Figure 4.5 – The geographic grid implicit in Pedro Reinel’s chart of ca. 1504 (‘Reinel ca.
1504’). The red diamonds represent the control points. Notice the distortion of meridians
and parallels in the vicinity of Newfoundland (upper left corner).
To the south of Cape Verde, and especially in the Gulf of Guinea, the meridians and
parallels of the three charts of the fifteenth century show a counterclockwise tilt of
about 5 to 10 degrees. Clearly, this is the effect of an eastward magnetic declination
at the time the information was collected17, which excludes the possibility of astronomical information having been used to represent the area. The comparison between these three charts and the Cantino planisphere reveals a dramatic improvement in the representation of the region, which is certainly the result of astronomically-observed latitudes having been incorporated. As for the local distortions of the
grids in some places of northern Europe and Newfoundland, in the charts of the sixteenth century, the subject is discussed later in this chapter, where the assessment
of the latitudes is presented (‘Reinel ca. 1504’), and also in Chapter 5 (‘Cantino’).
17
The value of 5° to 10° E does not match the output of the geomagnetic model for the region, during
the period 1450-1500, which is of the order of 2 to 3° E (Annex C). However, and considering the observations made by D. João de Castro in 1538, the magnetic declination may have been considerably
larger at the time (see Fig. 3.8, in Chapter 3).
96
6
Declination (deg)
4
2
0
-2
-4
-6
1250
1300
1350
1400
1450
1500
Madeira
C. Espichel
Gran Canaria
Terceira
Slea Head
S. Nicolau
1550
Figure 4.6 – Variation of the magnetic declination in the eastern Atlantic, between
1250 and 1550, according to the geomagnetic model of Korte and Constable (2005).
10
8
Declination (deg)
6
4
2
0
-2
-4
1300
1350
1400
1450
CALS7K2
1500
1550
1600
1650
1700
Historical sources
Figure 4.7 – Variation of the magnetic declination in Lisbon as yielded by the geomagnetic model of Korte and Constable, 2005 (CALC7K2) and observed by Portuguese pilots and cosmographers18.
Up to this point the results obtained do not permit detailed conclusions to be drawn
about the methods used for constructing these four particular charts. Theoretically it
18
The historical sources of the observed values, as given by Barbosa (1937), are: João de Lisboa, Livro
de Marinharia (ca. 1515); D. João de Castro, Roteiro de Lisboa a Goa (1538); Vicente Rodrigues, Roteiros Portugueses (1570); Gaspar Manuel, Roteiros Portugueses (1600); Manuel Pimentel, Arte de Navegar (1666, 1668).
97
is possible that a chart without a scale of latitudes, like ‘Aguiar 1492’, incorporates
information collected using some rudimentary form of astronomical navigation; mutatis mutandis, and accepting Barbosa’s thesis, a scale of latitudes could well have
been added to an old pattern based on routes only, producing a chart similar to ‘Reinel ca. 1504’. Even if no definitive conclusions can be achieved at this time concerning the two possibilities, the analysis done so far is enough to support the thesis of
Barbosa that the transition between the two cartographic models was facilitated by
the small values and the small variation (in time and space) of the magnetic declination, during the fifteenth century.
Carta Pisana
Carignano
A. de Virga
Vesconte Dulceto
Valsecha
Soleri
Prunes
Cantino
Aguiar
Viladestes
Olives
Anonymous
Maggiolo
D. Homem
Anonymous
Sideri
Barentszoon
Crescentius
Figure 4.8 – Variation of the magnetic declination in six locations of the Mediterranean and
Black Sea, between 1200 and 1600. The circles represent the angle of rotation of some extant portolan charts, as estimated by Lanman (1987). The two filled circles represent ‘Aguiar
1492’ and ‘Cantino’ (adapted from Gaspar 2008a, p. 201, Fig. 9).
As for the Mediterranean and Black Sea, and accepting the testimony of Pedro Nunes
(2002, p. 134-35) that the representations were copied from old Majorcan charts, it
is assumed that all cartographic information comes from earlier non-Portuguese
sources based on the method of the point of fantasy. Most (if not all) extant portolan
charts up to about 1600 represent the Mediterranean with a more or less constant
tilt of eight to ten degrees (Lanman, 1987, p. 23-32)19. That is also the case of the
19
As I have suggested in a previous work (Gaspar, 2008a, p. 200-202), the orientation of the Mediterranean basin in all portolan charts up to about 1600 reflects the spatial distribution of the magnetic
98
charts analyzed here, with the exception of ‘Modena ca. 1471’, where the Mediterranean is not depicted. In all remaining cases meridians and parallels in the region
appear rotated counterclockwise, though the angle of rotation decreases when approaching the Iberian Peninsula, showing values less than five degrees along the
western coast of Portugal. Using the method of Lanman (1985, p. 25), who estimated
the average angle of rotation of the Mediterranean as the inclination of the line connecting Gibraltar to Antioch, whose latitudes are almost identical, values of 8° and 9°
were obtained for, respectively ‘Aguiar 1492’ and ‘Cantino’. As for the two Reinel’s
charts, which depict only the western part of the basin, the rotation was estimated at
about 7°, which is the approximate inclination of the 38° N parallel (see Figures 4.2
and 4.5). Figure 4.8 compares the angle of rotation of some extant portolan charts,
as estimated using Lanman’s method, with the variation of the magnetic declination
in some locations of the Eastern and Western Mediterranean.
Scale measurements
In this subsection the analysis made to some metric properties of the charts is presented, which included the assessment of distance scales, latitude scales, the length
of the degree of latitude, and the length of the mile and the league. Before the results are presented and discussed, a broader view of the cartography of the fifteenth
and sixteenth centuries is necessary, concerning the questions related to the use of
the historical lengths of the degree (‘modules’) and the type of distance scales
adopted in the nautical cartography of the time.
Franco (1957) estimated the length of the degree of latitude in a number of charts
from the fourteenth to the seventeenth centuries. Two types of charts were analysed: charts without a latitude scale, in which the assessment was made on the basis
of the known distances between chosen places in the Mediterranean; and charts
with a latitude scale, in which the methodology described in Chapter 3 (p. 55-56) was
used. In the first case, 26 charts from 1339 to 1666 were analyzed and an average
value of 22.4 leagues per degree was found (Ibidem, p. 156-157). Table E.1 of Annex
E, compiled from Franco’s study, shows the results obtained in the second case,
where 36 charts of Spanish, Italian and Portuguese origin, made between 1502 and
1674, were analysed. All distance scales were considered to be subdivided in sections
of 12.5 leagues (50 miles). Table E.2 shows the results of a similar analysis made for
the present study, where 42 charts of Portuguese origin, from 1502 to 1646, where
declination in the middle of the thirteenth century, when the first charts were constructed. That is
supposed to be also the case of the Portuguese charts of the fifteenth and sixteenth centuries, in
which the representation of the region is concerned.
99
analyzed20. Three different graduations of the distance scales were considered: 12.5,
12 and 10 leagues per section. The values corresponding to the second option (12
leagues) are shown inside brackets, only for comparison purposes.
Table 4.1
Joint distribution of modules and types of scales
Franco, 1957
Module
Gaspar, 2010
TOTALS
N = 10
N = 12.5
N = 10
N = 12.5
18
3
19
5
13
40
17 1/2
5
5
3
11
24
16 2/3
0
0
0
2
2
Other
0
4
1
7
12
TOTALS
8
28
9
33
78
Table 4.1 shows the joint distribution of the modules and types of scales in the two
groups of data (the 12 leagues’ option was not considered). The most interesting
finding is the almost total absence of charts using the 16 2/3 module, the Atlas Miller
appearing as the only flagrant exception. Although this result contradicts the writings
of several well-known authors of the sixteenth century, including Pedro Nunes, Pedro de Medina and Martin Cortés de Albacar (see Table 2.1 in Chapter 2)21, it is reasonable to consider that direct measurements made on the charts should prevail
over the statements of cosmographers and pilots of the time. From the examination
of the results in Annex E and Table 4.1, the following conclusions can be drawn:
− The large majority of the charts adopt scales with the traditional sections of 12.5
leagues. These continued to be used even after the introduction of the 10
leagues’ modality, in the middle of the sixteenth century. The results of both
studies coincide on this point, although most of the charts are distinct and have
different origins;
− In the charts of Portuguese origin no preference is apparently given for any of the
17 ½ and 18 leagues’ modules. That is not the case of the charts analysed by
Franco, some of them of Spanish origin, where there is a clear preference for the
18 leagues’ module22;
20
The printed reproductions of Portugaliae Monumenta Cartographica (Cortesão and Mota, 1987)
were used. No special criteria were adopted for the choice of the charts rather than the legibility of
the reproductions.
21
There is at least one historical source, the Livro de Marinharia de João de Lisboa (Rebelo, 1903, p.
29), which associates a scale of 12.5 leagues with the module of 16 2/3 leagues per degree.
22
A similar result appears in a study presented by Marcel Destombes in the International Geography
Congress, celebrated in 1938, in Amsterdam. Franco (1957, p. 195) reproduces a table with the estimated length of the degree in 32 charts, most of them of Portuguese origin. The average value is 71.6
100
− There seems to be no correlation between the date of the charts and the adoption of a particular module. This is true for both Franco’s and my analysis;
− There are a few cases where the adoption of scales with sections of 12 leagues
could resolve aberrant values (Anonymous ca. 1535; Lopo Homem, 1554; and Diogo Homem, 1558) and many others where alternative modules would result, including 16 2/3 leagues per degree23. However the coincidence is not considered
to be sufficient to support the possibility. If those two types of scales (12.5 and 12
leagues) really coexisted in the sixteenth century cartography, the fact would
have caused an unacceptable ambiguity in the use of the distance scales and in
the identification of the module adopted by each chart.
The occurrence of some situations where the deduced length of the degree of latitude is aberrant or does not match any of the historical modules suggests the occurrence of errors in the drawing of the scales of leagues. That is not surprising if one
recalls that the large majority of the charts analysed here are richly decorated and
not intended to be used at sea. Also, the coexistence of different standards in the
nautical cartography of the sixteenth and seventeenth centuries, as well as the absence of any known criteria for adopting any of them, seem to indicate that the subject had little relevance for the routine practise of navigation and chart making. Once
the political issues related to the establishment of the Spanish and Portuguese zones
of influence have been resolved, in particular those concerning the longitude of the
Moluccas, the determination of the exact size of the Earth may have lost it relevance
as well. If one accepts this interpretation then the coexistence of different standards
may well be interpreted as an echo of those disputes and of the traditional models of
the Earth. The first accurate measurements of the Earth’s radio were made by JeanFelix Picard, in 1669-70. His results were referred to by the cosmographer major Manuel Pimentel, in his Arte de Navegar of 1712 (Cortesão et al., 1969, p. 54), who proposed a standard of 18 leagues per degree, due to its better convenience for calculations. This new standard, which was used in Portugal up to the end of the nineteenth
century, has nothing to do with the module referred to by Duarte Pacheco Pereira
ca. 1505-8, in the Esmeraldo de Situ Orbis (see Table 2.1, p. 39).
Having made an initial parenthesis to present a broader view of the cartography of
the sixteenth and seventeenth centuries, concerning the use of the different standards, the analysis of the five Portuguese charts is now retaken. Table 4.2 shows the
dimensions and approximate geographic limits of the charts. Table 4.3 shows the
miles, to which correspond 17.9 leagues. A notable outlier is a chart by Lopo Homem (Atlas Miller),
with a degree of 16 2/3 leagues.
23
This possibility comes from the similarity between the ratios 12.5/18=0.69 and 12/17.5=0.69, as
well as between the ratios 12.5/17.5=0.71 and 12/16.67=0.72.
101
approximate linear scale of each chart24 and the metric length of the degree of latitude, as estimated using two alternative methods:
− For the charts depicting an explicit (‘Reinel ca. 1504’) or implicit (‘Cantino’) scale
of latitudes, the value of R was determined using the expression R = ∆m/∆ϕ,
where ∆ϕ is a latitude difference and ∆m is the corresponding distance, in millimeters, between parallels or marks in the latitude scale;
Table 4.2 – Dimensions and geographic limits
width x
height (mm)
Approx. latitude limits
Approx. longitude limits
613 x 732
3°N – 50°N
32°W – 3°E
Reinel 15 century
711 x 948
3°S – 59°N
35°W – 16°E
Aguiar 1492
1030 x 770
7°N – 54°N
35°W – 42°E
Cantino 1502
2200 x 1050
45°S – 70°N
90°W – 160°E
893 x 620
14°N – 65°N
60°W – 16°E
Chart
Modena ca. 1471
th
Reinel ca. 1504
− For all charts, the length R’ of the degree was estimated from the average spacing
between interpolated parallels, as explained in Chapter 3 (p. 55-6). Notice that R
= R’ only when the latitude errors are zero or do not change with latitude25. For
the purpose of estimating the values of R’ it is desirable that only the parts of the
grids where parallels are approximately straight and east-west oriented are used.
However that was not always possible and the values estimated in such conditions are only crude approximations. To detect variations of scale with latitude,
two zones were considered in all charts, south and north of parallels 35° N or
36° N. In the Cantino planisphere, the south-most zone was extended to the
Equator26. In all four other charts the southern latitude limit was 15° N or 16° N.
When a high quality 1:1 digital copy of the chart was available, R and R’ were determined by direct measurements taken, respectively, on the graphical scales of latitude
and on the interpolated graticules, and the values found are considered exact. That is
the case of ‘Modena ca. 1471’, ‘Cantino’ and ‘Reinel ca. 1504’. For the remaining two
cases, the values had to be estimated taking into account the proportion between
the size of the available digital copies and the physical dimensions of the originals, as
indicated in the bibliography, and should be considered as approximate. However
24
7.0 M means 1:7,000,000. The scales were estimated as the quotient between the length of one
degree of latitude in the chart (R and R’) and the corresponding distance on the surface of the Earth
(about 111135 m).
25
If R’≠R there is a scaling error in the charted latitudes.
26
This analysis is restricted to the northern Atlantic. The assessment of the southern hemisphere in
the Cantino planisphere is presented in Chapter 5.
102
this procedure has no significant effect on the accuracy of the remaining parameters
or in the assessment of the latitudes. From the examination of Table 4.3 the following conclusions can be drawn:
− The linear scales of the three charts of the fifteenth century are similar, though
not identical, which is an indication that different patterns were used by each
cartographer;
Table 4.3 – Scales I
Chart
Modena ca.
1471
th
Reinel 15 cent.
Aguiar 1492
Cantino
15°N – 35°N
R (mm)
R’ (mm)
Scale 1:
--
15.1
7.4 M
16.0
6.9 M
15.4
7.2 M
16.2
6.9 M
14.2
7.8 M
15.5
7.2 M
35°N – 47°N
16°N – 36°N
--
36°N – 50°N
16°N – 36°N
--
36°N – 50°N
0° - 35°N
35°N – 55°N
8.7/8.33
16°N – 36°N
Reinel ca. 1504
36°N – 54°N
8.5
12.3 to 13.3 M
9.0
12.1
12.0*
12.7
8.8 to 9.3 M
* Average value
− The length of the degree, as estimated from the spacing between parallels, increases from south to north in both groups of charts. The differences between
the average values of R’ in the two zones are of 5% to 6% in all charts, except in
‘Aguiar 1492’, where it is 9%;
− In the charts of the sixteenth century, there is a mismatch between the length of
the degree of latitude, as measured in the latitude scales (R) and as estimated
from the spacing between parallels (R’)27. This result is discussed below, when
the corresponding lengths of the degree are presented;
− Two different values of R are presented for the Cantino planisphere. This is due
to the inconsistent placement of the tropics and the Arctic Circle relative to the
Equator. The values of 8.70 mm and 8.33 mm apply, respectively, to considering
the positions of the tropics or of the Arctic Circle to be correct. This subject is reexamined in Chapter 5.
27
The spacing between the degree marks in the graphical scale of latitudes of ‘Reinel ca. 1504’ is not
constant, showing variations from about 11.7 to 12.1 mm per degree, which is certainly caused by the
deformations of the parchment.
103
Table 4.4 – Scales II
Chart
Modena
ca. 1471
15°N – 35°N
Reinel
15th cent.
16°N – 36°N
Aguiar
1492
16°N – 36°N
Cantino
Reinel
ca.1504
Length of
Distance
one section
scales
(mm) (S)
35°N – 47°N
36°N – 50°N
36°N – 50°N
0° – 35°N
35°N – 55°N
16°N – 36°N
36°N – 54°N
Leagues
per section (N)
Length 1° latitude
(leagues)
L
L’
--
18.6
2
10.13
12.5
4
10.05
12.5
6
9.13
12.5
6
5.85
12.5
18.6/17.8
3
8.23
12.5
18.2
19.7
--
19.2
20.1
--
19.4
21.2
18.2
20.1
18.4
19.3
In Table 4.4 the following information is shown:
− The number of graphical scales of distance shown in each chart. This number varies between 2, in ‘Modena ca. 1471’, and 6, in ‘Aguiar 1492’ and ‘Cantino’. All distance scales are considered to be graduated in Spanish leagues28;
− The length S of each section of the scales of leagues, in millimeters. This is always
an average value, which was found by adding the total length of all distance
scales, with the exception of those showing severe distortions, and dividing the
result by the total number of sections. In the case of ‘Reinel 15th century’, measurements were made only in the two scales on the right side of the chart, where
the parchment is less deformed;
− The number N of leagues per section, which was considered to be 12.5 in all cases. The justification was given in the beginning of this subsection, where a broader view of the cartography of the sixteenth century is presented. The specific case
of the Cantino planisphere is addressed in Chapter 5;
− The length L of the degree of latitude, in leagues, as determined using the expression L = R x N/S, where the values of R are in Table 4.3. The two alternative
values given for ‘Cantino’ correspond, respectively, to a degree of 8.70 mm and
8.33 mm;
28
Leite (1923, p. 234) and Costa (1983, p. 210-14) refer to them as ‘Portuguese leagues’ but the two
units are probably identical and the term ‘league from Spain’ was used by both Spanish and Portuguese pilots. See also Chapter 2, Note 40 (p. 39).
104
− The length L’ of the degree of latitude, in leagues, as determined with the expression L’ = R’ x N/S, for the two latitude zones, where the values of R’ are in Table
4.3.
The first important fact to be noticed in Table 4.4 is, for both groups of charts, the
variation of the length of the degree with latitude. In the charts of the fifteenth century the value of L’ increases from about 19 leagues per degree, in the south, to
about 20 or 21 leagues per degree, in the north. These values are clearly larger than
any of the historical standards of the time (16 2/3, 17 ½ and 18 leagues per degree).
Such results should not be considered either anomalous or unexpected if one accepts that none of the charts of the fifteenth century incorporates observed latitudes
and no specific module was explicitly used in their construction. Considering now the
two charts of the sixteenth century:
− There are significant differences between the length L of the degree, as deduced
from the relation between the scales of latitudes and the scales of leagues, and
the length L’, as estimated from the spacing between interpolated parallels. In
the case of ‘Reinel ca. 1504’, the value of L is close to the value of L’ only in the
southern zone, suggesting that the scale of latitudes applies to this area; in the
case of ‘Cantino’, the same happens when a degree of 17.8 leagues is considered;
− While in the representation of the 0°-36° N zone, a degree of latitude close to the
standard of 18 leagues seems to have been adopted in both charts, confirming
the use of observed latitudes, the same does not happen with the northern zone,
where larger degrees are found. A finer analysis of this issue is made later in this
section, when the assessment of the latitudes is presented.
Up to this point, after the visual analysis of the interpolated grids and the assessment
of the length of the degree were made, the results seem to support two key ideas:
that the charts of the fifteenth century do not incorporate astronomically-observed
latitudes, having been constructed in accordance with the traditional portolan-chart
model; and that the introduction of the latitude model in the nautical cartography,
which took place probably in the last years of the fifteenth century, was not extended to the full area represented on the charts. As for the two charts of the sixteenth
century, nothing distinguishes them from the generality of the charts of the same
period, in which the adopted length of the degree is concerned.
Having concluded that the Portuguese charts of the fifteenth century, as well as parts
of the charts of the sixteenth, were based on the traditional portolan-chart model, a
comparison needs now to be made with older portolan charts of Italian and Majorcan origin aiming to confirm a common nature. Rather than interpolating the geo-
105
graphic grid implicit in each of those charts, estimate the length of the degree from
the spacing between parallels and comparing the results with the Portuguese
charts29, a simpler method was devised based on the distances measured along four
straight segments between coastal places, three in the Atlantic (C. Boujdour – C. S.
Vicente, C.S. Vicente – C. Fisterra and C. Fisterra – Ouessant) and one in the Mediterranean (Gibraltar – C. Corse), chosen as to be common to all charts. The method consisted in measuring the distances on the charts using the appropriate scales of miles,
normalize the results and make the comparisons. To normalize the results, all distances, in miles, were divided by the corresponding exact values, in meters, so that
an assessment of the metric length of the mile was obtained in each case. Though it
is not the objective of this analysis to determine the length of the mile30, but to compare the scales in different charts and regions, the average values of those estimates
may shed some light on the standards adopted in the Portuguese charts, and so contribute to better understand the origin of the information. As for the charts of the
sixteenth century the results should be taken with care, as the length of the distance
units were probably adjusted to conform to the adopted length of the degree or to
the latitude observations made in the coast of Africa. Together with the five charts of
Portuguese origin, nineteen portolan charts of Italian and Majorcan origin were analyzed31. The complete set of results is in Annex F.
In Table 4.5 the results of the five Portuguese charts are presented, where the miles
shown in Annex F were converted to Spanish leagues (four miles per league), together with some average values. The numbers inside brackets are the lengths of the degree (L), in leagues, which result from dividing the lengths of the league by the metric
length of the degree (111135 m). Because the results are very sensitive to small variations in the measurements, especially when the chart reproductions are small and
the places are difficult to locate with precision, no fine interpretation of the numbers
is justified. For example, an error of 1 mm in the measurement of a segment with 40
mm will cause an error of 2.5% in the resulting evaluation of the mile. The most noticeable feature in the data is the large variability of the results, both in time and
location. In the Atlantic (see Annex F) the length of the mile decreases with latitude
in almost all charts. The average values are: 1686 m (C. Boujdour – C. S. Vicente);
1461 m (C. S. Vicente – C. Fisterra), 1349 m (C. Fisterra – Ouessant) and 1258 m (Gibraltar – Cape Corse). This result supports the traditional idea that portolan charts
29
This would be inappropriate for the older portolan charts due to the scarcity of control points in the
Atlantic and the likely irregularity of the interpolated grid in most of them.
30
Such purpose would oblige to a much broader and detailed analysis, which is beyond the scope of
this research.
31
The measurements were made on the paper reproductions given in Pujades (2007). A common ruler
was used for the purpose.
106
were made by compiling information from different sources, using different units of
distance. With few exceptions, the ‘Mediterranean mile’ (Gibraltar – C. Corse) is the
shortest and the ‘African mile’ (C. Boujdour – C. S. Vicente) is the longest. In general,
the results for the Portuguese charts are well within the overall range of values. Still
some particular differences might be relevant as it is the smaller league in the Atlantic coast of Africa and western coast of Portugal, and the larger league in the Mediterranean. In none of the segments the Roman mile of 1480 m, referred to by Costa
(1983, p. 216), seems to have been used as a standard. For the Mediterranean (Gibraltar – C. Corse), an average value of 1239 m is obtained when the Portuguese
charts are excluded, which is close to the ‘geometric mile’ of ca. 1242 m, referred to
by some authors as the portolan chart standard32. In a study involving the measurement of six distances in the Mediterranean, made on 26 portolan charts from the
fourteenth to the seventeenth centuries, Franco (1957, p. 153-57) estimated a degree of 22.4 leagues, to which corresponds a league of 4961 m and a mile of 1240 m.
These values closely match the average length of the ‘Majorcan league’ (4946 m)
indicated by the same author (Ibidem, p. 63).
Table 4.5 – Metric length of the league
C. Boujdour
C. S. Vicente
C. S. Vicente
C. Fisterra
C. Fisterra
Ouessant
Gibraltar
C. Corse
6220 [17.9]
5440 [20.4]
5412 [20.5]
--
Reinel 15 century
6684 [16.6]
5232 [21.2]
5968 [18.6]
5728 [19.4]
Aguiar 1492
6400 [17.4]
5120 [21.7]
5164 [21.5]
5196 [21.4]
Cantino 1502
6456 [17.2]
5604 [19.8]
5424 [20.5]
5376 [20.7]
Reinel ca. 1504
6416 [17.3]
5736 [19.4]
5352 [20.8]
5000 [22.2]
Average Portuguese
6436 [17.3]
5428 [20.5]
5464 [20.3]
5324 [20.9]
Average all charts
6744 [16.5]
5844 [19.0]
5396 [20.6]
5032 [22.1]
Average Majorcan
6452 [17.2]
5828 [19.1]
5376 [20.7]
5132 [21.7]
Average Italian
6900 [16.1]
5708 [19.5]
5440 [20.4]
4992 [22.3]
Chart
Modena ca. 1471
th
No detailed conclusions can be drawn about the metric length of the Spanish league
used in the Portuguese charts from the above results only. However the specific goal
of this analysis was reached, as the comparison between the two groups of charts
clearly shows that they share the same basic cartographic model, use similar distance
units and are both piecewise constructions of information with similar scale variations between regions, probably compiled from different sources. The results also
32
In his Geographia and Hydrographia Reformata (Bologna, 1661), Ricciolli refers to a geometric mile
measuring 68/81 (close to 5/6) of a Roman mile, that is, 1242 m (Corradino Astengo, 2009, personal
communication).
107
support the idea that Portuguese cartography originated in the Majorcan school and
that the representation of the Mediterranean in the Portuguese charts of the sixteenth century was copied from Majorcan sources.
Only one of the charts, ‘Reinel ca. 1504’, depicts a graphical scale of latitudes. In this
case, the latitudes of the control points were measured directly by extending horizontally the graduation of the existing scale to the appropriate locations (see Figure
3.5). In the case of ‘Cantino’ a digital scale of latitudes was first constructed on the
basis of the spacing between the Equator and the Arctic Circle, from which the latitudes of the control points were read (see Figure 3.6) 33. In the charts of the fifteenth
century a linear scale of latitudes was first estimated from the spacing between the
interpolated parallels. Only the parts of the grids showing approximately straight and
horizontal parallels were used for the purpose and the resulting digital scales were
adjusted to the charts as to match the latitudes of the control points in those parts,
as well as possible. The latitude errors were determined by comparing the measurements with the exact values.
The complete set of results for all charts is in Annex B, where the error of a reading is
defined as the quantity ε = ϕ-ϕ0, where ϕ and ϕ0 are, respectively the latitude measured on the chart and the exact value. Figures 4.9 and 4.10 illustrate the distribution
of the errors with latitude for, respectively, the charts before and after 1500. Concerning the three charts made before 1500 (Figure 4.9), the results can be grouped in
two classes: for latitudes larger than about 30° N, errors are generally less than one
degree and approximately centered at zero; for latitudes less than 30° N, the dispersion is larger and there is a negative correlation of the errors with latitude, with the
largest values (of about 3°) occurring close to the Equator. These results are coherent
with the geometry of the interpolated grids of meridians and parallels in the region,
whose distortions were found to be caused by the magnetic declination. The negative correlation of the errors with latitude is not, in this case, the result of any scaling
error but caused by the counterclockwise tilt of the grid, which makes the average
north-south spacing between adjacent parallels to be larger than in the other regions34. As for the distribution of the errors for latitudes larger than 30° N, the results
confirm what was said before when the interpolated grids were examined, about the
33
The justification for considering the position of the Arctic Circle relative to the Equator, rather than
the position of the tropics, to estimate a linear scale of latitudes is given in Chapter 5, where the two
alternatives are analyzed in detail.
34
As explained in Chapter 3 (p. 61) a ‘scaling error’ is here understood as a latitude error proportional
to the latitude caused by mixing cartographic information with a different scale or adopting a different
length for the degree of latitude.
108
parallels being approximately straight and equidistant. The local irregularities in the
orientation of the parallels, especially in the vicinity of the Atlantic islands, are also
reflected in the error distribution. See, for example, the clusters of points corresponding to the Azores islands, between 37° N and 40° N, and to the Canary Islands,
between 28° N and 29° N. Though there is some variability among the results of the
three charts, especially in the dispersion of the errors, their distribution with latitude
is similar in all of them. This is an indication that they were all constructed using the
same charting method and, possibly, based on similar patterns. It is interesting to
realize that the chart with the best cartographic quality, in which the dispersion of
the errors is concerned, is ‘Aguiar 1492’. This doesn’t necessarily imply that more
accurate data were used in its compilation but, more likely, that its construction was
more careful.
Figure 4.9 – Distribution of the latitude errors in the northern Atlantic, in degrees, for the
charts made before 1500. The errors corresponding to the archipelagoes of Madeira and
Azores are included.
In a book dedicated to ‘Reinel 15th century’ chart, Amaral (1995, p. 138-41) asserts
that the only section of the coastline that incorporates observed latitudes is the part
of the Gulf of Guinea to the east of Cape Coast (ϕ = 5° 06’ N). The results clearly contradict this interpretation. Apparently Amaral was not aware of the effect of the
magnetic declination on the interpolated grid, which excludes the use of the set
point method, and also failed to realize that a good linear correlation between northsouth distances and the corresponding latitude differences is not sufficient to infer
that astronomical methods were used.
109
Figure 4.10 – Distribution of the latitude errors in the northern Atlantic, in degrees, for the
charts dated after 1500.
Figure 4.10 illustrates the distribution of the errors with latitude for the two charts of
the sixteenth century, ‘Cantino’ and ‘Reinel ca. 1504. Contrarily to the charts of the
fifteenth century, for which the ratios between north-south distances and latitude
differences were estimated from the spacing between interpolated parallels, the
latitudes of the control points in the two charts were measured using their latitude
scales, whether they are explicitly shown (‘Reinel ca. 1504’) or not (‘Cantino’).The
differences between these results and those previously presented for the charts of
the fifteenth century are dramatic and significant: the latitude-varying errors and
imprecision caused by the magnetic declination have been corrected, and the whole
African coastline and Atlantic islands, from the Equator to about 35° N, are represented with errors generally less than one degree. This is a clear indication that the
results of the astronomical survey ordered by King João II in Africa, at about 1485, is
already reflected in these two charts. Above 35° N the errors increase with latitude,
reaching values larger than 3° (‘Reinel ca. 1504’) and close to 5° (‘Cantino’) at about
60° N. Contrarily to the older charts, where the variation of the error with latitude in
the Gulf of Guinea was caused by the effect of magnetic declination, this is clearly a
scaling error, as the interpolated grids of meridians and parallels do not show significant signs of a similar effect in the representation of northern Europe. A close look at
the interpolated grids in Figures 4.4 and 4.5 permits to see that while meridians are
approximately straight and north-south oriented between 35° N and 60° N, which
excludes the occurrence of large values of the magnetic declination in the area, the
average spacing between adjacent parallels is larger than south of 35°N. This is an
110
indication that the representation of northern Europe, from about the strait of Gibraltar to the British Islands, was copied from a source with a larger scale. An estimation of the scale exaggerations can be made from the slopes of the regression lines
calculated for the error values north of 35° N, which are found to be coherent with
the length L’ of the degree, determined from the spacing between interpolated parallels (Table 4.4)35, as well as with the metric length of the league estimated from
some distances measured between places in the Atlantic (Table 4.5).
Figure 4.11 – Distribution of the latitude errors in the charts dated after 1500 (degrees), for
latitudes larger than 40° N, before and after the systematic components (mean values and
trends) were removed.
Figure 4.11 shows the variation of the errors in the two charts of the sixteenth century, for latitudes above 35 °N, before (‘original’) and after (‘corrected’) the trend and
mean components were removed36. The comparison between the corrected values
and the variations shown in Figure 4.9, for the charts of the fifteenth century, does
not suggest any improvement in the accuracy of the latitudes. On the contrary, the
dispersion of the errors for the points situated between 35° N and 55° N (the common domain) is a little larger for the sixteenth century’s charts, which seems to exclude the possibility of observed latitudes. In my opinion no astronomical surveys
had yet been made in northern Europe in the beginning of the sixteenth century,
which continued to be represented according to the old patterns.
A separate analysis needs still to be made of the representation of Newfoundland in
‘Pedro Reinel ca. 1504’. Table 4.6 sows the latitude errors of four control points, as
determined using the main latitude scale (‘Main’) and the oblique scale (‘Oblique’).
The results confirm what is suggested by the presence of the oblique scale and by
35
In theory, the slope of the regression line is equal to the quantity (L’-L)/L (see Note 64 on Chapter 3,
p. 61).
36
Not all values shown in Annex B have been used. The exceptions are those relative to Iceland, in the
Cantino planisphere, and to Greenland, in Reinel’s chart, both close to zero.
111
the distortion of the interpolated parallels in the vicinity of Newfoundland (see Figure 4.5), that while this region was certainly surveyed using astronomical methods,
its representation on the chart was not made relative to the main scale of latitudes,
which excludes the use of the set point method. Whether Newfoundland was plotted
according to the course and distance from some known location or its position is only
approximate is a point to be clarified in the next subsection, where the navigational
accuracy of some tracks is assessed.
Table 4.6
Latitude errors in Newfoundland (‘Reinel ca. 1504’)
Control points
Toponym
Cape Race
C. Raso
Miquelon
Horse Islands
I. dos bacalhaus
Belle Isle
Latitude
Main scale
Oblique scale
46.7
4.0
-0.3
47.0
3.7
-0.9
50.2
3.7
-0.2
52.0
4.2
-0.3
In this subsection a series of theoretical rhumb-line tracks connecting control points
is compared with the corresponding segments on the charts, with the purpose of
identifying the routes and charting methods used in the construction, as well as determining when the information relative to the various regions was collected. In Figure 3.14 (p. 72), some of these tracks are represented in a plane, with constant scale,
according to the successive courses and distances, as measured from C. Espichel on
the surface of the Earth. Notice that, because this type of representation is not geometrically consistent, the position of a point on the plane depends on the origin of
the track. That is the case of Madeira, whose location is different whether it is plotted relative to C. Espichel or to Terceira, and also of C. Farvel, whose location is different whether it is plotted relative to Terceira, to Slea Head or to C. Espichel.
In Tables 4.7 and 4.8 the courses and distances (C and D) measured on the charts of
the fifteenth century, between chosen control points in the northern Atlantic, are
presented and compared with the exact values (C0 and D0). All distances are given in
degrees. Because none of the three charts shows a scale of latitudes, the distances
were first measured in leagues, using the scales of the charts (see Annex G for all
values), and then converted to degrees using the appropriate value of L’, previously
112
determined and presented in Table 4.437. The average values of the magnetic declination along the tracks, as of 1500, are also shown38.
Table 4.7
Courses along tracks for fifteenth century charts
Track
C0
δ
Modena
ca. 1471
Reinel
15th cent
Aguiar
1492
C
C0 - C
C
C0 -C
C
C0 - C
Mean
C0 - C
229
3.5
229
0.0
227
2.0
226
3.0
1.7
271
-0.4
274
-3.0
275
-4.0
274
-3.0
-3.3
Terceira – Madeira
126
1.7
132
-6.0
132
-6.0
134
-8.0
-6.7
174
1.9
176
-2.0
175
-1.0
174
0.0
-1.0
202
2.0
200
2.0
201
1.0
198
4.0
2.3
356
1.3
--
--
353
3.0
353
3.0
3.0
Table 4.8
Distances along tracks for fifteenth century charts (degrees)
Track
D0
Modena
ca. 1471
D
D - D0
Reinel
15th cent
D
Aguiar
1492
D - D0
D
D - D0
Mean
D0 - D
8.6
9.0
0.4
8.6
0.0
8.2
-0.4
0.0
14.1
14.1
0.0
12.8
-1.3
12.3
-1.8
-1.0
10.0
10.3
0.3
9.6
-0.4
9.6
-0.4
-0.2
17.4
17.0
-0.4
15.8
-1.6
16.6
-0.8
-0.9
22.3
23.3
1.0
21.8
-1.5
22.6
0.3
-0.1
13.7
--
--
13.2
-0.5
13.8
0.1
-0.2
In the charts of the fifteenth century, and with the exception of the track TerceiraMadeira, the differences C0 – C between the exact courses and the values measured
on the charts are relatively small, as well as the corresponding dispersions. If it is
assumed that these differences are the direct effect of the magnetic declination,
then the average value of δ along each track at the time the directions were measured is approximated by the average value of C0 – C. This implies that the magnetic
declination was positive (eastward) in the tracks C. Espichel – Madeira, Madeira – S.
Nicolau and C. Espichel – Slea Head, and negative (westward) in the other cases. The
results are coherent with the values of δ in Figure 4.6, estimated by the geomagnetic
37
The values of L’ presented in Table 4.4 for the charts of the fifteenth century refer to the zones
15°N to 35°N and 35°N to 50°N. In the tracks ‘C. Espichel – Madeira’ and ‘Madeira – Terceira’ average
th
values were used for each chart: 19.2 leagues for ‘Modena ca. 1471’, 19.7 leagues for ‘Reinel 15
century’ and 20.3 leagues for ‘Aguiar 1492’.
38
As explained in Chapter 3, the magnetic declination for each track is the average between the values at the two control points, as shown in Tables 3.3 and 3.4.
113
model of Korte and Constable (2005) for the period 1400-1500, except in the tracks
Terceira – Madeira and Madeira – S. Nicolau, which present exaggerated values. No
detailed comparison aiming at determining the time when the courses were observed seems possible, given the relatively small value and variation of the magnetic
declination, and the uncertainty of the results yielded by the geomagnetic model.
The explanation for the mismatch in the track Terceira - Madeira can be found in the
geometric inconsistency of the charting method and is illustrated in Figure 3.14 (p.
74), where the position of Madeira varies whether it is plotted from Lisbon or from
Terceira. Clearly Madeira was plotted, in all three charts of the fifteenth century,
according to the course and distance as measured from Lisbon, causing the track
Terceira - Madeira to appear rotated clockwise relative to its true orientation. A similar cause is probably behind the discrepancy in the track Madeira – S. Nicolau.
Table 4.8 shows the corresponding values of distance, in degrees, for the same group
of charts. Due to the fact that distances are expressed in degrees and the length of
the degree varies with latitude in all charts, these numbers should be regarded as
approximations and no detailed interpretation is appropriate. Also there is a considerable uncertainty in the position of some control points due to poor legibility and to
the exaggeration of the size of capes and islands. It is interesting to notice that the
largest differences between the measured and the theoretical values, D-D0, occur in
the track ‘C. Espichel-Terceira’. This is also the case where the dispersion of the distances measured in all charts is larger (see Annex G, Table G.1).
Table 4.9 – Courses along tracks for sixteenth century charts
Reinel
Cantino
Mean
ca. 1504
Track
C0
δ
C0 - C
C
C0 - C
C
C0 - C
229
3.5
231
-2.0
227
2.0
0.0
271
-0.4
273
-2.0
274
-3.0
-2.5
Terceira - Madeira
126
1.7
131
-5.0
133
-7.0
-6.0
202
2.0
200
2.0
201
1.0
1.5
174
-1.9
174
0.0
174
0.0
0.0
356
1.3
353
3.0
353
3.0
3.0
292
-6.1
300
-8.0
283
9.0
--
314
-5.9
327
-13.0
315
-1.0
--
333
-7.8
003
-30.0
344
-11.0
--
293
-6.7
303
-10.0
301
-8.0
-9.0
Tables 4.9 and 4.10 show the corresponding results for the charts of the sixteenth
century. Two different groups of tracks need to be analyzed separately: those which
114
are common to the charts of the fifteenth century (the six first); and those appearing
for the first time, as the result of the exploration missions made in the end of the
fifteenth and beginning of the sixteenth centuries (the four last)39. It was shown before in this chapter that the scales of latitude in ‘Cantino’ and ‘Reinel ca. 1504’ only
apply to the areas where astronomical observations were made, which is not the
case of most control points used to construct the tables. For this reason, and to make
the results comparable with those obtained for the charts of the fifteenth century,
the values of the parameter L’ in Table 4.4 were used, instead of L, to convert the
distances from leagues to degrees40. As with the charts of the fifteenth century, the
results should be interpreted with care and no detailed conclusions are appropriate.
Table 4.10 – Distances along tracks for sixteenth century charts (degrees)
Cantino
Track
D0
D
D - D0
Reinel
ca. 1504
D
D - D0
Mean
D - D0
8.6
9.0
0.4
9.2
0.6
0.5
14.1
13.8
-0.3
14.2
0.1
-0.1
Terceira - Madeira
10.0
10.0
0.0
10.6
0.6
0.3
17.4
16.3
-1.1
16.0
-1.4
-1.3
22.3
22.3
0.0
22.5
0.2
0.1
13.7
13.4
-0.3
13.9
0.2
-0.1
20.2
13.0
-7.2
23.4
3.2
--
30.8
23.5
-7.3
31.1
0.3
--
23.6
18.9
-4.7
19.1
-4.5
--
20.6
15.7
-4.9
20.2
-0.4
-2.7
In the first group, no significant differences are found from the courses of the older
charts. It is interesting to notice the good match between the two Reinel’s charts,
which suggests that one was copied from the other or that they share a common
model. The distances measured on the charts of the sixteenth century are usually
larger than the corresponding values, in degrees, of the older charts (Table 4.8). No
special meaning is attributed to this fact other than the inaccuracy of the conversion
process from leagues to degrees. Notice that the same systematic difference does
not occur between the distances measured in leagues (Annex G).
39
Greenland is supposed to have been re-discovered by João Fernandes Labrador and Pedro de Barcelos between 1495 and 1498, and also visited by John Cabot, in the English expedition of 1498 (Peres,
1983, p. 309-19); Newfoundland was probably visited by an English expedition in 1497-98, and again,
by Gaspar Corte-Real in 1500 and 1501 (Ibidem, p. 350).
40
As with the charts of the fifteenth century, average values of L’ were used in the tracks C. Espichel –
Madeira and Madeira – Terceira: 19.0 leagues for ‘Cantino’ and 18.9 leagues for ‘Reinel ca. 1504’.
115
Considering now the second group, an apparent anomaly needs to be explained,
which is the large differences between the courses ‘Slea Head – C. Farvel’, ‘C. espichel – C. Farvel’ and ‘Terceira – C. Farvel’ in the two charts. In the Cantino planisphere,
the island is represented almost exactly north-south with the Azores, which is not the
case of ‘Reinel ca. 1504’, where Greenland is shown much closer to Newfoundland
and with a different shape. A possible explanation, to be confirmed below, is that
while in the Cantino planisphere the position of Greenland may have been plotted
relative to some place in northern Europe, in ‘Reinel ca. 1504’ the origin was probably the Azores. It should also be noted that, at the time Newfoundland and Greenland were visited by the Portuguese explorers, the astronomical methods of navigation were already established, which makes possible that the set point was used to
chart these two regions. To clarify the issue a finer comparison needs to be done
between the segments connecting some control points on the charts and the corresponding theoretical tracks. The task is somehow complicated by the coexistence, in
both cases, of two distinct charting methods applying to the same Atlantic area, each
of them adopting a different length for the degree. Rather than comparing numbers
it was found more effective to plot all relevant positions and tracks on the reproductions of the two charts, using the following conventions:
− A theoretical set point track is represented according to the exact latitude of its
end point, as measured in the latitude scale of the chart, and the magnetic
course relative to a given origin. Notice that, because the origin may be affected
by a latitude error, the length of the track does not necessarily coincide with its
theoretical value, Dm;
− A theoretical track using the method of the point of fantasy is represented according to the magnetic course and distance (in leagues) relative to a given origin.
To convert the distances from degrees to leagues two alternatives modules are
used: the nominal value L (as determined from the latitude scale of each chart)
and the interpolated value L’ (as determined from the spacing between interpolated parallels).
In Figures 4.12 and 4.13 the positions of C. Espichel, Slea Head, Iceland (south), C.
Farvel, Terceira and C. Race are represented together with some relevant theoretical
tracks. The analysis of the figure suggests the following comments:
− On both charts, the position of Newfoundland (C. Race) appears to have been
plotted using the method of the point of fantasy and a track with origin in the
Azores (Terceira). This interpretation is reinforced by the large latitude errors of
C. Race. The use of the nominal module (L) in the conversion from degrees to
116
leagues (white triangles) appears as the best option, confirming that Newfoundland was not copied from the old pattern used to represent Europe;
− The position of Greenland (C. Farvel) on ‘Reinel ca. 1504’ appears to have been
plotted according to a track with origin in the Azores (Terceira), using the set
point method;
− On the Cantino planisphere, the position of Greenland (C. Farvel) appears to have
been charted using a track with origin in northern Europe. Two options were considered: Ireland (Slea Head) and the southern tip of Iceland. This last option appears as the best match, when associated with the point of fantasy.
C. Farvel
Iceland
Slea Head
C. Race
Terceira
Figure 4.12 – Comparison between the locations of Cape Race and Cape Farvel in ‘Cantino’,
and as determined from the theoretical magnetic tracks with origin in Terceira, Slea Head
and Iceland. The green circles represent the control points on the chart; the white circles
represent the set point; the grey and white triangles represent the point of fantasy, where
the theoretical distances were converted from degrees to leagues using, respectively, the
nominal (L=17.8) and the interpolated (L’=20.1) modules.
Also notice how the shape of Greenland is very different in the two representations.
This fact, associated with the different routes used to plot the island on the charts,
indicate that distinct sources were used and suggest that new data from some ex-
117
ploratory mission sent to the region became available after 1502, when the Cantino
planisphere was already drawn.
Figure 4.13 – Comparison between the locations of Cape Race and Cape Farvel in ‘Reinel ca.
1504’ and as determined from the theoretical magnetic tracks with origin in Terceira, C. Espichel and Slea Head. The grey squares represent the control points on the chart; the white
circles represent the set point; the grey and white triangles represent the point of fantasy,
where the theoretical distances were converted from degrees to leagues using, respectively,
the nominal (L=18.2) and interpolated (L´=19.3) modules.
A strange fact still remains to be explained concerning ‘Reinel ca. 1504’, which is the
existence of an oblique latitude scale in the vicinity of Newfoundland only applying to
the region. An obvious conclusion is that while latitudes were observed and incorporated into the representation, the main latitude scale cannot be used for reading
them. A possible reason might be that the region was represented as an inset drawn
in a different scale, with no relation with the rest of the chart. Still such solution
would be highly inconvenient for navigation and is contradicted by the fact that the
length of the degree is equal in both latitude scales. Then the best explanation for
the presence of the extra scale must be that the main scale is not applicable to Newfoundland because its position was not plotted on the chart using the set point
method, as suggested by Gernez (1952). As shown before, the use of the method of
118
point of fantasy is confirmed by the large latitude error of C. Farvel in the chart,
which results from the effect of the magnetic declination.
In Chapter 2 (p. 37-38) the suggestion of Barbosa (1937) that the charts of the fifteenth and sixteenth centuries may reflect the manipulation of the marine compasses, with the purpose of compensating them for the magnetic declination at the
time they were constructed, was presented. According to this theory, which is supported by some excerpts taken from the Tratado da Agulha de Marear de João de
Lisboa and other sources, the compass needles were rotated clockwise by one to two
points during the fifteenth century (11 ¼ to 22 ½ degrees), and one to half a point
during the sixteenth (11 ¼ to 5 ¾ degrees), the manipulations having affected directly
the courses represented on the charts of the time. These numbers seem unrealistic
when compared with the values of the magnetic declination near the coast of Portugal. In 1500 the magnetic declination in Lisbon, as estimated on the basis of the
available historical observations, was about 1.5° (see Table 3.2 and Figure 4.7); in
1400, and according to the model of Korte and Constable (see Figure 4.6), it was
most probably less. Then, not only the values taken from the Tratado are overly exaggerated but also the implied variation with time seems incorrect, as the magnetic
declination had a local minimum at about 1400 and grew from there until about
1550, when it reached a local maximum of about 8° E (according to the historical
observations). The fact does not totally invalidate the theory though, as it seems still
possible that the courses presented in Tables 4.7 and 4.9 were measured with manipulated compasses. To verify the possibility suppose that all courses represented
on the charts have been corrected by +3.5°, which is the average value of the magnetic declination along the track C. Espichel – Madeira in 150041. If that were the case
then the non-manipulated mean values of C0-C, in the last column, should have been
closer to the corresponding values of the magnetic declination than they are now.
The verification, which consists in adding 3.5° to the last column of Tables 4.7 and 4.9
and comparing the results with the values of δ, is not conclusive42. Whether the
charts of the fifteenth and sixteenth centuries were affected by the use of manipulated compasses or not is still uncertain, as the relatively small values of the magnetic
declination do not permit the results to be more expressive. Anyway the large correction values referred to in the Tratado da Agulha de Marear and cited by Barbosa
are certainly not real, at least in the European area where this study applies.
41
Recalling that the magnetic declination, δ, is the angle between the true North and the magnetic
North, counted clockwise from the true North, then C0 = Cm + δ, where C0 is the true course and Cm is
the magnetic course.
42
The results are not considered to be significant enough to be shown and discussed here but can be
easily reproduced using the method explained.
119
Modeling the North Atlantic and the Mediterranean
With the results obtained in the previous sections concerning the routes and methods adopted in the construction of the charts, representations of the north Atlantic
and Mediterranean were simulated using the EMP model. Because the main purpose
of this simulation is only to reproduce the main geometric features associated with
the different charting methods, as well as with the choice of routes and the effect of
the magnetic declination, no attempt was made to replicate the details of each chart
or even to consider the effect of the scaling errors.
The input of the model consisted in a series of tracks with origin in C. Espichel, covering the north Atlantic coasts of Africa, Europe and Newfoundland, the Atlantic islands
of Azores, Madeira and Cape Verde, and the Mediterranean and Black Sea. Some of
the routes were already discussed in this chapter, like the ones connecting Lisbon (C.
Espichel) to Greenland and to Newfoundland; others were chosen on the basis of
common sense. Although it is likely that the representation of northern Europe, in
the charts analyzed here, was based on information collected in the fifteenth century, or even before, the magnetic declination as of 1500 was used. This is justified by
the relatively small accuracy of the estimations made by the geomagnetic model,
when compared with the available historical observations, as well as by the small
variations during the period 1400-1500. For the Mediterranean and Black Sea, the
magnetic declination as of 1300 was considered to be the best choice, for the reasons invoked before (see p. 98-99). Three separate simulations were made, in order
to cover the different routes and charting methods on which the construction of
each chart was considered to be based:
− Simulation A: only the method of the point of fantasy is considered. Greenland
and Newfoundland are not represented. The simulation is intended to reproduce
the geometry of the three charts of the fifteenth century: ‘Modena ca. 1472’,
‘Reinel 15th century’ and Aguiar 1492’;
− Simulation B: the method of the point of fantasy is used in all tracks except those
connecting Madeira to Cape Verde and to the Gulf of Guinea, where the set point
method was adopted. Cape Farvel, in Greenland, is represented according to a
track with origin in Iceland. This simulation is intended to reproduce the geometry of ‘Cantino’ in the North Atlantic and Mediterranean43;
43
The simulation of the entire chart, including the South Atlantic and Indian Oceans, is presented and
discussed in Chapter 5.
120
− Simulation C: similar to simulation B except that Cape Farvel is represented using
the set point method and taking Terceira (Azores) as origin. This simulation is intended to simulate the geometry of ‘Reinel ca. 1504’.
20W
10W
0
10E
20E
30E
40E
50N
30W
40N
30N
20N
10N
0
Figure 4.14 – Output of simulation A with the tracks used as input. Notice the counterclockwise tilt of the meridians and parallels in the Mediterranean (right) and Gulf of Guinea (bottom). Compare with the grids implicit in the charts of the fifteenth century (Figures 4.1 to
4.3).
Because of the geometric inconsistency associated with the charting methods of the
fifteenth and sixteenth centuries, which are reflected on the conception of the EMP
model, a note is due on the type of routes used as input and their influence on the
final outputs. When no closed loops exist, the final positions of all points are unambiguously determined by the courses and distances between them, which are conserved in the output; if closed loops exist, the final positions of the points are the
result of an optimization process in which the given courses and distances are not
necessarily conserved. In the present situation it was considered appropriate to use
closed loops not only in the Mediterranean and Black Sea but also in the northern
Europe, due to the uncertainty about the routes used to represent the region on the
charts. When applying the method of the point of fantasy, a value of 0.8 was assigned to the parameter w, whose function is to attribute a relative weight to distances and directions, during the optimization process (see explanation in Chapter 2,
121
p. 79-80). This choice is justified by the results obtained by Gaspar (2008a, p. 199200) in the modeling of portolan charts.
40W
20W
40W
0
60N
20W
0
20E
20E
60N
40E
50N
50N
40N
40N
30N
30N
20N
20N
10N
10N
0
Figure 4.15 – Outputs of simulations B (left) and C (right) with the tracks used as input. Notice the stronger convergence of the meridians near Newfoundland in simulation B. Compare, respectively, with the grids in Figure 4.4 (‘Cantino’) and Figure 4.5 (‘Reinel ca. 1504’).
Figures 4.14 and 4.15 show the outputs of the three simulations. As expected, no
perfect match was obtained with any of the interpolated grids of the five charts. Still,
the main geometric features associated with the different charting methods, the
choice of routes and the effect of the magnetic declination are reasonably reproduced. In all simulations the north-south axis of the Mediterranean appears rotated
to northwest, reflecting the effect of magnetic declination, whose average value in
1300 was about 8° E. In simulation A, a counterclockwise tilt of the grid also occurs in
the region south of about 20° N and in the Gulf of Guinea. The comparison with the
charts of the fifteenth century suggests that the magnetic declination is underestimated by at least five degrees in the Gulf of Guinea, where the tilt of meridians and
parallels is significantly larger. To the north, the output represents the parallels as
approximately horizontal and equally spaced, as in the three charts. This is a feature
shared by the outputs of simulations B and C (Figure 4.15).
There are two important differences between simulations B and C, and simulation A:
the representation of the northwestern Atlantic, due to the inclusion of the tracks
connecting Europe to Greenland and Newfoundland; and the correction of the counterclockwise tilt of the parallels in the south-most regions, as a result of the use of
the set point method. A subtle still relevant difference between outputs B and C is
the orientation of the meridians near Greenland and Newfoundland, as a result of a
122
different choice of routes. In simulation B, like in ‘Cantino’, Greenland was charted
relative to the Iceland, using the method of the point of fantasy and Newfoundland
was charted relative to Azores (Terceira), using the set point method. In simulation C,
like in ‘Reinel ca. 1504’, both Greenland and Newfoundland were charted relative to
Azores. This difference of criteria is reflected upon a stronger convergence of the
meridians in output B.
A relevant difference between the model outputs and the charts, not easily detected
by visual inspection, is the ratio between the longitudinal and latitudinal lengths of
the grids. This ratio may be estimated as the quotient, k = P/R, between the average
lengths of one degree of parallel at some chosen latitude (P) and one degree of meridian (R). Table 4.11 contains the values of k for the five charts and the three simulations, estimated for the 40° N parallel44. As expected, the value of k in all simulations
approaches cos (40°) =0.77, which is the theoretical ratio measured on the spherical
surface of the Earth. That is not the case of the charts, where the estimates are always larger than 0.77. Though other causes may contribute to the differences, one of
the most important is probably the scale variations inside each chart. This subject
was already addressed in a previous section (see Table 4.5, p. 107, and related discussion), when the length of the league in different parts of the charts was assessed
on the basis of various distances measured between places.
Table 4.11
Ratios between the lengths of parallels and meridians
Chart
Modena ca. 1471
th
Reinel 15 century
Aguiar 1492
Cantino
Reinel ca. 1504
k
EMP model
k
0.81
0.83
0.86
0.81
0.81
Simulation A
Simulation A
Simulation A
Simulation B
Simulation C
0.77
0.77
0.77
0.77
0.75
As stated in the beginning of this section, no detailed comparison between the outputs of the simulations and each individual chart is justifiable, as there are numerous
other factors, beyond the magnetic declination and the choice of routes, affecting
their geometry. Keeping in mind that the main objective of this simulation is to show
that the main geometric features of the charts can be reproduced by simulating the
charting methods of the time, under the influence of the magnetic declination, the
44
The values shown in Table 4.11 are coarse estimations based on the total length of the 40° N parallel and the total length of the 10° W meridian, as measured on a straight segment connecting the end
points. No allowance was made for the fact that parallels and meridians are not usually straight. In
‘Modena ca. 1471’ and ‘Reinel ca. 1504’ alternative meridians were used: 6° W and 14° W, respectively.
123
results just presented are satisfactory. In Chapter 5 the application of this type of
simulation to the South Atlantic and Indian Oceans is presented and discussed.
In the last section the results of the cartometric analysis made to four Portuguese
charts of the fifteenth and sixteenth centuries, depicting the northern Atlantic and
the Mediterranean, were presented and discussed. When appropriate, the corresponding results obtained for the Cantino planisphere were also shown and interpreted, for comparison purposes.
The visual inspection of the interpolated grids of meridians and parallels proved to
be a simple but effective way of quickly recognizing some important features of the
charts, to be later analyzed in detail. With this technique it was possible to assess the
effect of the magnetic declination on the geometry of the charts, to determine which
parts could, or could not, have been constructed on the basis of astronomicallyobserved latitudes and to make a first assessment of the cartographic accuracy in the
different regions. From the examination of the interpolated graticules, and taking
into account the small values of the magnetic declination at the time, it was concluded that conditions were favorable during the fourteenth and fifteenth century for the
cartographic representation of the Atlantic coastlines of Europe and northern Africa
to consolidate and easily accommodate a scale of latitudes, when astronomical navigation was introduced.
Assessments of the distance scales, latitude scales, the length of the degree of latitude and the metric length of the league were presented. The analysis was extended
to a number of Portuguese and non-Portuguese charts from the fourteenth to the
seventeenth centuries and included the discussion of previous studies. Two types of
distances scales were recognized: scales of 12.5 leagues per section, which originated
in the scales of miles of the portolan charts and were used throughout the fifteenth
and sixteenth centuries; and scales of 10 leagues per section, introduced in the middle of the sixteenth century. The scales with sections of 12 leagues, supposedly used
in the Cantino planisphere (1502), appear as a single exception in the Portuguese and
Spanish cartography and may be the result of an error made by the cartographer.
Three different standards for the length of the degree were identified in the Portuguese and Spanish charts depicting a scale of latitudes – 18, 17 ½ and 16 2/3 leagues
per degree – the last one appearing only in the Atlas Miller. The coexistence of these
three standards in the cartography of the sixteenth and seventeenth centuries indicates that the choice of a particular module had little relevance for the routine prac-
124
tice of navigation, being only an echo of the traditional models of the Earth and the
political disputes over the location of the Moluccas. The idea of Casaca (2005) that
each of the standard lengths of the degree used in navigation was associated with a
different league cannot be accepted, as the system would have caused an unacceptable confusion in the practise of navigation. Also, in the dispute that opposed
Portugal and Spain over the longitude of the Moluccas, it was the size of the Earth
that was relevant for determining if the islands were in the Portuguese or in the
Spanish hemispheres, not the length of the league.
When the length of the degree is estimated from the spacing between the interpolated parallels, instead of from the scales of latitudes, a more detailed interpretation
becomes possible. In the charts of the fifteenth century, none of them graduated in
latitude, the length of the degree is significantly larger than the known historical
modules, increasing from about 19 leagues, in the south, to about 20 or 21 leagues,
in the north. This is an indication that different sources with slightly different scales
were used in their compilation. A similar variation with latitude occurs in the two
charts of the sixteenth century, where the adopted length of the degree (assessed
from the scales of latitudes) is not identical to the values estimated from the spacing
between parallels. This suggests that only part of the area represented on the charts
was surveyed using astronomical methods, the other part (northern Europe) having
been copied from traditional patterns. Having concluded that the Portuguese charts
of the fifteenth century, as well as parts of the sixteenth’s, were based on the traditional portolan model, a comparison was made between these five charts and a
number of Italian and Majorcan charts of the fourteenth and fifteenth centuries. The
comparison, based on the assessment of the metric length of the mile along some
tracks in the Atlantic and Mediterranean45, clearly shows that the two groups of
charts share the same cartographic model, use similar units of distance and are both
piecewise constructions of information compiled from different sources with slightly
different scales.
A detailed assessment of the latitude accuracy of the charts has confirmed the conclusions drawn in the previous analyzes about the construction methods and the
effect of magnetic declination. Concerning the charts of the fifteenth century, the
errors are consistently less than one degree to the north of 30° N, increasing steadily
to the south, as a result of the magnetic declination. Despite the accuracy of the latitudes in the northern part of the Atlantic, there is no indication that astronomical
methods were used. A completely different distribution occurs in the charts of the
45
The length of the mile was first assessed and the results converted to leagues.
125
sixteenth century, with errors less than one degree between the Equator and 45° N,
strongly increasing with latitude from there, as a result of a scaling error.
A comparison was made between a set of tracks connecting chosen control points,
measured on the charts, and the corresponding theoretical rhumb-line tracks, with
the purpose of identifying the routes and charting methods used for constructing
each chart, to assess the effect of the magnetic declination on their geometry and to
contribute to better determine when the information was collected. Concerning this
last issue, no detailed interpretation of the results seemed possible, as the values of
the magnetic declination in the area were relatively small and didn’t vary much during the period 1400-1500. However the similarity of the courses and distances measured on the charts of the fifteenth and sixteenth centuries, connecting points in the
European coast and Atlantic islands, confirms that both use the portolan chart model
in the representation of the area. The difference in the position of Greenland in the
two charts of the sixteenth century was shown to be the result of using different
charting methods and tracks to locate the island.
No historical text has come to us documenting how the transition between the portolan chart and the latitude chart was made, after the introduction of astronomical
navigation. Also very few charts are extant belonging to the period when that transition supposedly took place. What the present analysis has shown is that the process
was relatively slow and smooth, as the two different cartographic models coexist in
the charts of the sixteenth century, when the astronomical methods were already
firmly established. The earliest known charts where observed latitudes were unmistakably incorporated are the Cantino planisphere and ‘Reinel’s ca. 1504’. A clear sign
of the use of the new methods is the dramatic improvement in the accuracy of the
Atlantic coastline of Africa, already reflecting the astronomical surveys made around
1485. None of the charts of the fifteenth century analyzed here show any evidence
of the use of astronomical methods, though the north-south relative positions of the
places to the north of the 30° N parallel are surprisingly accurate. From the comparison between the two groups of charts it was also possible to infer that no astronomical surveys were probably made in the coasts of Europe up to the time ‘Cantino’ and
‘Reinel ca. 1504’ were completed, which means that the representation of those areas continued to be copied from older patterns based on the portolan chart model.
The idea of Barbosa (1938a) that older charts, constructed in a time when the magnetic declination was relatively small, could have been used to support astronomical
navigation by simply overlaying a scale of latitudes, is confirmed in this study. That
was found to be the case of the three charts of the fifteenth century, in what the
representation of northern Europe is concerned. Paradoxically, the adoption of a
126
conventional degree of latitude in ‘Cantino’ and ‘Reinel ca. 1504’, considerably different from the value implicit in the models from which such representation was
copied from, made them unfit for astronomical navigation in the area. Assuming that
such methods were indeed practiced in European waters, maybe these two charts
are not representative of the remaining cartography of the sixteenth century or the
pilots relied more on the latitude information registered on their rutters than on the
charts.
Another suggestion of Barbosa (1937), that the charts of the fifteenth and sixteenth
centuries may reflect the manipulation of the marine compasses, as to compensate
for an eastward magnetic declination of as much as two points (22 ½ degrees), is not
supported in this study. Though that kind of manipulation was practiced in that period, as several sources confirm, it is not certain that it was reflected on the geometry
of the charts in a sufficiently expressive way as to be detected by cartometric analysis. On the other hand the values of magnetic declination indicated in the source referred to by Barbosa (the Tratado da Agulha de Marear de João de Lisboa) are unrealistic and not confirmed by the available historical observations.
The thesis proposed by Amaral (1995) that the coastline of the Gulf of Guinea, drawn
as an inset in ‘Reinel 15th century’, was added around 1505 using astronomicallyobserved latitudes, is not supported in this study. As with the other two charts of the
fifteenth century, the distortions caused by the uncorrected magnetic declination in
the interpolated grid prove that the representation of the area was based on the
method of the point of fantasy.
‘Reinel ca. 1504’ is the earliest extant nautical chart showing a graphical scale of latitudes. The existence of an extra latitude scale placed obliquely near Newfoundland,
and only applying to the area, is a further motive of interest and has represented a
puzzle for the historians of Cartography. In this study it was concluded that the reason for such peculiar solution is that the region was placed on the chart according to
a magnetic course and estimated distance, as measured from the Azores, notwithstanding the fact that latitudes were also observed and reflected on the representation. The interpretation of Gernez (1952) is then confirmed except for the origin of
the track, which was found to be in the Azores. Why the set point method was not
used for the purpose remains to be determined. A likely explanation is that the information of latitude was collected when the region was already represented in the
pattern charts. The different methods adopted for plotting Greenland on ‘Cantino’
and ‘Reinel ca. 1504’, as well as the very different shape of the island in the two
charts, indicate that distinct sources were used and that Greenland may have been
re-visited after 1502, when the Cantino planisphere was already drawn.
127
A series of numerical simulations of the cartography of the North Atlantic and Mediterranean was presented, with the purpose of reproducing the main geometric features of the charts and associate them with the effect of the magnetic declination
and charting methods. The objective of the simulations is considered to have been
achieved and the results are coherent with the expected influence of those factors,
notwithstanding some visible differences between the model outputs and the geometry of the individual charts. A good example of the effectiveness of the modeling
process was the simulation of the geometry of the North Atlantic in the two charts of
the sixteenth century, in which the effect of the different charting solutions was
clearly reflected on the outputs.
128
5. THE CANTINO PLANISPHERE
The Cantino planisphere, made by an anonymous Portuguese cartographer in 1502,
is one of the most precious cartographic monuments of all times1. It was important
at the beginning of the sixteenth century because it showed detailed and up-to-date
strategic data in a period when the geographic knowledge of the world was growing
continuously. And it is important in our days because it contains unique historical
information about the maritime exploration missions and the evolution of nautical
cartography in a particularly interesting period. With this chart, the traditional Ptolemaic depiction of Eastern Africa and the Indian Ocean was abandoned and the contours of the Americas are shown in a way suggesting that they are part of a new continent, clearly separated from India. Lands unknown to the European are represented in their correct geographic locations: Newfoundland, Florida and the coast of Brazil2. Other parts of the traditional knowledge of the world, transmitted by Ptolemy’s
Geography, are depicted with unprecedented detail and accuracy. The Cantino planisphere is also one of the few extant early Portuguese charts and the oldest known
nautical chart to represent places according to their latitudes, following the advent
of astronomical navigation. Although no graduated meridian is shown, a latitude
scale is implicit in the placement of the Equator, the tropical lines and the Arctic Circle. Contrarily to some portolan-charts of the sixteenth century, where latitude
scales were overlaid after the coastlines were drawn and have no relation with the
latitudes of most places, this scale plays a fundamental role in the new cartographic
model of which the Cantino planisphere is the earliest known example3.
In this chapter the results of the cartometric analysis and modeling of the Cantino
planisphere are presented and discussed. The text is organized in four sections. The
first (Overview and sources) contains a general overview of the chart and an intro1
The Cantino planisphere is now kept in the Biblioteca Estense Universitaria, Modena, Italy. A pagesize reproduction is in Annex H.
2
The coasts of Brazil and North America appear in Juan de La Cosa’s planisphere of 1500 but the representations are conjectural.
3
The planisphere of Juan de la Cosa also shows the Equator and the tropic of Cancer. But the position
of these lines are only approximate and some authors don’t accept that the chart was completed in
1500, mainly due to the fact that some of the information shows evidence of later exploration voyages (see Nunn, 1934, p. 51-52). To my knowledge no detailed assessment of the latitudes was ever
made in Juan de la Cosa’s planisphere.
129
CHAPTER 5 – THE CANTINO PLANISPHERE
duction to the exploration missions and cartographic sources from which its geographical information may have been compiled. In the second (Cartometric analysis)
the results of the cartometric analysis are presented and discussed. The third section
(The enormous isthmus) is focused on the interpretation of the longitudinal deformation of the African continent in the chart, in the light of the known historical
sources and the results of the cartometric analysis presented before. In the fourth
section (‘Modeling the Cantino’) the results of a numerical simulation of the geometry of the chart, using the model introduced in Chapter 3, are presented. The last
section (‘Synthesis and conclusions’) summarizes the most important results and
conclusions reached previously.
Overview and sources
The Cantino planisphere is a large manuscript chart drawn on six leaves of parchment mounted on a piece of cloth, measuring the total about 105 x 220 cm. On the
back there is an inscription transmitting some information about the intriguing story
behind its making: Carta de nauigar per le Isole nouamte. tr… in le parte de l’India:
dono Alberto Cantino Al S. Duca Hercole (‘Navigational chart of the islands recently
discovered in the parts of the Indies: from Alberto Cantino to Duke Hercole’). Alberto
Cantino was an agent of Hercole d’Este, Duke of Ferrara, who sent him to Lisbon in
the beginning of the sixteen century, searching for information about the Portuguese
maritime explorations. Cantino managed to be admitted to the court and to conquer
the favors of one or more cartographers, from whom he purchased a chart of the
world allegedly copied from the official pattern (the Padrão Real), kept in the House
of Guinea and India. The chart was then smuggled from Portugal and sent to Italy, in
15024.
The first detailed studies of the Cantino planisphere were made by Henry Harrise, in
1883 and 1891, and by Duarte Leite, in 1923. This last work is the most exhaustive on
the analysis of the geographical information and the sources used in the compilation
of the chart. More recent studies include those by Armando Cortesão (1935), Armando Cortesão and Teixeira da Mota (1987, Vol. I, p. 7-13), Edzer Roukema (1963)
and Moacyr Pereira (1994). No systematic analysis of the geometric properties and
4
The whole story about the making and smuggling of the Cantino planisphere is told by Leite (1923, p.
225-232). Most historians who have written about the subject consider that it was copied from the
Padrão Real, the Portuguese official pattern on which all sea-going charts were allegedly based. This
interpretation is justified by the up-to-dateness of its geographical information and the high price paid
by Alberto Cantino. On this matter it should be recalled that the disclosure of maps and globes showing newly discovered lands was to be forbidden in 1504 by a decree of King Manuel I of Portugal,
(Ibidem, p. 227-29), but it is almost certain that such policy was already in force in the last decade of
the fifteenth century.
130
navigational accuracy of the chart has ever been done, with the exception of the
simple measurements and scale assessments made by Harrise (1883) and by Leite
(1923, p. 232-35). Most authors have considered the Cantino planisphere to be
drawn on a cylindrical equidistant projection centered on the Equator (plate carrée)
though this assertion has never been supported by any quantitative study and can
be objectively denied by a careful reading of the available historical documents describing the navigational and charting methods of the Renaissance (see Chapter 2, p.
33-4).
Figure 5.1 – The sheets of parchment in the Cantino planisphere. The closed figure over the
northeastern coast of Brazil, in the lower left sheet, is an amendment. The dashed lines represent tears.
Four continents are shown on the chart: Europe, Africa, Asia and the Americas, occupying roughly 250 equatorial degrees, from about 90° W, in the West, to about
160° E, in the East. The depiction of an ocean eastward of the Chinese coast, significantly named Oceanus occideroriêtalis (which probably means ‘eastward of China
and westward of Europe’) suggests that Asia and America were already considered as
independent continents separated by a large mass of water, not represented in the
planisphere. The south and north-most regions represented in the chart are, respectively, the southern tip of South America, at about 38.5° S, and the northern part of
Scandinavia and Asia, truncated at about 70° N. One of the most striking features of
the planisphere is the representation of Africa, whose Atlantic and Indian coastlines,
from the entrance of the Mediterranean to the entrance of the Red Sea, are shown
for the first time with amazing accuracy and detail. Also new to the European eyes
were the island of Greenland (known to having been visited much earlier but never
depicted on a nautical chart), Newfoundland, Florida and the coast of Brazil. Little
131
was left of the Ptolemaic geographic view of the world: only the traditional shapes of
Scandinavia and Baltic Sea, as well as the Red Sea and Persian Gulf, not yet visited by
the Portuguese, and the designations mare prosodu and prasso promontorio, in the
eastern coast of Africa.
The Cantino planisphere is made of six rectangular pieces of parchment5, mounted
on a large sheet of canvas, measuring the total about 220 x 105 cm6. In the lower left
sheet there is an amendment strip replacing the former representation of the northeastern coastline of Brazil with a revised one. Two large tears are visible in this same
sheet, one going from the left margin of the chart to the coast, and the other, running from the coast of Brazil to the coast of Africa (Figure 5.1). There is a clear sign
that the upper part of the chart was truncated, as the legend over Greenland is incomplete (A ponta d…) and an ornament, which looks like the lower part of a capital
letter, is shown to the right of the Tordesillas’ line7. The fact that the two central
sheets of parchment have slightly larger widths than the other four further suggests
that the whole margin outside the reddish neatline, which is only partially visible,
may have been removed. However, I don’t consider these signs to be sufficiently
strong to prove the existence of a margin wide enough to depict written information
because the solution was unusual in the Portuguese cartography of the time. As for
the possible existence of a title, the hypothesis seems to contradict the accepted
theory that the planisphere is an unauthorized copy of the official pattern. Assuming
that such title existed and was removed, a more likely explanation is that the chart
was purchased (or in some way deviated from its original purpose) shortly after it
was made for a different client, possibly an important official or nobleman. The removal of the title would be an obvious way of hiding the name of the cartographer or
the original purpose of the chart8.
The Equator (Linha equinocialis), the tropical lines (Tropicus cãcer and Tropicus capricorni), the Arctic Circle (Circulus artcus) and the dividing line of Tordesillas (Este he o
marco dantre Castella y Portugual 9) are the only geographic gridlines depicted in the
5
Most authors refer to only three sheets of parchment mounted side by side but a close examination
of the original reveals three horizontal stitching lines running across those sheets (see Figure 5.1).
Whether they are the result of a cut made on the original sheets or not is irrelevant.
6
These are the dimensions indicated by Giuseppe Boni, Director of the Biblioteca Estense, in his written donation of 1873 (see Harrisse, 1883, p. 72). Because the margins of the chart are irregular, these
values are only approximations.
7
It is not clear when this strip was removed. The interpretation implicit in Leite (1923, p. 225), based
on the testimony of Giuseppe Boni, is that the damage was done during the years that the chart was
lost, in the nineteenth century. See also Cortesão e Mota (1987, Vol. I, p. 7).
8
The possibility of the title having been removed in the nineteenth century, during the period the
chart was lost, does not affect the argument. It is the very existence of a title which contradicts the
theory that the chart is an unauthorized copy of the official pattern, ordered by Alberto Cantino.
9
‘This is the boundary between Castile and Portugal’.
132
planisphere. It is interesting to notice that these lines make an angle of a little less
than 1° with the margins. Assuming that this is not a mistake, the anomaly suggests
that a strip was removed all around the perimeter of the chart and the present neatline added after10. Two circular systems of 32-point wind-roses are shown, one centered south of the Cape Verde Islands and the other over the Hindustan Peninsula, at
about 14° S. On the tangency line of the two systems, over the African Continent, a
large wind rose with a fleur-de-lis indicating North is drawn. There are six graphical
scales of distance graduated in leagues distributed over the chart’s area, with a variable number of sections. The chart has 39 inscriptions with valuable historical and
geographical information11, and numerous illuminations decorating Europe, Africa
and the Americas. An abundant toponymy is shown with the names written in a
semi-gothic calligraphy, perpendicularly to the coastline, as in the portolan charts of
the time. Numerous flags mark the territories and parts of the coast discovered,
claimed or in possession of Portuguese, Spaniards, English and Muslims.
The Cantino planisphere is a compilation of cartographic data from different sources
and times. The information representing the Mediterranean and Back Sea, probably
the oldest, may have been copied from Majorcan charts; the newest, including Brazil,
the eastern coast of Africa and the Hindustani Peninsula, is from the first two years
of the sixteenth century. Two distinct cartographic models have been used in its construction: the portolan-chart model, based on estimated distances and compass directions (‘point of fantasy’); and the latitude-chart model, incorporating astronomically-determined latitudes (‘set point’). The oriental part of the chart, not covered in
this study, is considered to be based on the Arabic sources contacted by Vasco da
Gama and Pedro Álvares Cabral in the period 1498-150012.
10
Also notice that the margin shows no discontinuities between adjacent sheets, though the parchment has some clear signs of distortion, especially near the vertical line joining the two upper left
sheets. This suggests that the truncation may have been made after the parchment was already distorted, possibly during the nineteenth century.
11
All the inscriptions are reproduced and translated into English in Portugaliae Monumenta Cartographica (Cortesão and Mota, 1987, Vol. I, p. 11-13).
12
It is usually accepted that the cartographic information of the oriental part of the Cantino planisphere was obtained from the Arabic pilots to whose services Vasco da Gama (1498) and Pedro Álvares Cabral (1500-1501) turned to for making the passage between the eastern coast of Africa and
India. With the exception of the ports visited by their fleets in the coast of Malabar, all representations to the east of the Hindustan Peninsula are not of Portuguese origin. Some inscriptions written
over those areas indicate the latitude of the places, expressed in inches (pulgadas), the unit used by
the Arabic pilots to measure the latitude. The considerable north-south distortion of the Malacca
peninsula may be the result of a poor conversion between inches and degrees. A more detailed analysis of the oriental part of the Cantino planisphere, including an assessment of the accuracy of the
latitudes, is in Albuquerque (1967). The hypothesis that Arabic portolan charts were used as the main
source for the representation of these areas, as suggested by Leite (1923, p. 236), is doubtful because
there is no historical evidence that such charts ever existed.
133
Mediterranean and Black Sea
No historical documents are known which identify the cartographic sources utilized
for representing the Mediterranean and Black Sea in the Cantino planisphere. The
oldest known testimony concerning the depiction of these regions in the Portuguese
cartography of the sixteenth century is from Pedro Nunes, in the ‘Treatise in defense
of the navigational chart’ (1537), where he complains about the fact that the places
in the Levant (the Mediterranean and Black Sea) are not represented according to
their latitudes and says that those parts were copied from Majorcan charts, where
they were made in the past (Nunes, 2002, p. 134-35). The visual inspection of the
Cantino planisphere seems to confirm the fact, as the longitudinal axis of the Mediterranean appears rotated to northwest by an angle of about 8°, which is close to the
average value of the magnetic declination in the region, during the thirteenth century13.
Northern Europe
According to Teixeira da Mota (1977, p. 2), the representation of the European and
African coasts of the Mediterranean, as well as of the Atlantic coasts between the
Iberian Peninsula and Denmark, comes from the so-called ‘normal portolan’ and was
based on estimated distances and courses given by the compass. To the north of this
area, the depiction of the Baltic Sea and Scandinavia, much coarser, would have been
based on compass-less navigation. However, the detail of the representation and the
fact that many toponyms in the British Isles, France and Holland are written in Portuguese raise the possibility of new surveys (including latitude measurements) having
been made in those areas. No earlier chart of Portuguese origin is known showing
the north-most part of the Atlantic, with the Scandinavia, Iceland and Greenland. The
inscription written to the southeast of Greenland, in the Cantino planisphere (see
Figure 5.2), reads: ‘This land is discovered by order of the very excellent prince Dom
Manuel King of Portugal […] and according to the opinion of the cosmographers it is
believed to be the point of Asia’14. This does not mean, as explained by Leite (1923,
p. 238-9), that the Portuguese considered Greenland to be connected to Asia by the
west. On the contrary, the island was thought to be a western extension of Asia,
connected to Scandinavia15. Anyway, the memory of the earlier settlements made by
13
See also Chapter 2 (p. 25-26) and Chapter 4 (p. 98-9).
As translated by Cortesão and Mota (1987, Vol. I, p. 11). The original reads: Esta terra he descober
per mandado muy escelentissimo pncipe Dom manuel Rey de portugall […] polla quall segum a opiniom dos cosmofricos se cree ser a ponta dasia.
15
According to Leite (Ibidem) the truncated upper strip of the Cantino planisphere might have shown
the connection between Greenland and Scandinavia, as represented in the Caverio planisphere, of ca.
1505, and in earlier Ptolemaic maps. The oldest known cartographic representation of Greenland is in
14
134
Europeans in the region was apparently forgotten, as well as the previous cartographic depictions of the island, and Greenland appears in the Cantino planisphere as
if it were a new discovery16. There is a considerable eastward shift of the island,
which is represented northward of the Azores, when their longitudes differ by more
than fifteen degrees. The possibility of the distortion having been caused by the
charting method, as first suggested by Mota (1973, p. 9), was already confirmed in
Chapter 4 (p. 116-18) and is re-addressed below. Other early cartographic representations of Greenland are found in the King-Hamy chart (ca. 1502), Pedro Reinel (ca.
1504), Caverio (ca. 1505) and the Pesaro Oliveriano world map (ca. 1505-08), but
only the Caverio map depicts a similar eastward displacement.
Figure 5.2 – Greenland and Scandinavia in the Cantino planisphere, both identified as ‘part of
Asia’. The truncated upper strip of the chart might have shown the connection between
them, as in the Caverio planisphere, of ca. 1505.
North Atlantic islands
With the exception of the British Islands, which already appear in the Carta Pisana
(ca. 1385) and other early portolan charts, the first unambiguous cartographic repre-
a map by Claudius Clavus, included in a manuscript edition of Ptolemy’s Geography, the ‘Nancy manuscript’ of 1427, where Greenland appears as a mass of land flanking Scandinavia to the north and
west. In later manuscript editions of Geography, of the end of the fifteenth century, Greenland appears as a peninsula connected to Scandinavia. See Mead (2007, p. 1783-85).
16
The island is supposed to have been re-discovered by João Fernandes Labrador and Pedro de Barcelos, between 1495 and 1498, and also visited by John Cabot, during the English expedition of 1498.
See Peres (1983, p. 309-19).
135
sentation of the Atlantic Islands is found in Dulceto’s chart of 133917: three islands in
the Madeira archipelago - Madeira, Porto Santo and Desertas − and three in the Canary Islands − Lanzarote, Lobos and Fuerte Ventura (Cortesão, 1971, p. 55-60). While
some of the Azores islands have been depicted in nautical charts as early as in the
mid-fourteenth century, together with some imaginary ones18, the oldest correct
depiction of the archipelago only appears in Zuane Pizzinago’s chart of about 1424.
By the time the Cantino planisphere was made, the cartographic representation of
the Atlantic islands had already achieved a good degree of accuracy as shown, for
example, in the chart of Jorge de Aguiar (1492).
Africa
The systematic exploration of the western coast of Africa began about 1421-22, under the leadership of Prince Henry (1394-1460), the fifth legitimate son of King João I
of Portugal. The Cabo Bojador (present Cap Boujdour, 26° 08’ N, 14° 29’ W), a strong
physical and psychological obstacle to the southward progression of the exploration
ships of the fifteenth century, was crossed by Gil Eanes in 143419. From this important date on several expeditions were sent in succession. At about 1470, the
whole coast between the cape and São Jorge da Mina (5° 06.5’ N, 1° 21’ W), where
an important fortress started to be built in 1483, had already been explored. The
fraction of the coast between Cabo Catarina (present Pointe Sainte Catherine: 1°
16’ S, 8° 58’ W) and south of Cape Cross (21° 46’ S, 13° 57’ E) was explored by Diogo
Cão in the two missions of 1482-84 and 1485-86. At about 1485, an astronomical
survey of the coast of Guinea20 was ordered by King João of Portugal21. In this mission participated João Vizinho, physician and cosmographer of the court, and probably also Duarte Pacheco Pereira (ca. 1460-ca. 1533), who later published an extensive list of latitudes in his important work Esmeraldo de Situ Orbis, of ca. 1505-8 (see
17
The Dulceto chart of 1339 is now kept in the Bibliotèque Nationale de France, Paris. Pujades (2007,
p. 255) has recently shown that the names ‘Dulcert’ and ‘Dalorto’ are both misspellings of the name of
the Genoese cartographer Angelino Dulceto.
18
Cortesão shows the outlines of the Atlantic islands in the cartography of the fourteenth century,
together with a table making the correspondence with the present toponyms.
19
This was an important achievement for the Portuguese ships of the time, not because it was difficult
to navigate to the south of the cape, but due to the contrary northerly winds and currents which
made the return trip long and hard. Much easier than sailing (or rowing) against the elements was to
drive away from the coast and come back to Portugal through the open sea and the Azores, a practice
that was initiated around the middle of the fifteenth century, after the introduction of the caravel in
the exploration trips.
20
To the Portuguese of the fifteenth century the term Guiné designated a large fraction of the northwestern African coast, southward of the Senegal River (about 16° N).
21
This is known from a handwritten note attributed to Columbus, or to his brother Bartolomeo, on the
margin of a copy of the Historia Papae Pii (Venetiis, 1447). A facsimile of the note is in Raccolta di
Documenti e Studi publicati della Comissioni Colombiana. Autografi di Cristoforo Colombo. Parte I, Vol.
III. Roma, 1892.
136
Pereira, 1954). The Cape of Good Hope, close to the southern tip of Africa, was
reached by Bartolomeu Dias in 1488, who explored the stretch of coast between
near Cape Cross, the south-most point reached by Diogo Cão, and Rio do Infante
(present Great Fish River: 32° 41’ S, 28° 24’ E)22. The eastern coast of Africa up to
Mõmbaça (present Mombasa, in Kenya: 4° 05’ S; 39° 42’ E) was first visited by the
fleet of Vasco da Gama, in its voyage to India, and again by the ships of Pedro Álvares
Cabral (1500-1501) and João da Nova (1501). Cape Guardafui, in the northeastern tip
of Africa, and the entrance of the Red Sea were reached by the ship of Diogo Dias in
1501 after being lost from Cabral’s fleet, near the Cape of Good Hope, and having
suffered a terrible storm that killed most of the crew. A Portuguese flag and an inscription are depicted in the Cantino planisphere, near the southern end of the Gulf
of Aden, referring to this trip: ‘unto here is discovered by the King of Portugal’23. Another possible source of information for the eastern coast of Africa is the mission of
Pero da Covilhã, who was sent by King João II in an overland expedition to Africa and
India, and to whom a chart was given in 1487, before his departure. He is known to
have visited Calecute and Goa, in India, and also the eastern coast of Africa, during
the period 1489-90. Pero da Covilhã was not allowed to leave Ethiopia, where he
spent the rest of his life, but the important information collected by him was probably passed to King João II and the story of his adventure was written by Francisco
Álvares in the Verdadeira Informação do Preste João, of 1540 (see Álvares, 1943)24. A
notable exception to the accuracy with which the African coast is depicted in the
Cantino planisphere is the island of Madagascar, whose representation is certainly of
Arabian origin, as there is no evidence that it was visited by the Portuguese up to
1502.
The earliest known cartographic source representing the fraction of the African coast
explored during the first voyage of Diogo Cão (from about Cape Lopez to Cape Santa
Maria) is the chart of Cristoforo Soligo of ca. 148925. The second voyage of Cão was
first registered in the world map of Henricus Martellus Germanus (ca. 1489) and also
in the globe of Martin Behaim (1492). During his two missions, Diogo Cão left in the
22
Only in the return trip from Rio do Infante did Bartolomeu Dias sight the Cape of Good Hope and
sailed along the southern and southwestern coast of Africa up to Luderitz Bay (26° 40’ S), from where
he came back to Portugal. No log or original journal of Dias’ mission has survived. For a detailed description and discussion of his trips see Ravenstein (1908), Costa (1990), Randles (1988b) and Axelson
(1988).
23
The original reads: fasta aqui e descoberto por el Rey de portugall (Cortesão and Mota, 1987, Vol. I,
p. 12).
24
Cortesão (1974, p. 172) was of the opinion that the chart given to Pero da Covilhã before his departure was returned to Portugal enriched with new information, and raises the possibility of unknown
missions having been sent by King João II to the eastern coast of Africa, up to Sofala and even Malindi,
after he received the chart from Pero da Covilhã. See also Albuquerque (1989b, p. 127).
25
The chart of Soligo is kept in the British Museum, London.
137
coast of Africa four padrões, two of them are represented in the Soligo chart and, all
four, in the Cantino planisphere26.
America
On the western side of the Cantino planisphere, to the left of the Tordesillas’ line,
‘the Antilles of the King of Castile’ (Las antilhas del Rey de castella) are shown. These
were first discovered by Cristopher Columbus, in his voyages of 1492 and 1493-96,
and later explored by several Spanish expeditions. Four large islands are represented:
Yssabela (Cuba), Jamayqua (Jamaica), Espanhola (Haiti, with a Spanish flag) and
Boriquem (Puerto Rico), together with numerous others from the Lesser Antilles and
Bahamas. To the south, the coasts of Venezuela and Guiana are shown, from the Gulf
of Venezuela, in the west, to the estuary of the Maranhão (golfo fremosso), close to
the line of Tordesillas. Delimiting this fraction of the coast three Spanish national
flags are depicted: two at the eastern and western limits and one over the Peninsula
of Paria. This region was first reached by Columbus, in his third voyage of 1498-1500,
and later explored by Alonso de Hojeda (1499-1500), who visited the province of
Coquibacoa (present Gulf of Venezuela), and by Vicente Yañez Pinzon, who is supposed to have entered the Amazon estuary in 1500 (see Harrisse, 1892, p. 662-80).
Another mass of land is shown to the west of the Caribbean Sea, identified by most
researchers as Florida27. It is significant that no national flag, either Spanish or a Portuguese, was drawn over this land, which was officially discovered by Ponce de Léon
in 1513, and that all toponyms are written in Portuguese. That is a sign that the region was probably first reached by a Portuguese expedition, who could not reclaim
the land for being within the Spanish side of the Tordesillas line28. Two distinctive
features in the representation of the Caribbean Sea are revealed by visual inspection:
the exaggerated size of the islands, when compared with the land that surrounds
them, suggesting that this part of the chart might have been copied from a larger
scale map; and their apparent displacement to northeast. To the north, a fraction of
Newfoundland’s coast is shown with a Portuguese flag and an inscription, saying that
the discovery was made by Gaspar Corte-Real, by order of the King of Portugal. It is
26
A padrão was a stone monument with a Croce on top, laid by the Portuguese explorers along the
coast of Africa, to sign the newly discovered lands.
27
That is, in my opinion, the simplest and most consensual interpretation. Other suggestions have
been made in the past, like being the Yucatan Peninsula or an erroneous duplication of Cuba. A brief
summary of these theories is in Peres (1983 p. 322-26).
28
See Peres (1983, p. 322-26). The discovery might have been made by Duarte Pacheco Pereira, in
1498, or by Gaspar Corte-Real, in 1499.
138
interesting to notice that this land is represented as if it were an island, just to the
east of the line of Tordesillas, thus belonging to the Portuguese hemisphere29.
The earliest known cartographic depiction of Central America and the Caribbean Sea
is found in Juan de la Cosa’s planisphere of 1500. The comparison between both
maps shows that although the general outline of the Caribbean islands is similar,
there are notable differences both in their shapes and positions relative to the mainland on the south. The two charts are also different in the outline of the northern
coast of South America, in the fraction between the Gulf of Venezuela and the delta
of the Maranhão. Finally, as noticed by Harrisse (1892, p. 88-92), there is a total discrepancy between the geographic names in both maps. In Juan de la Cosa’s map, the
whole coastline starting in the Gulf of Venezuela and then going to west and north to
join the present region of New England, explored in 1497-98 by the English expedition of John Cabot, is conjectural and idealized, probably in support of Columbus’
conviction that he has reached Asia. From the above it seems clear that, although the
main source of the Cantino planisphere for the Caribbean was certainly of Spanish
origin (with the exception of Florida), it is unlikely that the La Cosa map was used for
the purpose.
Brazil
Much has been written about the sources used in the representation of Brazil in the
Cantino planisphere, the most exhaustive works being those of Leite (1923), Roukema (1963) and Moacyr Pereira (1994). According to Roukema (p. 7-8), the Brazilian
part of the map was the last to be added and reached its present form in three phases: to the first belong all geographical names written in semi-gothic and an initial
coastline running to southeast from Golfo fremosso to Cabo Sam Jorge, and from
there, south-southwesterly to north of porto seguro, continuing further south to the
tip of the landmass. Only a relatively small portion of the coast, between the flag
near the Vera cruz inscription and the northern side of the baia de todos os santos
would have been surveyed, in 1500, by Pedro Álvares Cabral and the provision ship
sent back home with the news. To the second phase belongs the pasting of the strip
of parchment between Rio de sã franc° and Golfo fremosso, altering the position of
Cabo Sam Jorge and the orientation of the coastline from there to north of Porto
seguro, which became southerly oriented. This correction would have been based on
the information brought by the fleet of João da Nova, who arrived in Lisbon in September 1502, after its mission to India. In the third phase the toponyms written in
29
The accuracy of the location of Newfoundland in the chart, as well as the possibility of its position
having been manipulated with political purposes, is discussed below.
139
cursive would have been added, as well as the island named quaresma30 and the
blob representing the Cabo de Sacta Marta31. The information for these last inputs
would have been obtained during the exploration voyage sent to Brazil by King Manuel I in 1501, which returned to Lisbon in July 1502. As noted by Pereira, these additions were certainly made by an Italian hand, after the chart was delivered to Alberto
Cantino32.The entire coastline between baia de todos os santos and Cabo Sam Jorge,
as well as between Cabo Sam Jorge and the line of Tordesillas, appears conjectural,
as no names are shown and the drawing is conventional. Two distinctive features lay
eastward of Cabo sam Jorge: the golfo fremosso and rio grande, which were identified by Pereira (1975, p. 718) as, respectively, the gulf of Maranhão and the delta of
the Amazonas. At the mouth of Rio grande an inscription is shown reading: todo
este mar he de agua doçe (‘all this sea is of fresh water’).
As for the long stretch of coast from Porto Seguro to about 39° S, no trustable information came to us on any exploration voyages made in the region. The opinion of
Leite (1923, p. 268) is that the entire representation is conjectural and that the only
fraction of the coast where any landings took place, in the period 1500-1502, is the
one delimited by the two Portuguese flags, visited by Cabral’s fleet. Roukema (1963,
p. 23) accepts that the whole coast between the island of quaresma, in the north,
and Cabo de Sacta Marta might have been explored in the expedition of André Gonçalves (1501) and gives a probable chronology of the voyage33. Whatever the historical truth is, it is clear that no corrections were made to the original drawing in the
section laying south of the amendment, which might explain the latitude errors in
the placement of the new toponyms, written in cursive lettering. Concerning the unrealistic orientation of the coast to the south of Cabo de Sacta Marta, it is probably
the product of the imagination of the cartographer as no exploratory mission is
known to have reached the region. Rather than an attempt to drive the Spaniards to
think that the whole region was within the eastern side of the Tordesillas’ line, as
suggested by some authors34, the representation seems inspired by the Ptolemaic
30
Which was identified by Leite (1923, p. 275) as the island of Fernando de Noronha (ϕ=3° 51’ S), by
Roukema (1963, p. 22) as the Atol das Rocas (ϕ=3° 50’ S) and by Moacyr Pereira (1994, p. 712) as the
island of Santo Aleixo (ϕ=8° 37’ S).
31
Which Roukema (1963, p. 23) considers to be, either Ponta do Tubarão (ϕ=20° 17’ S) or Cabo de S.
Tomé (ϕ=22° S), and Moacyr Pereira (1994, p. 707) identifies as Cabo de Santa Marta Grande (ϕ=28°
37’ S).
32
The new toponyms are, in general, incorrectly placed on the chart and contain spelling errors that
point to an Italian origin of the author. See Pereira (1994, p. 711).
33
Roukema suggests a departure from Portugal in the Summer of 1501, the arrival to the Brazilian
coast in September, reaching the farthest south land in January 1502 (the Cabo Sacta Marta = Cabo de
S. Tomé?), discovering the quaresma island in March and returning to Lisbon in July 1502.
34
Mota (1977, p. 12-15) lists some charts of the beginning of the sixteenth century with a falsified
coast of Brazil, made with political purposes. However he is of the opinion that the Cantino plani-
140
conception of a closed world ocean35. If that is indeed the case, it seems hard to believe that it was copied from a Portuguese official pattern, which was supposed to be
free of fantasy and keep a reliable up-to-date register of the newly discovered lands.
In this section a systematic cartometric analysis of the Cantino planisphere is presented and discussed. Some of the results, concerning the representation of the
North Atlantic, were already presented in Chapter 4, for comparison purposes. The
text is structured in four subsections:
− In Scale measurements, the analysis made to some metric properties of the chart
related to the type of distance scales and the length of the degree of latitude
adopted in the representation is presented and discussed;
− In Meridians and parallels the geographical grid of meridians and parallels implicit in the representation, estimated on the basis of a sample of control points, is
presented and interpreted, with the purpose to quickly recognize the most important features of the chart, identify the areas where different charting methods
were used and make a first assessment of its cartographic accuracy;
− In Assessing the latitudes, the latitudes of a sample of control points measured
on the chart, are compared with the exact values. The results are presented in
the form of distributions of the errors with latitude and interpreted in the light of
the various sources, standards and charting methods that may have been used in
the compilation;
− In Assessing courses and distances a series of theoretical rhumb-line tracks connecting chosen control points is compared with the corresponding segments
measured on the chart, with the purpose of contributing to the identification of
the routes on which the chart is based and better identifying the charting methods used in each region.
sphere is free of such intentional mistakes and that the apparent positional errors are the result of the
navigational and charting methods of the time. On the contrary, Fernandes (1998, p. 25-6) suggests
that the errors in the positions of Greenland, Newfoundland and Brazil are part of a hoax aiming to
fool the Spaniards.
35
A more radical example of this conception appears in the world map of Lopo Homem (1519), considered to have been once part of the Miller Atlas, where a long strip of land starting in South America
and coming to southeastern Asia encircles the Atlantic and the Indian Oceans in an immense closed
lake. An apparently similar conception is shown in the known fragment of the Piri Rei’s map, of 1513,
with an extensive southern continent running from South America to about a longitude of 10° W,
where it reaches the right margin of the parchment. See also Pereira (1994, p. 715-16).
141
All measurements were made on a 1:1 high resolution digital image of the Cantino
planisphere.
Scale measurements
The Equator, tropical lines and Arctic Circle are depicted as straight lines, approximately parallel to each other, and making an angle of a little less than 1° degree with
the upper and lower margins of the chart. It has always been assumed that the spacing between these lines was approximately proportional to the corresponding latitude differences on the sphere, so that a linear scale could be inferred from their
locations. However, a careful measurement reveals that those distances are inconsistent with a unique scale of latitudes, as an error seems to have been made in the
placement of either the Arctic Circle or the tropical lines.
Table 5.1 – Spacing between the Equator, tropics and
Arctic Circle and corresponding values of R
Lines
∆ϕ
Equator – Tropic of Cancer
23.5°
Equator – Tropic of Capricorn 23.5°
Equator – Arctic Circle
66.5°
Spacing (mm)
205
204
554
R (mm)
8.72
8.68
8.33
Table 5.1 shows the average spacing between the Equator, the tropics and the Arctic
Circle, as determined on the basis of several measurements made in different locations of the sheets of parchment. For a perfectly linear scale of latitudes, the ratio R
between these lengths and the correspondent latitude differences (R represents the
length, in millimeters, of a degree of latitude on the chart) would be constant. That is
not the case, as the value of R in the tropical zone (8.70 mm, average) is significantly
larger than between the Tropic of Cancer and the Arctic Circle (8.33 mm). For the
latitude scale to be constant, either the Arctic Circle should have been drawn about
24 mm to the north of its actual position or both tropical lines should have been
placed 9 mm closer to the Equator. A possible explanation is that the cartographer
used a latitude difference of 24°, instead of 23.5°, between the Equator and the tropics. However the explanation is historically implausible and only accounts for about
half of the difference36. Assuming that the tropical lines are correctly placed relative
to the Equator, then the cartographer might have considered the latitude of the Arctic Circle to be 63.5° N, instead of 66.5° N, an easy mistake to make. But the alternative possibility, that the tropical lines are misplaced relative to the Equator, should
36
This approximation was used by Leite (1921, p. 234) when assessing the length of the degree in the
chart. However the correct value of about 23° 30’ was well known at the time the Cantino planisphere
was made, as admitted by the author. See also Note 40, below, on the calculations made by Leite.
142
also be considered. This issue is re-examined below, where the number of leagues
contained in each degree of latitude is estimated, and again, in ‘Assessing the latitudes’ (p. 150).
Figure 5.3 – Scale of leagues over the North Atlantic. The Cantino planisphere
has six scales of leagues, with a variable number of sections.
Figure 5.4 – The line of Tordesillas and the Cape Verde archipelago in the Cantino planisphere. According to the treaty celebrated between Spain and Portugal, in 1494, the dividing
line was supposed to pass 370 leagues westward of Cape Verde but no precise location was
defined.
The chart contains six distance scales with a variable number of sections, from 18 to
23 (Figure 5.3), assumed to represent Spanish leagues37. Except for some minimal
variations, all sections are of equal length, which was found to have an average value
of 5.85 mm. No explicit information is given in the chart on the number of leagues
contained in each section and on its relation with the length of the degree of latitude. However these elements can be estimated recalling that the demarcation line
37
That is, the leagues used by both the Spanish and Portuguese pilots in the Iberian Peninsula. See
Note 28 on Chapter 4, p. 104.
143
of Tordesillas was agreed to run 370 leagues to the west of the Cape Verde Islands
(see Figure 5.4). In the chart, the distance between the west-most tip of the Island of
Santo Antão and the line of Tordesillas is 180 mm, to which correspond 30.8 sections
of the scale of leagues38. The quotient 370/30.8 = 12.0 indicates that each section
has 12 leagues. This was also the result found by Leite (1923, p. 234) and later repeated by Costa (1983, p. 251) and other authors. Still, and as noted before (see
Chapter 2, p. 42-43; Chapter 4, p. 101), this type of division is not referred to in any
known historical source and its coexistence with the 12.5 standard would have
caused a serious ambiguity in the use of the charts. Also, and because all sections are
subdivided in five parts, to each one would correspond 12/5 = 2.4 leagues, a value
too awkward to be practical. It is not easy to reject this result though, as the dividing
line of Tordesillas is clearly depicted on the chart and its agreed distance from the
islands of Cape Verde, 370 Spanish leagues, is a well established historical fact. A
possible explanation is an error in the placement of this line, either made by accident
or purposefully, as a way to give the idea of a larger Portuguese area of influence in
the Atlantic. An alternative way of determining how many leagues are contained in
each section of the distance scales is to measure a series of distances on the chart
and compare the results with the corresponding values in other charts of the same
period. In Table 5.2 the distances between some chosen control points in the Atlantic, as measured in leagues on the Cantino planisphere and in other four charts of
about 1500, are presented. In the first case both alternatives, 12 and 12.5 leagues
per section, were considered. The shaded cells indicate the best matches.
Table 5.2 – Distances, in leagues, as measured in the
Cantino planisphere and in other charts
th
Reinel 15
cent. (1)
Aguiar
1492 (2)
Reinel ca.
1504 (3)
Average
(1)-(3)
Cantino
[12]
Cantino
[12.5]
C. S. Vicente – C. Fisterra
127
130
119
125
116
121
270
259
279
269
268
279
173
168
177
173
167
174
202
194
205
200
184
192
772
751
780
767
735
766
Tracks/charts
SUMS
The results are expressive: in average, the distances measured on the Cantino planisphere are comparable with the corresponding distances measured on the other
charts only when sections of 12.5 leagues are considered. If all averaged distances
are added (767 leagues, in the fourth column), the result closely approaches the cor38
As Leite (1923, p. 234), it is assumed here that the west-most limit of the archipelago was chosen as
origin in order to widen to the largest possible size the Portuguese area in the Atlantic.
144
responding value in the Cantino planisphere (766 leagues, in the last column). Without surprise, the numbers which are closest to Cantino’s are those of Reinel’s chart
of ca. 1504. One may then conclude, with some confidence, that the distance scales
of the Cantino planisphere use the same standard as all other charts of the same
period (12.5 leagues per section) and that the dividing line of Tordesillas is placed on
the chart about 7 mm to the west of its correct position39. Having settled this question, the determination of the length of the degree of latitude can now proceed on
the basis of the available information.
The first author to determine the length of the degree in the Cantino planisphere
was Leite (1923, p. 234), who found a value of 17.5 leagues. However, and in order to
arrive to this precise number, he had to round off the latitude difference between
the Equator and the tropics to 24°. If the correct value of 23.5° were used instead the
resulting length of the degree of latitude would have been 17.9 leagues40. In my
opinion Leite was driven by a strong conviction that the 17.5 module was adopted in
the construction of the chart because this is the standard more often referred to in
the historical sources. Probably for the same reason, the measurements and conclusions of Leite were cited by several authors after him and never contested. Now, and
recalling that the average length of one section of a distance scale is 5.85 mm and
that each degree of latitude measures either 8.70 mm or 8.33 mm, depending on
which reference is considered (the tropics or the Arctic Circle), the length L of a degree can be estimated either as 8.70/5.85 × 12.5 = 18.6 leagues (tropics are well
placed) or as 8.33/5.85 x 12.5 = 17.8 leagues (Arctic Circle is well placed).
It is not easy to interpret the value of 18.6 leagues per degree in the light of the historical sources, mostly because it is certain that astronomically-observed latitudes
were incorporated in the construction of the Cantino planisphere, which probably
implied the explicit adoption of one of the standards of the time. The value is close to
the ratios of 18.4 and 18.8 estimated, respectively, by Franco (1957, p. 162) and
Marcel Destombes (as cited by Franco, Ibidem, p.195), which indicates that these
authors have both considered scales of 12.5 leagues and used the spacing between
the tropics as a reference. A possible explanation for the adoption of this value is
that the model used for constructing the chart was some older pattern not based on
39
To be consistent with sections of 12.5 leagues, the distance between Santo Antão and the line of
Tordesillas should be about 173 mm, instead of 180 mm.
40
The average distance between the Equator and the tropics is about 204.5 mm, as shown in Table
5.1. Dividing this value by 24 degrees, one gets 8.52 mm per degree, instead of 8.70 mm. To the
180 mm separating Santo Antão from the Tordesillas’ line would then correspond 180/8.52 = 21.1
degrees of latitude. The length of each degree could then be estimated as 370/21.1 = 17.5 leagues. If
an angular distance of 23.5° between the Equator and the tropical lines were used instead, the resulting length of the degree of latitude would have been 370x8.7/180 = 17.9 leagues.
145
astronomical methods, and only representing the northern Atlantic area, later complemented with additional information from more actualized sources. The value of
17.8 leagues per degree is, on the other hand, a reasonable match with the module
of 18 leagues referred to by Duarte Pacheco Pereira in the Esmeraldo de Situ Orbis
(ca. 1505-8) and a more plausible choice of the cartographer. Additionally, it is close
to the value of 18.2 leagues found for ‘Reinel ca. 1504’, made shortly after the Cantino planisphere (see Table 4.4, p. 104).
It should be emphasized that the deformation of the parchment with age hardly explains the inconsistency of the spacing between the Equator, the tropical lines and
the Arctic Circle, because the process would have distorted all north-south lengths in
a more or less proportional way. However, a non-isotropic deformation might be
reflected in the value of the module, as the determination of the length of the degree was made on the base of north-south measurements, while all distance scales
but one, from which the length of the league on the chart is estimated, are east-west
oriented. Incidentally, this possibility can be easily checked by assessing the distortion of the two circular patterns of wind-roses, one centered south of the Cape Verde
and the other over the Hindustan Peninsula. The average horizontal and vertical radiuses of those patterns measure, respectively, 252.0 mm and 249.5 mm, to which
corresponds a difference of 1%. While the sign and value of this deformation cannot
account for the value of 18.6 leagues per degree found above41, it matches perfectly
the difference between the value of 17.8 leagues per degree and the historical
standard of 18 leagues per degree. This effect is easily understood if one recalls that
any enlargement of the horizontal dimensions of the chart makes the leagues in the
distance scales (which are horizontal) to appear larger, which results in fewer leagues
per degree of latitude (which are measured in the vertical).
The arguments produced so far seem to indicate that the second possibility (17.8
leagues per degree) is probably the correct one, from which we may infer that both
the tropics and the line of Tordesillas are incorrectly placed on the chart. This conclusion is to be revisited in the next subsection, when assessing the accuracy of the latitudes.
While it is not possible to determine the longitudinal extent of the Cantino planisphere with accuracy, it is certain that only about three quarters of the circumference of the Earth at the Equator are represented. Leite (1923, p. 235) found a value
41
To explain the value of 18.6 as a distortion of the 18 leagues per degree module, the average horizontal radius of the wind rose patterns would have to be 3% smaller than the average vertical radius,
as to make the leagues apparently larger. In fact, it is 1% larger.
146
of 257°, later repeated by other authors42. If an average value of 8.7 mm is used for
the length of the degree of latitude (see Table I), then the longitudinal extent can be
estimated as 2200/8.7 = 253°; for a degree of 8.33 mm, the longitudinal extent is
264°. However, these estimations only made sense if the scale along the Equator
were identical to the scale of latitudes, which is not necessarily the case43.
Another parameter referred to by some authors is the numerical, or nominal, scale of
the chart. Leite (1923, p. 235) considers two different numerical scales: the one determined by dividing the length of one degree of latitude on the chart by the corresponding distance on a spherical model of the Earth; and the one intended by the
cartographer, on the basis on his assumptions of the size of the Earth, which Leite
calls the ‘projected scale’44. While it is true that charts were drawn using a single
scale of leagues, this scale strictly applies only along certain routes, exactly the ones
which were used to construct a particular chart. And since the meridians are not
generally represented by straight vertical lines, such scale is also not applicable along
the north-south direction. Furthermore the concept of numerical scale, as applied to
a map, was foreign to the charting methods of the time. The pattern charts, from
which subsequent copies were made, were constructed as to use the whole surface
of the available sheets of parchment, with no previous considerations about the resulting numerical scale.
No meridians or parallels are depicted on the Cantino planisphere other than the
diving line of Tordesillas, the Equator, the tropics and the Arctic Circle. However, the
geographical graticule implicit in the representation can be revealed through the
georeferencing technique described in Chapter 3, on the basis of a sample of control
points. In the present study, it wasn’t always possible to establish a firm correspondence between the places depicted on the chart and in the modern maps, even when
a toponym exists. In some cases, the places are clearly identified in the chart, either
by their names (for example, Lixbonna = Lisboa) or by some obvious geographical
context (for example, the position of Cape Espichel, south of Lisbon). In some others,
42
This value was probably found on the assumption that a degree of latitude on the chart, as estimated on the basis of the spacing between the Equator and the tropics, which were considered to be 24
degrees of latitude apart, measured 8.5 mm instead of 8.7 mm (see Note 40).
43
Most authors have assumed that the chart is drawn on the cylindrical equidistant projection centered at the Equator (plate carrée), for which the lengths of one degree of latitude and longitude are
equal. Putting aside this assumption, which is obviously wrong, the question is whether distances
measured along the Equator are conserved or not. The answer is negative because that would only
happen, in theory, if the routes used to construct the chart were all taken along the Equator. In general, and for this type of representation, the average scale along the Equator is always less than the
scale inferred by the spacing between parallels.
44
Leite (Ibidem, p. 235) found a value of 1:12,820,000 for the first and 1:12,600,000 for the second.
147
more or less firm identifications were obtained from previous studies (for example,
the case of Rio do Infante, identified as the Great Fish River, in South Africa). In the
remaining cases, the identifications are considered as approximations and should be
used with care (for example, the Cabo de Sacta Marta in the southern coast of Brazil,
which has been identified as the Cape of Santa Marta Grande).
Figure 5.5 – Interpolated geographic grid of the Cantino planisphere. Meridians and parallels
are spaced five degrees. The rectangles identify the areas with major grid distortions. The
small red diamonds are the control points.
Figure 5.5 shows the grid of meridians and parallels interpolated using MapAnalyst,
on the basis of a sample of about 240 control points. The five rectangles, labeled A to
F, identify the areas with major distortions. From the visual inspection of the figure
one may conclude that:
− Parallels are approximately straight, east-west oriented and equally spaced, and
meridians are curves, making variable angles with the parallels. The exceptions to
this general rule are the Mediterranean and Black Sea, which appear rotated to
northwest by an angle of about 8° (rectangle A), and the Caribbean Sea (rectangle
E), where the gridlines are significantly distorted;
− The spacing between adjacent meridians generally decreases with latitude, grossly reflecting the convergence of meridians on a spherical Earth. In some areas,
their orientation appears locally distorted, as in northern Europe (rectangle B),
148
northeastern Africa (rectangle D), Caribbean Sea (rectangle E) and Brazil (rectangle F);
− The deformation of the grid in the Caribbean Sea (rectangle E) confirms what has
been mentioned before (see p. 138), that the representation of these regions was
copied from a larger scale source, as the spacing between meridians and parallels
is clearly inflated;
− The exaggerated longitudinal extent of the African continent causes the meridians in the area between the entrance of the Red Sea and the Mediterranean to
show an anomalous orientation (rectangle D). This distinctive feature of the Cantino planisphere is discussed below, when assessing the routes on the chart, and
also in the section ‘The enormous isthmus’;
− Both the meridians and the parallels are deformed in the region demarcated by
rectangle B (northern Europe). As for the orientation of the meridians, showing
an exaggerated convergence with latitude, it was already shown to be the result
of the placement of Greenland on the chart, which was plotted according to a
track with origin in some place in northern Europe (see Chapter 4, p. 117-18);
− The deformation of the meridians near the eastern coast of Brazil (rectangle F) is
certainly the result of a longitudinal misplacement of the quaresma island on the
chart, which has been identified in this study as the island of Santo Aleixo;
− The deformation of the parallels in the southern coast of Africa (rectangle C) may
be caused, either by the misidentification of some control points or by latitude
errors introduced in the construction of the chart. This subject is further discussed below, when assessing the latitudes.
Figure 5.6 depicts a new version of the interpolated grid of meridians and parallels,
based on a corrected sample of control points, from which some places known to be
misplaced on the chart were excluded: all points located in the Caribbean Sea (excepting Trinidad), due to the obvious scale exaggeration of the area, and the island of
quaresma, in the Brazil, due to its longitudinal error. This procedure is justified by the
fact that those points do not add any useful information to the grid, in which its main
geometric features are concerned. Still, it should be stressed that the more regular
aspect of the new graticule, in the northern and western parts of the chart, is mainly
due to the scarcity of control points rather than to its intrinsic cartographic accuracy.
On the other hand, this new version emphasizes the regular east-west orientation of
the parallels in most of the area and makes clearer how the convergence of the meridians is reflected into the chart’s geometry. It is interesting to note that the lengths
149
of the parallels in the Atlantic are approximately proportional to the cosine of their
latitudes, as in the spherical surface of the Earth and in the Flamsteed projection45.
Figure 5.6 – Interpolated geographic grid of the Cantino planisphere for a corrected set of
control points, from which positions known to be wrongly placed on the chart were excluded. The small red diamonds are the control points. Compare with Figure 5.5.
Some preliminary conclusions can already be drawn from this analysis. First, that the
coasts of Africa and Brazil, are probably depicted according to observed latitudes,
while the Mediterranean and Black Sea, as well as Central America, are represented
on the basis of magnetic courses and estimated distances. As for the representation
of the Atlantic European coasts, it was already concluded in Chapter 4 that no astronomical surveys were probably made in those areas up to 1502, from which it may
be inferred that they were copied from an older pattern. This conclusion is to be confirmed below, when assessing the accuracy of the latitudes.
45
In the Flamsteed, or sinusoidal projection, the parallels are straight and equally spaced, and the
meridians are sinusoids, cutting the parallels in a way that all east-west distances are conserved. As
noticed by Barbosa (1938b, p. 246-48) this representation would be expected if the chart were constructed on the basis of a series of east-west tracks, represented with a constant scale, complemented
with a north-south track, at the longitude of Lisbon.
150
While it is certain that extensive parts of the Cantino planisphere were surveyed by
astronomical methods, no systematic assessment of the latitudes was ever done and
some doubts remain about the exact areas where such techniques were applied. To
assess the accuracy of the latitudes on the chart a sample of about 150 control points
was used, covering the regions where navigational astronomy is known, or supposed,
to have been utilized. That is the case of Europe (excluding the Mediterranean), Africa, the Atlantic Islands, the coast of Brazil and part of the central and northern America. Also excluded is the representation of Central America and the Caribbean Sea,
for the reasons invoked in the previous subsection.
Figure 5.7 – Distribution of the latitude errors in the Atlantic for a degree of latitude of
8.70 mm (top) and 8.33 mm (bottom). The shaded areas contain the points with errors of less
than one degree. The slopes of the regression lines are proportional to the scaling errors. A
positive slope (line going from bottom left to top right) indicates a positive scaling error.
Two methods were used to determine the latitudes on the chart: the measurement
of the north-south distances, in millimeters, between the control points and the
151
Equator, whose values were divided by the length R of the degree of latitude (see
Table 5.1); and the overlapping of a digital ruler graduated in degrees of latitude on
the image of the chart. This later procedure proved to be accurate enough and the
most convenient in the majority of the situations. To take a measurement, the ruler
was put on the vertical line containing the point of interest and its position was adjusted as to make its origin to coincide with the Equator. To compensate for some
visible distortions, the ruler was sometimes rotated as to become approximately
normal to the Equator, and the length of the degree was locally adjusted46. However,
some uncertainty couldn’t be avoided as it was not always possible to make a perfect
adjustment.
Annex B contains all latitude errors, in degrees. Figure 5.7 shows their distribution in
the Atlantic, excluding Brazil and North America. The data are organized in categories, according to location: North Atlantic, from Iceland to the south of Portugal, including Greenland and Newfoundland (red circles); Azores (orange squares); Africa
NW, from the strait of Gibraltar to the Equator (green triangles); Madeira and Canary
Islands (yellow circles); Cape Verde (yellow squares); Africa SW 1, from Cabo Lopez to
Cabo Negro (red circles); Africa SW 2, from Cape Cross to Dreimasters Ridge (blue
diamonds); and Africa S, from Saint Helen Bay to Great Fish River (red triangles). These categories were further grouped in four classes, according to their apparent scaling error, and a regression line was determined for each. The shaded area contains
the control points with errors of less than one degree. Two different sets are illustrated: one corresponding to the a degree of latitude of 8.70 mm, based on the spacing between the Equator and the tropical lines (top), and the other, to a degree of
latitude of 8.33 mm, based on the spacing between the Equator and the Arctic Circle
(bottom).
If the region to the north of 40° N is excluded, the second version is clearly superior
to the first in terms of the overall latitude errors. This is more noticeable in the
southern coast of Africa (between 30° S and 35° S), where the average error changes
from about 2.7° to 1.4°. In the African coast to the north of the Equator, known to
have been surveyed in the fifteenth century using astronomical methods, the average value of the error is small in both cases but its variation with latitude is close to
zero in the second version (the same happens in the southeastern coast of Africa,
whose data are shown in Figure 5.12). This suggests that the linear scale of latitudes
adopted in the chart may have been established using the places in the region as a
reference. Taking into account the conclusion reached in Chapter 4, that the repre46
The local adjustments of the digital scale of latitudes were made as to always conserve the latitudes
of some horizontal lines of the chart, known to be east-west oriented. These lines include the Equator,
the tropics and some of the rhumb-lines of the wind-rose system.
152
sentation of northern Europe in all five charts was based on traditional nonastronomical patterns, it is now possible to conclude that the position of the Arctic
Circle is correct and a value of 8.33 mm is to be accepted as the length of one degree
of latitude. A consequence of this result, following the discussion initiated in the previous section, is that the module adopted in the Cantino planisphere is indeed the
one referred to by Duarte Pacheco Pereira ca. 1505: 18 leagues per degree47.
Figure 5.8 – Distribution of the latitude errors in the North Atlantic
(Europe and Azores).
Figure 5.9 – Distribution of the latitude errors in the North Atlantic (Africa).
47
This result takes into account the anisotropic deformation in the left-right and top-bottom directions, which accounts for the difference between the values of 17.8 leagues per degree found before
and the historical module of 18 leagues per degree (see explanation in p. 145-46).
153
Having clarified which length of the degree and version of the error distribution are
to be accepted, it is now possible to proceed with the analysis of the data. The error
distribution shown in Figure 5.7 clearly reveals that the coastline depicted in the Cantino planisphere is a piecewise construction based on information compiled from
different sources, with different scales and accuracies. Also, there is no continuity in
the regression lines from one zone to the other (with the exception of Europe),
which suggests a poor precision in the adjustment of the various parts. Figure 5.8
illustrates the distribution of the latitude errors in the North Atlantic and Azores
group, for a degree of 8.33 mm. A scaling error of about 15% affects most latitude
values, with the exception of Iceland. This means that the representation of the area
was copied from a non-astronomical pattern, where the implicit length of the degree
of latitude was close to 20 leagues. As for the small error associated with the representation of Iceland, it does not necessarily implies that astronomical observations
were made in the region.
Figure 5.9 represents the distribution of the latitude errors in the northwestern coast
of Africa, where the astronomical survey was made, and the Atlantic islands of Madeira, Canary and Cape Verde. Notice the relatively small scaling error and dispersion.
Figure 5.10 – Distribution of the latitude errors in the southwestern and
southern coast of Africa. The blue diamonds correspond to the fraction
of the coast visited by Bartolomeu Dias in 1487-88. The cluster of red
triangles corresponds to the southern coast of Africa.
Figure 5.10 shows the distribution of the latitude errors in the southwestern and
southern coast of Africa, from the Equator to about 35° S. Three sets of control
154
points are shown: the red circles symbolize the western coast, from the Equator to
about 16° S, first surveyed by Diogo Cão in two exploration voyages, from 1482 to
1486; the blue diamonds, the section of the coast between Cape Cross (21.8° S) and
about 27.5° S, known to have been explored by Bartolomeu Dias in 1487-8848; and
the red triangles represent the southern African coast, from St. Helen Bay (G. Sta
ellena) to the Great Fish River (Rio do Infante), explored by Bartolomeu Dias, in 1498,
and by the ships of Vasco da Gama and Álvares Cabral, in 1497-150049 (see also Figure 5.11).
Figure 5.11 –The African coast in the Cantino planisphere from Pelican Point in the west, to
Cabo das Correntes, in the east.
The examination of the error distribution suggests that two distinct sources were
used: one for representing the region explored by Diogo Cão (Africa SW 1) and the
southern coast of Africa (Africa S), and the other for representing the stretch of coast
visited by Bartolomeu Dias (Africa SW 2). In the first group, the distribution of the
error indicates a scale about 6% smaller then the scale of the chart, which suggests
48
Bartolomeu Dias sailed away from the coast due to bad weather or contrary winds, in 8 January
1488, and made a large anticlockwise turn before heading north and reaching the coast again, near
Mossel Bay (34° 13’S; 22° 11’E).
49
Bartolomeu Dias reached the eastern-most point of its exploration voyage in April 1488, near Great
Fish River, and then turned back surveying the southern and southwestern coast of Africa up to Luderitz Bay, where he returned to Lisbon. Vasco da Gama first touched the western coast of Africa at St.
Helen Bay, in 8 November 1497, where he made careful astronomical observations and then proceeded to the eastern coast and to India.
155
that the source from which this part was copied was based on a degree of 16 2/3
leagues (16.7/17.8 = 0.94). Nevertheless it is somehow surprising that the latitudes
of the southern coast of Africa, which were well known at the time the chart was
made, are represented with so little accuracy50. As for the second group, the exaggeration of the scale is so large (76%) that the only logical explanation is that a gross
mistake was made by the cartographer when transferring this fraction of the coast to
the chart. If the scaling error were compensated for, by removing the trend of the
data, the resulting latitude errors would be quite small, which is an indication that
accurate astronomical observations were made.
Figure 5.12 – Distribution of the latitude errors in the eastern coast of Africa
and western coast of Hindustan.
Figure 5.12 shows the distribution of the errors in the eastern coast of Africa, from C.
Santa Maria (25° 58’ S) to Bab-el-Mandeb (12° 26’ N), at the entrance of the Red Sea
(Africa SE and Africa NE, in the figure), and also for the western coast of Hindustan,
between Kochi (9° 56’ N) and Angediva (14° 45’ N) (Indian Ocean, in the figure). For
the first series (red circles), the average error and scaling error are both close to zero.
The dispersion is also relatively small, with the exception of the two control points at
about 8° S and 9° S (Quillua, present Kilwa, and Mafia Island). In the second series,
the values of the error concentrate between -0.5° and -1.3°, indicating a slight
southward displacement in the representation of the region. In the Hindustan Peninsula, only the places known to have been visited by the Portuguese up to 1502 were
50
According to the chronicler João de Barros, accurate latitude measurements using a large astrolabe
mounted on land are known to have been made by Vasco da Gama in St. Helen Bay, in 1487 (Barros,
1932, p. 280). In 1502, when the Cantino planisphere was made, the latitude of the Cape of Good
Hope was known with accuracy better than 0.5°.
156
considered: Angediba (Angediva Island, 14° 45’ N), Calicut (Calecute, 11° 15’ S) and
Coçim (Kochi, 9° 56’ S). The dispersion of the errors is a little larger than in the other
two groups of data.
Figure 5.13 – Distribution of the latitude errors in the coast of Brazil (red circles) and
Caribbean Sea (yellow squares).
Figure 5.13 illustrates the distribution of the latitude errors in Central America and
Brazil, from Florida (about 25° N) to C. Santa Marta Grande (about 29° S). Only the
fraction of the coast situated between Cabo de sam Jorge (present Cabo Branco) and
Porto Seguro, known to have been visited by the fleets of Álvares Cabral and João da
Nova, have latitude errors less than one degree. As for the northern coast of Brazil
and the Caribbean Sea (with the exception of Trinidad), the results clearly show that
the area was not surveyed with astronomical methods, as most errors are larger than
eight degrees. Also, the fact that their values strongly increase with the latitude is a
confirmation that this section was copied from a representation with a much larger
scale51. According to Mota (1973, p. 10), the exceptional small error for the island of
Trinidad is probably a coincidence52.
Using the methodology introduced in Chapter 3, a series of idealized rhumb-line
51
Mota (1973, p. 10) indicates a scale exaggeration of 50%. A larger value, of the order of 70%, is
suggested by the data in Figure 13.
52
Mota suggests that the effect of the magnetic declination, during Columbus’ trip from Cape Verde
to the coast of Venezuela, may have been compensated for by a strong equatorial current.
157
tracks were compared with the corresponding routes on the chart. Two types of
comparisons are presented: between individual tracks connecting pairs of control
points, with the purpose of determining the corresponding charting methods; and
between sets of tracks, with the purpose of identifying the routes used to draw the
chart. Some of these routes are known, such as the ones followed by Vasco da Gama,
from Cape Verde to Calecute (India), by Pedro Álvares Cabral, from Cape Verde to
Porto Seguro, and by Columbus, from the Canary Islands to Cuba and from Cape
Verde to Trinidad. In such cases, it is expected the analysis to confirm that those
routes were indeed used in the construction of this particular chart. Others are uncertain, as it is the route to Cape Farvel (Greenland) and to Cape Race (Newfoundland), or the tracks connecting the Atlantic islands.
Table 5.3
Courses and distances along tracks
From Lisbon to the Atlantic, Cuba and the Mediterranean
Track
C0
Cm
C1
D0
Dm
D1
271
272
273
14.1
--
15.6
Terceira - Madeira
126
126
131
10.0
10.1
10.8
174
175
174
22.3
22.2
22.8
229
226
231
8.6
8.1
9.7
164
158
163
5.3
5.4
5.2
202
200
200
17.4
17.2
16.7
Madeira – Punta Tarifa
072
068
073
10.1
8.6
10.8
Gran Canaria – São Nicolau
216
214
215
13.8
13.3
12.9
356
354
353
13.7
13.8
15.1
292
298
300
20.2
16.1
14.7
314
320
327
30.8
28.0
26.6
340
342
345
12.1
12.0
8.7
253
262
264
12.8
28.1
10.6
333
341
003
23.6
22.3
21.3
293
299
303
20.6
16.2
17.8
Punta Tarifa – C. Carbonara
076
069
072
12.4
8.7
14.5
C. Carbonara – Alexandria
115
108
106
18.5
25.2
22.1
Gran Canaria – Cuba
262
261
273
54.0
49.2
56.7
In Tables 5.3 and 5.4, the following quantities are shown, for each track:
158
− The theoretical rhumb-line courses and distances C0 (true course), D0 (true distance), Cm (magnetic course) and Dm (equivalent distance), as defined in Chapter
3 (p. 69);
− The course and distance in the Cantino planisphere, C1 and D1, as estimated
measuring the length and the direction of the segment between the two control
points, and converting it to degrees using the ratio R = 8.33 millimeters per degree53.
In the analysis of the results the typical cases defined in Chapter 3 (p. 70-71), concerning the comparison between the theoretical values and those measured on the
chart, were considered. Table 5.3 shows the quantities defined above for the North
Atlantic, Caribbean Sea and Mediterranean areas. The first eight lines refer to the
tracks connecting Lisbon (C. Espichel) and Punta Tarifa to the Atlantic islands of
Azores (Terceira), Madeira, Canary Islands (Gran Canaria) and Cape Verde (São Nicolau). It is interesting to notice how, in the majority of the cases, C0 and D0 best approach C1 and D1. As already mentioned in Chapter 4, where the results for the whole
set of early Portuguese charts are presented, this is an indication that the courses
were observed in a time when the magnetic declination was smaller, probably in the
beginning of the fifteenth century. Having already concluded that the northern Atlantic is represented in all of them using the portolan-chart model, this result was
expected. Some small differences between the routes measured on the chart and the
corresponding spherical tracks are due to the impossibility of conserving all relative
positions when representing the tracks in a plane. That is the case of the line connecting Terceira to Madeira, which appears rotated clockwise from its true orientation due to the fact that both Madeira and Terceira were represented according to
the courses and distances as measured from Lisbon (see Figure 3.14). Others are the
result of the scale exaggeration to the north of 35° N, which was previously detected
from the spacing between interpolated parallels (see Tables 4.3 and 4.4, in Chapter
4), from the distances measured in the northern Atlantic (Table 4.5) and from the
distribution of the latitude errors (Figure 5.8). That is the case of all distances measured from C. Espichel, which show an exaggeration of about 10% relative to the theoretical values. Not knowing with sufficient accuracy the spatial distribution of the
53
A different solution was adopted in Chapter 4, where the conversion from leagues to degrees in the
North Atlantic was made on the basis of the latitude-varying parameter R’ (estimated from the interpolated graticule), with the objective of making these distances comparable with those measured on
the charts of the fifteenth century. Here, it was considered more convenient not to mask the scaling
errors introduced in the compilation of the chart.
159
magnetic declination in the area at the time the information was collected54, no finer
interpretation of the results is possible.
In the second group, seven tracks connect C. Espichel and Terceira to Greenland (C.
Farvel) and Newfoundland (C. Race). These were already analyzed in Chapter 4 (p.
116-18), where it was concluded that while the position of Greenland was plotted on
the chart relative to some place in northern Europe, Newfoundland was represented
according to a track with origin in the Azores (Figure 4.12). The comparisons made
with the various theoretical alternatives have also shown that the method of the
point of fantasy was used in both cases. Concerning the representation of Greenland
in ‘Cantino’ and ‘Reinel ca. 1504’, it seems obvious that different sources and methods were used in the two charts, probably resulting from a new exploratory mission
sent to the region. The possibility of the position of Newfoundland having been manipulated for political reasons, so that it appeared on the eastern side of the Tordesillas diving line, seems unnecessary for explaining the relatively small difference between the measured (17.8°) and the theoretical distance (20.6°), given the scale variations of the chart and the inaccuracy of the estimation process.
The next two tracks in Table 5.3 connect Punta Tarifa, near the Strait of Gibraltar, to
Alexandria, in the Mediterranean. Contrarily to the Atlantic tracks, where the values
of the magnetic declination all refer to 1500, the year of 1300 was chosen as the reference date for this case. This is justified by the fact that most portolan charts up to
about 1600 show a counterclockwise tilt of 8° to 9°, which is comparable to the average value of the magnetic declination in 1300 in the region (see Chapter 4, p. 98-99).
Though a perfect match was not achieved for this group of tracks, especially in the
one connecting C. Carbonara to Alexandria, the results confirm that the method of
the point of fantasy was used for representing the Mediterranean. The significant
differences between the distances measured on the chart and the theoretical ones,
of more than 10%, indicate that the length of the Mediterranean is exaggerated,
probably as a result of a poor conversion between the distances units used in the
Mediterranean and in the Atlantic55. As for the track connecting Gran Canaria to Cuba, representing the route followed by Columbus in 1492, the large difference between the theoretical course and the one measured on the chart reflects the fact,
already mentioned in this chapter, that the representation of the Antilles was copied
from a larger scale chart and that they were placed much to the north of their correct position. Though it is not possible to draw detailed conclusions about the chart54
The estimates yielded by the geomagnetic model of Korte and Constable (2005) are considered not
to be accurate enough due the relatively small values and variation during the fifteenth century.
55
This subject was addressed in Chapter 4 (Table 4.5), when assessing the metric length of the mile
from distances measured in the Atlantic and the Mediterranean.
160
ing method of the original source, it seems certain that no astronomical methods
were used.
Figure 5.14 illustrates some of the tracks presented in Table 5.3. The green lines and
circles represent the tracks measured on the chart; the black lines represent the theoretical tracks as determined using the method of the point of fantasy (triangles and
squares) or the set point method (circles and squares). The same conventions presented in the last chapter for constructing Figures 4.12 and 4.13 (p. 116) were adopted: a theoretical track using the set point method was represented according to the
exact latitude of its end point, as measured in the latitude scale of the chart, and the
magnetic course relative to its origin; a theoretical track using the method of the
point of fantasy was represented according to the magnetic course and distance (in
leagues) relative to its origin, where the conversion from degrees to leagues was
made using the module of the chart, R = 17.8 leagues per degree. There is an important difference between the two representations though: while in Figure 4.12
individual tracks where compared by aligning the two corresponding start positions,
in Figure 5.14 all tracks are connected in an ordered sequence, with origin in C. Espichel. Rather than identifying the charting method used in each individual track it is
the objective of this representation to help clarifying what composite routes were
used in the construction of the chart. Concerning the area covered by Table 5.3 (the
Atlantic and the Mediterranean), there is reasonable agreement between the theoretical composite tracks and the corresponding routes on the chart. Some obvious
discrepancies, like the positions of Cuba and Alexandria, are explained by the scaling
errors of the chart. Others are probably the result of the difficulty in identifying the
exact tracks used in the construction of the chart, like in the position of C. Farvel, or
the uncertainty in the values of the magnetic declination. Notice that a good match
between some theoretical track and the corresponding segment measured on the
chart doesn’t necessarily imply that the two points coincide in the representation
because errors are cumulative in the composite routes. That is the case, for example,
of C. Farvel, whose final position is affected by the differences in the tracks ‘C. Espichel – Slea Head’ and ‘Slea Head’ – Iceland’.
Table 5.4 contains the information relative to the tracks connecting Cape Verde (S.
Nicolau) to the Americas, Africa and India. The first entry refers to the route followed
by Pedro Álvares Cabral in 1500, from Cape Verde to Porto Seguro. The numbers eloquently confirm that the set point method was used to place the coast of Brazil on
the chart, contradicting the theory that a purposeful manipulation was made as to
show a larger area of the newly discovered land in the Portuguese hemisphere. It is
also interesting to notice that this good agreement between the theoretical and the
161
Figure 5.14 – Tracks measured on the chart versus theoretical routes. The triangles represent positions determined with method of the point of fantasy; the circles (course prevails) and squares (distance prevails), with the set point method.
162
charted track only occurs when the observations of the magnetic declination made
by D. João de Castro in 1538, which are significantly different from the ones yielded
by the geomagnetic model, are considered (see Figure 5.14). The track ‘S. Nicolau –
Trinidad’ refers to the second voyage of Columbus, made in 1494, between Cape
Verde and the coast of Venezuela. As noticed earlier, the small latitude error in the
position of Trinidad cannot be taken as an indication that astronomical methods
were used. However, the better agreement between the theoretical and the charted
tracks, when compared with the one connecting Gran Canaria to Cuba, suggests that
the representation of the Venezuelan coast was imported from a different source.
Table 5.4
Courses and distances along tracks
from the Canary Islands and Cape Verde to the Americas, Africa and India
Track
C0
Cm
C1
D0
Dm
D1
São Nicolau – Porto Seguro
São Nicolau – Trinidad
Porto Seguro – C. Good Hope
204
264
109
199
261
10
195
262
107
36.0
36.0
54.7
34.9
35.2
94.7
35.9
40.8
61.8
São Nicolau – C. Palmas
C. Palmas – Ilhéu Rolas
Ilhéu Rolas – C. Negro
126
107
161
162
127
103
157
157
126
104
158
161
20.4
14.9
16.6
19.6
21.0
19.4
17.0
20.2
23.6
18.8
17.6
18.8
C. Correntes – I. Moçambique
I. Moçambique - Malindi
Malindi – Mogadishu
Mogadishu – C. Guardafui
C. Guardafui – Bab-el-Mandeb
111
079
056
036
029
357
045
031
274
105
075
054
038
034
003
051
037
280
086
074
060
046
031
003
043
047
269
1.3
5.4
1.9
10.6
10.3
11.8
7.4
11.4
7.8
1.8
4.2
1.9
10.8
10.9
11.8
8.2
12.3
3.6
1.6
6.0
2.8
8.8
11.2
11.8
5.9
15.0
6.3
Malindi - Calecute
068
075
071
38.3
56.6
41.4
The long route between Cape Verde (São Nicolau) and Bab-el-Mandeb, at the entrance of the Red Sea, comprising thirteen individual tracks, is the most difficult to
analyze. Two reasons explain why: first, the historical observations of the magnetic
declination made by D. João de Castro in 1538 do not fully cover this area and the
values yielded by the geomagnetic model are probably far from reality; and second,
the quality of the representation is variable, as seen during the assessment of the
latitudes. However, and having already concluded that the coast of Africa was represented according to astronomically-observed latitudes, no detailed comparison between individual tracks is justified, except when there is some doubt about what
163
modality of the set point method was used (latitude and course or latitude and distance)56. More important is to be able to confirm that the representation of the African coastline, as a whole, is well reproduced with the set point method, using these
particular routes.
In Figure 5.14 two series of tracks are shown connecting Cape Verde (S. Nicolau) to
the Cape of Good Hope: one along the western coast of Africa and the other through
the coast of Brazil (Porto Seguro). In the second option two modalities of the set
point method were considered in the track connecting P. Seguro to C. Good Hope:
latitude and course (white circles), and latitude and distance (white squares).
It is clear from the figure that the geometry of the African coast is better reproduced
with the first series of tracks, although there is a slight longitudinal displacement
between the theoretical routes and those of the chart. This is easily explained by the
high sensitivity of the simulation to small differences in the values of the magnetic
declination in the two tracks connecting São Nicolau to I. Rolas. For example, a difference of only 2° in the course between C. Palmas and I. Rolas causes a longitudinal
displacement of this last point of about three equatorial degrees, making the whole
route connecting I. Rolas to C. Good Hope to be displaced by the same amount. As
emphasized in Chapter 3 (p. 64-66), there is a considerable uncertainty in the estimation of the magnetic declination for the points located in the Gulf of Guinea, which
include C. Palmas and I. Rolas. The good overall agreement between the theoretical
routes and those measured on the chart along the western coast of Africa may be
taken as an indication that the estimated values of the magnetic declination for the
area are not too far from the correct ones.
Most individual tracks of the following group, connecting C. Good Hope to the entrance of the Red Sea (Bab-el-Mandeb), show considerable differences from the corresponding theoretical tracks, making the overall orientations of both routes to diverge along the eastern coast of Africa. The effect is better perceived if the longitudinal positions of C. Good Hope are forced to coincide, as illustrated in Figure 5.15.
The figure depicts four sets of tracks: the one measured on the chart (green circles)
and three versions of a theoretical route with origin in the C. Good Hope, depending
on the distribution of the magnetic declination: magnetic declination zero everywhere (crosses); using the values yielded by the model of Korte and Constable (2005)
for the year 1500 (red triangles); and using the values observed by D. João de Castro
in 1538, as discussed in Chapter 3 (white circles) (see Table 3.2). There are some
56
As noted before, it is doubtful that estimated distances were used in the making of the chart, as the
magnetic courses were a much more useful navigational element of information than the distance.
However, such solution may have been adopted when courses were very close to East or West.
164
slight differences between this representation and the one in Figure 5.14, beyond
the longitudinal displacement of the tracks, which are caused by the deformations of
the medium in the Cantino planisphere. However these differences are minor and
don’t affect the outcome of the analysis.
15
C. Guardafui
10
5
Muqdisho
0
Malindi
Distance N-S
-5
-10
Moçambique
-15
-20
C. Correntes
-25
-30
-35
-40
0
5
10
15
20
25
30
35
40
Distance E-W
Theoretical (João Castro)
Cantino
Theoretical (no dec)
Theoretical (CALC7K2)
Figure 5.15 – Comparison between three theoretical routes connecting the
Cape of Good Hope to Cape Guardafui and the corresponding route measured
on the Cantino planisphere (green circles). All sets have been aligned in longitude at the position of Cape of Good Hope (west-most point).
Two important facts are revealed by the comparison between the four routes in the
figure: the considerable relevance of the magnetic declination when simulating the
orientation of the coast; and the superiority of Castro’s observations over the results
of the geomagnetic model. It is worth noticing how the values yielded by the model
produce the worst result of the three. A close examination of the data reveals that
most of the divergence between the theoretical set of tracks adopted here (white
165
circles) and the corresponding route on the chart (green circles) is generated between C. Agulhas and C. Correntes, mainly due to an exaggeration of the longitudinal
distances on the chart, and between Mogadishu and C. Guardafui, due to a large difference in the courses. In this last case, the likely reason for the divergence is the
undervaluation of the magnetic declination in the area57. In the next section, ‘The
enormous isthmus’, this subject is re-examined in a broader context. The next and
last track connects Malindi, in the eastern coast of Africa, to Calecute, in the coast of
Malabar. In this case, there is a good match between the course and distance measured on the chart and the theoretical values of Cm and D0, suggesting that either the
method of the point of fantasy was used or that the set point was amended by the
estimated distance. Since the latitude error of Calecute is small and this track has a
long east-west component, making any error in the course to strongly affect the position of the set point, the last possibility is probably the correct one.
The enormous isthmus
One of the most distinctive features of the Cantino planisphere is the enormous size
of the Isthmus of Suez. Three factors contribute to this apparent distortion: the
width and orientation of the Red Sea; the width and orientation of the Mediterranean; and the longitudinal extent of the African continent at the latitude of Cape Guardafui.
The representation of the Red Sea in the Cantino planisphere is certainly of Ptolemaic origin, as the first exploratory missions in the region only occurred during the sixteenth century, well after the chart was made. Its traditional shape and orientation,
as represented in the Ptolemaic mappae mundi of the fifteenth century, appears to
have been pasted directly into the chart, making the distance between its northern
tip and the Mediterranean to appear much larger than it should. Regarding the width
and orientation of the Mediterranean, Pedro Nunes writes in 1537 (Nunes, 2002, p.
136):
[…] the charts seem to be different from the tables of Ptolemy, because he puts
sixty three degrees and a half from the meridian of Canarias to the end of Africa
[…] where Pelusio is, which is a mouth of the Nile in the strait of land that lies
between the two seas […]. But in the charts there are no more than fifty two
degrees, and because of this, as well as because the end of this coast of the Le57
The average orientation of the eastern coast of Africa in some Portuguese charts of the sixteenth
and seventeenth centuries, between Cape Agulhas and Cape Guardafui, was measured and compared
with the theoretical value, in the Mercator projection. The results show systematic differences of the
order of ten degrees in the charts of the sixteenth century, decreasing to about six degrees, in the
charts of the seventeenth.
166
vant is too high on the charts, which is thirty six degrees of height […] when it
should be thirty one, this strait of land, to which we call in cosmography Isthmus, appears enormously large, being a little more than thirty leagues, as represented by Ptolemy, who lived in Alexandria […]58
Figure 5.16 – The Red Sea and the Isthmus of Suez in the Cantino planisphere. Inside the
blue rectangle the exercise of Pedro Nunes to reduce the size of the isthmus, by displacing
Pelusio ten degrees to the east and five degrees to the south (Nunes, p. 136), is illustrated.
Pedro Nunes gives two reasons for the exaggerated size of the isthmus, as shown on
the charts of his time: the latitude errors in the representation of the Mediterranean;
and its small length, when compared with Ptolemy’s standard. Regarding the length
of the Mediterranean, he recognizes that the charts were correctly drawn for navigational purposes because those fifty two degrees are (contrarily to those used by
Ptolemy) equatorial degrees, to which correspond about 900 leagues (Ibidem). He
then proceeds with a conceptual exercise in which the position of Pelusio, at the
mouth of the Nile, is shifted 10 degrees to the east, to compensate for its longitude
58
The original text reads: as cartas parecem que são nisto diferentes das tauoas de Ptolomeu: porque
elle põe sesenta e três grãos e meo do meridiano das Canarias ao fim de Africa em leuante onde esta
pelusio: que he ua boca do Nilo […] que jaz entre os dois mares […] mas nas cartas nam há mais que
cinqoeta e dous graos: e assi por isto: como por esta costa de leuante: no fim della estar nas cartas
muyto alta: que he em trinta e seys graos da altura a costa de África auedo de ser trinta e hu: fica este
estreyto de terra:, a que chamamos em cosmografia Ismo: descompassadamente grande: sendo ele
pouco mais que de trinta legoas como parece per Ptolomeu que viuia em Alexandra […].
167
error, and then 5 degrees to the south, to compensate for its latitude error. The result is illustrated in Figure 5.16, where P1 and P2 are, respectively, the initial and the
corrected positions of Pelusio in the Cantino planisphere. Pedro Nunes correctly addresses two of the reasons for the exaggerated size of the isthmus in the charts,
namely the need to conserve the distances between places in the east-west direction, which makes the meridians to converge, and the existence of large latitude errors in the representation of the Mediterranean, causing its eastward limit to be
shown to the north of the correct position. However he fails to identify the most important reason, which is the effect of the magnetic declination on the geometry of
the charts.
Before proceeding with the analysis of the second factor mentioned in the beginning
of this section, the longitudinal extent of the African continent, it is still necessary to
clarify what should exactly be understood as an ‘exaggerated longitudinal extent’ in
the present context. In other words, to what kind of representation should the distances measured on the Cantino planisphere be compared in order to quantify the
distortions? Like Pedro Nunes, who referred to the length of the Mediterranean
measured in equatorial degrees when citing the Ptolemaic standard, I think that one
appropriate reference is the plate carrée projection, in which meridians and parallels
are straight and equidistant, forming a square graticule. A longitudinal distance on
the chart is then considered to be ‘exaggerated’ when its value is larger than the
spacing between the corresponding meridians in the plate carrée. An alternative reference is the Flamsteed projection, in which the meridians are curves and distances
are conserved along all parallels, there represented as equidistant straight segments.
A longitudinal distance measured on a chart is then considered to be ‘exaggerated’
when its value is larger than the corresponding distance measured on the Flamsteed
projection. The relevance of this second assessment comes from the fact that, as
mentioned by Pedro Nunes, charts should conserve distances between places in order to be useful for navigation.
In Figure 5.17, the geographic area comprising the eastern Mediterranean, the Red
Sea and the Persian Gulf is represented in two different projections: the plate carrée
(left) and the Flamsteed projection (right). In both representations an outline of the
Cantino planisphere was overlaid, so that the position of Lisbon and all parallels were
forced to coincidence. The red and the green circles represent, respectively, the positions of two places (C. Guardafui and Alexandria) in the projections and in the Cantino planisphere. The crosses and white circles represent the positions of the same
two places as determined using the theoretical routes with origin in Lisbon, without
and with magnetic declination, respectively. The comparison between the various
representations in the figure suggests the following considerations:
168
− The position of the east-most point of the Mediterranean on the chart is about
two degrees to the west of the corresponding representation in the plate carrée
and six degrees to the east of the corresponding representation in the Flamsteed
projection. This means that its width is significantly larger than it should if longitudinal distances were to be conserved. The reason for the discrepancy is the
scale exaggeration already discussed in Chapter 4 (see Table 4.5 and related discussion). Also notice how the longitudinal difference of two degrees to the plate
carrée is much less than the ten degrees indicated by Pedro Nunes. From these
results it may be concluded that, contrarily to the opinion of Nunes, the length of
the Mediterranean on the chart does not contribute to the large size of the isthmus; on the contrary, it contributes to reduce the longitudinal spacing between
the Mediterranean and the entrance of the Red Sea;
50º
50º
40º
40º
Alexandria
Alexandria
30º
30º
20º
20º
10º
0º
20º
10º
C. Guardafui
C. Guardafui
0º
30º
40º
50º
60º
70º
Theoretical (no magnetic declination)
Theoretical (with magnetic declination)
20º
30º
40º
50º
60º
70º
Cantino
Projected
Figure 5.17 – The representation of the Red Sea and Eastern Mediterranean in the Cantino planisphere (green dashed lines) compared with a plate carrée (left) and with a Flamsteed projection (right). The overlapping was made as to align the meridian of Lisbon and
all parallels in the three different representations.
− The effect of the northward shift of the eastern Mediterranean on the size of the
isthmus, caused by its counterclockwise tilt, is relatively small. This may be visualized by bringing the position of Alexandria on the chart (green circle) a little to
the west of the corresponding position in the plate carrée (red circle);
− The longitudinal distance between Alexandria and C. Guardafui, measured in
equatorial degrees, is about 21° in the plate carrée and 36° in the Cantino planisphere. This means that the distance on the chart is significantly exaggerated.
The examination of the figure also shows that most of the difference is due to the
169
position of C. Guardafui, which is about 14° to the west of the corresponding
plate carrée representation.
From the above results one may conclude that the main reason for the exaggerated
longitudinal distance between the eastern Mediterranean and the entrance of the
Red Sea is not the length of the Mediterranean or its latitude errors, as Pedro Nunes
suggested, but the position of C. Guardafui in the chart. The next step will be to identify its causes. Two possibilities are considered: the geometric distortions associated
with the latitude chart; and the effect of the magnetic declination. In Figure 5.17
(left), the black cross at about 11° N represents the position of C. Guardafui, as determined using the theoretical route discussed in the last section, not affected by
magnetic declination. Surprisingly this point is almost coincident with the corresponding plate carrée position. On the contrary, when the magnetic declination is
considered, the position of C. Guardafui (white circle) comes very close to the corresponding representation on the chart. The obvious conclusion is that the charting
method alone has no significant influence on the eastward elongation of the African
continent, which is mainly caused by the effect of the magnetic declination on the
courses plotted on the chart. This result is somehow unexpected in what the influence of the charting method is concerned and can only be considered as a fortuitous
coincidence, caused by the use of this particular route along the coast of Africa.
An alternative explanation for the anomalous orientation of the eastern coast of Africa in the Cantino planisphere was proposed by Semedo de Matos (2003, p. 184),
who asserts that the few exploratory missions made in the years that preceded the
making of the chart (by Vasco da Gama, Pedro Álvares Cabral and João da Nova) are
not sufficient to explain the accuracy with which the shape of Africa is represented,
and suggests that the longitudinal extent of the continent was imported from the
Ptolemaic tradition. The cartographer would have started to plot the position of
Cape Guardafui (the Ptolemaic Cape Aromata), 83 degrees to the east of the Canary
Islands (the Fortunate Islands), as indicated in Ptolemy’s Geography, and then proceeded to draw the eastern African coast as to make the connection with the representation of the southern region of the continent. The fact that such distance was
measured in equatorial degrees would explain the enormous size of the Isthmus of
Suez. About this subject, Pedro Nunes wrote, in his ‘Treatise in defense of the navigational chart’ (Nunes, 2002, p. 137-38):
‘Ptolemy lived in Alexandria [and] strived to have true information at least of
the Levant and most neighboring parts […] Nevertheless he found from his information of the inland that Cape Guardafui, which he called Cape Aromata, is
eighty three degrees from the meridian of the Canary Islands. This same cape
170
was discovered by the Portuguese, not by eclipses59, like Ptolemy, or by land, or
sailing to the East [from the Mediterranean], but with so large detours, as it is
done in such long ways like the one of India, and experiencing so many storms
and diversity of weather […]. I was expecting that we would find this Cape Aromata in a very different longitude from the one given by Ptolemy, and opening
the compass on it I find it to dist from the meridian of the Canary Islands the
same 83 degrees. Now it is manifest that the Portuguese didn’t make it with this
longitude to be conform with Ptolemy: from whom most of the time are different: neither I know if there are any Portuguese who remember that Ptolemy
talked about the Aromata promontory: and that this is Cape Guardafui: furthermore our charts are so well delineated: that to do it would be necessary to
change all routes: which cannot be done.’ 60
Indeed, a careful measurement made on the Cantino planisphere yields a longitudinal distance between the western limit of the Canary Islands and Cape Guardafui of
82.8 equatorial degrees. Pedro Nunes acknowledged the coincidence but considered
it to be the result of the available navigational information, of which he praises the
excellence, rather than the reflex of the Ptolemaic information. The charts were
made on the basis of observed latitudes and courses between places and were supposed to be used exactly the same way. To construct them otherwise ‘cannot be
done’, as it would affect their accuracy and usefulness as navigational tools. The geography of the eastern Mediterranean and Red Sea was a common knowledge of the
European culture much before the Portuguese made the periplus of Africa, and the
only reason to keep the apparent discrepancy in its representation can only be of
navigational nature. But if the object of the analysis is restricted to the Cantino planisphere, the counter argument used by Pedro Nunes makes all sense (Matos, 2003, p.
184). Indeed, how could the navigations be so accurate in determining the position
of Cape Guardafui after a so long and dangerous trip around a whole continent? We
know that the only ship reaching Cape Guardafui and the entrance of the Red Sea
before 1502 was the one of Diogo Dias, in 1501. She was lost from the fleet of Pedro
59
That is, by using the eclipses of the Moon to determine the longitude.
The original text reads: Ptolomeu veuia em Alexandria [e] trabalhaua per ter verdadeyras enfomações: ao menos de Leuante e das partes mais vezinhas […] E porem sem embargo disto achou: per
suas enformações do Sartão: que o cabo de Gardafuy: que elle chama Aromata: distaua do meridiano
das Canarias per .83. graos. Este mesmo cabo descubrirão os Portugueses: nam per eclipses como
Ptolomeu: nem por terra: nem nauegando per leuante: mas com tamanhos rodeos: como se faze em
tam comprido caminho: como he o da India: e passando tantas tormentas: e diuersidade de tempos
[…] Esperaua eu este cabo Aromata: nos saysse em muito difer̃ te longura da que Ptolomeu lhe deu:
e lançandolhe ho compasso: acho que dista do meridiano das Canarias pelos mesmos oytenta e tres
graos. Ora manifesto he: que os portugueses nam lhe foram por esta longura: pera conformarem com
Ptolomeu: do qual as mais vezes sam diferentes: ñ sey se ha Portugueses a quem lembre: que Ptolomeu falou no promontorio Aromata: e que este he ho cabo de Gardafuy: quanto mais que andam as
nossas carta tam gizadas: que pera fazer isto era necessario mudar todalas rotas: o que se nam podera sofrer.
60
171
Álvares Cabral near the Cape of Good Hope, after a terrible storm which sunk four of
the ships, and arrived at the area with only seven men.
15
C. Guardafui
10
5
Mogadishu
Mogadishu
0
Malindi
Distance N-S
-5
-10
Moçambique
-15
-20
Moçambique
C. Correntes
-25
C. Correntes
-30
-35
-40
0
5
10
15
20
25
30
35
40
Distance E-W
Manuel Álvares
André Pires
João de Lisboa
Theoretical (João Castro)
Cantino
Figure 5.18 – Tracks along the eastern coast of Africa as taken from four Portuguese rutters of the sixteenth century, from the Cantino planisphere (green circles) and from the theoretical route, affected by magnetic declination (white
circles). All sets have been aligned in longitude at the position of the Cape of
Good Hope (west-most point). All distances were converted to degrees assuming a module of 18 leagues per degree.
Maybe the incorporation of the Ptolemaic length was only a temporary measure, to
be corrected as soon as more accurate and detailed observations were made in the
172
region. However, even that possibility is denied by the fact that all nautical charts of
the sixteenth century show the same eastward shift of the African continent. Matos
(2009)61 recognizes the fact but argues that the persistence of certain errors in the
nautical cartography of the time was common and may be explained by the easiness
with which they were corrected by the pilots in their navigations. If that were indeed
the case, then more exact courses along the eastern coast of Africa would have to be
registered in the rutters of the sixteenth century, differing significantly from those of
the Cantino planisphere.
In Figure 5.18, the representation of the eastern coast of Africa, from the Cape of
Good Hope to Mogadishu, which results from the information of courses and distances registered in three rutters of the sixteenth century, is illustrated62. For comparison purposes, the figure also shows the tracks measured on the Cantino planisphere, as well as the theoretical route, affected by magnetic declination. Though
there is a considerable variability among the tracks, the average orientation of the
coast, as inferred from the rutters’ information, eloquently agrees with the Cantino
planisphere. In my opinion this result invalidates the application of the previous argument to this particular situation, though the practice described by Matos certainly
applies to later periods, when the variation of the magnetic declination with time
had already made the directions indicated by the charts obsolete63.
It is a well-known fact that Ptolemaic information (as well as information from other
sources64) was incorporated into the nautical cartography of the Middle Ages and
Renaissance, but that resource was almost exclusively used in the areas not yet visited by the maritime exploratory missions. In the case of the Cantino planisphere, it
applies to the representations of the Red Sea and Persian Gulf, as well as of the Malay Peninsula and the Baltic Sea. The theory that the longitudinal width of Africa in
61
Personal communication.
These rutters are the Livro de Marinharia de João de Lisboa (Rebelo, 1903), the Livro de Marinharia
de Manuel Álvares (Albuquerque, 1969) and the Livro de Marinharia de André Pires (Albuquerque,
1989b). Although no precise dates can be assigned to any of these rutters, they were all compiled
during the sixteenth century. The earliest information concerning the eastern African coast is the one
in the Livro de Marinharia de João de Lisboa, with parts that may come from the beginning of the
century. Due to the fact that ships going to India usually passed at a considerable distance from land,
the southeastern coast of Africa was poorly known up to 1576, when a detailed survey was ordered by
King D. Sebastião. Before that date, a reconnaissance is known to have been made in 1506, from the
Cape of Good Hope to Sofala (Albuquerque, 1970b, p. 5-7).
63
As with the portolan charts of the Mediterranean, the reaction of the chart makers to changes in
the directions indicated by the magnetic compass, as a result of the variation of the magnetic declination with time, was extremely slow (to say the least). In the case of the Portuguese nautical cartography, this is confirmed by the little variation in the orientation of the eastern African coastline represented in most charts of the sixteenth century.
64
See Guerreiro (1993) for a description of the sources used in the Catalan Atlas, the globe of Martin
Behaim and the Cantino planisphere.
62
173
the cartography of the sixteenth century has Ptolemaic origin is elegant and historically attractive. However it is not explicitly confirmed by any written source and remains superfluous for explaining the geometry of the charts of the time. The hypothesis defended in the present thesis that such distortions are the result of the uncorrected magnetic declination appears as the most plausible explanation and is corroborated by the navigational data registered in the extant rutters. However, it still remains to be explained how this long coastline could be represented with such relative accuracy and detail on the basis of so few explorations missions. While it is possible that undocumented surveys may have been done in the region (by sea as well
as by land), I can’t resist citing the phrase with which Pedro Nunes ended the discussion on this issue, in his ‘Treatise’ (2002, p. 138):
‘And these ways are so different in the manner of discovering this cape [of
Guardafui], and both of them finally agree, [that] we should have in mind that
the navigations in Portugal are more accurate [certain], and better founded
than any others.’ 65
It was shown how two independent factors have contributed to the enormous size of
the Isthmus of Suez, as represented in the Cantino planisphere: the direct pasting of
the traditional Ptolemaic representation of the Red Sea on the chart and the exaggerated longitudinal spacing between the entrance of the Red Sea and the eastern
limit of the Mediterranean, caused by magnetic declination. Concerning the first factor, it is worth noting that the cartographer could well have adjusted the size and
orientation of the Red Sea in order to harmonize the representation with the known
length of the isthmus. This solution was adopted in some charts of the beginning of
the sixteenth century, as in the anonymous chart of ca. 1506, usually known as Kunstmann III (Cortesão and Mota, 1987, Vol. I, p. 15-16), and the chart of 1510 attributed to Jorge Reinel (Ibidem, p. 39-31). But the discrepancy continued to appear in the
Portuguese nautical cartography for a long time, which is a clear indication of its little
navigational relevance.
Modeling the Cantino planisphere
Having presented a systematic cartometric analysis of the chart and clarified some
relevant questions related to the details of its construction, a simulation of the geographic graticule of the Cantino planisphere is now presented and discussed. As with
the modeling of the North Atlantic (see Chapter 4), the main purpose of this exercise
65
The original reads: E pois estas vias sam tam diferentes no modo de descubrir este cabo: e vem ambas nisso a conformar: he bem que cuidemos: que as nauegações em Portugal: sam as mais certas: e
milhor fundados: que nenhuas outras.
174
is to reproduce the geometric features that result from the mixed use of the latitude
and portolan models, under the influence of the magnetic declination. No attempt
was made to replicate such local errors and distortions as are the scaling errors in
northern Europe, Mediterranean and Caribbean Sea, the exaggerated size of the
Isthmus of Suez or the latitude errors in the African coast. The input of the model
consisted in a set of tracks with origin in C. Espichel, covering the area already considered in the simulation of the North Atlantic, plus the Caribbean Sea, the southern
Atlantic and the part of the Indian Ocean between the eastern coast of Africa and the
western coast of Hindustan, excluding the island of Madagascar. The choice of the
tracks and charting methods was made in accordance with the results obtained previously. Closed loops were used only in the areas were a dense network of maritime
routes is supposed to have existed, as in the Mediterranean and northern Europe.
Three simulations were run, where only the spatial distribution of the magnetic declination varied. The following parameters were chosen (see Figure 3.17):
− Method: loxodromes, mixed model, w = 0.8 66. The method of the point of fantasy was used for the Mediterranean, Europe and the Caribbean Sea, and the set
point method for Africa, Brazil and the Indian Ocean;
− Geographic grid: the geographic limits were chosen as to cover the area defined
by the set of tracks used as input;
− Domain: a set of tracks supposedly representative of the routes utilized to construct the Cantino planisphere was used as input in accordance with the conclusions reached previously;
− Magnetic declination: a value of the magnetic declination was attached to each
point of the tracks. All values refer to 1500, except in the Mediterranean, where
the year 1300 was chosen.
−
Simulation A: values derived from the observations of D. João de Castro (South Atlantic and Indian Oceans) and as yielded by the geomagnetic model (North Atlantic,
Mediterranean and North Sea) (see Table 3.2);
−
Simulation B: values yielded by the geomagnetic model of Korte and Constable
(2005);
−
Simulation C: magnetic declination zero everywhere.
Figure 5.19 depicts the graphic output of simulation A, in the form of a geographical
graticule, together with the tracks used as input. In the tracks represented as solid
lines, the method of the point of fantasy was used; in the tracks represented as
dashed lines, the set point method was used. Only in one case, the track connecting
66
This value is justified by the results previously obtained by Gaspar (2008a) in the simulation of three
portolan charts.
175
Malindi to Calecute, the distance was used to determine the set point. In Figure 5.20,
the graticule produced in simulation A is shown side to side with the interpolated
geographical grid of the chart. From the comparison between the two representations the following conclusions can be drawn:
40W
60N
20W
0º
20E
40E
60W
40N
60E
20N
0º
20S
Figure 5.19 – Output of simulation A showing the tracks used as input. Meridians and
parallels are spaced five degrees. Dashed lines indicate the use of the set point method.
− In general, the model reproduces well the main geometric features of chart. Examples of good agreement are: the convergence of meridians in northern Europe; the tilted grid in the Mediterranean and Black Sea, due to the effect of
magnetic declination (rectangle E); and the distorted meridians in the eastern
coast of Africa (rectangle F);
− As expected, the areas of the chart where major distortions and errors have been
identified are not well simulated. These include: the Caribbean Sea, whose representation is affected by a large scale distortion (rectangle B); the eastern coast of
Brazil, where the meridians are distorted due to the longitudinal misplacement of
the island of quaresma; and the southern coast of Africa, where large latitude errors have been detected (rectangle D).
In the quantitative analysis presented next the model outputs of the three different
simulations are compared with the corrected graticule depicted in Figure 5.6, where
176
some control points known to be affected by large errors (in the Caribbean Sea and
Brazil) were not considered. As explained before, this procedure is justified by the
fact that those points do not add any useful information to the grid, in which its main
geometric characteristics are concerned. On the contrary, the orientation of meridians and parallels in the areas contiguous to the points is significantly affected by
their influence in the interpolation process, like in the Atlantic region to the west of
the Azores.
A
A
E
E
B
B
F
C
F
C
D
D
Figure 5.20 – Comparison between the interpolated the Cantino planisphere (left) and the
model output of simulation A (right). In both cases meridians and parallels are spaced five
degrees. The dashed rectangles indicate areas where there are significant differences; the
solid rectangles indicate areas where there is a good agreement.
Figure 5.21 – Displacements vectors from the comparison between the corrected graticule of
the Cantino planisphere (right) and the output of simulation A (left). The area of the circles is
proportional to the displacements.
In Figure 5.21 the output of simulation A (left) and the corrected graticule of the Cantino planisphere (right) are shown, together with the displacement vectors resulting
from the quantitative comparison between both, calculated with MapAnalyst. Figures 5.22 and 5.23 show the displacement vectors of the comparisons made be-
177
tween the outputs of simulations B and C, and the corrected Cantino graticule: using
the spatial distribution of the magnetic declination yielded by the geomagnetic model only (simulation B); and considering the magnetic declination to be zero everywhere (simulation C). It is interesting to realize that a considerable part of the strong
meridian convergence near the eastern limit of the representations, between 10° N
and 40° N, results from the charting method only (see Figure 5.23). The increase of
the convergence caused by magnetic declination is apparent in Figures 5.21 and 5.22.
Figure 5.22 - Displacements vectors from the comparison between the corrected graticule of
the Cantino planisphere (right) and the output of simulation B (left). The area of the circles is
As expected from the analysis presented before in this chapter, where the values of
the magnetic declination observed by D. João de Castro were found to agree much
better with the directions measured on the charts than the estimations of the geomagnetic model, both outputs of simulations B and C compare unfavorably with the
output of simulation A. This visual assessment in confirmed by a simple quantitative
analysis of the results. Table 5.5 contains the values of the following quantities, calculated for each of the three outputs, where s and µ are measured in arbitrary units
close to the degree of latitude:
− s: root-mean-square positional error, s =
∑d
2
i
N , where di is the distance be-
tween the positions of control point i in the chart’s graticule and in the model
output. A value of 0 indicates a perfect match between both;
− µ: average positional error, µ = ∑ di N , where di is the distance between the
positions of control point i in the chart’s graticule and in the model output. A value of 0 indicates a perfect match between both.
178
Figure 5.23 - Displacements vectors from the comparison between the corrected graticule of
the Cantino planisphere (right) and the output of simulation C (left). The area of the circles is
These results confirm that the output of simulation A is closer to the geometry of the
Cantino chart than the other two, thus validating the spatial distribution of the magnetic declination used in the process. As expected, the output of simulation C (no
magnetic declination) is the worst of the three. No detailed analysis of the outputs is
justifiable as there are numerous other factors, beyond the magnetic declination and
the scale variations, affecting the geometry of the chart. But it may be concluded, as
when the geometry of the North Atlantic in the charts of the fifteenth and sixteenth
centuries was simulated, that the main geometric features of the Cantino planisphere can be satisfactorily reproduced using the proposed methodology.
Table 5.5
Root-mean-square (s) and average positional errors (µ) of the
model outputs relative to the corrected Cantino graticule
(degrees of latitude)
Outputs
s
µ
Simulation A
1.7
2.5
Simulation B
1.9
2.7
Simulation C
2.2
3.1
A systematic cartometric analysis of the Cantino planisphere was presented which
included an estimation of the standard length of the degree of latitude, an assessment of the accuracy of the latitudes and a comparison between a set of theoretical
rhumb-line tracks, calculated on a spherical Earth, and the corresponding routes,
179
measured on the chart. Also, the geographical grid of meridians and parallels implicit
to the representation was interpolated, using digital techniques. From these analyses, relevant conclusions were drawn on the navigational accuracy of the chart and
its relation with the various cartographic sources from which the information was
compiled, as well as on the methods used in its construction.
From the analysis made on the distance scales and the spacing between the Equator
and the Arctic Circle it was possible to conclude that the module of 18 leagues per
degree was adopted in the Cantino planisphere, a result that contradicts previous
researches. Two mistakes explain the difficulty in reaching the correct conclusion:
the first is the misplacement of the Tordesillas’ line on the chart, fifteenth leagues to
the west of its correct position, from which a non-existent type of distance scales,
with sections of 12 leagues, is implied; the second is the inconsistency in the spacing
between the Equator, the tropical lines and the Arctic Circle, preventing a unique
scale of latitudes to be determined. The conclusion that normal distance scales with
sections of 12.5 leagues were used in the chart, from which it was inferred that the
line of Tordesillas was misplaced, was confirmed by a comparison made between
some distances measured on the Cantino planisphere and on the four other charts
analyzed in this study. As for the position of the parallels, it was concluded that the
correct latitude scale is given by the spacing between the Equator and the Arctic Circle, which implies that both tropical lines are represented about 9 mm further from
the Equator than they should. Supporting this conclusion is the implied module of 18
leagues per degree, mentioned by Duarte Pacheco Pereira, and the small latitude
errors in the part of the African coast surveyed ca. 1485. It is worth noticing that the
precise value of 18.0 leagues was obtained after the longitudinal deformation of the
chart, assessed through measurements made on the circular pattern of the wind roses, was corrected for.
The analysis of the geographic graticule implicit in the representation, as well as a
comparison between the routes measured on the chart and on a spherical model of
the Earth, firmly confirms that the Cantino planisphere was constructed on the basis
of the usual navigational and charting methods of the time: the method of the point
of fantasy, based on magnetic courses and estimated distances; and the set point
method, based on astronomically-observed latitudes. The old thesis that the Cantino
planisphere, as well as the other latitude charts of the time, is based on the plate
carrée projection is wrong and should be definitely abandoned.
The mistakes found in the position of the tropical lines relative to the Equator and in
the longitudinal position of the dividing line of Tordesillas, not detected in previous
researches, do not support the popular theory that the Cantino planisphere was cop-
180
ied from an official pattern. Also contradictory to this interpretation are the large
latitude errors in the representation of southern Africa and the lack of precision with
which the cartographic information taken from various sources was copied into the
chart, not taking into account the respective scales. Paradoxically it was the occurrence and nature of these errors that has permitted to draw some relevant conclusions about the details of the construction. That was the case of the scale exaggeration in northern Europe, from which it could be concluded that the representation
was copied from a traditional portolan-chart source, and the variation of the latitude
errors along the African coast, from which the different sources could be individualized. Interesting examples of this kind of ‘error signature’ are the northwestern coast
of Africa, where the astronomical surveys made around 1485 are clearly reflected on
the accuracy of the latitudes, the long coastline between the Equator and the Cape
of Good Hope, where the older module of 16 2/3 leagues per degree seems to have
been used, and the relatively small stretch visited by Bartolomeu Dias in 1487-88,
whose representation is affected by a very large scaling error.
A detailed comparison between some routes measured on the chart and a set of
theoretical tracks has permitted to confirm the idea that Africa was drawn according
to a route with origin in Lisbon and bordering its western and eastern coastlines. The
observations of the magnetic declination made by D. João de Castro in 1538, and
here extrapolated to 1500, were found to be of an extraordinary relevance and accuracy, having permitted to fully explain the position of Brazil and the orientation of
the eastern coast of Africa on the chart. To this respect, the theory that the longitudinal width of Africa at the latitude of Cape Guardafui was adopted from the Ptolemaic tradition was shown to be superfluous for explaining the shape of the continent, as the orientation of the eastern coastline is coherent with the use of the set
point method, under the influence of magnetic declination, and agrees with the information registered in the rutters of the sixteenth century.
The geometry of the Cantino planisphere was modeled using the EMP model application. Although a detailed simulation was not considered to be adequate or useful,
due to the numerous spurious errors affecting the chart, it was possible to reproduce
its main geometric features using the results obtained previously on the routes and
charting methods. Of the three simulations made, the one adopting the spatial distribution of the magnetic declination deduced from the observations of D. João de
Castro has shown to be the best.
The theory regarding a possible manipulation in the representation of Brazil and
Newfoundland, with the purpose of placing these lands inside the Portuguese zone
of influence, was found to be wrong, as their positions on the chart are coherent
181
with the navigational information presumably used to plot them. On the other hand
it is uncertain whether the mistake in the representation of the Tordesillas’ line was
purposeful or not. Ironically the result obtained, an enlargement of the Portuguese
area of influence in the Atlantic, has no effect on the navigational accuracy of the
chart.
The thesis that the Cantino planisphere was ordered by Alberto Cantino to a Portuguese cartographer, who made a copy of the official pattern, has been popular
among historians. Supporting facts are the up-to-dateness of the chart and the high
price paid for it. Still many significant geometric details challenge the interpretation,
as is the likely existence of a title and its mutilation, the mistakes made in the position of the tropics and the line of Tordesillas, and the significant latitude errors in the
representation of southern Africa. A better interpretation of the known facts is that
Alberto Cantino did not order the making of the chart, which was probably reserved
for some nobleman or official client, but found some way of deviating it from the
original purpose shortly after it was completed.
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6. CONCLUSION
The main objectives of the present thesis, as stated in the Introduction, are:
− To propose and test a methodology for the systematic cartometric analysis and
modeling of early nautical charts, aiming at a better understanding of their geometry and methods of construction;
− To characterize the main geometric features of the earliest nautical charts of Portuguese origin and clarify their relations with the contemporary navigational and
charting methods.
These objectives were accomplished in Chapters 3 through 5, where the application
of a set of digital cartometric and modeling techniques to the study of five early nautical charts was proposed and presented. Though only a limited number of charts
were analyzed, the use of those tools permitted to characterize their common geometric properties and clarify their connection with the navigational and charting
methods of the time. In general, the results obtained confirm the study hypotheses
introduced in Chapter 1, concerning the construction and use of pre-Mercator nautical charts and the possibility of simulating them. As stated there, no explicit theories
or study hypotheses were established for specific historical matters related to the
origin and dating of each chart or even for such important subjects as are the transition between the portolan chart and the latitude chart, and the standard length of
the degree of latitude. However, and as expected, the effectiveness of the techniques used in this study and the fact that they were applied for the first time in a
systematic way, made possible to draw original and interesting conclusions on some
historical matters. Significant examples are the standard length of the degree of latitude adopted in the Iberian nautical cartography and the construction of the Cantino
planisphere.
In this final chapter the most relevant results and partial conclusions presented in the
previous chapters are integrated and discussed, and some suggestions are made for
future research. The chapter is organized in five sections: in the first (Discussion of
thesis hypotheses), the results and conclusions are analyzed in the light of the study
hypotheses established in the Introduction; in the second (Cartometric analysis and
modeling), the use of the various cartometric and modeling techniques is briefly
summarized and discussed; in the third section (Conclusions with historical rele-
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CHAPTER 6 – CONCLUSION
vance), some of the partial conclusions on historical matters reached in this study,
considered to have special historical relevance, are summarized; in the fourth section
(Future research) suggestions for the continuation of the present research are presented; in the sixth and last section (Concluding remarks) a final comment is made
about the methodology adopted in the present study and the contribution of this
thesis to the study of old nautical charts.
Discussion of the thesis hypotheses
Five study hypotheses were established concerning the construction and use of early
nautical charts, and the possibility of simulating them:
Hypothesis 1: pre-Mercator nautical charts were constructed to be used at sea and
reflect the needs of marine navigation and the navigational methods of the time.
It is now consensually accepted by most researchers that nautical charts were developed during the thirteenth century with the purpose of supporting marine navigation. Although the majority of the manuscript charts that survived to our days were
not probably intended for being used at sea, as suggested by their sumptuous decoration or large size, they were certainly drawn by the same chart makers and copied
from the same patterns. As for the main geometric features of the representations
and their connection with the navigational methods of the time, all five Portuguese
charts analyzed here share the same cartographic models. No significant differences
were found between the most decorated charts (Jorge de Aguiar and the Cantino
planisphere) and the other three, in which the navigational accuracy in concerned.
The theory of Fernández-Armesto (2006, p. 749) that sea charts ‘may have been a
visual aid to illustrate – for the enlightenment of passengers, landlubbers, and such
interested parties as merchants – the data pilots preferred to carry in their head or
rutters’ can hardly be applied to the nautical charts of the Renaissance, as their use
at sea is documented in several sources of the time. As for the alleged preference of
pilots to use the data registered in their rutters, it is certainly applicable to some particular regions for which the available charts didn’t show the necessary detail or accuracy. However charts and rutters should always be considered – in the past as well
as in the present – as complementary rather than mutually exclusive sources of navigational information. To this respect, it is interesting to notice the good agreement
found between the orientation of the eastern coast of Africa, in the Cantino planisphere (which is a sumptuary chart, obviously not intended to be carried aboard),
and the data registered in three different rutters of the sixteenth century.
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Hypothesis 2: pre-Mercator nautical charts were constructed by transferring directly
to the plane the directions and distances measured on the spherical surface of the
Earth, with a constant scale, as if it were flat. This method made the resulting representations geometrically inconsistent, in the sense that they were dependent on the
particular set of routes used for constructing each chart, and caused certain distortions that can be identified through cartometric analysis.
The methods of chart construction used in the pre-Mercator period are documented
in Portuguese and Spanish historical sources, of which the texts of Pedro Nunes
(1537), Martin Cortés de Albacar (1551), Francisco da Costa (1596) and Manuel Pimentel (1712) are well known. In all of them it is clearly stated that places are represented on the charts according to their latitudes and courses relative to other places
or, in the case of the older charts, to the courses and distances. The use of a unique
scale, though not explicitly referred to by these authors, is implicit in all descriptions.
In his ‘Treatise in defense of the navigational chart’ (1537), Pedro Nunes shows to be
aware of the geometric idiosyncrasies of this charting method and elaborates on its
effect on the orientation of the meridians on the chart, which he finds cannot be
straight and parallel, as he had supposed in the beginning of the text. However he
considers that the charts of the time are the best possible instrument to support marine navigation, provided that they are well understood and used by the pilots. Pedro
Nunes specifically refers to the fact that the north-south direction is not usually represented as such on the charts and that these are only accurate along the specific
tracks that were practiced by the pilots. This important concept was usually ignored
by the historians of the twentieth century, even after the important work of António
Barbosa (1938), which had little impact against the well established myth of the
square chart. In the present thesis comparisons made between theoretical tracks
defined on the spherical surface of the Earth and the corresponding tracks measured
on the charts have shown that their geometry is closely dependent on the particular
set of routes used in their construction, thus confirming the interpretation of Barbosa. An interesting example of this dependence in two charts of the sixteenth century, the Cantino planisphere and the chart of Pedro Reinel of ca. 1504, is the impact
on the geometry of the representations caused by the different ways used to plot the
position of Newfoundland: relative to northern Europe, in the first case, and to the
Azores, in the second. Another significant case confirming the same principle is the
position of the Cape of Good Hope in the Cantino planisphere, which was found to
have been represented according to a set of tracks bordering the western coast of
the continent, rather than to the routes followed by Vasco da Gama and Pedro Álvares Cabral, who approached the Cape of Good Hope sailing from west. Although
only a limited number of exemplars were subjected to a systematic cartometric anal-
185
ysis, some measurements made on numerous other charts of the sixteenth century
indicate that they all share the same cartographic model. I consider the nature and
quality of the results to firmly support the hypothesis that pre-Mercator nautical
charts were drawn by plotting directly on the plane, with a constant scale, the latitudes, courses and distances observed on the curved surface of the Earth.
Hypothesis 3: most pre-Mercator nautical charts were drawn on the basis of uncorrected magnetic directions and their geometry reflects the spatial distribution of the
magnetic declination at the time the navigational information was collected.
The phenomenon of magnetic declination was unknown probably until the last quarter of the fifteenth century. Although the pilots of the time were aware that the maritime compasses did not usually indicate true North, the anomaly was attributed to
poorly magnetized needles and sometimes compensated for by manipulating the
position of the wind roses. The earliest documented mention to a spatially variable
magnetic declination is a hand note from Columbus, written during his first voyage to
the Americas. In 1538 and 1541, D. João de Castro made the earliest known systematic survey of the magnetic declination, in his voyages from Lisbon to Goa and from
Goa to the Red Sea. Based on the Livro de Marinharia de João de Lisboa, which mentions the manipulation of compasses by pilots with the purpose of compensating
them for the magnetic declination, Barbosa suggested that the Portuguese cartography of the fifteenth and sixteenth centuries may reflect this practice. However no
historical source mentions that charts were constructed on the basis of corrected
courses and the extant cartography of the time clearly show the effect of magnetic
declination. That was the conclusion drawn in the present study, concerning the five
Portuguese charts that were subjected to cartometric analysis. Furthermore the differences between a set of directions measured on the charts and the corresponding
exact values usually match the magnetic declination at the time, as yielded by the
geomagnetic model of Korte and Constable (2005) (North Atlantic and Mediterranean) or observed by D. João de Castro (South Atlantic and Indian oceans). This coincidence is particularly obvious in the case of the Cantino planisphere, where the distorted shape of the African continent is well explained by the effect of the uncorrected magnetic declination.
Hypothesis 4: the equidistant cylindrical projection was not, implicit or explicitly, used
in the construction of the nautical charts of the fifteenth and sixteenth centuries.
The thesis that the Portuguese charts of the fifteenth and sixteenth centuries were
drawn according to the principles of the cylindrical equidistant projection centered at
the Equator (plate carrée) may have originated in a wrong interpretation of Pedro
186
Nunes’ ‘Treatise in defense of the navigational chart’. The theory was repeated and
accepted by successive generations of cosmographers and historians, and managed
to survive to our times, despite the work of António Barbosa, who emphatically explained that the cylindrical equidistant projections could never have been used in the
nautical cartography of the fifteenth and sixteenth century because it was incompatible with the navigational methods of the time. To the logical arguments of Barbosa
the present study have added additional evidence that: (i) the charting method described in the extant historical sources, in accordance with which new places were
plotted on the chart according to their latitudes and directions relative to other places, cannot produce a square or rectangular graticule. Various factors concur for this
impossibility, the most obvious being that the use of a constant linear scale is forcedly reflected on the orientation of the meridians, which always converge to the poles.
This is illustrated in the various outputs of the EMP model application, when simulating the main geometric features of the charts using the charting methods described
in the historical sources; (ii) the geometry of the charts, as estimated through
georeferencing, is objectively different from the geometry of the plate carrée. This is
confirmed by a quick visual inspection of the interpolated graticules, which show
approximately straight and equidistant parallels, and curved meridians converging to
the poles. Although the thesis that the cylindrical equidistant projection was explicitly used in the construction of the old charts is probably not defended by any modern
author, the idea that their geometry approximates the plate carrée is still common
among historians. While it cannot be denied that, near the Equator and in the absence of the magnetic declination, the interpolated graticules of the old charts may
locally approximate a square grid, this property is shared by many other map projections and has nothing to do with the charting method. In my opinion, the idea contributes to perpetuate the myth and is detrimental to a correct interpretation of the
geometry of the pre-Mercator charts. It is worth mentioning that, although the plate
carrée is not generally suited for marine navigation, it would have been a good solution for representing the inter-tropical zones during the Renaissance if the spatial
distribution of the magnetic declination at the time were known and the longitude
could be determined at sea. However that was not the case, as Pedro Nunes failed to
recognize when he proposed the solution in 1537.
Hypothesis 5: the geometry of pre-Mercator charts can be numerically replicated by
simulating the charting methods of the time, taking into account the routes supposedly used to construct them and the spatial distribution of the magnetic declination.
Two types of simulation were made in the present study: the simulation of specific
tracks, or sets of tracks, defined on the spherical surface of the Earth and then compared with the corresponding segments measured on the charts; and the simulation
187
of the graticules of whole charts or geographic areas. The first method aimed at determining what charting methods were used for representing each region (point of
fantasy or set point method) and which routes were used to construct the charts.
The second method was used to simulate the main geometric features of the charts,
on the basis of the routes identified before and the spatial distribution of the magnetic declination, and was implemented with the EMP model application. Both
methods proved to be effective and easy to use, and permitted to identify some of
the routes used in the construction of the charts and to simulate their main geometric features. The theory that old nautical charts are only approximate representations, not susceptible of accurate analysis or simulation, was proven to be incorrect.
Although the charts analyzed in this study have shown mistakes and errors of various
natures, these were usually possible to identify and do not affect significantly the
geometry of the charts. Paradoxically it was the occurrence of these imperfections
that has permitted to draw relevant conclusions about the methods used to draw the
charts, the details of the construction and the probable sources of information.
Cartometric analysis and modeling
A set of cartometric techniques was used for analyzing the geometry of five nautical
charts of Portuguese origin. These included georeferencing, the assessment of scales
and distance units, the assessment of latitudes, and the comparison between directions and distances measured on the charts with the corresponding theoretical values. All techniques require that an accurate correspondence between the old chart
under analysis and the modern world is first established. This was done by compiling
a sample of more than two hundred control points of known geographic coordinates,
which have been identified both in the old and in a modern representation. Although
the use of most of these tools in historical cartography is not original, their systematic application to the study of nautical charts was done, to my knowledge, for the first
time.
The visual inspection of the interpolated grids of meridians and parallels implicit to
the representations, which were obtained through georeferencing, proved to be a
simple yet very effective way of recognizing the main geometric features of the
charts. With this technique it was possible to quickly assess the effect of the magnetic declination on the interpolated graticule, to identify the areas where astronomically-observed latitudes might have been incorporated and to make a preliminary qualitative assessment of the cartographic accuracy in the different regions, to be later
addressed with finer techniques. The computer application MapAnalyst proved to be
a valuable tool in various phases of the research and was used, not only for georefer-
188
encing and producing the interpolated graticules, but also for making quantitative
comparisons between the old charts and the outputs of the numerical simulations.
Assessments of latitudes, distances and courses were made by comparing the quantities measured on the charts with their theoretical values calculated on the surface of
the Earth. From these results it was possible to make a finer characterization of the
geometry of each chart, to identify the different cartographic models used to represent the various regions and, in some cases, to estimate the maritime routes used in
the charting process. The analysis of the distribution of the latitude errors permitted
to establish interesting connections with the historical exploratory missions and to
shed some light into the complex issue of the length of the degree adopted in the
cartography of the time. Because the geometry of most (if not all) pre-Mercator
charts is affected by magnetic declination, an estimate of its spatial distribution at
the time the cartographic information was collected was found necessary. Two primary sources were used: the historical observations made by D. João de Castro in
1538 and 1541, for the South Atlantic and Indian Oceans, and the outputs of the geomagnetic model of by Korte and Constable (2005), for the North Atlantic and the
Mediterranean. Because most directional data used by the model are concentrated
in the northern hemisphere, its results for the coasts of Africa and Brazil can only be
considered as crude approximations and were not used in the study. On the contrary,
the observations made by D. João de Castro were found to be reliable and accurate,
being used whenever possible for the assessment of directions and simulation purposes.
In general, the methodology of cartometric analysis proposed in this thesis, consisting in the orderly application of a set of techniques to each chart, proved to be effective and accurate. In most situations, preliminary conclusions that were drawn in
some phase of the process could be confirmed and detailed using a different tool;
that was for example the case of the scaling errors in the representation of northern
Europe, detected by the visual inspection of the interpolated graticules and later
detailed when assessing the latitudes. In other cases, it was found necessary to use
more than one tool to draw a firm conclusion; that was the case of the identification
of the length of the degree adopted in the Cantino planisphere, which was made on
the basis of the analyses made on the scales of leagues, the distances measured on
various charts, the assessment of latitudes and the estimation of the distortion
caused by the parchment’s aging.
A numerical model was developed, the EMP model application, for simulating the
geometry of the old charts. Its working concept is similar to what it is known in Geodesy as ‘geodetic adjustment’ and, in social sciences, as ‘multidimensional scaling’.
189
Starting with a sample of distances between points on the surface of the Earth, the
principle consists in numerically adjusting their positions on the plane, so that the
sum of the squares of the differences between the given and the final distances is
brought to a minimum. This concept, whose application to mapmaking was first proposed by Tobler (1977), was here generalized to distances and directions measured
on the curved surface of the Earth. The input of the EMP model application is a sample of rhumb-line courses and distances defined either by the intersections of a regular geographic grid or by a set of pre-defined tracks between places, affected by the
magnetic declination. The output is the cartographic representation which results
from the optimization process, in the form of a geographic graticule interpolated
from the final positions of the points. The EMP model proved to be an effective research tool and was used, not only for producing the simulations presented in this
thesis, but also for quickly assessing the influence of the various factors affecting the
geometry of the charts. It is worth mentioning that only a limited number of its capabilities was used in the research and presented in the thesis.
Conclusions with historical relevance
Two types of conclusions were drawn from the results of the cartometric analysis
and modeling presented in the thesis: those concerning the use of the techniques
and methodology, already presented in the previous section; and those pertaining to
the historical aspects related with the making of the charts and the acquisition of the
geographic information, summarized in this section.
Leagues and degrees
Considerable attention was given, in this study, to the cartographic standards adopted in the charts of the fifteenth and sixteenth centuries, namely the types of distance
scales and the length of the degree of latitude. Two usually accepted interpretations
were challenged here: the existence of distance scales with sections of 12 leagues;
and the pretense evolution of the standard length of the degree, from 16 2/3 to 17 ½
leagues, as a result of more accurate measurements made by the Portuguese pilots
at sea.
Concerning the first issue, no extant historical source mentions the existence of
scales of distance with sections of 12 leagues. Only two types are referred to: sections of 12.5 leagues, which were adapted from the graphical scales of the Mediterranean charts and used throughout the fifteenth and sixteenth centuries; and sections of 10 leagues, explicitly graduated, which first appeared during the second half
of the sixteenth century. The only known cartographic specimen where sections of
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12 leagues might have been used, as inferred from the longitudinal position of the
line of Tordesillas on the chart, is the Cantino planisphere. However the adoption of
such standard would have made each of its five subdivisions to represent 2.4
leagues, an improbable value. Also, the comparison of various distances measured
on the chart with the corresponding values in a number of other charts, considering
both the 12.5 and the 12 leagues’ options, has shown a much better agreement with
the first one. The conclusion drawn was that the line of Tordesillas is misplaced on
the chart, either purposively or not, and that the normal scales of 12.5 leagues per
section were used. This issue is closely related with the length of the degree of latitude adopted in the representation. If the 12 leagues’ option were accepted, the
resulting length would have been 18.6 leagues per degree, a module not referred to
in any historical source. On the contrary, if the 12.5 leagues option is chosen instead,
a module close to 18 leagues per degree is inferred, which coincides with the standard referred to by Duarte Pacheco Pereira ca. 1505, and used in many other Portuguese and Spanish charts of the sixteenth century, including Pedro Reinel’s chart of
ca. 1504.
Three different modules are mentioned in the historical sources – 16 2/3, 17 ½ and
18 leagues – the first one being usually considered as the oldest in the Iberian cartography. Measurements were made on 42 Portuguese charts of the sixteenth and seventeenth centuries, to determine which module was used in each of them, and the
results were associated with the output of a similar survey made by Franco (1957) on
36 charts of Portuguese, Spanish and Italian origins. The results show that all three
standards coexisted in the nautical cartography of that period, though the 16 2/3
module was only detected in the group of charts belonging to the Atlas Miller (1519).
Furthermore no apparent correlation exists between the adopted modules and the
dates of the charts. These two facts clearly deny any meaningful evolution in the
standard length of the degree. The popular idea that the 17 ½ module resulted from
the astronomical survey ordered by King João II ca. 1485, in Africa, cannot be accepted. Not only much better conditions existed along the coast of Portugal to make such
measurements, but also the necessary information for deducing a practical standard
was already available in the traditional cartography of the area. In my opinion the
coexistence of those modules for such a long period is merely an echo of the traditional models of the Earth and of the political disputes over the location of the Moluccas, and clearly suggests that the choice of a particular one had little relevance for
the practice of navigation. The latitude charts were drawn and used on the basis of
observed latitudes and magnetic courses, and the distances between places were
known to be affected by substantial errors, most of them resulting from the use of
the set point method, as D. João de Castro recognized in 1538. Under these circum-
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stances it is likely that the distance information that could be measured from the
charts was usually superseded by the estimations made by pilots at sea and registered in their rutters. Formally, leagues of different lengths resulted from the use of
the different modules. However, these differences could hardly be reflected on the
practice of navigation because they would have caused an unacceptable confusion.
Considering that the length of the degree in the latitude chart was conventional, rather than experimental, the league used by the pilots in their assessments of the distance sailed was most probably shorter than the leagues of the charts. This comes
from the fact that the metric length of the league in the charts of the fifteenth century, as estimated on the basis of a series of distances measured on the charts, is
smaller than in the charts of the sixteenth’s, where it is the indirect result of the
adoption of a specific module.
Knowing that a much better assessment of the length of the degree could have been
made by simply overlaying a scale of latitudes on the traditional charts of the northern Atlantic, which were constructed on the basis of estimated distances, it remains
unclear why the traditional modules were adopted instead. The political issues related with the size of the Earth, preceding Columbus mission, and with the location of
the Moluccas hardly explain the persistence of such irrational solution throughout
the sixteenth and seventeenth centuries, which can only be justified by its relatively
little impact on navigation.
The advent of the latitude chart
The advent of the latitude chart is one of the most interesting subjects in the history
of nautical cartography. Still no historical text has come to us explaining how the
transition between the two cartographic models was made. The analysis of the few
extant Portuguese charts of the end of the fifteenth and beginning of the sixteenth
centuries has shown that the two solutions coexisted throughout the sixteenth century, with the newly discovered regions being represented with the new model,
while the representations of the Mediterranean, Black Sea and western Europe continued to be based on the old one. The earliest extant chart to clearly incorporate
astronomically-observed latitudes is the Cantino planisphere, of 1502. Though the
three charts of the fifteenth century analyzed here show no explicit or implicit evidence of those methods, such as the existence of a scale of latitudes or the adoption
of one of the historical modules, the possibility of some rudimentary form of astronomical navigation having been used in the collection of the cartographic information cannot be discarded.
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The theory of António Barbosa (1938a) that the transition between the two cartographic models was facilitated by the small values of the magnetic declination occurring in Europe during the fifteenth century, permitting a graphical scale of latitudes
to be overlaid on the old charts without significant error, is supported by this study.
The assessment of the latitudes in the three charts of the fifteenth century revealed
remarkably small errors along the western European coast, between 30° N and
55° N. Having already concluded that these charts were not constructed on the basis
of observed latitudes, this result can only be explained by the occurrence of small
values of the magnetic declination in the region, when the information was collected.
This was confirmed by the output of the geomagnetic model of Korte and Constable
(2005), which indicates that absolute minimums occurred between 1300 and 1500 in
the eastern Atlantic. Ironically, the adoption of a conventional length for the degree
of latitude in the charts of the sixteenth century, considerably different from the value implicit in the older charts, from which the representation of Western Europe was
copied from, made this representation unfit for astronomical navigation. That was
found to be the case of the Cantino planisphere and Pedro Reinel’s chart of ca. 1504,
both showing large latitude errors north of the 40° N parallel, strongly increasing
with latitude. This result was unexpected and seems to contradict the idea that astronomical navigation was practiced in the region in the beginning of the sixteenth
century. Assuming that such methods were indeed used, two not mutually exclusive
reasons may explain the fact: either the two charts of the sixteenth century analyzed
here are not representative of the nautical cartography of the time, in what the representation of Europe is concerned; or the navigation in the European waters and
Atlantic islands relied more on the latitude information registered in the pilot’s rutters than on the charts. Whatever the correct explanation is, it seems obvious that a
more extensive and detailed research on the cartography of the sixteenth century, as
well as on the information registered in the existing rutters, is required.
The Cantino planisphere
The geometry of the Cantino planisphere is rich and complex. This results from the
methods used in its construction, the diversity of sources of cartographic information
from which it was compiled and the multiple factors affecting its accuracy. All cartometric techniques used to analyze the chart’s geometry have confirmed that the
Cantino planisphere was drawn on the basis of the navigational and charting methods of the time: the portolan-chart model (method of the ‘point of fantasy’), for representing the northern Atlantic, the Mediterranean, Black Sea and Caribbean Sea;
and the latitude model (‘set point’ method), for representing the southern Atlantic
and Indian Oceans.
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A systematic comparison between a set of courses and distances measured on the
chart with the corresponding theoretical tracks has permitted to conclude that Africa
was drawn in accordance with a route with origin in Lisbon, bordering its western
and eastern coastlines. The eastward displacement and exaggerated longitudinal
width of the continent is fully explained by the use of the set point method, under
the effect of the magnetic declination. The theory that the distance between the
Fortunate Islands (the Canary Islands) and Cape Aromata (Cape Guardafui) was imported from Ptolemy’s Geography was found to be superfluous, as the navigational
information registered in the rutters of the sixteenth century coincide, not only with
the routes measured on the chart, but also with the theoretical rhumb-line tracks
along the African coast, when the magnetic declination as of 1500 is taken into account. To this respect, it is interesting to recall the opinion of Pedro Nunes in 1537,
who rejects the same interpretation on the basis that such procedure would have
made the charts unfit for navigation.
The significant eastward shift in the representation of Greenland, which appears
north-south with the Azores, was shown to be the result of the track used to plot the
island on the chart, adopting some place in northern Europe as origin. The theory
that the location of Brazil and Newfoundland was manipulated so that they would
appear inside the Portuguese hemisphere, after the Tordesillas’ agreement, was
shown to be unfounded, as their positions are consistent with the magnetic courses,
estimated distances and observed latitudes used to plot them. However, an error
was spotted on the location of the Tordesillas’ line, which is represented some 15
leagues to the east of its historical position (370 leagues westward of the Cape Verde
archipelago). Whether this mistake was purposeful or not is uncertain but it is interesting to notice that it does not affect the navigational accuracy of the chart.
The distribution of the latitude errors with latitude has permitted to unveil what may
be called the ‘error signature’ associated with each of the sources used in the compilation. Two significant examples are the representation of the northwestern African
coast, where the astronomical survey made ca. 1485 is clearly reflected on the accuracy of the latitudes, and the stretch of the southwestern coast visited by Bartolomeu Dias in 1487-88, affected by a very large scaling error.
The inconsistency in the placement of the tropical lines and Arctic Circle relative to
the Equator, not detected in previous researches, was resolved in favor of the position of the Arctic Circle. By relating the resulting length of the degree on the chart
with the length of one section of the distance scales, a module of 17.8 leagues per
degree of latitude was deduced, later corrected to 18 leagues per degree, after the
anisotropic deformation of the parchment was taken into account. This is the module
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referred to by Duarte Pacheco Pereira in the beginning of the sixteenth century and
closely matches the corresponding result found for Reinel’s chart of ca. 1504. It is
also coherent with the small latitude errors in the northwestern coast of Africa,
where the astronomical survey was made, and with a number of distances measured
on the chart and compared with the corresponding values in the other four charts
analyzed in the study.
The theory that the Cantino planisphere was ordered by Alberto Cantino to a Portuguese cartographer, who made a copy from the official pattern, is not supported by
the present study. Some significant evidences challenge this interpretation, as is the
likely existence of a title and its mutilation, the mistakes made in the position of the
tropics and the line of Tordesillas, and the large latitude errors in the representation
of the southeastern and southern coasts of Africa. A more plausible interpretation of
the known historical facts is that the chart was surreptitiously acquired shortly after
it was made for some nobleman or official client. That would explain the existence of
the title, the sumptuous decoration (incompatible with a furtive copy) and the numerous errors and mistakes, not easy to explain in an official pattern.
The chart of Pedro Reinel of ca. 1504
The chart of Pedro Reinel of ca. 1504 is the earliest known chart showing a graphical
scale of latitudes. The cartometric analysis has shown that, like in the Cantino planisphere, only the region south of about 35° N was charted using astronomicallyobserved latitudes, the representation of the European coastlines having been copied from an older portolan-type pattern. A further motive of interest in this chart is
the existence of an extra scale of latitudes, positioned obliquely near Newfoundland
and only applying to the region. This study concluded that the reason for such
strange solution is that the area was placed according to a magnetic course and distance measured from the Azores, notwithstanding the latitude of some points in the
coast having been observed and reflected on the chart. Another interesting feature
of Reinel’s chart is the representation of Greenland. Contrarily to the solution adopted in the Cantino planisphere, the island was plotted on the chart according to its
latitude and magnetic course, measured from the Azores. This is an indication that
the region may have been re-visited and new information made available after the
Cantino chart was already completed.
Future research
The use of digital techniques in the analysis of old maps is a relatively recent development and the geometry of the vast majority of the extant pre-Mercator nautical
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charts was never studied. This fact is confirmed by the significant number of historically relevant findings of the present study, albeit no specific hypotheses concerning
any of the individual charts were established and only a limited number of them,
belonging to a relatively short period, were analyzed. The research can now proceed
in two complementary directions: the improvement of the cartometric and modeling
tools presented here; and their application to a larger number of charts of other periods and origins.
Concerning the methodology used to make the cartometric analysis, more sophistication is needed. Although most measurements were made on digital copies of the
charts, the operation was almost always ‘manual’, in the sense that a standard drawing application and a plain hand calculator were used to measure angles and lengths,
and to make the necessary calculations and conversions. The process was time consuming and prone to error, forcing to frequent double checks and corrections. Some
kind of automation would be welcome in future works, especially when analysing
larger numbers of charts. The improvement could take the form of a dedicated computer application to calculate the distances, directions and latitudes on each chart,
after the positions of the control points and other relevant information was loaded.
Although the specific ‘cocktail’ of cartometric tools used here was found to be effective and accurate for the type of information required by the study, other types of
measurements and comparisons could be added to the process or even replace some
of the original ones, depending on the objectives.
As an empirically-developed prototype, the EMP model application is a relatively
inefficient instrument and could be improved in several ways. It was already mentioned that no attempt was made to mathematically formalize the method or to
prove the convergence of the numerical algorithm, and how the results were validated using a small number of typical cases of known exact solutions. A proper formalization of the adjustment process is desirable, not only to prove its convergence to
the exact solution (assuming it exists) but also to improve the computational efficiency of the algorithm, which is based on geometric considerations.
As for the application of this kind of methodology to a larger number of preMercator charts, aiming at better understanding how they were constructed and
evolved with time, almost everything is to be done. Hundreds of charts of various
periods and origins need to be taken out of the archives, copied into high quality
digital copies and analyzed. We have seen in this study how the geometry of the
charts was dependent on the particular set of routes used in their construction, especially in the representation of large oceanic basins. A systematic study needs now
to be done to confirm that this basic geometric feature applies to the generality of
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the pre-Mercator cartography and to determine how the different areas were charted. It was also shown in this study how charts were drawn on the basis of uncorrected magnetic directions, a process which affected the shape of the coastlines, and the
orientation and length of the tracks between places. Whether the cartography of the
sixteenth and seventeenth centuries reflects or not the variation of the magnetic
declination with time is uncertain. In some areas, like in the Mediterranean and Black
Sea, the initial representations may have been left unchanged for long periods; in
other areas, the magnetic declination may have been corrected for. It was also
shown that the portolan-chart model, based on magnetic courses and estimated distances, coexisted with the latitude model in the representation of some areas, after
the introduction of astronomical navigation. It is still to be determined how long this
solution persisted and how the evolution took place in the different regions. A particularly important case, already mentioned in this chapter, is the representation of
Western Europe.
The cartometric tools proposed in this study have shown to be useful not only for
determining the charting methods used in the construction of the charts and assessing their navigational accuracy, but also for unveiling interesting connections
between their geometry and the exploratory missions behind the cartographic information. Three suggestions for a complete cartometric analysis of individual charts
are made here: the Juan de la Cosa planisphere, allegedly drawn in 1500 but whose
dating has been contested on the ground that some of the information depicted is of
a later period; the planisphere of ca. 1504, by Nicolo Caveri, which shows a graphical
scale of latitudes and was copied from Portuguese sources, including the Cantino
planisphere; and the Carta Marina of 1516, by Martin Waldseemuller, the earliest
known printed nautical chart of the world, significantly named Carta Marina Navigatoria Portugallen Navigationes Atque Tocius Cogniti Orbis Terre Maris (‘A Portuguese
Navigational Sea-chart of the Known Earth and Oceans’).
Concluding remarks
In the beginning of this thesis the principle of parsimony, the well-known Occam ’s
razor, was enunciated. That was not by chance, as it has served as a permanent
frame of reference throughout the whole research, especially when interpreting the
results of the cartometric analysis in the light of the historical sources and navigational methods of the time. Ironically a good deal of complexity was needed to prove
that the pilots and cartographers of the Middle Ages and Renaissance have generally
used the easiest methods for solving their practical problems. The long lasting theory
of the square chart was shown to be wrong, as the nautical charts of the fifteenth
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and sixteenth centuries were drawn by plotting directly on the plane, with a constant
scale, the directions, distances and latitudes observed on the curved surface of the
Earth, as if it were flat. Not due to the ignorance of the cartographers about the real
shape of our planet but because that was the best possible practical solution in a
time when longitude could not be determined directly at sea and the spatial distribution of the magnetic declination was unknown. The empiricism, rather than the
adoption of any conceptual model of the world and of the ways to represent it on
the plane, has prevailed in old nautical cartography. Charts were drawn in accordance with what was observed by pilots at sea using the same basic principles of marine navigation. The fact that those principles were simple doesn’t make the resulting
representations also simple. On the contrary, pre-Mercator nautical charts show
considerable complexity, as a result of the various factors affecting their geometry,
the choice of the routes used in the construction, the diversity of the sources and the
errors made by the cartographers. That is why it was first necessary to deal with the
complex meanders of the charts’ geometry before being able to prove their conceptual simplicity.
Not armed with the sophisticated digital tools of our time, António Barbosa stated
and defended, more than 70 years ago, some of the most important conclusions of
this research, on the basis of a careful analysis of the historical sources and a profound knowledge of the navigational methods of the time. His conclusions addressed
the method of construction of the charts and the influence of the magnetic declination in their geometry, as well as the transition from the portolan-chart to the latitude chart. The results presented in this thesis clearly confirm Barbosa’s findings and
are an adequate homage to his valuable contribution to the history of Cartography.
As for my own contributions, I expect that the methodology here proposed may facilitate a fresh start and open new perspectives in the study of pre-Mercator nautical
cartography. The variety and richness of the conclusions drawn in the present research, from which those concerning the length of the degree, the advent of the latitude chart and the Cantino planisphere are probably the most relevant, are an eloquent confirmation of the utility and effectiveness of the proposed methodology.
Hopefully they will arouse the enthusiasm of others and help recognizing the need
for a multidisciplinary approach when studying old nautical charts.
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210
ANNEX A – CONTROL POINTS
North Atlantic
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Newfoundland & Greenland
Belle Isle
Horse Islands
Cape Race
Miquelon
Cape Farvel
51.95
50.21
46.67
46.94
59.77
-55.37
-55.78
-53.07
-56.33
-43.93
I. de frey Luis
C. Raso
Europe
21121120Lisboa
Iceland (northwest)
Iceland (west)
Iceland (south)
Orkney Islands
Tory Island
Slea Head
Carnsore Point
Isle of Man
Ramsey
Land's End
Isles of Silly
Isle of Wight (south)
Dover
66.43
63.82
63.47
58.98
55.27
52.10
52.17
54.23
51.87
50.07
49.93
50.58
51.13
-23.13
-22.75
-18.23
-3.07
-8.23
-10.48
-6.37
-4.53
-5.33
-5.72
-6.32
-1.30
1.32
torrey
b. asrey ?
tone ?
I de ina ?
c. de galez
b. asques ?
Jllanda
Jllanda
Jllanda
ilhas de orcam
Torra
biascua ?
torrey
deimam
Y. mã
porlinga ?
?ulinga
porlinga ?
buis ?
sanduc ?
dobra
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Europe (cont.)
Skagen
Zeebrugge
Cap Gris Nez
Le Havre
Guernsay
Île d'Ouessant
Île de Sein
Belle-Ille
Île de Ré
Pointe de Grave
Santander
Cabo de Peñas
Cabo Ortegal
Cabo Fisterra
Cabo Mondego
Ilhas Berlengas
Cabo Espichel
Cabo S. Vicente
57.75
51.33
50.87
49.52
49.47
48.47
48.03
47.33
46.20
45.57
43.47
43.67
43.77
42.88
40.18
39.42
38.42
37.00
10.63
3.20
1.58
0.06
-2.58
-5.08
-4.85
-3.18
-1.40
-1.07
-3.77
-5.85
-7.87
-9.27
-8.92
-9.52
-9.22
-8.95
garnasoy ?
bxam
Saym
bella illa
rey
cordan ?
Sandre ?
penas de ?
mondego
berlenga
c. despichel
mila
miranco
c. de cano ?
garnasoy
bxamte
saim
bela I.
Rey
santa Rita ?
samtander
penas de goca
ponta de ganta ?
c. finisterra
mõndego
berlemgas
c. de spichel
te
C. de sam b
bruxas
caliz
bruges
cales
garnasy
bxamte
saim
bela Ilha
Rey
garnasoy
bxam
Saym
Bella ilha
Rey
bela yilha
Rey
samtander
penas
Santandre
as penas de goça ?
santandre
torros
mondego
Cabo de Finisterra
mondego
as Berlengas
c. de fisterra
mondego
gerlemgas
Cabo de Sam Viçente
C. de sam b
Sta Maria
Samiguell
a Terceira
a palma
o pico
o fayall
ilha das flores
samta maria
sam miguel
Y. terceira
graciosa
pico
faial
froles
te
Azores
Santa Maria
São Miguel
Terceira
Graciosa
Pico
Faial
Flores
36.98
37.78
38.73
39.05
38.45
38.57
39.43
-25.10
-25.47
-27.22
-28.02
-28.37
-28.68
-31.22
a
Sta m
S. miguel
terceira
Grosa ?
o pico
faiall
Ilha da flores
a
de samta m
Y: de sammigell
graciosa
piquo
faiall
Y das frolles
a
I. Santa m
Y. terceira
graciosa
pico
Ilha do faiall
Y das frolles
212
Modern name
Mediterranean & Black Sea
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Spain & France
Punta Tarifa
Gibraltar
Malaga
Cabo de Gata
Cabo de Palos
Cabo de la Nao
Valencia
Barcelona
Cabo Creus
Marseille
Iles d'Hières
Albenga
36.02
36.12
36.72
36.72
37.63
38.73
39.45
41.42
42.32
43.30
43.02
44.05
-5.61
-5.35
-4.42
-2.20
-0.68
0.23
-0.32
2.23
3.32
5.28
6.48
8.23
zubalmar ?
malica
c de gata
gibaltar
malega
c. de gata
C. pala
C. de martim
balença
barcelona
c. de creos
marselha
gibal ?
malega
arbeniga
arbenamglia
Gibraltar
Malaga
C. de gata
C. de palla
C. de martim ?
balençia
barcelona
C. de cres ?
marselha
Ilhas de Rex
Arbenga
cabreira
formentor
cabraira
valença
barcelona
marselha
tamigere ?
gibraltar
malaga
c. de gata
c. dalcodia ?
balença
barcelona
c. de creos
marselha
Baleares
Cabo de Formentor
Cabrera
Punta Prima
39.95
39.15
39.8
3.22
2.95
4.28
cabraira
21321320Lisboa
Cap Corse
Cap Pertusato
Capo Caccia
Capo Carbonara
43.00
41.37
40.57
39.10
9.35
9.20
8.17
9.53
Corse & Sardinia
forti.. ?
cabreira
p. malio ?
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Italy
Genoa
Pisa
Piombino
Elba (west)
Roma
Ischia
Punta Licosa
Punta Vaticano
Punta de Faro
Capo San Vito
44.40
43.72
42.93
42.78
41.73
40.73
40.25
38.62
38.27
38.18
8.93
10.27
10.50
10.10
12.23
13.90
14.92
15.83
15.65
12.73
Ienoa
pissa
peambin
Ielba
Roma
Isola
pisa
plombi
Ielba
Roma
Isola
lenoba
Pissa
Pionbino
Roma
Isola
Dilicosa
bibarra
Adriatic Sea
Capo Passero
Capo Spartivento
Capo Rizzuto
Otranto
Vieste
Ancona
Ravena
Venezia
Trieste
Rt Kamenjak
Sibenik
Lastovo
Kepi Rodonit
36.68
37.93
38.90
40.10
41.88
43.62
44.63
45.42
45.65
44.77
43.72
42.75
41.58
15.15
16.07
17.10
18.52
16.18
13.52
12.27
12.42
13.70
13.92
15.85
16.87
19.45
C. de Spotabemto
otranto
ravena
beneçia
tieste
rabinto ?
sibanico
melada
c. de lipan
Greece & Aegean Sea
Akra Kyllinis
37.95
21.13
ancona
Ravena
Leneça
trieste
parenco
Sibinico
melada
pisa
plumbo
Roma
214
Modern name
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Greece & Aegean Sea (cont.)
Akra Akritas
Akra Tainaro
Akra Maleas
Kriti (west)
Kriti (est)
Kriti (south)
Korinthus
Akra Kafireas
Skiros (north)
Thessaloniki
Akra Paliouri
Akra Pines
Tassos (south)
Istanbul
36.72
36.38
36.43
35.30
35.30
34.92
37.95
38.17
38.98
40.62
39.92
40.12
40.57
41.08
21.88
22.48
23.20
23.52
26.32
24.73
22.97
24.58
24.48
22.93
23.75
24.30
24.65
29.05
c. de galo ?
actapas ?
pandico
serpo
s. mada ?
constantinopla
Black Sea
42.67
43.18
45.22
46.62
45.35
44.38
45.02
45.15
42.13
41.03
41.02
27.75
27.93
29.75
31.55
32.48
33.75
35.43
36.42
41.68
40.50
39.72
Mesombre
barnia ?
Salina
G. ote de doni ?
C. paro ?
Cafa
trapazamba
Facho
Risso
Trapasonda
21521520Lisboa
Nesebur
Varna
Sulina
Ochakov
Mys Tarthankut
Mys Ayya
Feodosyia
Korenkovo
Poti
Rize
Trabzon
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Black Sea (cont.)
Sinop
Amasra
42.03
41.75
35.18
32.38
silnipo
sarnastro
Sanastro
Turkey, Eastern Aegean Sea & Middle East
Baba Burun
Lesbos (southeast)
Chios (north)
Rodos (northeast)
Antalya
Tarsus
Iskenderun
Cyprus (east)
Cyprus (south)
Cyprus (west)
Tartus
Saida
Tel-Aviv
Gaza
Dumyat
39.47
39.02
38.60
36.47
36.85
36.78
36.62
35.70
34.57
35.12
34.90
33.57
32.05
31.53
31.50
26.07
26.62
26.00
28.22
30.75
34.80
36.13
34.58
33.03
32.28
35.87
35.38
34.75
34.43
31.92
C. de pantarna
Sardami ?
rodes
Xios
Rodas
Satalicos
Terrasso
Alexandreta
Chipre
Chipre
Chipre
Tortosa
Saitos
Jaffa
Garzaia
Dannata
alexandreta
Ilha chipre
tarta
Jafa
Garzra
damiata
Mediterranean African coast
Ras al Hamamah
Banghazi
Tripoli
Gabes
Cap Bon
Zalita
Annaba
32.95
32.12
32.90
33.90
37.08
37.53
36.90
21.72
20.05
13.18
10.12
11.05
8.93
7.87
c. de rapralon ?
bonança ?
triponell
Caparneus
C. buõ
tripoli de barbaria
G. de bona
bona
Tripoli de Barbaria
capasse ?
tripoli de barbaria
galita
G. de bona
galatias
216
Modern name
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Mediterranean African coast (cont.)
Dellys
Tenes
Oran
Mellila
Cap Trois Fourches
Ceuta
36.92
36.52
35.75
35.18
35.43
35.90
3.90
1.18
-0.63
-2.83
-2.97
-5.28
tanes
Cabo das forchas
ceuta
Melilla
C. de fulea ?
ceupta
tidellea
teney
ouram
melila
Tradelis
Monte Tenes
Ouram
melilla
C. das trez forcas
ceuta
tadelis
tenere
ouram
C. amte furca ?
ceuta
Africa
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Africa northwest
35.78
33.37
32.55
30.63
28.75
26.12
24.70
24.13
23.63
20.85
20.60
15.97
14.75
14.67
13.55
-5.77
-8.30
-9.28
-9.88
1.05
-14.52
-14.90
-15.53
-16.00
-17.12
-16.47
-16.52
-17.53
-17.40
-16.63
espartel
azamour
C. de ?
C denon
C debojador
angra dos ruivos
angra dos cavallos
rio douro
C bnco
arguim
Rio de canaga
Cabo verde
arzila
azamor
c. de samtini ?
C. de ger
C. denam
C. de bojador
G. dos ruivos
G. dos cavalos
R. do ouro
C. branco
arguim
R. de canaga
Cabo Vde
C. de nam
C. de bojador
angra dos Ruivos
angra dos cavallos
Rio do ouro
C. bramco
arguim
Rio de canaga
C. Verde
Arzila
Azamor
C. de ?
C. de grez ?
C. de nom
C. de boxador
Angra dos Ruivos
G. dos caballos
Rio douro
C. branco
arguim
Canaga
C. Verde
rio de gambia
R. de gambia
Rio de lagoa ?
R. de gãbia
tanigere ?
c. de nom
C. de bojador
G. dos Ruyvos
G. dos cavalos
R. do ouro
C. branco
arguym
R. de canaga
C. Verde
21721720Lisboa
Cap Spartel
Azmour
Cap Beddouza
Cap Rhir
Cap Chaunar
Cap Boujdour
Angra de los Rubios
(Angra dos Cavalos)
Rio de Oro
Ras Nouadhibou
Arguin
Sénégal River
Cap Vert
Isle de Gorée
Gambia River
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Africa northwest (cont.)
Cabrousse
Rio Geba
Cap Verga
Cestos River
Cape Palmas
Cape Three Points
Cape Coast
Lagos
Niger river
Malabo (south)
Ilha do Príncipe
Ilhéu das Rolas
12.48
11.70
10.20
5.43
4.37
4.73
5.10
6.42
4.27
3.20
1.62
0.00
-16.80
-15.60
-14.47
-9.60
-7.73
-2.05
-1.25
3.40
6.08
8.68
7.40
6.52
c. roxo
Rio grande
C. Rouxo
Cabo das palmas
C. das baixas
Cabo corso
Rio do lago
C. Rouxo
C. das palmas
C. das pontas
C. fermoso
Do princepe
Ilha bramca
Cabo Roxo
Rio grande
C. da Vga
R. dos Cestos
C. das palmas
C. das três pontas
C. Corço?
Rio do Lago
C. Formoso
Fernando Pó
Ilha do Príncipe
Madeira & Canary Islands
Madeira
Porto Santo
Selvagem Grande
Palma
Tenerife
Gran Canaria
Alegranza
32.80
33.05
30.15
28.68
28.24
27.97
29.40
-17.27
-16.35
-15.87
-17.85
-16.56
-15.58
-13.52
a madeira
p. sto
salvage
a palma
tenerife
gram canaria
I da Madeira
porto samto
salvages
a palma
tanarife
gram canaria
alegrança
Ilha da Madeira
porto samto
salvagens
a palma
tanarife
gram canaria
alegrança
a madeira
Porto sto
Selvagens
a palma
tanarife
a gram canaria
de samto antonio
samnicolaão
do sall
Ilha de samtiago
I. do fogo
santantom
sam nicolao
y. da madeira
porto samto
palma
tanarife
gram canaria
Cape Verde
Santo Antão
São Nicolau
Sal
Santiago
Fogo
17.07
16.62
16.75
15.07
14.92
-25.17
-24.32
-22.95
-23.62
-24.40
Snycolao
?sal
S tiago
fogo
samtantonio
ao
sam n
do sall
fogo
santiago
illa dei fogo
samtamtam
sam niculao
y. do sal
samtiago
fogo
218
Modern name
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Africa southwest
Cap Lopez
Annobón
Ponta do Padrão
Rio Quanza
Cabo de Santa Maria
Cabo Negro
Ascension Island
Cape Cross
Pelican Point
Sandwich Bay
Conception Bay
Hotentot Bay
Douglas Point
Luderitz Bay
Possession Island
Jammer Bucht Bay
Dreimaster Ridge
-0.62
-1.43
-6.08
-9.87
-13.42
-15.68
-7.95
-21.77
-22.93
-23.37
-23.90
-26.13
-26.30
-26.67
-27.02
-27.17
-27.68
8.72
5.62
12.33
13.32
12.53
11.93
-14.37
13.95
14.42
14.48
14.47
14.95
14.95
15.13
15.18
15.27
15.52
C. de lopo gllz
Anno bom
Rio do padrom
C. de Lopo Gonçalves
Ano Bom
Manicongo
Rio de Sam Lazaro
Cabo Lobo
C. Negro
Asçenssam
C. do padrom
apõnta dangsa
emseada branca
G. da conçepçam
G. de san bitoria
põta dos ilheos
G. de Sanxpoball
Terra de S. Silvestre
a lonba da pena
Africa south
-32.72
-34.35
-34.83
-34.47
-34.13
-33.88
-33.83
-33.77
18.08
18.50
20.02
20.87
22.18
25.93
26.28
26.47
G. Sta ellena
C. boa esperança
C. das agulhas
C. do infante
G. san bras
baía da Roca
ilheos chaos
puta do carrascall
21921920Lisboa
Saint Helen Bay
Cape Good Hope
Cape Agulhas
Cape Infanta
Mossel Bay
Algoa Bay
Bird Island
Cape Padrone
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Africa south (cont.)
(Praia das Lagoas)
Great Fish River
-33.57
-32.68
27.02
28.40
praia das alagoas
Rio do infante
Africa southeast
Cabo Santa Maria
Cabo das Correntes
Beira
Quelimane
Ilhas Primeiras
Ilha de Moçambique
Ilha Metundo
Kilwa Island
Mafia island
Zanzibar I. (north)
(Baixos de S. Rafael)
Pemba I. (northeast)
Mombasa
Malindi
Pate Island (east)
-25.97
-24.10
-19.88
-18.33
-17.10
-15.03
-11.15
-8.98
-7.90
-5.70
-5.20
-4.88
-4.08
-3.20
-2.12
32.98
35.50
34.82
36.98
39.10
40.73
40.68
39.60
39.75
39.30
39.17
39.87
39.70
40.15
41.15
Rio da lagoa
Cabo das Correntes
Çaffalla
Rio dos bons sinaes
Ilhas Primeiras
moçambique
Ilhas de Sam lazaro
Quillua
zamzibar
baixos de sam Rafaell
mõmbaça
melinde
pate
Africa northeast
Mogadishu
Cape Hafun
Cape Guardafui
Socotra
Bab-el-Mandeb
2.03
10.45
11.83
12.55
12.43
45.33
51.42
51.28
53.30
43.33
mogodoxo
çocotorá
Reinel ca. 1504
220
Modern name
India
Modern name
Angediva Island
Calecute
Kochi
Latitude Longitude
14.75
11.25
9.93
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
74.17
75.77
76.25
Cantino 1502
Reinel ca. 1504
angediba
caliqut
coçim
Americas
Modern name
Latitude Longitude
Modena ca. 1471
Aguiar 1492
Reinel 15th cent.
Cantino 1502
Reinel ca. 1504
Central America
Florida (south)
Cuba (East)
Puerto Rico (East)
Cabo Engaño
Jamaica
Guadeloupe
Trinidad (northeast)
25.28
20.22
18.25
18.60
18.12
16.25
10.85
-80.27
-74.13
-65.58
-68.32
-77.27
-61.17
-60.92
C. do fim de Abrill
Yssabela
boriquem
ilha espanholla
Jamaiqua
ilha de guadalupe
ilha de los cambales
Brazil
0.47
-2.37
-7.15
-16.30
-8.60
-28.62
-49.53
-44.17
-34.80
-39.01
-35.03
-48.80
Rio grande
golfo fremosso
Cabo de Sam Jorge
porto seguro
quaresma
Cabo de Sacta Marta
22122120Lisboa
Amazonas
Goldo do Maranhão
Cabo Branco
Porto Seguro
Ilha de S. Aleixo
C. Sta Marta Grande
ANNEX B – LATITUDE ERRORS
All latitude errors are in decimal degrees. A positive error means that the latitude
measured in the old map is to the north of the modern value; a negative value means
it is to the south. In the charts of the two last columns (Cantino and Reinel) the latitudes were measured using the existing (or inferred) scale of latitudes. In the other
cases, they were estimated on the basis of the implicit geographic graticules. The
shaded cells indicate errors equal or larger than one degree.
North Atlantic
Modern name
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
Cantino
1502
Reinel
c. 1504
3.3
-0.2*
-0.2*
-0.4*
-1.0*
-0.5
Newfoundland & Greenland
Belle Isle
Horse islands
Cape Race
Miquelon
Cape Farvel
51.95
50.21
46.67
46.95
59.77
2.4
Europe
Iceland (northwest)
Iceland (west)
Iceland (south)
Orkney islands
Tory Island
Slea Head
Carnsore Point
Isle of Man
Ramsey
Land's End
Isles of Silly
Isle of Wight (south)
Dover
Skagen
Zeebrugge
Cap Gris Nez
Le Havre
Guernsay
Île d'Ouessant
Île de Sein
Belle-ille
Île de Ré
Pointe de Grave
66.43
63.82
63.47
58.98
55.27
52.10
52.17
54.23
51.87
50.07
49.93
50.58
51.13
57.75
51.33
50.87
49.52
49.47
48.47
48.03
47.33
46.20
45.57
0.1
-0.4
0.0
0.1
0.0
0.1
-0.1
-0.1
0.0
0.0
-0.2
-0.2
-0.2
-0.2
0.0
-0.4
0.1
0.0
0.0
0.1
0.1
-0.2
0.5
-0.2
0.5
0.3
0.3
0.3
0.2
0.3
0.4
0.5
0.5
0.2
0.3
0.3
-0.1
-0.5
0.0
0.0
3.9
4.1
3.7
2.3
3.6
4.1
3.9
4.4
3.7
4.1
4.9
4.0
4.1
3.7
3.9
3.7
3.4
3.3
3.2
2.6
2.3
3.3
1.4
1.2
2.4
1.8
1.6
1.6
1.6
1.3
1.2
1.4
1.5
1.5
0.2
0.0
1.0
0.8
0.4
223
Modern name
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
Cantino
1502
Reinel
c. 1504
0.0
0.1
0.2
0.1
0.0
0.2
-0.1
-0.1
-0.2
0.1
0.5
0.8
0.6
0.4
-0.1
1.6
1.8
1.8
1.6
1.3
1.3
1.1
1.0
0.9
1.1
1.7
1.9
1.1
1.0
1.1
0.1
0.3
0.3
0.5
0.3
0.4
0.3
0.2
0.0
0.4
1.0
1.1
0.3
0.5
-0.4
Europe (cont.)
Santander
Cabo de Peñas
Cabo Ortegal
Cabo Fisterra
Cabo Mondego
Ilhas Berlengas
Cabo Espichel
Cabo S. Vicente
Santa Maria
São Miguel
Terceira
Graciosa
Pico
Faial
Flores
43.47
43.67
43.77
42.88
40.18
39.42
38.42
37.00
36.98
37.90
38.73
39.05
38.45
38.57
39.43
-0.3
0.0
-0.1
0.0
0.0
0.3
0.0
-0.2
0.3
0.5
0.7
0.3
-0.1
-0.1
0.8
0.0
0.0
0.0
0.3
0.2
0.2
0.1
-0.1
0.1
0.3
1.0
1.0
0.5
0.5
0.3
* Latitudes were measured on the oblique scale to the east of Newfoundland.
Africa
Modern name
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
Cantino
1502
Reinel
c. 1504
-0.3
0.1
0.3
0.1
0.4
1.3
1.1
0.7
0.7
0.8
0.8
1.0
1.3
0.2
0.6
0.9
0.4
0.6
1.3
1.1
0.4
0.2
0.3
0.2
-0.1
0.3
-0.1
0.3
-0.4
-0.3
-0.2
0.1
-0.4
-0.1
0.0
1.1
1.2
0.5
0.6
0.0
0.0
0.0
0.1
0.0
0.1
0.6
0.3
-0.1
-0.1
-0.2
-0.2
-0.6
-0.1
Africa northwest
Cap Spartel
Azmour
Cap Beddouza
Cap Rhir
Cap Chaunar
Cap Boujdour
Angra de los Rubios
Angra dos Cavalos
Rio de Oro
Cap Blanc
Arguim
Senegal river
Cap Vert
Isle de Gorée
Gambia River
Cabrousse
Rio Geba
Cap Verga
Cestos River
Cape Palmas
Cape Three Points
Cape Coast
Lagos
Niger river
Malabo (south)
Ilha do Príncipe
Ilhéu das Rolas
224
35.78
33.37
32.55
30.63
28.75
26.12
24.70
24.13
23.63
20.85
20.60
15.97
14.75
14.67
13.55
12.48
11.70
10.20
5.43
4.37
4.73
5.10
6.42
4.27
3.20
1.62
0.00
-0.1
0.1
0.4
0.3
1.3
0.7
0.8
0.6
0.6
0.8
0.7
0.4
0.8
0.9
0.7
0.4
0.7
1.6
1.5
3.1
3.2
-0.3
0.0
0.1
0.2
0.6
1.3
1.2
0.7
0.7
1.1
0.5
0.5
0.9
0.6
0.6
0.8
0.9
0.8
1.3
1.6
2.6
2.7
2.8
2.7
1.7
1.7
1.4
1.5
1.5
2.3
3.3
3.5
Modern name
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
Cantino
1502
Reinel
c. 1504
-0.2
0.0
0.2
0.5
0.3
0.5
0.4
0.1
0.1
0.2
0.4
0.3
0.2
0.3
0.6
0.8
0.4
0.7
0.1
0.3
0.4
-0.4
0.0
-0.1
-0.2
-0.5
-0.4
-0.1
1.0
1.5
1.1
1.3
1.1
1.0
1.4
1.3
1.4
1.0
1.2
1.0
0.4
0.4
0.1
0.7
0.7
-0.1
0.2
-0.4
Madeira & Canary Islands
Madeira
Porto Santo
Selvagem Grande
Palma
Tenerife
Gran Canaria
Alegranza
32.80
33.05
30.15
28.68
28.24
27.97
29.40
0.0
0.0
0.0
0.3
0.0
-0.3
0.0
Cape Verde
Santo Antão
São Nicolau
Sal
Santiago
Fogo
17.07
16.62
16.75
15.07
14.92
0.9
1.0
1.3
0.9
0.8
Africa southwest
Cap Lopez
Annobón
Ponta do Padrão
Rio Quanza
Cabo Santa Maria
Cabo Negro
Ascension Island
Cape Cross
Pelican Point
Sandwich Bay
Conception Bay
Hotentot Bay
Douglas Point
Luderitz Bay
Possession Island
Jammer Bucht Bay
Dreimaster Ridge
-0.62
-1.43
-6.08
-9.87
-13.42
-15.68
-7.95
-21.77
-22.93
-23.37
-23.90
-26.13
-26.30
-26.67
-27.02
-27.17
-27.68
1.7
1.4
2.3
-0.4
-1.6
0.1
0.0
1.1
-0.4
0.7
2.3
1.6
0.7
0.7
0.1
-0.4
-1.1
-1.9
-1.8
-3.0
Africa south
Saint Helen Bay
Cape Good Hope
Cape Agulhas
Cape Infanta
Mossel bay
Algoa bay
Bird islands
Cape Padrone
(Praia das Lagoas)
Great Fish River
-32.72
-34.35
-34.83
-34.47
-34.13
-33.88
-33.83
-33.77
-33.57
-32.68
0.3
0.5
1.1
1.4
1.6
1.9
1.8
1.9
2.1
1.9
Africa southeast
Cabo Santa Maria
Cabo das Correntes
Beira
Quelimane
Ilhas Primeiras
Ilha de Moçambique
-25.97
-24.10
-19.88
-18.33
-17.10
-15.03
0.1
-0.4
-0.3
0.4
-0.1
0.1
225
Modern name
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
Cantino
1502
Reinel
c. 1504
Africa southeast (cont.)
Ilha Metundo
Kilwa Island
Mafia island
Zamzibar I. (north)
(Baixos de S. Rafael)
Pemba island (northeast)
Mombasa
Malindi
Pate Island (east)
-11.15
-8.98
-7.90
-5.70
-5.20
-4.88
-4.08
-3.20
-2.12
-0.7
1.2
0.7
-0.2
-0.3
-0.4
-0.4
-0.1
-0.2
Africa northeast
Mogadishu
Cape Hafun
Cape Guardafui
Socotra
Bab-el-Mandeb
2.03
10.45
11.83
12.55
12.43
-0.9
-0.6
-0.5
-0.5
-1.3
India
Modern name
Angediva Island
Calecute
Kochi
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
14.75
11.25
9.93
Cantino
1502
Reinel
c. 1504
1.2
-0.6
-1.4
Americas
Modern name
Latitude Modena
(deg)
c. 1471
Reinel
th
15 cent.
Aguiar
1492
Cantino
1502
Central America
Florida (south)
Cuba (East)
Puerto Rico (East)
Cabo Engaño
Jamaica
Guadeloupe
Trinidad (northeast)
25.28
20.22
18.25
18.60
18.12
16.25
10.85
13.8
10.5
8.7
8.6
9.9
8.6
0.9
Brazil
Amazonas
Goldo do Maranhão
Cabo Branco
Porto Seguro
Ilha de S. Aleixo
Cabo Santa Marta Grande
226
0.47
-2.37
-7.15
-16.30
-8.60
-28.62
5.0
8.8
0.1
-0.9
-1.1
1.8
Reinel
c. 1504
ANNEX C – DISTRIBUTION OF
MAGNETIC DECLINATION
4
3
6
0
-1
0
1
-1
2
-4
1
4
-3
-3
-5
-20
-1
1
-1
-4
-6
0
0
-4
-5
3
-8 7
-40
2
20
40
60
80
-60
-7 -6
-8
-9
-
-1 0
11
3
-12
-1 3 4
-1
-40
2
-4 -2
-1
1
-1
-3
-2
2
3
-2
1
-8
-9 0
-1
-20
4
0
4
-3
-5 4
1
0
1
-7
0
6
5
3
2
-2
-4
-3
-5
-6
-20
-6
4
5
-4
-3
0
3
3
-1
-40
7
4
1
2
-5
4
2
-8
-6
4
0
-60
-1
2
3
5
-2
20
5
-4
-40
2
7
1
-8
0
8
6
2
-6
-1 -2
-7
-6
7
6
7
9
3
20
-1
2
4
-7
-1
-5
-9
40
4
8
40
8
3
3
6 5
-1 -1
4 5
-1
3
-1 1
- 10
-8 -9
10
-3-4
8
10
5
-6
1
-4
5
7
-1 3
7
-1 1 6
-
60
2
0
8
-2
-3
10
-1 1
60
5
4
9
0
-20
0
20
40
60
80
Figure C.1 – Spatial distribution of magnetic declination in the Atlantic and Indian Oceans, in
1200 and 1300, as yielded by the geomagnetic model of Korte and Constable (2005).
-3
-1
- 90
-8
-1
2
40
3
4
6
2
-2
3
-5 6
-1
60
-40
-7
-20
0
-5
-1
3
1
-5
-6
-60
1
4
-5
-4
-5
80
-7
-2
-1
-4
-2
-3
-5
-3
-1
0
-4
-3
20
-40
1
-6
0
-3
-20
-2
3
2
-1
5
-40
-7
6
-3
0
-3
-2
-6
-4
0
2
-1 0
4
5
-6
-4
-2
-8
-5
5
3
2
0
-2
-6 7
-
-1
-20
5
4
3
-3
1
0
0
-4
-9
-60
-2
1
2
5
1
-3
-20
-40
0
-4
-1
4
4
-3
-3
-3
-1
3
-1
3
2
-4
-1
-2
4
0
0
1
-2
20
5
-5
3
2
1
2
1
0
-9
-7
6
4
5
-4
-7
0
-1 1
6
20
3
-1
0
1
40
2
-4
4
4
2
1
5
2
3
3
-1
-9
60
-1
1
-1
- 198
-1
-1 7
-1 65
-1
-1 4
-1 3
5
2
-1
6
6
-5
4
5
7 7
40
-1 4
6
4
-1 0 11
-8
-7
-6
-1187 6
- -1 1 5
-
60
5
1
0
2
-3 -
2
0
20
40
60
80
227
ANNEX C – DISTRIBUTION OF MAGNETIC DECLINATION
2
-6
-7 -8
1
3
1
4
-4
-3
-1
0
1
-7
-3
1
-1
-6
3
-9
-6
2
0
-11
60
-9
40
-8
20
2
-40
4
0
-7
2
4
-20
-5
3
1
0
-1
-40
-1
3
5
3
0
-2
2
5
-20
4
5
3
5
-8
-5
-3
-2
6
-4
0
4
1
3
3
-7
4
4
-10
-6
-4
1
0
2
-20
-60
-8
2
3
-1
2
0
-40
-6
-3
1
3
-5
-2 -1
2
-2
2
1
-4
0
-1
-4
-6
4
0
-2
-3
-5
20
3
-3
-2
4
0
-6
-5
-3
-2
-5
-4
-1
1
40
-4
1
-8
20
2
3
4
2
0
-2
-2
5
40
-1
-2 -3
-6
0
1
2
3
4
1
-1 0
-1 6
-1 5 4 -1 3
-1
-1 2 0
1 9
-1 1 - -
60
0
-1
2
-7 -9
-8
-4
-1 -1
0 1
3
-12
-1
2
1
-5
-5
-1 7
-1 6
-1 5
-1 4
60
80
-60
-40
-20
0
20
40
60
80
-1
3
-7
2
-4
-5
-1
-1
-2
-8
-4
-4
2
-7
-3
2
2
-9
0
-5
3
2
-3
-4
-5
1
-3
0
0
20
1
3
-2
-7
1
0
-2
5
-1
3
-2 -3
-6
40 -5
4
-1
-2
-6
-4
20
-1
1
-6
-6
-9
-5
-6
2
0
-3
3
2
-1
-5
-8
-4
-2
-3
-1 3
60 -1 2
-1
4
40
-1 0
-9
1
-4
4
60 -1 3
-11
0
2
1
-7
-1 0
-8
0
4
5
6
-1 3
-5
3
0
20
40
-1
8
-10
60
2
-6
1
3
0
-20
4
-40
-8
-40
4
-60
-1
5
-14
3
-1 2
5
4
-40
-13
7
-1 0
-9
-1 1
-20
-12
-4
-2
-1 1
2
-9
-5
-4
3
4
-6
-7
-20
0
1
-3
3
2
-7
1
2
2
-3
4
-8
-2
0
-1 0
0
3
1
-1
-6
-1
3
80
-60
-40
-20
0
20
40
60
80
228
ANNEX D – THE EMP MODEL
In this annex the interface and formulae of the EMP model application are described.
The annex has two sections: in the first (General description and use), the general
structure and working options are explained in detail; the second (Formulae) contains the mathematical expressions used in the application.
General description and use
The EMP model application was developed with the MatLab® interpreted language
and contains the following modules:
•
EMP: the main module of the application, which controls the interface window;
•
loxo: the module dealing with rhumb-line tracks;
•
ortho: the module dealing with great circle tracks;
•
world: data file containing the geographic coordinates of the world coastlines
used in the application.
Options
All options available to the user are accessed through the interface window in Figure
D.1. They are organized in seven categories, corresponding to the following boxes:
−
Method: in this box the type of track and charting method are selected:
•
Orthodromes: the initial distances and directions between points are calculated
along great circles;
•
Loxodromes: the initial distances and directions between points are calculated along
rhumb lines;
•
−
Point of fantasy: both distances and directions between points are adjusted in
the optimization process, according to the weighting parameter w;
−
Set point: positions of the points in the plane are adjusted as to conserve their
original ordinates, which represent the latitudes;
−
Mixed model: the charting method (‘point of fantasy’ or ‘set point’) is defined
for each particular pair of points. This choice is only applicable when the set of
tracks used as input is provided by an external file.
Sliding scale and input box distances/directions: used to define the value of the
weighting parameter w, between 0 and 1. If 0 is chosen only distances are considered; if 1 is chosen, only directions are considered; in general, the adjustments made
229
to the positions of the points during the optimization process vary with the value of
w, according to expressions D.11 and D.12.
Figure D.1 - Interface of the EMP model application.
−
Geographic grid: definition of the geographic limits and spacing between meridians and parallels in the output.
•
S/N: the lower and upper latitude limits, in decimal degrees (N is positive and S is
negative);
•
W/E: the lower and upper longitude limits, in decimal degrees (E is positive and W is
negative);
− Spacing (deg): spacing between meridians and parallels, in decimal degrees.
−
•
Parallels: parallels are depicted when this check button is selected;
•
Meridians: meridians are depicted when this check button is selected;
•
Coastline: coastlines are depicted when this check button is selected;
Input points: choice of the set of points used as input:
•
230
Use geographic grid: the latitude and longitude intersections of the geographic grid
defined in the Geographic grid box are used as input;
− Spacing: the spacing between parallels and meridians defined in the Geographic
grid box may be subdivided for the purpose of creating the set of input points. For
example, a value of 2:1 indicates that the original spacing is halved.
−
•
Use track: the tracks provided by the external file indicated in the text box are used
as input;
•
Load new track: an external file containing a set of tracks is imported to be used as
input. The file contains a list of latitudes and longitudes, the associated values of
magnetic declination and a matrix defining what type of charting method is to be
used for each pair of points;
•
Show tracks: the external tracks are depicted in the output when this check button
is selected.
Distortion info: allows tor the depiction of distortion information in the output.
•
Tissot ellipses: plots Tissot ellipses in each grid intersection;
− size: the size of the ellipses can be chosen using a number between 1 and 4.
•
−
−
Max angular distortion: plots isolines of maximum angular distortion.
Magnetic declination: allows for the inclusion of magnetic declination affecting
all directions. Pre-calculated matrices of 1° x 1°, containing the world spatial distribution for the years of 1200 through 1500, can be chosen. Two special cases
are considered:
•
mixed: the magnetic declination refers to the year 1500 everywhere, except in the
Mediterranean, where it refers to 1300;
•
file: the values of the magnetic declination in each point are provided by the external file containing the tracks used as input.
Show lines: allows for the plotting of great circle or rhumb lines, and the corresponding distance circles, centered in a chosen geographic position.
•
Loxodromes: projected rhumb lines radiating from a chosen position are plotted;
•
Orthodromes: projected great circles radiating from a chosen position are plotted;
•
Distance circles: lines of constant rhumb-line or great circle distance from chosen
position.
− Origin (lat, long): latitude and longitude, in decimal degrees, of the origin of the
spherical lines and distance lines.
−
Constraints: allows for the imposition of some restrictions to the pairs of points
to be used as input. The choices do not apply when an external file of tracks is
used.
•
No constraints: all possible pairs of points are considered;
231
•
Only from central meridian: only the tracks containing, at least, a point on the central meridian are considered;
•
Only from parallel: only the tracks containing, at least, a point on the parallel whose
latitude is defined in the input box are considered;
•
Distances less than: only the tracks with lengths less or equal the distance specified
in the input box are considered (distances in decimal degrees);
•
Only from position: only the tracks starting from the geographical position defined
in the input boxes (latitude and longitude in decimal degrees) are considered.
Formulae
In this section the mathematical expressions used to determine the rhumb-line
courses and distances, to numerically adjust the positions of the points on the plane
and to determine the various quantities shown on the output are presented and
briefly explained1.
Rhumb line distances and directions
For each pair of points of geographic coordinates (ϕ1, λ1) and (ϕ2, λ2), the corresponding rhumb-line course, C, and distance, D, are calculated using the following
expressions:
tan C =
∆λ
∆Ψ
[D.1]
D = ∆ϕ sec C
[D.2]
  π ϕ 
Ψ = ln  tan  +  
  4 2 
[D.3]
∆λ = λ2 − λ1
[D.4]
∆ϕ = ϕ 2 − ϕ1
[D.5]
∆Ψ = Ψ2 − Ψ1
[D.6]
where
and ∆ϕ, ∆λ and ∆Ψ are, respectively, the differences of latitude, longitude and meridional parts. During the initialization phase of the loxo module, the values of C, D
and δ, where δ is the magnetic declination, are determined for each track. These
quantities will be later used in the optimization process, to adjust the position of all
1
Although the application also allows for the use of great circles tracks, the possibility is not explored
in the present thesis and the corresponding formulations are not shown here.
232
points. Two alternative charting methods may be used to determine the position of
points 1 and 2 in the plane: the method of the point of fantasy, in which the relative
positions of the two points are given by a segment of length D oriented in the direction of the magnetic course, Cm = C – δ; and the set point method, in which the relative positions of the two points are given by the difference of latitudes ∆ϕ and either
the magnetic course Cm (course prevails) or the distance D (distance prevails) between them. When the magnetic declination is zero, or is not considered, the three
elements of information are coherent and the relative positions obtained using all
methods coincide.
Coordinate adjustments
Once the quantities defined above are calculated, an optimization routine starts during which the plane coordinates of the points are adjusted. Starting with some arbitrary initial positions in the plane (the application assumes that the longitude and
latitude are used for that purpose), the optimization process consists of a series of
iterations during which those coordinates are gradually adjusted so that the sum of
the differences between the rhumb-line and the plane distances and directions in all
pairs of points are minimized. At the end of each iteration, the root-mean-square
errors of distances and directions are calculated, using the expressions:
S dist
1
2
=  (D k − d k ) 
N  n

S dir
1
2
=  (Ck − ck ) 
N  n

1/ 2
∑
[D.7]
1/ 2
∑
[D.8]
where N is the number of pairs, and dk and ck are, respectively, the present distance
and direction between points in pair k. The iteration process ends when the successive values of Sdist and Sdir no longer show significant variations or a pre-defined maximum number of iterations is reached.
In Figures D.2 (point of fantasy) and D.3 (set point), A is the present position of some
point, whose adjustment relative to point B is being calculated at iteration i. O represents the mid-point of the segment connecting A to B. The adjustments dx and dy to
the position of A are calculated using the following expressions:
Point of fantasy
dx =
∆x
− [dx0 cos(wθ ) + dy0 sin(wθ )]
2
[D.9]
233
dy =
∆x
− [− dx0 sin(wθ ) + dy0 cos(wθ )]
2
[D.10]
where
dx0 =
∆x 
d − D
1 − (1 − w)

2 
D 
[D.11]
dy 0 =
∆y 
d − D
1 − (1 − w)

2 
D 
[D.12]
θ = Cm − arctan(∆x ∆y ) is the angle between the course Cm and the direction of
the line connecting the two points on the plane, d is the present distance, and
∆x and ∆x are the abscissa and ordinate differences between A and B.
∆x/2
O
dx0
dy0
∆y/2
D/2
Cm
A
θ
θ’
dx
A’
d/2
dy
Figure D.2 – Coordinate adjustment for the method of the point of
fantasy, with w = 0.5.
Set point
Course prevails:
dx =
∆x ∆y
−
tan C m
2
2
[D.13]
dy = 0.
Distance prevails:
dx =
∆x 1
±
D 2 − ∆y 2
2 2
dy = 0.
234
[D.14]
O
∆x/2
O
∆x/2
D/2
∆y/2
∆y/2
Cm
A
A’
A
A’
dx
dx
Figure D.3 – Coordinate adjustment for the set point method. Left: magnetic course prevails;
right: distance prevails.
Tissot ellipses and angular distortion
The following expressions were used for calculating the orientation and size of the
ellipses of distortion at each grid node2:
F
cos i =
[D.15]
EG
tan 2 β =
G sin (2i )
E cos 2 ϕ + G cos (2i )
[D.16]
 ∂x ∂ϕ 

tan γ = 
∂
y
∂
ϕ


[D.17]
a = sin i
GE
E cos ϕ sin β + G sin 2 (i − β )
[D.18]
b = sin i
GE
,
E cos ϕ cos β + G cos2 (i − β )
[D.19]
2
2
2
2
where a and b are the major and minor semi axes of the projected ellipse, i is the
angle between the meridian and the parallel, β is the angle between the meridian
and the major axis of the ellipse and γ is the angle between the y-axis and the meridian (see Figure D.4), and E, F and G are the Gauss coefficients:
2
 ∂x   ∂y 
E =   +  
 ∂ϕ   ∂ϕ 
2
2
[D.20]
The formulae in Bugayevskiy and Snyder (1995, p. 15-20) were used.
235
F=
∂x ∂x ∂y ∂y
+
∂ϕ ∂λ ∂ϕ ∂λ
2
 ∂x   ∂y 
G =  + 
 ∂λ   ∂λ 
[D.21]
2
[D.22]
N
y
γ
b
β
i
a
E
Figure D.4 – Projected ellipse of distortion
At grid node (i,j), the partial derivates of x and y are calculated by the approximate
expressions:
∂x xi −1, j − xi +1, j
≈
∂ϕ
2∆ϕ
[D.23]
∂x xi , j +1 − xi , j −1
≈
∂λ
2∆λ
[D.24]
∂y yi −1, j − yi +1, j
≈
∂ϕ
2∆ϕ
[D.25]
∂y xi , j +1 − xi , j −1
,
≈
∂λ
2∆λ
[D.26]
where ∆ϕ and ∆λ are, respectively, the latitude and longitude spacing between parallels and meridians, and the indexes i and j refer, respectively, to the lines (parallels)
and columns (meridians) of the geographic grid.
The maximum angular distortion, ω, at each grid node is yielded by the expression:
sin 2ω =
236
a −b
a+b
[D.27]
ANNEX E – SCALES AND
MODULES
Table E.1
Estimated lengths of the degree of latitude, in leagues,
on charts depicting a scale of latitude (Franco, 1957, p. 162)
#
Author
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Pedro Reinel
Anonymous (Reinel?)
Anon. Portuguese
Pedro Reinel
P. Fernandes
Diogo Ribeiro
Gerolamo Verrazano
Jorge Reinel
Gaspar Viegas
Anonymous, Spanish
Anonymous, Spanish
Anonymou, Spanish
João Freire
Lopo Homem
Diego Gutiérrez
Anon. Spanish
Bartolomé Olives
Lázaro Luís
Lázaro Luís
Fernão Vaz Dourado
Fernão Vaz Dourado
Fernão Vaz Dourado
Fernão Vaz Dourado
J. Martinéz
Anonym. Portuguese?
Anonym. Portuguese?
J. Martinéz
Juan Riezo
Juan Martinéz
Spanish
1504
1506
1502
ca. 1520
1528
1529
1529
> 1534
1534
1536
1541
1545
1546
ca. 1550
1550
16th cent.
1562
1563
1563
1568
1568
1570
1570
1576
1576
1576
1579
1580
1586
1588
N=12.5 N=10
17.9
17.4
18.4
17.9
17.6
18.0
17.8
17.6
18.1
Notes
Numbered scale
Cantino planisphere
17.8
17.4
17.7
Numbered scale
Numbered scale
Numbered scale
17.5
Numbered scale
17.4
Numbered scale
17.4
Numbered scale
18.2
18.4
17.9
17.8
17.9
17.8
17.8
17.7
17.8
18.1
17.8
17.4
17.1
17.8
17.8
237
ANNEX E – SCALES AND MODULES
Table E.1 – Cont.
#
31
32
33
34
35
36
Author
J. Martinéz
J. Martinéz
J. Martinéz
J. Martinéz
Spanish
Denis de Rotis
Year
1591
1591
1591
1591
1640
1674
N=12.5 N=10
Notes
17.9
17.9
17.0
18.1
18.0
17.9
Note: The information in the first column refers to the numbering given by Franco (1957).
The identification of the charts was found, whenever possible, from the sources given by
Franco.
Table E.2
Estimated lengths of the degree of latitude, in leagues,
on Portuguese charts depicting a scale of latitude
Chart
Anonymous, 1502
Pedro Reinel, c. 1504
Anonymous, c. 1505
Anonymous, c. 1506
Anonymous, 1510
Anonymous, ca. 1517
Anonymous, ca. 1518
Anonymous, ca. 1535
Jorge Reinel, ca. 1540
Atlas Miller, 1519
Atlas Miller, 1519
Atlas Miller, 1519
Diogo Ribeiro, 1529
Diogo Ribeiro, 1529
Anonymous, 1545
João Freire, 1546
Anonymous, ca. 1560
Anonymous, ca. 1560
Lopo Homem, 1554
Diogo Homem, 1558
Sebastião Lopes, 1558
Bartolomeu Velho, 1560
238
Plate
5
8
7
6
9
10
11
14
15
17
22
24
39
40
79
75
80
96 A
27
108
390
227
201
202
203
204
N=12.5 N=12
17.8
18.2
17.2
19.3
18.1
18.1
18.1
18.9
18.3
16.5
16.6
16.2
17.6
17.7
17.5
18.2
17.8
17.3
18.6
18.6
17.3
N=10
(17.1)
(17.5)
(16.6)
(18.6)
(17.4)
(17.4)
(17.4)
(18.1)
(17.5)
(15.8)
(15.9)
(15.6)
(16.9)
(17.0)
(16.8)
(17.5)
(17.1)
(16.6)
(17.9)
(17.8)
(16.6)
17.9
17.9
17.8
18.0
18.7
Notes
Cantino planisphere
Atlantic
Atlantic & Mediterranean
Kunstamnn III, Atlantic
Indian Ocean
Indian Ocean
Indian Ocean
Atlantic
Atlantic
Northern Europe
South Atlantic
Atlantic
Planisphere
Planisphere
Planisphere
Gulf of Guinea
Planisphere
Africa northwest, red Sae
Planisphere
Brazil
Atlantic
Strait of Magellan
Western Pacific
Americas
Atlantic
Indian Ocean
ANNEX E – SCALES AND MODULES
Table E.2 – Cont.
Chart
Diogo Homem, 1563
Lázaro Luís, 1563
Lázaro Luís, 1563
Anonymous, ca. 1565
Anonymous, ca. 1565
Fernão Vaz Dourado, 1568
Diogo Homem, 1568
Anonymous, 1583
Luís Teixeira, ca. 1600
J. Teixeira Albernaz, 1626
António Sanches, 1641
João Teixeira, 1646
Plate
127
212
219
405
406
244
131
270
280
284
330
408
360
446
530
508
N=12.5 N=12
18.3
17.3
17.1
18.1
18.1
17.5
18.1
17.9
19.4
17.6
17.2
17.6
N=10
(17.6)
(16.6)
(16.4)
(17.4)
(17.4)
(16.8)
(17.4)
(17.1)
(18.6)
(16.9)
(16.6)
(16.9)
17.9
17.6
17.5
17.4
Notes
Mediterranean
Atlantic
Caribbean Sea
Atlantic
Caribbean Sea
Eastern archipelago
Brazil
Ceylon to Japan
Africa northwest
Ceylon to Japan
Caribbean Sea
Planisphere
Atlantic & eastern Pacific
Brazil
South Atlantic
Atlantic & Caribean Sea
Note: All measurements were made on the chart reproductions of Portugaliae Monumenta
Cartographica (Cortesão and Mota, 1987). The second column (Plate) indicates the number
of the plate containing each reproduction. The numbers inside parentheses, relative to sections of 12 leagues, are given for comparison purposes.
239
ANNEX F – MILES AND METERS
Chart/Track
C. Boujdour
C. S. Vicente
d (miles)
M (m)
Dulceto, 1330
C. S. Vicente
C. Fisterra
d (miles)
M (m)
C. Fisterra
Ouessant
d (miles)
M (m)
Gibraltar
C. Corse
d (miles)
M (m)
429
1525
543
1291
1262
1171
507
1383
1253
1180
1187
1245
Dulceti, 1339
647
2038
430
1521
Cresques, ca. 1375
867
1521
406
1611
Soler, 1385
420
1557
500
1402
1179
1254
F. Beccari, 1403
457
1431
551
1272
1162
1272
Virga, 1409
462
1416
500
1402
1262
1171
393
1664
491
1428
1044
1416
Anon. Venice, 1420
424
1543
563
1245
1264
1169
Cesanis, 1421
418
1565
488
1437
1176
1257
Anon. Magreb, 1421
457
1431
1250
1182
1142
1294
Viladesters, 1413
823
1602
Viladesters, 1423
722
1826
385
1699
Giroldi, 1426
639
2064
493
1327
475
B. Beccari, 1435
476
1473
1377
529
1325
Vallseca, 1439
864
1526
492
1329
548
1279
1194
1238
At. Valseca, ca. 1440
820
1608
455
1437
517
1356
1129
1309
439
1490
470
1492
Vallseca, 1449
1254
1179
Rosell, 1449
1189
1243
Bianco, 1448
Ripol, 1456
458
1428
688
1019
Modena, ca. 1471
848
1555
481
1360
518
1353
Reinel 15th cent.
789
1671
500
1308
470
1492
1032
1432
Aguiar, 1492
824
1600
511
1280
543
1291
1138
1299
Cantino, 1502
817
1614
467
1401
517
1356
1100
1344
Reinel, ca. 1504
822
1604
456
1434
524
1338
1172
1250
Averages
790
1686
450
1461
523
1349
1179
1258
Averages Italian
769
1725
460
1427
517
1360
1189
1248
Averages Majorcan
820
1613
452
1457
527
1344
1155
1283
Averages Portug.
820
1609
483
1357
514
1366
1113
1331
Note: d is the distance along the track, in miles, as measured on the charts; M is the corresponding length of the mile, in meters.
240
ANNEX G – COURSES AND
DISTANCES IN CHARTS
Table G.1
Courses and distances in the northern Atlantic:
charts of the fifteenth century (D0 in degrees, d in leagues)
Modena ca. 1471
Track
C0
Reinel 15th cent
Aguiar 1492
D0
C
d
C
d
C
d
229.3
271.3
8.6
14.1
228.9
274.2
173
277
227.0
275.0
170
258
225.5
273.9
166
260
Terceira - Madeira
356.3
126.3
173.5
13.7
10.0
22.3
-132.3
175.5
-198
434
352.5
132.2
175.0
265
190
419
353.2
133.7
174.3
293
194
439
201.5
17.4
200.4
316
201.0
303
197.8
325
Table G.2
Courses and distances in the northern Atlantic and Mediterranean:
charts of the sixteenth century (D0 in degrees, d in leagues)
Cantino 1502
Track
C0
Reinel ca. 1504
D0
C
d
C
d
229.2
8.6
230.7
172
227.4
174
271.3
356.3
313.8
14.1
13.7
30.8
273.3
352.9
326.8
278
269
473
274.2
352.6
315.1
274
269
601
Terceira - Madeira
126.3
173.5
333.1
10.0
22.3
23.6
130.5
173.9
003.2
192
406
380
133.3
174.0
344.2
200
414
369
292.7
163.9
20.6
5.3
303.2
162.9
316
93
300.8
164.3
390
091
Madeira – S. Nicolau
Madeira – P. Tarifa
P. Tarifa – C. Carbonara
201.5
071.5
075.6
17.4
10.1
12.4
200.3
073.4
071.5
297
193
258
200.5
069.1
073.0
295
203
283
C. Carbonara - Alexandria
Gran Canaria - Cuba
114.9
261.7
18.5
54.0
105.6
273.1
394
1010
---
---
Gran – Canaria – S. Nicolau
216.0
292.3
340.2
13.8
20.2
12.1
214.5
299.6
345.2
230
261
155
214.2
287.7
--
228
358
--
253.1
12.8
264.2
189
--
--
241
ANNEX G – COURSES AND DISTANCES IN CHARTS
Table G.3
Courses and distances in the southern Atlantic
and Indian Ocean (D0 in degrees, d in leagues)
Cantino 1502
Track
242
C0
D0
C
d
S. Nicolau – P. Seguro
S: Nicolau - Trinidad
203.7
260.8
36.0
36.0
195
262
639
726
S. Nicolau – C. Palmas
C. Palmas – I. Rolas
I. Rolas – C. Negro
126.9
107.1
161.2
20.4
14.9
16.6
126
104
158
420
335
313
162.4
111.2
19.6
1.3
161
086
334
29
078.7
056.1
036.0
5.4
1.9
10.6
074
060
046
107
50
156
C. Correntes – Moçambique
Moçambique – Malindi
Malindi – Muqdishu
028.5
357.2
044.7
10.3
11.8
7.4
031
003
043
199
209
105
Muqdishu -– C. Guardafui
C. Guardafui – Bad-el-Mandab
031.0
274.4
11.4
7.8
047
269
268
112
Malindi – Calecute
P. Seguro – C. Good Hope
067.8
109.2
38.3
54.7
071
107
736
1101
ANNEX H
CHART REPRODUCTIONS
Figure H.1 – Anonymous chart of the Atlantic coasts of Europe and Africa, ca. 1471.
Figure H.2 – Chart of the Mediterranean, Western Europe and the African coast by Jorge de
Aguiar, 1492
Figure H.3 – Chart of the Western Mediterranean, Western Europe and the African coast by
Pedro Reinel, fifteenth century.
Figure H.4 – Anonymous Portuguese chart of the world, 1502 (Cantino planisphere).
Figure H.5 – Chart of the North Atlantic and Western Mediterranean by Pedro Reinel, ca.
1504.
243
ANNEX H – CHART REPRODUCTIONS
Figure H.1 – Anonymous chart of the Atlantic coasts of Europe and Africa, ca. 1471. Size of
the original: 617 × 732 mm. Biblioteca Estense Universitaria, Modena (C.G.A.5c).
244
Figure H.2 – Chart of the Mediterranean, Western Europe and the African coast by Jorge de
Aguiar, 1492. Size of the original: 1030 × 770. Beinecke Rare Book and Manuscript Library,
University of Yale, New Haven.
245
Figure H.3 – Chart of the Western Mediterranean, Western Europe and the African coast by
Pedro Reinel, fifteenth century. Size of the original: 711 x 948 mm. Archives Départementales de la Gironde, Bordeaux (2 Fi 1582 bis).
246
Figure H.4 – Anonymous Portuguese chart of the world, 1502 (Cantino planisphere). Original
size: 2200 x 1050 mm. Biblioteca Estense e Universitaria, Modena (C.G.A.2).
247
Figure H.5 – Chart of the North Atlantic and Western Mediterranean by Pedro Reinel, ca.
1504. Original size: 893 x 620 mm. Bayerisch Staatsbibliotek, Munique (Cod Ican 132).
248
AUTHOR INDEX
Albacar, Martín Cortés de 29, 40, 88, 100, 185
Albuquerque, Luís de 2, 13-15, 17, 28, 30, 34,
37, 39, 42, 43, 63, 65, 87, 133, 137, 173
Alegria, Maria Fernanda 26, 87, 88
Álvares, Francisco 137
Amaral, Joaquim Ferreira do 27, 87-89, 109,
127
Astengo, Corradino 107
Axelson, Eric 137
Azurara, Gomes Eanes de 35, 43
Balletti, Caterina 48, 53
Barbosa, António 3, 13, 34-38, 41, 92, 94, 97,
98, 119, 126, 127, 150, 185-187, 193, 198
Barros, João de 14, 156
Boutoura, Chrysooula 48, 51
Bugayesky, Lev 235
Campbell, Tony 22, 85
Casaca, João 39-41, 125
Castro, D. João de 7, 18, 20, 21, 38, 40, 62-65,
96, 97, 163-165, 175, 178, 181, 186, 189,
191
Chaves, Alonso de 29
Constable, Catherine 21, 25, 26, 62, 63, 93, 97,
114, 119, 159, 160, 164, 175, 177, 178, 186,
189, 193, 196, 226, 227
Cortesão, Armando 2, 15, 16, 21, 26, 31, 34,
39, 42, 43, 63, 65, 85-90, 100, 101, 130,
132-134, 136, 137, 174, 239
Costa, Abel Fontoura da 16, 17, 34, 39-41, 86,
104, 107, 137, 144
Costa, Francisco da 15, 30-31, 42, 88, 185
Coutinho, Carlos Viegas Gago 14, 34, 63
Destombes, Marcel 100, 145
Fernández-Armesto, Felipe 6, 184
Franco, Salvador García 39, 41, 42, 99-101,
107, 145, 191, 237
Gaspar, Joaquim Alves 25, 28, 32, 34, 95, 96,
98, 100, 121, 175
Genevey, A. 21, 63
Gernez, Winter D. 90, 118, 127
Gonçalves, António Manuel 16
Guerreiro, Inácio 26, 89, 173
Hardy, Rolland 53
Harrisse, Henry 132, 138, 139
ICA (International Cartographic Association) 45
Jenny, Bernhard 52-54
Korte, M. 21, 25, 26, 62, 63, 93, 97, 114, 119,
159, 160, 164, 175, 186, 189, 193, 196, 226,
227
Lanman, Jonatham 2, 23, 24, 98, 99
Leite, Duarte 3, 34, 88, 104, 130-134, 139, 140,
142, 144-147
Lisboa, João de 16, 17, 37, 39, 40, 42, 63, 97,
100, 119, 127, 173, 186
Livieratos, Evangelos 48, 51
Loomer, Scott Allen 2, 24, 25, 47, 61
Maling, Derek 45
Marques, Alfredo Pinheiro 26, 43, 87-89
Matos, Jorge Semedo de 170, 171, 173
Matos, Luís de 28
Mead, William 135
Mitchell, A. Crichton 18
Monmonier, Mark 34
Mota, Avelino Teixeira da 2, 26, 34, 39-43, 8590, 100, 130, 132-135, 137, 140, 157, 174,
239
Nordenskiold, Adolf Erik 22
Nunes, Pedro 12, 21, 27-29, 31, 33, 38, 40, 63,
71, 98, 100, 134, 166-171, 174, 185, 187,
194
Pereira, Duarte Pacheco 14, 39-41, 43, 101,
102, 136, 138, 139, 146, 153, 180, 191, 195
Pereira, Moacyr 130, 139-141
Peres, Damião 86, 115, 135, 138
Pimentel, Manuel 15, 16, 39, 97, 101, 185
Pujades, Ramón 3, 6, 22, 23, 29, 38, 106, 136
Randles, W. G. L. 11, 40, 137
Ravenstein, Ernest George 14, 137
Rebelo, Jacinto de 15, 16, 39, 42, 100, 173
Roukema, Edzer 130, 139, 140
Sandman, Alison 29
Siemon, Karl 73
Silva, Luciano Pereira da 2, 34
Snyder, Jonh 34, 73, 235
Tobler, Waldo 4, 50, 51, 73, 74, 78, 190
Webster, Adrian 52
Winter, Heinrich 85, 90
Woodward, David 3
249

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