Certaine errors in navigation
considered as a turning point in the literature about navigation and
a crucial step towards its mathematization.
Edward Wright (1561
– 1615) studied at Cambridge University and in 1589, after some
years teaching there, he took part on an expedition to the Azores
with the goal to explore and pirate the area. In that same year he
started working in his book
and, in 1592, he submitted the first copy to the Earl of Cumberland.
Between 1594 and 1597 he lived in London where he made essential
studies and observations for his work.
Errors in Navigation1
published in 1599.
It’s a work of great importance for the history of
navigation and had two more editions in the 17th
In that same year, Wright also ordered the publishing of his
translation of the important work of Simon Stevin,
with the title
The Haven-finding Art.
Errors in Navigation
is a book with some
original characteristics for its time: one
can notice the absence of the usual introduction to the
of chapters on the calculation of Holy days
and chapters on tides and winds. The book is divided in 4 main parts
– deals with the errors associated to the common nautical chart.
Mathematical basis of Mercator’s projection.
– deals with the variation of the magnetical compass. Method for
knowing its value.
– deals with the use of the cross-stafe and ways to avoid errors.
– corrects/updates values of sun’s declination’s and stars tables
and of other constants necessary to navigation.
To find Pedro Nunes’
name in Wright’s
is not a difficult task, alongside with other notable names as
Mercator, Frisius, Brahe, Ortelius, Cortés, Ramus, etc. Recently,
Henrique Leitão pointed out a preoccupying lack of references to any
relation between Nunes’ and Wright’s works in international
historiography. This would not be, for sure, Wright’s intention
since he keeps “no secret about his intellectual debt. Not only does
he cite the Portuguese by name, but he even explains in the Preface
that the problems he will treat have been previously addressed by
others «especially by Petrus Nonius» out of whom most of the first
Chapter of the treatise following is almost word for word translated”.
The case of Edward
Wright is paradigmatic and exemplary but it is far from being the
only one in England. For instance, John Davis wrote about
“paradoxical navigation” (that is, the loxodromic navigation studied
for the first time by Nunes); Robert Hues published his
Tractatus de globis et eorum usu
in 1594 and refers to several subjects previously studied by Pedro
Nunes; William Barlow published his
in 1597 and he mentions the work done by the “learned
He even adapted a
(nonius scale) to an instrument called
Thomas Harriot worked on the loxodromic curve. The list could go on.
This shows that the scientific work of Pedro Nunes was highly
recognized and regarded among English mathematical practitioners.
In 1569, a few
years after Nunes published his
Mercator presented his map
ad usum navigatium
though he didn’t provide a mathematical explanation for it. This
would only be accomplished 30 years later by Edward Wright, who
would finally show how to avoid the errors of the common sea chart’s
and also that Mercator’s cartographic proposal was conformal. In
fact, in the common plain sea chart, the North-South distances were
maintained, contrasting with the east-west distances that became
gradually exaggerated when the latitude was increased, due to the
convergence of the meridians in the polar regions.
Before 1590, Wright
was already interested in the problems of the sea chart and worked
to express mathematically a cartographical projection where the
loxodromes were straight lines. In his
Wright would explain the construction of his “nautical planisphere”
totally based on mathematical calculus – the Mercator-Wright’s
Fig. 1 - Wright's “nautical planisphere”.
“his” chart affirming that it would bring advantages when compared
to the previous proposals and also called the attention to the fact
that the “new” planisphere made the drawing of routes on globes
easier, and “By help of this planisphaere (…) the rumbs may much
more easily and truly be drawn in the globe then by these mechanical
ways which Petrus Nonius taught
cap.26 lib.2. de
obser. Reg. et Instr. Geom.
imagined by Pedro Nunes was indeed slower. Wright improved it and
introduced some variants that made it easier to use.
influence extended to more subjects. In the end of his book, Wright
explained the use of solar tables to calculate the latitude of a
place - the known
Regiment of the Sun
- pointing out a technical detail previously analysed by the
portuguese and ignored on calculations: the variation and correction
of the values of the solar declination with the longitude. He also
informed that the sailors should correct the value of the distance
of the pole star to the polar region, an issue also addressed by
Nunes, stating that these values were calculated for a given and
constant latitude and therefore should be corrected for each
latitude. This was what Nunes suggested in chapter 7 of his
Wright didn't present a mathematical explanation, excusing himself
of the fact that he didn’t linger more on this problem in the
To know more:
David Waters, The
Navigation in England
in Elizabethan and Early Stuart
Times, (London: Hollis and Carter,
“English navigational books,
charts and globes printed down to 1600”, Revista da Universidade
de Coimbra, 33 (1985), 239–257.
Edward Wright, Certaine
Errors in Navigation, arising either of the Ordinarie Erroneous
Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and
Tables of Declination of the Sunne, and Fixed Starres Detected and
Corrected, (London: Valentine Sims, 1599) .
E. G. R. Taylor,
The Haven–Finding Art: a History of Navigation From Odysseus to
Captain Cook, (London: Hollis & Carter, 1971).
Henrique Leitão, “Maritime
discoveries and the discovery of Science: Pedro Nunes and Early
Modern Science”, in: Victor Navarro Brotóns e William Eamon (eds.),
Más allá de la Leyenda Negra: España y la Revolución Científica.
Beyond the Black
Legend: Spain and the Scientific Revolution
(Valencia: Instituto de Historia de la Ciencia y Documentación López
Piñero, Universitat de València, C.S.I.C., 2007), pp. 89–104.
“Ars e ratio: A náutica e a constituição
da ciência moderna”, in: La ciencia y el mar, Maria Isabel
Vicente Maroto, Mariano Esteban Piñeiro (coords.), (Valladolid: Los
autores, 2006), 183–207.
J. S. Parsons, W.
F. Morris, “Edward Wright and his work”, Imago Mundi, 3
(1931), p. 61–71.
Pedro Nunes, Obras, vol. I,
(Lisboa: Fundação Calouste Gulbenkian, 2002).
Pedro Nunes, Obras, vol. IV,
(Lisboa: Fundação Calouste Gulbenkian, 2008).
D’Hollander, “La théorie de la loxodromie de Pedro Nunes”, in: Luís
Trabucho de Campos, Henrique Leitão, João Filipe Queiró (eds.),
International Conference Petri Nonii Salaciensis Opera Procedings,
Lisbon, Coimbra, 24–25 May 2002 (Lisboa: Departamento de Matemática
da Faculdade de Ciências da Universidade de Lisboa, 2003), 63–111.
Johnston, “The identity of the mathematical practitioner in
(ed.), Der “mathematicus”: Zur Entwicklung und Bedeutung einer
neuen Berufsgruppe in der Zeit Gerhard Mercators, Duisburger
Mercator–Studien, vol. 4 (Bochum: Brockmeyer, 1996), 93–120.
Errors in Navigation, Detected and Corrected with Many
Additions that were not in the Former Edition... [with an
Addition Touching the Variation of the Compasse],
(London: [s.n.], 1610) .
Edition: Edward Wright,
Certaine Errors in
Navigation Detected and Corrected, with Many Additions that
were not in the Former Edition...,
(London: Joseph Moxon, 1657).
The Haven-finding art, or, The way to find any Haven or
place at sea by the Latitude and variation. Lately published
in the Dutch, French, and Latine tongues, by commandement of
the right honourable Count Mauritz of Nassau, Lord high
Admiral of the united Provinces of the Low countries,
enioyning all Seamen that take charge of ships under his
iurisdiction, to make diligent observation, in all their
voyages, according to the directions prescribed herein: And
now translated into English, for the common benefite of the
Seamen of England.
(London: G. Bishop, R. Newbery, and R. Barker, 1599).
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