The World of Magellan

With this kind of language the poor gentleman lost his wits, and distracted himself to comprehend and unravel their meaning; which was more than Aristotle himself could do, were he to rise again from the dead for that purpose alone."

"Over conceits of this sort the poor gentleman lost his wits, and used to lie awake striving to understand them and worm the meaning out of them; what Aristotle himself could not have made out or extracted had he come to life again for that special purpose."

Don Quixote de la Mancha, Miguel de Cervantes.

Back in the days of Magellan, what was the size of the Earth that Magellan himself and the rest of his coevals cosmographers considered? Might Columbus be right when he indicated that Asia would not be far from America if sailing to the West? How much information did those people could know about the dimensions of the Earth before they left on their journeys? All these questions are certainly important and would come into our minds once we check the course and route followed by Magellan across the Pacific Ocean. In this article, we will get into the skin of a generic man of science that lived on the early s. XVI and unravel those questions since the course followed by Magellan in his trip shows a critical fact: Magellan was certainly aware that he would face an extremely long journey when he entered into the Pacific Ocean.

Picture shows the course followed by Magellan in the Pacific Ocean. Magellan followed this course in the Pacific Ocean for more than 10,000 Km. He was targeting the Moluku islands that beforehand he knew were located in the equator. From that observation, we can deduct that he knew from up-front the extreme magnitude of the Pacific Ocean that he had to face in his voyage, although the actual size exceeded his initial expectations.

First of all, we shall highlight that the question about the sphericity of the Earth (as opposed to the flat Earth theory), was already solved at this point in History. In those days, the Earth’s spheroid shape was no questioned and was totally accepted. On the other hand, Copernicus’ theories regarding the heliocentrism would still take some years to be developed, so the Cosmos was still understood according to the Ptolemy's model. This model considers the Earth as the center of the Universe being surrounded by the spheres of the Moon, the Sun and the other visible planets, with a lager over sphere that would content the fixed stars. Ptolemy was inspired by the ideas of the classic astronomers of the ancient Greece. In the Western world, as well as in the Muslim World, the spherical shape of the Earth was taken for granted following this ancient Greek tradition. Therefore, this expedition did not “discovered” the spherical shape of the Earth, contrasting to what we may have heard many times, but rather confirm it.

Would be right to say that at least all men of a high cultural level were aware that the Earth was round. Round and spherical. The perfect spherical shape of the Earth was in fact not discussed, since it was believed that God must undoubtedly rely on pure forms when He created the Universe. This was the belief of the time and was not questioned by any of the most reputable men of science at that time. The flattening of the Earth by the poles was not discovered until the XVIII century by a French-Spanish expedition in where the Spanish scientific Jorge Juan y Santacilia took part.

However, the actual size of the Earth was not known. This was a question of debate at that time, with the issue lit after the discovery of America by the Spanish and the arrival to India and Indonesia by the Portuguese after surrounding Africa, with both powers mired in frenetic race to expand their domains and control the “Especieria” (NB the land where the spices grow) and trade.

Sizing the Earth was a challenge. Although Eratosthenes had completed a calculation with astonishing precision around the 230 BC, Ptolemy had subsequently greatly reduced the expected size. During the Middle Age, until the days of Columbus, the Ptolemaic idea of a “small” Earth was considered, but as it has been said, after the discovery of America, this issue came to the fore. The map of Toscanelli, that has not made it to our days although probably inspired Columbus on his idea that Asia was not far from Europe across the Atlantic ocean, and the later Erdapfel map of Martin Behaim, also followed the Ptolemaic idea of a “small” Earth.

How Eratosthenes was able to measure the size of the Earth in the ancient times? The astronomer Carl Sagan did successfully explained it in the 80s TV series Cosmos.

The model of Ptolemy's Universe, with the Earth at its center surrounded by the spheres of the Moon, the planets, the Sun and the fixed stars. It was considered valid even after the publication the heliocentric theory of Copernicus in the year 1543.

Across the 25 years that followed from the time that Columbus brought the news regarding the new discovered lands until Magellan and Rui Falero showed up in the retinue of Charles V introducing to him the most audacious project of reaching the Islands of the “Spices” sailing to the West, both cartography and geography had become the sciences of the moment, fostered by the La Casa de Contracion de Sevilla, which could be considered as the equivalent to the Cape Canaveral site for the NASA on the XVI century. Seville was at that time the center of the most advanced research, technology and logistics for every new expedition. This condition was very attractive to a great number of Portuguese sailors of great nautical experience that brought with them the knowledge acquired through their expedition journeys, and who preferred to serve in Seville to the Spanish crown rather to their own kingdom.

erdapfel, behaim, magallanes, colon, tamaño de la tierra,

The globe of Martin Behaim, or Erdapfel, from 1492, is the oldest globe representation conserved until our days. The continent of America does not appear and Asia is represented on the western side of the Atlantic ocean.

This image shows the model of the Behaim map from the excellent Benhaim Globe app, available on Google Play for Android. The app allows to zoom-in and read even the smallest texts of the image. In this screenshot of the app, Asia is represented in the West, the Atlantic ocean in the center and both Europe and Africa in the Eastern part.

The basis of the knowledge of the Earth’s geography were well founded in the XVI century, since even the Tropics, that are represented in Behaim’s globe, and the Polar Circles were known. A very important source of information that indicates the level of knowledge at the time of Magellan, is the book Suma de Geographia, by the major bailiff of Castilla de Oro, Martin Fernández de Enciso, which was published in 1519, the same year when Magellan began the journey.

In the Suma de Geographia, a paragraph shows with special relevance some of the aspects that we are dealing with in this section:

“Because each degree is set into 16.5 leagues and a sixth part, and you shall note that the entire globe counts around 360 degrees adding a total of 6,000 leagues”

In the previous quote, Enciso provides the dimensions of the sphere of the Earth, which he establishes in 6,000 leagues. He can reach that conclusion through a quite straight forward reasoning consisting in measuring the length of a degree, that he accounts for 16.5 leagues and a sixth, and multiplying that value by 360, that is the number of degrees contained in a complete circumference.

Since Enciso considered the Earth as a perfect sphere, the easiest way to find the distance comprised in one degree is to measure the length in the North-South direction, finding out the difference in latitude between two points that are contained in the same meridian. The length of the equator was assumed to be the same as the length of the meridian, because otherwise the sphere would not be perfect and, as we said, it was considered that God must have used perfect forms during the Creation. The way to calculate the latitude of any place was well known at that time, as we explain in the section “How they measured their position”.

In such a way, the last challenge that Enciso faced on his calculation was to measure the distance between two points over the Earth’s surface separated by one degree in the North-South direction, which Enciso establishes in 16.5 leagues and one sixth, to find the total length of the meridian by multiplying the distance by 360, as the number of degrees contained in a perfect circumference.

Suma de Geographia by Martín Fernández de Enciso. Year 1519. It provides the dimension of the World with an error of 17.5% in the circumference of the meridian: 6,000 leagues. These transformed at a rate of 5.5 Km per league, makes a total of 33,000 Km compared to the 40,000 Km as the actual length.

As per today, we know that the length of one complete circumference that contains a meridian in the Earth measures exactly 40,000 Km. What a coincidence that this is an exact figure, right!? Well, in this case this is clearly not a coincidence, since the choice of the “meter” as an unit of measure was initially established as a portion of the length of the meridian equivalent to a ten of a millionth part of the distance between the pole and the equator. As an anecdote, we shall mention that was Napoleon Bonaparte who signed in 1799 the new law that established the meter as an unit of measure in French territories, although he had universal ambitions for this as we can read from his own words: “…for all peoples and for all times”.

In the XVI century the unit of length was not standardized or uniform. Length was measured in leagues, but the leagues were not equivalent across different territories, and furthermore, their value did change across time. The league began to refer to the distance that one person could walk in one hour. Therefore we can find values for a league measuring anywhere between 4 and 7 Km. However, if we focus to the territory and time that we are analyzing, when Magellan was preparing his expedition, the Castilian league was equivalent to 20,000 Castilian feet, in other terms, it was very close to 5.5 Km.

Although Martín Fernández de Enciso established the length of a degree in the mentioned 16.5 leagues and one sixth, or the equivalent, 16.5 leagues plus two thirds, this matter was a key argument for the heated debate that was taking place at that time between the Spanish and Portuguese cosmographers about the possession rights of the Moluccas Islands. Because the Moluccas archipelago was close to the antemeridian demarcation that the kingdoms of Spain and Portugal had established during the reign of the Catholic Monarchs in the famous Treaty of Tordesillas. The fact that Earth was larger or smaller would make the Molucca Islands to be placed at one or the other side of the mentioned antemeridian determined by the rival kingdoms. Let’s analyze how this important topic was conceived in order to fully understand about it:

Only two years after the discovery of America, when Christopher Columbus had only found the few islands on his first trip, the Catholic Monarchs and King Juan II of Portugal signed the Treaty of Tordesillas. Both kings divided the world, with the lands and seas both discovered and to be discovered into two separated demarcations: “all of what is found and to be found, conquered or discovered further away of what is already found or discovered”. The border between both demarcations was established in a meridian that crosses the Atlantic ocean, and later found that it also crosses over Brazil, in this way: “…that is made and signed by the mentioned Ocean a stripe or a straight line from pole to pole, namely, from Artic pole to Antarctic pole, that is from North to South, the line must be placed at three hundred and seventy leagues from the Cape Verde islands, to the west, by degrees or by the best way that would provide the best accuracy, in a way that the distance is not increased”.

In other words, it was established that the meridian that separated both demarcations would lay at 370 leagues to the West of the Cape Verde islands, without specifying which island of the archipelago, or what was the exact length given to these mentioned leagues.

The Earth is not a perfect sphere, as the length of the equator is somewhat greater than the length of the largest meridian -in particular, 43 km-. However, in the sixteenth century they were still far from finding this out.

The demarcation meridian of the Treaty of Tordesillas generated, at 180 degree, an antemeridian that would also be the limit between Spanish and Portuguese kingdoms. The Moluccas islands were close to this antemeridian, which was a source of dispute that enhanced the study of geography.

The place where the Treaty of Tordesillas was signed. In the front; a sculpture of Doña Juana I de Castilla. Tordesillas, Valladolid, (Spain).

Representation of the demarcation meridian between the Spanish and Portuguese kingdoms according to the Treaty of Tordesillas (year 1494) defining the 370 leagues west of the Cape Verde archipelago. The Portuguese rights would begin on the eastern side of such meridian, and the Spanish on the western one. In order to produce this sketch, the length of the league is established at 5.5 Km.

The Memorial write up of Magellan justifying to the king Charles V the location of the Moluccas within the Castilian demarcation: the size of the Earth.

The General Archive of the Indies (Seville) custodies an unsigned document that a large number of historians attribute to Fernando Magellan, in which the author provides a series of geographical facts that would show that the Moluccas archipelago are within the Castilian demarcation of the Treaty of Tordesillas. By looking in detail and analyzing the document, we will find some really interesting data. Magellan begins in this way:

“Because it could be that the King of Portugal want, at some point, to indicate that the Moluccas islands are within (his) demarcation, and could order to change the course of the coast lines and shorten the gulfs of the sea, without anyone understanding as I understand and I know how this could be achieved, and I wanted, as a service to the King, leave this declaration with the latitude of the lands and capes discovered, and with this your Highness will be warned to that, so in the case I was deceased, your Highness is aware of the truth:

The island of San Anton, which is one the Cape Verde islands, off the coast from Guinea, where the partition of this Kingdom was completed with the Kingdom of Portugal, is the island located twenty two degrees eastern of the line of demarcation.”

The memorial continues to reference several geographic points. By analyzing what has been already introduced in this article, we will realize that we have enough information to find the size that Magellan attributed to the world.

In the previous paragraph, Magellan is actually providing a lot of non-implicit information. Since he establishes that the distance from the demarcation line defined by the Treaty of Tordesillas to Cape Verde is equivalent to 22 degrees, and is already known that Treaty defines the line at 370 leagues western of Cape Verde, it would be straight forward to calculate the number of leagues per degree that Magellan assumes by just dividing the 370 leagues by 22 degrees, with the result of 16.81 leagues/degree. This figure means an increase of the number of leagues per degree compared to the ratio established by Martín Fernández de Enciso as 16 leagues plus 2/3.

Furthermore, the previous estimation would be accurate enough, since the degrees in logintude shall be measured on the equator and not at the parallel that crosses over Cape Verde, since the distance measured in degrees would be smaller. Therefore, we can only ensure that for Magellan, each degree was equivalent to 16.81 leagues. In fact, there is major possibility that Magellan would already assumed that each league was equivalent to 17.5 leagues at the equator, that is the ratio that was later agreed in the Treaty of Zaragoza in 1529. In fact, if we use Google Earth to check the distance between both meridians – the one established in the Treaty of Tordesillas and the one at the island of San Anton in Cape Verde – we will see that it matches the actual value with a high accuracy.

Memorial attributed to Ferdinand Magellan, justifying by different geographical data that the Moluccas Archipelago was within the Castilian demarcation of the Treaty of Tordesillas.

Archivo General de Indias, Seville.

The parallels are shorter as they are closer to the poles, being the equator the largest parallel. Magallanes considered a length of 17.5 leagues for each degree in the equator, as it can be deduced empirically through Google Earth and his statements in the Memorial justifying that the Moluccan Archipelago was in the Castilian demarcation of the Treaty of Tordesillas.

Once this is considered, it is straight forward to deduce that for Magallanes the terrestrial circumference was equivalent to 6,300 leagues as the result of multiplying 17.5 leagues per degree by 360 degrees, or what is the same: 34,650 km. This value of the Earth size is a 13% smaller than the actual one, meaning that the Pacific Ocean would have a width reduced in 5.350 km with respect to the real size of 17,500 km at the equator, measured from the American coast to the Asian coast line.

This is, therefore, the dimension of the Earth assumed by Magallanes before starting this expedition: 34,650 km on the equator, compared to the 40,075 km that we know today is the real length. Undoubtedly, after the first voyage of Columbus, the knowledge of the world took a giant step forward in a short number of years, so that Magellan, even before departing, knew already that would face a vast ocean on the other side of America before he could reach the Asian continent.

The route followed by Magellan in the Pacific partly demonstrates his knowledge of the size of the planet. He believed that the Earth measured 5,350 km less than the actual size and for that reason he takes 10,500 km of voyage to reach the equator, since he knew that the Moluccas archipelago was still further ahead. It is very striking that he surpassed the equator and deviated so much to the north, and this was the reason why he ended up arriving in the Philippines archipelago. In fact, Elcano declared on this matter that "Magallanes [...] never wanted to follow that course [the course that leads to the Moluccas], although he was required to do so, because this witness [Elcano] being a pilot in his ship saw him." Almost with total certainty, Magallanes wanted to first secure for himself the government and control of some of the islands that he would discovered, as he had signed in the Capitulaciones de Valladolid of 1518 with Charles V.

Another surprise

The analysis of the aforementioned Magellan Memorial about the possession of the Moluccas still has one more final conclusion, since thanks to it we can deduce the exact location where Magellan located the meridian of demarcation between Spain and Portugal according to the Treaty of Tordesillas. This deduction can be made as for the first stop of Magellan in America, he waited to surpass over the Demarcation Meridian, only when he was certain that he was landing in Castilian territory.

This decision could have either been a coincidence or intentioned. However, and above all, we can conclude based on the description above that Magellan dominated at a truly amazing level the science of both navigation and cosmography at his time.

The first stop that Magellan orders on the American coast is at the Santa Lucia Bay, which today is identified as the Bay of Sepetiba. It is somewhere at the West of Rio de Janeiro, Brasil. If we pay attention to it, it coincides exactly with the location of the line of demarcation of the Treaty of Tordesillas taking 370 leagues to the west of the island of San Antón de Cabo Verde (assuming leagues of 5.5 km). Did Magellan wait until crossing into the Spanish demarcation to take a break? In the view of this, and despite his lack of the sufficient technical means to determine its geographical longitude accurately, it seems difficult to believe that this location was chose just by chance.