Magellan's Earth

"With these reasons did the poor gentleman lose his wits, and tried to comprehend and unravel their meaning, which was more than Aristotle himself could do if he were to rise again"

Don Quixote de la Mancha, Miguel de Cervantes.

What was the size of the Earth for Magellan and the cosmographers of the time? Was Columbus right when he said that, navigating towards the West, Asia would not be too far away? How much did they know about the size of the Earth before they parted? All of these questions are important when one thinks of following the tracks of Magellan through the Pacific Ocean. We will embody a man of science from the early 16th Century, and will seek to unravel these questions, as his route tells us something important: Magellan knew he was facing a long journey when he entered the Pacific Ocean.

The route followed by Magellan through the Pacific. Because he knew that the Moluccas were in the Equator, Magellan demonstrates with the course he followed that he knew the magnitude of the ocean he was facing, since to reach the Equator he had to traverse the Pacific Ocean for over 10.000 Km. However, its size exceeded his expectations.

First of all, it is important to mention that the debate over whether the Earth was round or not was already over. No one doubted the Earth was round. However, Copernicus’ heliocentric theory was still to come, and the understanding of the Cosmos still followed the Ptolemaic tradition, according to which the Earth was the centre of the universe, surrounded by the moon, the sun, the visible planets and the stars, which were considered to be fixed to a celestial sphere. Ptolemy was inspired by the ideas of the classic astronomers of ancient Greece. In the Western and Muslim world, the Earth was considered round within the Ptolemaic tradition. This expedition did not “discover” that the Earth was round, as it has sometimes been said, but rather confirmed it.

At least all of the men of a certain cultural level knew that the Earth was round and spherical. This was not discussed, since God must have created the Universe with pure. This was the thinking of the time, and it was not discussed, not even among the most prominent men of science. The fact that the Earth is flattened at the poles was not discovered until the 18th Century, in a Franco-Spanish expedition in which our distinguished Jorge Juan y Santacilia participated.

However, the size of the Earth was unknown. This was the issue on debate at the time, following the discovery of America by the Spanish, and the arrival of the Portuguese to India and Indonesia after surrounding Africa. The two powers were involved in a race to expand their domains and control the lands were spices grew, as well as its commerce.

Establishing the dimension of the Earth was a challenge. Despite the fact that Eratosthenes had done so with astonishing precision in 230 B.C., Ptolemy reduced its dimension notably years after.  During the Middle Ages, and up until the times of Columbus, the Ptolemaic idea of a “small Earth” was considered right, but this changed after the discovery of America. Toscanelli’s map, which has not endured time, but from which Columbus took the idea that Asia was not too far away over the Atlantic, in addition to the Erdapfel of Martin Behaim, led Columbus to take the seas in search of the spices.

How was Eratosthenes capable of measuring the Earth in antiquity? The famous astronomer Carl Sagan explained it masterfully in the 80s with his successful TV series Cosmos.

Ptolemaic’s model of the Universe, with the Earth at the centre, surrounded by the spheres of the moon, the planets, the sun, and the fixed stars. This idea was predominant until the publication of Copernicus’ heliocentric theory in 1543, and even after that it was still partly supported.

During the 25 years that passed since Columbus came back giving notice of the newly discovered lands, and the time where Magellan and Rui Falero presented themselves at the court of Carlos I of Spain to show their more than audacious project of reaching the Islands of the Spices navigating West, cartography and geography had become the sciences of the time. This was favoured by the House of Trade of Seville, which was the Cape Canaveral of the 16th Century. Seville had cutting edge technology, and was leader in investigation and logistics regarding exploratory trips. This also attracted a large number of Portuguese with great nautical experience and that preferred Seville to their own kingdom.

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

Martin Behaim’s globe, or Erdapfel, in 1492, is the most ancient that has been conserved. America is not in it, it is Asia that is at the West of the Atlantic Ocean.

Model of Behaim’s map in the excellent app Behaim globe, available in Google Play for Android. We can amplify and see even the tiniest details. In this screenshot we can see West Asia, the Atlantic Ocean at the centre, and Europe and Africa on the East.

The pillars of the knowledge regarding the Earth were well founded at this time, in the sense that even the tropics- which were already included in Behaim’s globe-and the Polar Circles, were already known. A very important source of information on how much knowledge surrounded the preparation of an expedition can be found in the Suma de Geographia, from the clerk of Castilla del Oro, Martín Fernández de Enciso, published in 1519, the same year that saw Magellan depart.

In the Suma de Geographia, we find an especially relevant paragraph. It says as follows (translated from antique Castilian):

Because one degree corresponds to 16,5 leagues and a sixth, you shall know that the whole world had approximately 360 degrees, which amount for six thousand leagues.

 

Enciso is giving us the dimensions of the sphere of the Earth, which he establishes in 6,000 leagues. He obtained it by what seems a simple method that consisted in measuring the length of a degree- established in 16,5 leagues and a sixth-, and then multiplying this value by the 360 degrees that make a complete circumference.

Because to Enciso the Earth was a perfect sphere, the easiest way to measure the length of a degree was to measure on the North-South axis, finding out the difference in latitude between two points of the same meridian. The length of the Equator was considered to be exactly the same as the meridian, because if it weren’t, the sphere would not be perfect, and as mentioned previously, there was no doubt that God would have created a perfect sphere. The calculation of the latitude of a place was well known, as we will explain in the section “How they measured their position”.

Therefore, to measure the total length of the meridian, they had to measure the distance between those two points of the Earth that were separated by a degree in the North-South axis- which was established by Enciso in 16,5 leagues and a sixth- and multiply it by the 360 degrees that make a perfect circumference.

Suma de Geographia of Martín Fernández de Enciso. Year 1519. It shows the dimension of the world with an error of 17,5% on the circumference of the meridian- 6,000 leagues, which converted to kilometres on a rate of 5,5 km per league make 33,000 km, instead of the 40,000 km it has in reality.

Nowadays we know that the length of a complete circumference containing a meridian measures exactly 40,000 Km. It is quite surprising that this figure is so exact, isn’t it? Obviously, this is not casual. The meter was initially set as a unit of measure that was a portion of the length of the meridian, and it was equal to a ten millionth part of the distance comprised between the Equator and the pole. On a different note, it was Napoleon who signed, in 1799, the law that set the unit of measure as the meter in the French territories, although he added that he did it “for all the people and for all times”.

In the 16th Century there was no standardised unit of measure. The league was commonly used, but a league had a different value in different places, and its value even changed through time. The league was first measured as the distance that a person could walk in one hour, which made its value range from 4 to 7 km. However, at the time and place of Magellan’s expedition preparation, a Castilian league was equivalent to 20,000 Castilian feet, approximately 5,5 km.

Although Martín Fernández de Enciso established the length of a degree in 16,5 leagues and a sixth (16 leagues and 2/3), the debate was still ongoing among the Spanish and Portuguese cosmographers, as this question would determine the possession rights of the Moluccas Islands. The Moluccas were close to the demarcation antemeridian that was established by the Spanish and Portuguese kingdoms during the times of the Catholic Kings through the famous Treaty of Tordesillas. The Earth being bigger or smaller would directly affect the Moluccas being at one side or the other of the demarcation antemeridian, and therefore under the domains of different kingdoms. Let’s explore this issue in more detail to better understand it.

After only two years from the discovery of America, and when only the islands that Columbus had found in his first trip were known, the Catholic Kings and the king Juan II of Portugal signed the Treaty of Tordesillas, that divided the world, the land and water that had been discovered and were to be discovered, in two demarcations, “all that were found o were to be found, conquered or discovered in said terms, beyond what is occupied or discovered”. The limit was established through a meridian that sits in the Atlantic Ocean, which divided what is now Brazil as it follows: “…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

The meridian that was established was therefore separating both demarcations at 370 leagues from the islands of Cape Verde, without specifying from which one, or the units a league corresponded to.

The Earth is not a perfect sphere, as the length of the Equator is slightly bigger than the meridian- 43 km more, to be precise. However, this was still unknown in the 16th Century.

The position of the demarcation antemeridian established by the Treaty of Tordesillas created another meridian, at 180 degrees, that would also mean the limits between Spain and Portugal. The Moluccas were close to this antemeridian, and it was the debate surrounding this issue that promoted the study of geography.

The place where the Treaty of Tordesillas was signed, in front of a statue to Juana I of Castile. Tordesillas (Valladolid, Spain).

Representation of the demarcation meridian between the kingdoms of Spain and Portugal according to the Treaty of Tordesillas (year 1494) defined in 370 leagues west from the islands of Cape Verde. The Portuguese part would be east of the meridian, while the Spanish part would be west of the meridian. To elaborate this graph, the value of a league is established in 5,5 km.

 

The memorial to Magellan justifying to King Carlos I the location of the Moluccas inside the Castilian demarcation: the size of the Earth.

In the General Archive of the Indies (Seville) there is an unsigned document, attributed to Ferdinand of Magellan, which contains some knowledge on geography that would demonstrate that the Moluccas islands were indeed inside the Castilian demarcation of the Treaty of Tordesillas. If we analyse it, we can find interesting data. Magellan says as follows:

Because it might be that the King of Portugal wanted, at some point, to say that the Moluccas islands were inside his demarcation, and could order to change the courses of the main coasts and the gulfs of the seas, without no one understanding as I do, I could, at the orders of His Majesty, declare to him the heights of the main lands and capes, and the altitudes in which they are, and with this H.M. would know, in the event of my death, the truth.

 

The island of Santo Antao, which belongs to the islands of Cape Verde, in the Guinea coast, where the partition of these lands was done with Portugal, is 22 degrees east the demarcation line.

The memorial continues by referencing several geographic points, but analysing what we know so far, we can see that we have enough information on the size that Magellan attributed to the Earth.

In the previous paragraph, Magellan was actually saying more than it seems. Since he establishes that there are 22 degrees between the demarcation of Tordesillas and Cape Verde, and we know that in the Treaty the line would be set 370 leagues to the west of Cape Verde, we can know the leagues per degree that Magellan is considering by dividing 370 leagues by 22 degrees, with the result of 16,81 leagues/degree. This unit increases the leagues per degree respect to those established by Fernández de Enciso, 16 and 2/3.

In addition, the previous calculation is not quite correct, since the degrees, in the geographic length, should be measured at the Equator, and not in the parallel of the Cape Verde islands, where the distance between degrees is less. Therefore, what we can establish is that to Magellan, each degree contained more than 16,81 leagues. In fact, it is possible that he already considered each degree to contain 17,5 leagues, the measure that was established years later in the Treaty of Zaragoza, in the year 1529. This would be coherent with our calculations.  In fact, if we measure on Google Earth the distance in the Equator between the two meridians of Tordesillas and the island of Santo Antao in Cape Verde, we can see that they are almost the same.

Memorial attributed to Ferdinand of Magellan in which he justifies, with different geographic data, that the Moluccas islands where inside the Castilian demarcation of the Treaty of Tordesillas. General Archive of the Indies.

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The parallels measure less the more you approach the poles, whilst the Equator is the one with the longest length. Magellan attributed a length of 17,58 leagues to each degree in the Equator, as it can be empirically deducted through Google Earth, taking as a starting point his declaration in the memorial, where he justified that the Moluccas islands were in the Castilian demarcation of the Treaty of Tordesillas.

It can be deducted that to Magellan, the terrestrial circumference equalled 17,58 leagues per degree multiplied by 360 degrees, which makes 6,331 leagues, or 34,822 km. He therefore thought that the size of the Earth was a 13% smaller of what it really is, and that the world had a width that was 5,253 km less of what it really is.

This is therefore the size of the Earth for Magellan before starting his expedition: 34.822 km in the Equator, while in reality it is of 40,075 km. After Columbus’ first trip the knowledge on the Earth had advanced greatly, and Magellan already knew, before parting, that he would be confronting a very vast ocean before reaching Asia.

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The course followed by Magellan in the Pacific partly shows his knowledge about the size of the planet. He thought it was 5,350 km less than what it really is, reason why it took him 10,500 km more to reach the Equator, as he knew the Moluccas were further away. It is surprising that he surpassed the Equator and then went up north, reaching the Philippines. In fact, Elcano said about this that “Magellan never wanted to follow that course, but he had to, as I witnessed as a member of his crew”. Magellan almost certainly wanted to make sure he governed some of the islands discovered by him, as signed with Charles V in the Capitulaciones de Valladolid in 1518.

 

Another surprise

The analysis of the previously cited Memorial of Magellan about the possession of the Moluccas still holds another conclusion. Because we can deduct from it where exactly did he establish the demarcation meridian between Spain and Portugal, we know that, before his first stop in America, he waited to having surpassed the meridian of demarcation to stop in the territories of Castile. It could have been by chance, or not. Anyhow, the best conclusion we can get to is that Magellan had an extensive knowledge of navigation and cosmography.

Magellan’s first stop in the American coast was in what he called Bay of St. Lucia, which nowadays is the Bay of Sepetiba, west from Rio de Janeiro. It matches perfectly with the line of demarcation of the Treaty of Tordesillas, 370 leagues west from the Saint Antao island of Cape Verde, being a league 5,5 km. Did Magellan wait to be in the Castilian area to stop? Although he did not have the necessary equipment to determine exactly his geographical situation, it seems difficult to believe that it was fortuitous.