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How long is a league?

We are talking about length, of course. Though, even after disambiguation, the answer may change depending on our definition. If we take metres to be the standard unit of length, ?a unit of length equal to X metres? could be an acceptable definition. So easy, isn't it? Now we only have to answer the question, how many metres are there in a league?

Here is where we could get lost trying to be more precise again. Conversion values change from one place to another since the early periods of history. Furthermore, we would first need to use standard units other than metres, such as stades and feet, then convert to metres again.

So, here we are, tracking Mendes Pinto with distances given in leagues. The issue is that, after working with a huge bibliography, I haven't found a definitive explanation on how the values were calculated if any values were given at all. The most secure point I got is that of a league being equal to 17.5 intervals of a degree.1 Having this as a given value, I approached the issue as follows:

• Mendes Pinto reports measures for distance and position being taken after the sun.

• Now, what Fernão Mendes Pinto really measures is an angle of the Earth's circumference, taking relative positions on its surface with the sun as a point of reference.

• The value of the sphere is well known for this period (Pedro Nunes, Sacrobosco), as nowadays, it has 360 degrees.

• Now, FMP is giving distances proportional to 360/17.5. FMP doesn't need to know how long planet Earth is on the meridian, he just measures parts of it and calls a unit of length in his path a league. This universal unit would be finally transferable to whatever the local common unit of length, be it stades, feet, and so on.

• Since we want to know the value nowadays, we don't need to solve how many stades or feet a league has either. It is enough to know the value of what FMP measures in metres, that is, the circumference of Earth, which is 40,000,000 m (round number, so a metre can also be exactly defined after the distance between the poles and the equator).2

• Now, the maths. 40,000,000 m % 360° = 111,111.1 m, that we further divide 111,111.1 % 17.5 = 6,349 m (6,350 m for the length of Earth's circumference being equal to 40,007,863 m.)

Therefore, following this approach, a league is 6.349 km.

Let's check it! According to FMP, distance from Nanjing to Beijing is 180 leagues. So 180 leagues x 6.349 km = 1,142.82 km. Actual distance, round number, 1,150 km!3

More examples needed to actually bring evidence. Close enough to be on the right track!

(1) Albuquerque, L. (1987). As navegações e a sua projecção na ciência e na cultura. Lisboa: Gradiva. P. 49. ^

(2) Wikipedia. Sub voce Earth. http://en.wikipedia.org/wiki/Earth ^

(3) Alves, J. (ed.) (2010). Fernão Mendes Pinto and the Pegrinação. Lisbon: Fundação Oriente. (Notes by M. Ollé, Vol. III, p. 126) ^