How to Measure the Earth’s Circumference?

I have completed the second chapter of my book. This section tells about different approaches to the issue of estimating the Earth's circumference. You can read the first page where I explain how I picked up the medium for the estimation.

 If the earth is a globe, its circumference can be roughly determined.

The two giants of the ancient world endeavored to carry out this tremendous task. Both of them estimated the angle of elevation of heavenly bodies above the horizon at distant points presumably located on the same meridian in order to reach the measure of one degree. They also assessed the distance between these spots by converting travel days on land (1) or at sea (2) into an accepted standard of length.

The fact that each of these estimations held versions proves that the scholars were not happy with their initial scores and, being confronted with sound criticism, had to improve their performance. The degree of uncertainty only grows if we take into account the inconsistency between ancient and modern units of measurement.

          The modern science rates the equatorial circumference of the earth at 40,075 kilometers where each meridian degree stands for 111.319 kilometers. (3) Medieval academics possessed a wide choice of measurement techniques, processing a variety of values. 

In the Greek-speaking world, a conventional unit of length to estimate distances both on land and at sea was a stadium, whose value would differ from region to region. The problem with this standard lies in its ambiguity: there are no fewer than five different variants and any talk of “precision” of an ancient estimation leaves an uneasy sense of misjudgment.

Table 2: Stadium to meters conversion (4)

          As we can see, the maximum gap between the opposite values can reach 25 percent (157:209=0.75).  The mean or “consensus” equivalent (184.6), which cuts by half the span of error in this ocean of uncertainty, approaches the Attic stadium.  It also allows contrasting various estimations and matches the Roman mile to stadium conversion (1,480 meters: 8 =185 meters), as reported by Strabo: “if one reckons as most people do, eight stadia to the mile” (5).

Accidentally, the modern metrical value of nautical mile-1.85 kilometers-coincides with our assessment. We will apply this amount for our further calculations to appreciate the charms and wonders of mathematical geography.  

Writing a book

I'd like to thank all my readers who give me the greatest respect that a writer deserves: to learn his opinion. More than one hundred readers perused my blog last month and my total auditorium has exceeded 500.

I'm happy to inform you that I have completed my long-term historic research on the conception of the East on the Latin West throughout the Late Middle Ages. The study has been conducted for six or seven years and its results contain the manuscript which includes dozens of articles.

At the current stage, I have started converting the manuscript into my second book. This is time to remind that my first book, Dawn and Sunset: A Tale of the Oldest Cities in the Near East, was published in 2015 as a second edition. It tells the story of the earliest urban communities on earth that mushroomed in Mesopotamia in the course of the fourth and the third millennia BCE. You may view seven chapters of this book on my Author's Page at scriggler.com
https://scriggler.com/Profile/michael_baizerman

The working title of my second book is

The Enchanting Encounter with the East:

Breaking the Medieval Ice between Latin Europeans and the World beyond Islam 

I have managed to edit the chapter titled ,What If the Earth Is the Sphere? In this chapter the reader learns that all European well-educated people conceived the Earth as an immobile globe, visualizing it in different shapes. I upload an extract from this chapter:

“Thus when the God, whatever God was he,

Had form’d the whole and made the parts agree,

That no unequal portions might be found,

He moulded Earth into a spacious round."

-Ovid, Metamorphoses (1)

"Of what importance is it to know whether the Earth is a sphere, a cylinder, a disk, or a concave surface?"  -Basil of Caesarea (2)

 

The term “geography” would fall out of use among medieval European scholars. This subject never pertained to the canon of “liberal arts” worthy to become part and parcel of the university curriculum. The western literati would not recognize the “earth description” in its own terms, treating it as a handmaid of Cosmography at best or as a concubine of Theology at worst.

Geographic ideas that held and refined medieval intellectuals originated in Ancient Greece. By adhering to these old-fashioned and partly erroneous tenets, western academics followed the path of “universal wisdom”, pouring the old wine into new wineskins.

In compliance with their classical mentors, Latin disciples unanimously adopted the image of the spherical Earth. They perceived our planet as a tiny anchored eyeball inside an enormous socket of the heaven; the globe surrounded by a number of concentric circles-the orbits of the revolving planets.

The geocentric vision of cosmographers placed the immobile Earth at the heart of the universe whose rotating celestial spheres (3) were spinning around non-stop, endowing the “Blue Marble” with an ability of constant innovation and improvement. This stationary center was protected by concentric circles of water, air, and fire.

In a renowned illustration to a Latin poem, Vox Clamantis ("The voice of the one crying out"), its author, John Gower, is shown shooting arrows at the sinful world. The poet blasts humankind for their wickedness at the backdrop of the Earth fashioned as a sphere with compartments for air, earth, and water. 

  

Image 1: The author as a shooter raining his satirical arrows on the wicked and sparing the righteous (4) 

                This image of the spherical Earth would not surprise an “extraterrestrial” onlooker, for whom the convexity of our planet was an undeniable fact. However, all human observers were “insiders” and based their assumptions on circumstantial evidence such as…