The story of how ancient thinkers grappled with the size and shape of our planet is a fascinating chapter in the history of science. While Eratosthenes often takes the spotlight for his remarkably accurate measurement of Earth’s circumference, another significant attempt, made by the polymath Posidonius of Apamea, comes to us primarily through the writings of a later scholar: Cleomedes. Without Cleomedes, our understanding of Posidonius’s specific contribution to this grand endeavor would be far murkier, perhaps even lost entirely.
The Man Who Wrote It Down: Cleomedes
Cleomedes, a Greek astronomer and Stoic philosopher, likely lived sometime between the 1st century BC and the 2nd century AD, though the exact dates remain a subject of scholarly debate. His principal surviving work, “On the Circular Motions of the Celestial Bodies” (often referred to by its Latin title, De motu circulari corporum caelestium), isn’t just a dry textbook of astronomical facts. It’s a valuable window into the astronomical knowledge and philosophical thought of his time, and, crucially, it preserves ideas from earlier figures whose own works haven’t survived the ravages of time. Cleomedes wasn’t necessarily an innovator of groundbreaking theories himself, but his role as a careful compiler, explainer, and preserver of earlier Hellenistic science is invaluable. He meticulously documented methods and arguments, providing context and clarity, and it’s within these pages that Posidonius’s method for measuring the Earth finds its most detailed exposition.
The Thinker Behind the Measurement: Posidonius
Posidonius (circa 135 BC – 51 BC) was a true intellectual heavyweight of his era. A Stoic philosopher, historian, geographer, astronomer, and politician, his influence was widespread. He taught on Rhodes, and his lectures attracted prominent Romans, including Cicero and Pompey. His writings were voluminous, covering an astonishing range of subjects, but sadly, only fragments and testimonies from later authors remain. Strabo, the geographer, relied heavily on Posidonius, as did Seneca and Plutarch. However, for the specific details of his Earth measurement technique, Cleomedes stands out as our primary guide. Posidonius wasn’t just an armchair philosopher; he was an observer, keen to connect theoretical understanding with empirical data, a trait clearly reflected in his approach to Earth’s measurement.
Unveiling Posidonius’s Method Through Cleomedes’s Pen
Cleomedes lays out Posidonius’s method with a clarity that allows us to reconstruct the ancient astronomer’s thought process. Unlike Eratosthenes, who used the sun and observations at Syene and Alexandria, Posidonius turned his attention to a different celestial body and a different pair of locations.
The Star and the Cities
The star chosen by Posidonius was Canopus (Alpha Carinae), one of the brightest stars in the night sky, particularly prominent in the Southern Hemisphere. The key to his method lay in observing Canopus from two cities that were, importantly, thought to be on roughly the same meridian (north-south line):
- Rhodes: At Rhodes, an island where Posidonius himself lived and taught, he observed that Canopus, at its highest point in its daily arc (its culmination), appeared to just graze the southern horizon. Essentially, its altitude was considered to be zero, or very close to it.
- Alexandria: Further south, in Alexandria, Egypt, Canopus was observed to culminate at a measurable altitude above the horizon. According to Cleomedes’s account of Posidonius, this altitude was determined to be 1/48th of the zodiacal circle. Since a full circle is 360 degrees, 1/48th of that is 360/48 = 7.5 degrees.
The critical insight here is that this difference in the apparent altitude of Canopus between Rhodes and Alexandria directly corresponds to the difference in latitude between the two cities. If Canopus is on the horizon at Rhodes and 7.5 degrees above it at Alexandria, then Alexandria is 7.5 degrees further south in its arc relative to the celestial sphere. This angular difference represents a segment of the Earth’s total circumference.
The Distance Dilemma
The next piece of the puzzle was the terrestrial distance between Rhodes and Alexandria. This was, and often remained, the trickiest part of such ancient measurements. While Eratosthenes had the benefit of professional bematists (surveyors trained to measure distances by counting steps) for the Syene-Alexandria leg, Posidonius likely relied on estimates from mariners or perhaps his own calculations based on sailing times. Cleomedes reports that Posidonius used a figure of 5,000 stadia for the distance between the two cities.
The accuracy of this distance is a major point of contention and directly impacts the final result. Sea routes are rarely straight lines, and estimations based on travel time can be notoriously unreliable due to winds, currents, and the skill of the navigator.
Cleomedes meticulously details how Posidonius utilized the star Canopus, observing its apparent zero altitude at Rhodes and its culmination at 7.5 degrees altitude in Alexandria. This angular difference, equivalent to 1/48th of a great circle, was then combined with an estimated north-south distance of 5,000 stadia between the two cities. These two key pieces of information—angular separation and terrestrial distance—formed the basis of Posidonius’s calculation for Earth’s circumference.
The Calculation
With the angular difference (7.5 degrees, or 1/48th of a circle) and the surface distance (5,000 stadia) in hand, the calculation itself was straightforward, relying on the principles of proportionality, much like Eratosthenes’s method:
If 1/48th of the Earth’s circumference is 5,000 stadia, then the total circumference is:
Total Circumference = 48 * 5,000 stadia = 240,000 stadia.
This is the figure that Cleomedes attributes to Posidonius’s method. It’s a neat, round number, and its accuracy hinges significantly on two factors: the precision of the 7.5-degree observation and, even more critically, the actual length of the “stadion” Posidonius was using and the accuracy of the 5,000 stadia distance.
Cleomedes’s Role: More Than Just a Scribe
It’s important to appreciate that Cleomedes wasn’t merely copying down figures. In his “On the Circular Motions of the Celestial Bodies,” he presents these arguments within a broader discussion of cosmology and astronomy. He explains the underlying geometric principles, such as the Earth being a sphere and the immense distance of the stars making their rays effectively parallel (though for a star on the horizon versus one at a slight altitude, this specific parallelism assumption is less critical than in Eratosthenes’s solar method; the key is consistent observation of celestial position relative to the local horizon). Cleomedes’s work contextualizes Posidonius’s measurement, showing it as part of a rational, observational approach to understanding the cosmos. He critiques other theories and presents these measurements as evidence for a spherical Earth, a concept well-established among educated Greeks by this period.
Without Cleomedes, we might have only vague references to Posidonius having measured the Earth, perhaps like the one Strabo gives, which mentions a different, smaller figure (180,000 stadia) that Posidonius might have later adopted or that Strabo himself derived or misremembered. Cleomedes provides the methodology, the specific star, the locations, the angular measurement, and the distance used for the 240,000 stadia calculation, which is invaluable for historians of science.
Evaluating the Result: Stadia, Stars, and Speculation
The figure of 240,000 stadia is, on its face, quite different from Eratosthenes’s famous 252,000 stadia. How accurate was Posidonius? This depends almost entirely on the length of the stadion he employed. The “stadion” was not a universally standardized unit in the ancient world. Its length could vary from about 157 meters to over 210 meters.
- If Posidonius used an “Egyptian” stadion of around 157.5 meters (similar to what some believe Eratosthenes might have used for his more accurate figure, although Eratosthenes’ value might be better if using a 185m stadion and his 250,000 result), then 240,000 stadia would be 37,800 kilometers. This is impressively close to the modern value of Earth’s circumference (around 40,075 km at the equator), with an error of only about 5.7%.
- If he used the more common “Attic” or “Olympic” stadion of about 185 meters, then 240,000 stadia becomes 44,400 km, which is an overestimate of about 10.8%.
Several sources of error were inherent in Posidonius’s method, as documented by Cleomedes:
- Observation of Canopus at Rhodes: Determining that a star is *exactly* on the horizon is tricky due to atmospheric refraction, which makes celestial objects appear slightly higher than they actually are, especially near the horizon. Obstructions on the horizon could also affect this observation.
- Measurement of Canopus’s altitude in Alexandria: While 7.5 degrees is a precise-sounding figure, the instruments of the time had limitations.
- Distance between Rhodes and Alexandria: As mentioned, 5,000 stadia was an estimate. If this distance was significantly off, the entire calculation would be skewed. Modern estimates place the great-circle distance closer to 3,200-3,300 nautical miles, which is significantly more than 5,000 of any common stadia. This suggests the 5,000 stadia was perhaps a “corrected” or “adjusted” figure based on some other reasoning, or simply a rough estimate from sailors. It’s the weakest link in the chain. If the 5000 stadia were a more accurate measure for that 7.5-degree arc, then the stadion would have to be very long, or the angular measurement itself flawed. It is more likely the distance was the primary source of error in the initial inputs.
- Assumption of the same meridian: Rhodes and Alexandria are not perfectly on the same line of longitude. Alexandria is slightly to the east of Rhodes. This introduces a small error, though likely less significant than the distance uncertainty.
The fact that Strabo, a near-contemporary and admirer of Posidonius, later reported a figure of 180,000 stadia for Posidonius’s Earth measurement adds another layer of complexity. This smaller figure, if using the 185m stadion, yields 33,300 km, a significant underestimate. Why the discrepancy? Perhaps Posidonius revised his calculations using a different distance estimate for Rhodes-Alexandria, or a different angular observation. Or maybe Strabo was citing a different attempt or a misunderstanding. Cleomedes, however, is quite specific about the 240,000 stadia figure and the observational data leading to it.
A Different Approach than Eratosthenes
It’s worth noting the elegance in both Eratosthenes’s and Posidonius’s methods. Both understood the fundamental geometry. Eratosthenes used the sun, relying on the assumption of its rays being parallel due to its vast distance, and a gnomon (a vertical stick) to measure shadow lengths, deducing angles from these. Posidonius used a star and direct altitude measurements. Both methods were conceptually sound, with their accuracy limited primarily by the precision of their input data – particularly the terrestrial distance between their chosen observation points.
The Enduring Legacy of a Preserved Idea
Cleomedes’s documentation of Posidonius’s method is a testament to the intellectual vitality of the Hellenistic world and the early Roman Empire. It shows a continued engagement with fundamental questions about the cosmos, driven by observation and mathematical reasoning. While Posidonius’s result of 240,000 stadia might have been less accurate than Eratosthenes’s (depending on the stadion and the true accuracy of Eratosthenes’ inputs, which also have their debates), the method itself was ingenious and demonstrated a deep understanding of spherical geometry and astronomical observation.
Thanks to Cleomedes, we don’t just know that Posidonius measured the Earth; we know how he attempted it, the data he used, and the reasoning he applied. This detailed account allows us to appreciate the scientific mindset of the era and to understand the challenges and triumphs of early geodesy. It highlights the interconnectedness of ancient scholarship, where the work of one philosopher-scientist is preserved and transmitted by another, allowing these ancient sparks of brilliance to illuminate our understanding centuries later. Cleomedes, in his role as a diligent chronicler, ensured that Posidonius’s intellectual labor was not entirely lost to the shifting sands of time.
