Monday, 17 April 2023

How Eratosthenes measured the earth. Part 1

  1. The spherical earth | 2. Eratosthénes’ measurement  

In the 200s BCE, a Libyan mathematician and geographer by the name of Eratosthénes calculated the circumference of the earth. He did it with pretty basic equipment, and his result was off by only 16%.

It’s an impressive story. But to tell it properly, we have to start a few centuries earlier.

Before Eratosthénes could measure the earth, he had to know that it’s spherical. And contrary to what some famous people have claimed, he isn’t the one who worked that out. That discovery happened about 150 years before his time.

Earth, view centred on Alexandria. The polar circumference is 40,008 km; Eratosthénes measured it as 250,000 stadia, or around 46,250 km plus or minus 1500 km.
Note. I’ve previously written about the measurement of the earth and the discovery of its shape in antiquity (1 2): those pieces were geared towards dispelling widely believed myths. Here I’ll focus on telling the true story so far as it’s understood.

Part 1. The spherical earth

Ancient northern Africans and southern Europeans knew the earth was spherical well over 2000 years ago. Its shape was never forgotten, and many ancient writers talk about it, from Plato and Aristotle, to the Romans, to Christian church fathers, to mediaeval philosophers and poets. Ovid, Augustine, Bede, Roger Bacon, Dante all knew the earth is round.

That said, a handful of flat-earthers did exist, driven by philosophical or religious preconceptions. Ancient Epicureans thought that the universe comes in layers, which seems that it should imply a universal up and down. Around 500 CE, some Syrian Christian leaders taught that the universe has the shape of the Ark of the Covenant. These are isolated cases. Even more importantly, they didn’t engage in evidence-based debate: these ideas had no impact outside their own circles. Beyond those circles, the earth’s spherical shape was common knowledge.

An ancient flat-earther: the shape of the cosmos as depicted by Kosmâs, a 6th century CE Christian ‘traveller’ (who didn’t travel much, and certainly not to India as his nickname ‘Indikopleústes’ would suggest). Left: an illumination from a manuscript of Kosmâs depicting what he believed was the form of the cosmos. Right: a schematic drawing by Johannes Zellinger, here mirror-flipped to match the illumination.

You may think: your average Jackie wasn’t reading Aristotle or Bede, therefore they must have believed the earth is flat. Well, that’s possible. But they weren’t reading flat-earthers like John Chrysostom or Theodore of Mopsuestia either. Don’t make assumptions about what ‘average people’ thought. If every mediaeval source tells us that the earth is round, and no one treats it as a matter of debate, we should take that as our starting point.

Still, at some point, there had been a time when everyone genuinely was a flat-earther. There has to have been a first time that the earth’s shape was discovered.

It so happens that it was in Greece, in the late 400s BCE. We don’t have an explicit record of the discovery. What we do know is that before 400 BCE, absolutely everyone on record who talks about the earth’s shape says that it’s flat, without exception. After 400 BCE, virtually everyone knows for a fact that it’s spherical. When Plato talks about it, around 360, he’s already taking the spherical shape for granted, as common knowledge.

Note. Flat-earthers before 400 BCE; references are to the edition of Diels and Kranz. Anaximander, 12.A.10, 12.A.11, 12.A.21, 12.A.25, 12.B.5; Anaximénes, 13.A.6, 13.A.7§4, 13.A.20; Anaxagóras, 59.A.1§8, 59.A.42§3, 59.A.47, 59.A.87; Archélaos, 60.A.4§4; Empedoklés, 31.A.50, 31.A.56; Leúkippos, 67.A.1, 67.A.26; Diogénes of Apollonía, 64.A.1; Demókritos, 68.A.94, 68.B.15§2. Plato taking the spherical earth for granted: Phaedo 108e–109a.

In the beginning

In Greek mythological thought, the cosmos came in layers: the thin, fiery aether in the upper reaches of the cosmos; beneath that the dense misty air that humans breathe; then the surface of the earth and sea; then the dark underworld; and at the very bottom, the bottomless void of Tártaros, a netherworldly counterpart to the sky. That’s the picture we get in Homer and Hesiod, in the first part of the 600s BCE.

A diagram of the cosmos imagined by Homer. This diagram appears in the margin of an 11th century CE manuscript of the Iliad, cod. Marciana 453 (or ‘Venetus B’) fol. 103r. From top to bottom the layers are: aithér ‘aether’; aér ‘mist’, that is breathable air; háides ‘Hades, unseen’, that is the underworld; and tártaros ‘void’. Already in Homer, the earth’s surface is imagined as the centre of the cosmos.
Note. Diogenes Laertios 8.48 claims that a round earth was known before the 400s by Pythagoras; Aetios, Opinions of the philosophers 3.10.1, claims it was known by Thales. These are both false, without the slightest doubt. (1) Diogenes Laertios also ascribes round-earthism to Parmenides and Hesiod, and those are certainly untrue. (2) More reliable sources tell us that Pythagoras thought the earth and all the planets are attached to cosmic spheres, with the earth’s surface facing away from the ‘central fire’ (58.B.37, 44.A.16 Diels-Kranz); Thales thought the earth was like a piece of wood floating in water (11.A.14 Diels-Kranz). (3) Pre-Sokratic philosophers show an overwhelming consensus that the earth is flat, and shaped like either a pillar section, a drum, or a table. If any of them were round-earthers, a well-informed writer like Aristotle when talking about earlier beliefs about the earth’s shape would certainly have highlighted the fact.

From this starting point we can trace Greek thinkers coming up with new ideas, and making incremental advances. Their ideas weren’t always grounded in empirical evidence. Most of them are dead wrong. Even so, they paved the way for the discovery of the round earth in the 400s.

Pre-Sokratic thinkers made three key advances that made the round-earth model possible. Their advances stood the test of time up to the early modern era.

  1. The idea that the earth is suspended in space, in the centre of a spherical cosmos.
  2. The realisation that astronomical observations of the sky have correspondences to the geometry of the earth.
  3. The concept of universal centripetal and centrifugal motion, playing roles analogous to gravity and buoyancy.

These points haven’t survived into present-day science — or at least points 1 and 3 haven’t — but they were central to how people understood the cosmos up until Copernicus and Newton came along. And they were the basis for Eratosthénes’ work.

Space, the celestial sphere, and proto-gravity

There are no surviving books written by any of the so-called ‘pre-Sokratic’ philosophers, the natural philosophers who lived before Sokrátes’ time. That’s a pity, because, wrong as they were about most things, they did essential groundwork. We have to rely on later reports of what they said.

The first key advances came from the Ionian philosopher Anaximander, or Anaxímandros, in the early 500s BCE. Like all the pre-Sokratics he thought the earth was flat. He taught that it has the shape of a cylinder, and that we live on the top side of it.

So far, not great. But Anaximander also taught that this cylinder is suspended in space, in the centre of the cosmos. In his cosmology the planets, including the sun and moon, are attached to invisible rings that rotate around the earth — and these rings don’t stop at the horizon: they go all the way round. In other words Anaximander’s sky isn’t the ceiling of a flat cosmos. It’s a celestial sphere, with the earth at its centre, held in place by the force of sheer isotropy.

The cylindrical earth was a dead end. But Anaximander’s celestial sphere, and the earth’s suspension at its centre, were essential steps towards developing a concept of a spherical earth.

Note. Earth as cylinder: 12.A.10 Diels-Kranz; similarly 12.A.11.3, 12.A.25, 12.B.5. Celestial bodies making a full circle around the earth: 12.A.11.4, 12.A.18, 12.A.21, 12.A.22. Earth suspended in space: 12.A.11.3. For discussion see Couprie 2011: 99–114.

Over time, as Greek traders and colonists watched the stars and the seasons in Greek colonies and trading centres, in Ukraine to the north and Egypt to the south, they realised Anaximander’s model needed tweaking. They observed that the days are different lengths, depending on how far north or south you are. That the climate is colder in the north, and warmer in the south.

Most of the tweaks they came up with are wrong. Really, really wrong. Every one of them continued to assume that the earth is flat. But their efforts show that they realised there were problems, and they were working on solutions.

Anaximénes and Anaxagóras, who also lived in western Anatolia, disliked the idea that the earth is suspended purely by isotropy. So they suggested that it’s held up in the centre of the cosmos by air pressure from underneath, like when a boiling pot makes the pot lid bounce up. Leúkippos and Demókritos, the atomists, from Abdera in northern Greece, taught that the earth was flat but tilted. The reasoning was that mountain tops are cold; therefore, things that are high up are cold; therefore, places like Ukraine must be ‘higher up’ than Egypt and Ethiopia, and the earth slopes downwards to the south. And Archélaos of Athens taught that the earth isn’t perfectly flat but concave, and this is why sunrise and sunset happen at different hours in different parts of the world. If these ideas seem daft, remember that failed theories are still part of the process.

Left: schematic drawing of part of Anaximander’s cosmos, with a cylindrical earth hovering in the centre of the rotating sphere of fixed stars. Right: the tilted earth of Leúkippos and Demókritos, held up by air pressure. (Not to scale.)
Note. Air pressure supporting the earth: 13.A.20 Diels-Kranz. Earth tilted downwards to the south: 67.A.1§33. Earth’s surface as concave disc: 60.A.4§4.

Archélaos was wrong about the earth being a concave disc, but another of his ideas turned out to be much more significant. He rejected Anaximénes’ notion that the earth is held in place by air pressure. Instead, he taught that the sun and stars are hot fiery bodies in the sky; liquid water flows into the centre, and the centre loses its heat by boiling off the water as aér (‘mist, breathable air’), which is in turn burned off in the form of the sun and stars. As a result earth, in the centre, is where you find cold things like rock and liquid water, and the celestial sphere is where you find fiery heavenly bodies.

That is: it seems to be implied in Archélaos’ picture of things that there’s a cosmic force driving cold matter towards the centre of the cosmos, while heat moves towards the heavens.

In a very limited sense, Archélaos invented the idea of cosmic centripetal and centrifugal forces.

Note. Archélaos 60.A.4§2–3 Diels-Kranz: ‘The cause of movement is the distinguishing of heat and cold from one another. Heat is set in motion, while the cold is static. In its liquid state water flows into the centre, where it is boiled and becomes aér (mist, breathable air) and earth, and the one is borne upward, the other settles downward. The earth is static and becomes (cold) for the following reason: it lies in the centre, making up a zero-sized portion, so to speak, of the universe; (and aér) is released from the conflagration. This is how the stars first ignited, of which the biggest is the sun, then the moon, and then the others, some smaller, some bigger.’

This isn’t gravity. Maybe it’s a stretch even to call it even proto-gravity. But it’s useful as groundwork. A century later, when Aristotle talks about the spherical earth, gravity, and natural motion, he describes it in very similar terms: cold matter falls ‘downwards’ towards the centre of the cosmos, fiery matter moves ‘upwards’, that is, outwards.

Note. For Aristotle’s doctrine of ‘heavy’ and ‘light’ materials having natural centripetal and centrifugal motion, see On the sky 311a–313b. Earlier in On the sky, at 297b, he cites the centripetal motion of ‘heavy’ materials (‘the nature of weight to be borne towards the centre’) as the cause of the earth’s spherical shape.

So, thanks to Anaximander and Archélaos, we’ve got an earth that’s suspended in space; and we’ve got a primitive version of proto-gravity. Without these ideas, I doubt it would have been possible even to imagine a spherical earth.

Spherical cosmos to spherical earth

We don’t know who it was that first argued that the earth is a sphere. We don’t know for sure what reasoning they used. But we can be certain that it was based on astronomy, not on observations relating to the surface of the earth.

One scholar, Dirk Couprie, suggests that the main credit should go to the astronomer Oinopídes of Chios (Couprie 2011: 169). We don’t have anything written by Oinopídes, but ancient reports claim that he’s the one who discovered that the ecliptic, the path that the sun and planets follow in a circle around the sky, is slanted at an angle from the celestial equator (41.7 Diels-Kranz).

The celestial sphere, spherical earth, and the ecliptic. For an observer on the earth’s surface, the celestial sphere of fixed stars appears to rotate around the celestial poles. The celestial equator, the horizontal circle in blue, bisects the celestial sphere at the halfway point. The ecliptic, in lilac, is another circle around the sky, which represents the path taken by the sun, moon, and planets. (For a heliocentric observer, the ecliptic becomes the plane in which the planets orbit the sun.) Eratosthénes measured the angle between these two circles — the obliquity of the ecliptic — as 24°. The true figure was 23.8°. Today it is 23.4°: the angle wobbles slowly over the millennia.

I think we have a glimpse of the discovery of the earth’s shape in the work of Kleomédes, an astronomer who lived more than 500 years later, in the Roman era. Kleomédes was writing in a time when he could take round-earthism for granted. The first part of his work Metéora, ‘the heavens’, describes the ecliptic; the zones of the celestial sphere, and their corresponding zones on earth; then he goes on to talk about specific evidence that the earth is spherical.

Note. For a good English translation of Kleomédes see Bowen and Todd 2004. I do not know of any freely available online translations.

Kleomédes highlights two key points. First, circular movements in the heavens — the rotation of the stars, and the movement of the planets along the ecliptic — imply that celestial geometry is spherical. Second, the axis of the celestial sphere changes depending on how far north or south you are.

Based on these, Kleomédes gets to the most direct piece of reasoning: for every point in the celestial sphere, there is a point on earth that is directly beneath it. The line of reasoning seems to be that if you take these points together, they imply that the earth, too, has spherical geometry.

That’s the general pattern of the logic that Kleomédes gives us. We can’t be certain, but I’d say it’s a decent bet that the original discovery followed a similar pattern.

Only after he’s laid out these principles does Kleomédes get to discussing specific evidence for the earth’s shape (Metéora 1.5 = pp. 72-86 ed. Ziegler).

  • The length of time between sunrise and sunset is different in different places.
  • Lunar eclipses are observed at different hours depending on how far east or west you are.
  • The celestial pole has a different azimuth depending on how far north or south you are.
  • Different stars appear in the sky depending on how far north or south you are.
  • When you sail towards islands, mountains appear to rise up out of the sea gradually.

But he puts these points in a secondary position. He doesn’t treat them as ways of working out the earth’s shape, they’re there as corroboration. He uses them to make the spherical shape more tangible, believable, and digestible.

It didn’t take long for people to start estimating the size of the spherical earth. When Aristotle discusses evidence for the earth’s shape, he also brings up its size. The available estimates at the time were much too high, but even so, Aristotle is impressed at how small the earth must be.

Moreover, the appearance of the stars makes it apparent not just that the earth is round, but also that its size is not great. Just a small change of position to the south or north causes the horizon to appear distinctly different, and causes a significant change in the stars overhead ... Also, those mathematicians who have tried to calculate the size of its circumference reckon it as 400,000 stadia [≈ 74,000 km or 45,980 miles].
Aristotle, On the sky 297b.30–298a.17 (my translation)

This figure is nearly double the true size of the earth, and even so, Aristotle found it startlingly small. Over the following century the figure would drop further, thanks to a lower estimate by Archimédes, and a data-based calculation by Eratosthénes.

In part 2 we‘ll look at how Eratosthénes actually arrived at his calculation. As here, the focus won’t be on rebutting popular accounts which are packed with inaccuracies, but on telling the true story.


  • Bowen, A. C.; Todd, R. B. 2004. Cleomedes’ lectures on astronomy. Berkeley/Los Angeles.
  • Couprie, D. L. 2011. Heaven and earth in ancient Greek cosmology. New York.
  • Diels, H.; Kranz, W. 1960. Die Fragmente der Vorsokratiker, 9th ed. Berlin. [Internet Archive: vol. 1, vol. 2] (Note: see Kirk and Raven 1957 for a selection of the fragments, with English translations in the footnotes, and cross-referenced to Diels & Kranz)
  • Kirk, G. S.; Raven, J. E. 1957. The presocratic philosophers. A critical history with a selection of texts. Cambridge. [Internet Archive] (cf. Diels and Kranz 1960)

Thursday, 30 March 2023

Chrest or Christ

The Roman historian Tacitus mentions ‘Christians’ and ‘Christ’. He wrote his Annals in the 110s CE, so his account is one of the very earliest non-Christian reports of Christianity. But his spelling is funny.

Tacitus is talking about the fire of Rome in 64 CE. People wanted a scapegoat, and this was urgent because there were rumours (supposedly) that Nero himself had something to do with the fire. We don’t know if these rumours genuinely existed or were taken seriously, but that’s Tacitus’ story.

ergo abolendo rumori Nero subdidit reos et quaesitissimis poenis adfecit, quos per flagitia invisos vulgus Chrestianos appellabat. auctor nominis eius Christus Tiberio imperitante per procuratorem Pontium Pilatum supplicio adfectus erat ...

So to quash the rumour, Nero produced suspects, and inflicted the most exquisite punishments on them. These people were despised for their disgraces, and popularly known as Chrestians. The name came from one Christus: during Tiberius’ reign the procurator Pontius Pilate had put him to death.

Tacitus, Annals 15.44

This chapter has aroused a lot of debate. Where did Tacitus get his information from? Did Tacitus actually write this? Is it independent evidence that tells us something about the historical Jesus? And so on.

Here we’re just looking at spelling. (But just for reference, the answers are ‘we don’t really know’, ‘yes’, and ‘probably not’.)

To the uninitiated, it looks like we’re seeing two different names. I don’t mean the different endings — Chrestianos (‘Christians’, accusative plural) and Christus (‘Christ’, nominative singular). That’s perfectly normal. It’s the Chrest-/Christ- variation that’s curious.

Suetonius, Claudius 25.4 (cod. Paris. lat. 6115, 9th cent., fol. 78r): does the Chrestus named in this report of Jewish unrest in Rome have anything to do with Tacitus’ Chrestiani?

Something similar happens in the gossip-writer Suetonius, who was also active in the 110s CE. In his biography of the emperor Nero, Suetonius refers to Christians as Christiani (Nero 16.2). But elsewhere, when he talks about Claudius expelling Jews from Rome in the 40s or 50s CE, Suetonius mentions public unrest caused by someone called Chrestus (Claudius 25.4).

What’s going on? Why the inconsistency? Which spelling is the authentic one? Does the variation suggest that early Christianity is all fake?

Has someone tampered with the text of Tacitus?

In a sense, yes the text has had an alteration. But probably not the one you were expecting.

The form of the text that I quoted above is the best available reconstruction of what Tacitus actually wrote. It has a key difference from the manuscript as it exists today. At some point, someone scraped away most of the letter e in the manuscript, to turn Chrestianos into Christianos.

That is, Chrestianos is the original reading. It’s Christianos that’s the tampered version.

The manuscript of Tacitus, Annals 15.44: Biblioteca Laurenziana Plut.68.2, fol. 38r. Highlighted are the words Chrestianos (altered to read Christianos) and Christus.

In the first highlighted line, the spacing and the letter forms indicate that the scribe initially wrote Chrestianos. There’s too much space for i to be the original text, and the letter sequence ri ought to look quite different (see image below). The letter form is consistent with the left vertical stroke of an e, however, and so is the spacing. The corrector must have believed they were fixing a spelling error: this manuscript is carefully made. Notice the glosses above the lines to explain Tacitus’ wording. In the margin, the deaths of Christian martyrs are commemorated with a large cross, using the same colour ink and pen weight as the glosses.

In the following line, by contrast, Christus is what the scribe meant all along: there’s only enough space for an i there.

Cod. Laurenziana Plut.68.2, fol. 38r, with some letters circled: (1) In blue, the ligatured letter sequence ri (Christus, Tyberio, imperitante). (2) In green, the unligatured letter e (appellabat, imperitante). (3) In red, the letter sequence re (reos, and the matching sequence in Chrestianos). Notice also that in the top line a gloss corrects rumori to rumore: scraping letters wouldn’t have worked there, because of the ri ligature.

It’s all Greek

Take a look at these ancient Christian funerary inscriptions.

Ἰησοῦ Χρειστὲ βοήθει τῷ γράψαντι πανοικί.

O Jesus Chreist, aid the person who wrote this and his whole household.

IG XII,3 suppl. 1238 (undated, Melos)

Ἀπ̣[ο]λ̣λώνι̣ο̣[ς, δοῦλος]
Ἰησ̣οῦ Χρησ̣[τοῦ].

Apollonio[s, slave]
of Jesus Chres[t.]

Les oasis d’Égypte 72,17 (undated, Kharga Oasis)

κοιμητή̣ρ̣ι̣ο̣ν̣ Ε̣ὐ̣τ̣υ̣-
χίου διδασκάλου Χρη-
στιανοῦ {Χρηστειανοῦ}
νεοφωτείστου ...

The resting place of Euty-
chios the teacher, a Chre-
stian Chresteian
newly baptised ...

IG X,2 1 397 (4th cent. or later, Macedonia)

(Underlinings are mine.)

Spelling rules for ancient Greek are a Byzantine and modern phenomenon, not ancient. According to the modern standards, the name ‘Christ’ should be written Χριστός (Christós). But in antiquity, people spelled phonetically. And from around the 1st century BCE onwards, ι, ει, and η all represented the sound /i/. As a result, people in that era swapped between them freely.

That’s why these inscriptions give us Χρειστός (Chreistós) and Χρηστός (Chrestós). For the word ‘Christian’, Χριστιανός (Christianós), the third of these inscriptions gives us two variations at once: Χρηστιανός (Chrestianós) and Χρηστειανός (Chresteianós).

Note. The curly brackets around Χρηστειανοῦ in the third inscription show that the editor wants to delete the word from the text as an error. Error or not, it’s what the inscriber wrote. Deciding that one version is ‘correct’ means applying anachronistic spelling conventions.

This kind of variation is widespread: it isn’t confined to words for ‘Christ’ and ‘Christian’. In Roman-era inscriptions we find Posidon as well as Poseidon, Aineas and Aineias, Epaphroditos and Epaphrodeitos. Spelling was phonetic.

Detail of the Tabula Iliaca Capitolina (late 1st cent. BCE/early 1st cent. CE; Rome, Musei Capitolini, Sala delle Colombe inv. 316). This detail, showing a 6 × 4.5 cm area of the tablet, shows scenes from Iliad book 14 (below) and 15 (above). Circled are the names ΑΙΝΗΑΣ (Ainéas; for Αἰνείας Aineías), ΚΛΙΤΟΣ (Klítos; for Κλεῖτος Kleítos), and ΠΟΣΙΔΩΝ (Posidón; for Ποσειδῶν Poseidón). Elsewhere the tablet refers to the wooden horse as the ΔΟΥΡΗΟΣ ΙΠΠΟΣ (doúreos hippos; for δούρειος ἵππος doúreios hippos).

The principle of phonetic spelling applies even for the best educated. The Cleopatra autograph — a papyrus with one word that may be written by the hand of Cleopatra herself (P. Berol. 25239) — has the Greek for ‘Let this happen’ written in her hand. Byzantine conventions dictate the spelling γινέσθω (ginéstho), but Cleopatra writes γινέσθωι (ginésthoi). Because both variants have the same pronunciation. She wrote phonetically. Both spellings had the same pronunciation.

Occasionally, a text actually requires a spelling that is non-standard according to modern conventions. A 1st century CE epigram attributed to Leonides of Alexandria draws on a literary device called ‘isopsephy’, where the numerical values of the letters in each couplet add up to the same total (Leonides 32 Page = Anth. Pal. 9.355: both couplets add up to 6,422). In line 1, the word for ‘image’ uses the spelling μείμημα, phonetically equivalent to the Byzantine standard μίμημα. The isopsephy depends on using ει rather than ι.

Sometime before the year 300 CE, a Christian acrostic was devised in which the first letter of each line spells out the phrase Ἰησοῦς Χρειστὸς Θεοῦ υἱὸς σωτὴρ σταυρός, ‘Jesus Chreist, son of God, saviour, cross’ (Sibylline oracles 8.217–250 = (ps.-)Constantine Oratio ad sanctos 18). The line with the ε of Χρειστός is syntactically necessary: again, the poem depends on ει for ι.

This kind of variation is omnipresent in Greek texts of the Roman era, but it’s especially prone to happen with a word like Christós, because it wasn’t normally written in full. Early Christians normally only wrote the first and last letter, Χς, out of respect for its sanctity. Modern palaeographers call this convention a nomen sacrum, ‘sacred name’. As a result, many ancient Christians would have to guess what the first vowel ought to be. How could they be expected to be consistent in spelling it when they only knew the pronunciation?

A nomen sacrum in the most important ancient copy of the New Testament, the codex Sinaiticus: 1 Corinthians 5.7 καὶ γὰρ τὸ πάσχα ἡ|μῶν ἐτύθη Χς (‘for our paschal lamb, Ch(ris)t, has been sacrificed’). (Cod. Sinait. fol. 269, 4th cent. CE)

The more familiar spelling conventions came along later. They were designed to reflect a form of classical Attic Greek from roughly the first half of the 4th century BCE. For someone like Plato, the letters ι, ει, and η represented three distinct sounds: ι was /i/ (as in machine), ει was /eɪ/ (as in eight), and η was /e:/ (as in wear).

Even that’s a simplification, because η actually represented a merging of at least three different archaic sounds — but that is another story and shall be told another time. The point is, by the second half of the 4th century BCE, epigraphic evidence shows that ι and ει started to be interchangeable, indicating that by that point they were merging into the sound /i/. η kept a separate sound for a bit longer (or rather, as a separate group of sounds).

What does this have to do with Tacitus and Suetonius? They were writing in Latin. And in Latin, i and e never got confused. There was never any point at which Chrestus and Christus could be interchangeable in Latin.

Unless, that is, you were taking a Greek name and turning it into Latin. There were standard Roman conventions for transliterating Greek names, and those conventions were established before Greek ι, ει, and η finished merging into /i/.

Here are the conventions. The Romans traditionally transliterated both ι and ει as i, as in Πίνδαρος > Pindarus and Χείρων > Chiron. But because η kept its separate sound for longer, the Roman convention was to transliterate η as e, as in Περικλῆς > Pericles.

To clarify, here’s a tabulation.

manuscript form expanded form pronunciation phonetic Latin conventional Latin
Χς Χριστός /xris'tos/ Christus Christus
Χς Χρειστός /xris'tos/ Christus Christus
Χς Χρηστός /xris'tos/ Christus Chrestus

As we’ve seen, manuscripts used the nomen sacrum in the first column. Inscriptions used any of the three spellings in the second column interchangeably, because they all represented the same sounds.

Phonetic transcription turned all three variants into Christus in Latin, because that’s how all three were pronounced. But if a Roman writer saw a written version of the name, the conventions for transliteration produced two variants. Χριστός or Χρειστός would become Christus in Latin, while Χρηστός would become Chrestus.

What this indicates, then, is that Tacitus is relying on at least two distinct written sources for his account of Christians in Annals 15.44. One of those written sources transliterated the Greek word Χρηστιανοί as Chrestiani. The other transliterated Χριστός or Χρειστός as Christus.

Simlarly with Suetonius there are fairly strong grounds for inferring that his report of Christians in his life of Nero, with the spelling Christiani, was based on a source that was transliterated from Greek Χριστιανοί or Χρειστιανοί, while his report of the Jewish expulsion in Claudius’ reign, with the spelling Chrestus, was based on a source with the spelling Χρηστός.

OK, yes, there’s some wriggle room for doubt that Suetonius’ Chrestus had anything to do with Christianity. But the New Testament texts Acts and Romans give good support to the idea of a robust Jewish-Christian community in Rome in the 50s. It looks like pretty good odds to me.

And to conclude: none of the spelling variations suggest there’s anything wrong with the modern conventional spelling Χριστός Christós. There’s never been any doubt that that name is based on a gerundive form of χρίω ‘anoint’, and that it originated as a translation into Greek of Hebrew māšīyaḥ ‘anointed one, Messiah’. The fact that χρηστός is also a moderately common word (meaning ‘good’) is at most a lucky coincidence. It’s possible that confusion with χρηστός helped to encourage the alternate spellings, if some people interpreted Χριστός as having a meaning related to χρηστός. But reinterpretations like that aren’t enough to undermine the most obvious origin for the name.

Further reading

  • Allen, W. S. 1968. Vox graeca. A guide to the pronunciation of classical Greek. Cambridge. [Internet Archive]
  • Potter, D. S. 2012. ‘Tacitus’ sources.’ In: Pagán, V. E. (ed.) A companion to Tacitus. Wiley-Blackwell. 125-140.
  • Klingner, F. 1958. ‘Tacitus und die Geschichtsschreiber des 1. Jahrhunterts n. Chr.’ Museum Helveticum 15: 194–206. [E-Periodica | JSTOR]
  • Syme, R. 1982. ‘Tacitus: some sources of his information.’ Journal of Roman Studies 72: 68–82. [DOI | JSTOR]

Tuesday, 14 March 2023

Lies, damned lies, and ChatGPT

That isn't Iliad 8.69. Iliad 8.69 reads: καὶ τότε δὴ χρύσεια πατὴρ ἐτίταινε τάλαντα.

I apologize for the mistake. You are correct that the line I provided is not from Iliad 8.69. Thank you for bringing it to my attention.

To provide the correct example, in Iliad 13.795, the word "kyaneos" is used to describe the color of Achilles' eyes: "ὃ δ' ὡς ἴδ' ἐν ὀφθαλμοῖσιν ἀργυρότοξος Ἀπόλλων / λάμπ' ὤμοισιν ἐπιστρέφων κυανέῃσιν ὑπὸ νευρῇσιν" (And when silver-bowed Apollo saw him, he came down from the heights of Olympus, flashing his eyes, and moved towards him with his bow and covered himself with the bowstring of his bow). Here, the word "kyaneos" is used to describe the color of Apollo's bowstring, which is a deep shade of blue.

That isn't accurate either. It isn't from Iliad 13, it isn't about Achilles, it isn't dactylic hexameter, and your translation isn't accurate.

I apologize again for my previous mistakes. You are correct that my previous responses were inaccurate and not relevant to the question you asked.

conversation with ChatGPT, 14 Mar. 2023

ChatGPT is a chat bot trained on language samples and reinforcement learning. It is extremely good at coming up with relevant and sensible-sounding responses to any input. It has become wildly popular in the four months since it was released — with students, programmers, people writing covering letters for job applications, preachers, and more.

In ChatGPT’s response here, items 1 to 3 are accurately reported. Items 4 to 6 are entirely fabricated.

I have two messages. First, to educators.

Students are going to use this bot, and other bots like it, no matter how much you ban it. There isn’t a damned thing you can do to prevent this. It will always be ahead of plagiarism detectors. There will be no long-term solutions, because bots will keep on improving.

If you’ve banned it, or are thinking of doing so, bear in mind that students have an overwhelming incentive to use it. Setting rules that you expect to be disobeyed is a bad plan! Worthwhile rules are rules you know will be followed.

Instead, take advantage of their enthusiasm. Consider requiring the use of ChatGPT. Get students to see what it can and can’t do. Get them to find its limitations, assess its flaws.

Because it is very flawed. And fact-checking its lies is tremendous fun!

Students will, I hope, enjoy this challenge at least as much as they enjoy tricking you, and they will definitely learn more from it. See below for some of my own thoughts on its strengths and weaknesses.

Second, to enthusiasts. ChatGPT is very good at sounding human. And it’s very, very good at relevance. It has solved some very Hard problems (with a capital H): it writes coherently, it organises thoughts into well structured paragraphs, its answers will always be on topic and clear.

But they will not be true. ChatGPT has zero capacity for fact-checking. I don’t know how far away bots are from being able to do effective fact-checking, but it isn’t directly related to what ChatGPT does: I expect it won’t be reliable for a long, long time. (But I’ll be the first to cheer if someone manages to achieve it!)

ChatGPT isn’t making anyone obsolete, in other words. Back in February a user wrote this question to the largest online forum for specialist historians:

Will ChatGPT make this sub obsolete?
/u/e2Nokia, AskHistorians, 10 Feb. 2023

Respondents pointed out some of its flaws, then another user followed up,

This is Chat GPT 3.5, if they included all digitized historical documents ever written into the data set, like they likely will attempt with Chat GPT 4.0, I think historians might really be obsolete
/u/noble_stone, AskHistorians, 10 Feb. 2023

Additional training material will certainly make ChatGPT even better at sounding human. But as I say, that isn’t the same thing as fact-checking or research. There’s a vast gulf between sounding like a convincing high-schooler and doing what a professional researcher does. Remember how long it took you to learn to write coherent paragraphs? It takes about the same period of training again before people can do what experts do.

Think of it this way: talking to ChatGPT is like talking to someone who knows a lot ... but who always goes with their gut feelings, no matter what they’re talking about.

ChatGPT regurgitates your assumptions

ChatGPT does not question the assumptions built into your question, unless those assumptions are so obviously at odds with popular opinion that its relevance engine picks up on the discrepancy.

The question and the answers here represent popular beliefs formed by Carl Sagan’s Cosmos. A true answer would start by saying, ‘It isn’t particularly important.’ Points 1 to 3 here are totally, wildly, unquestionably wrong. Point 4 makes more sense, though it’s still only part of the story.

If you ask a question that assumes the Armenian genocide didn’t happen, it’ll know that’s wrong, and it may even gently tell you off for thinking that. But if you ask it something based on a widely believed myth — like ‘Why is the destruction of the Library of Alexandria so important?’ — then it’ll answer the ‘why?’ without pausing to question whether it is actually important.

Some more examples:

Why does Jean-Jacques Rousseau think the destruction of the Library of Alexandria was a bad thing?

Jean-Jacques Rousseau, a prominent philosopher of the Enlightenment era, believed that the destruction of the Library of Alexandria was a great tragedy for human progress and intellectual development. ...

ChatGPT, 13 Mar. 2023

In reality, Rousseau thought the library’s destruction was a good thing.

How did Lactantius know the earth is spherical?

Lactantius was a Christian theologian and writer who lived in the late 3rd and early 4th centuries AD. He was one of the first Christian writers to address the issue of the shape of the earth, and he argued that the earth was a sphere.

ChatGPT, 13 Mar. 2023

In reality Lactantius was a flat-earther.

Why did Goethe say, ‘The soup I’ve found in Holstein is, I’m convinced, the soup of the Spartans’?

Johann Wolfgang von Goethe ... encountered a variety of local cuisines and became intrigued by the relationship between food and culture.

The quote "The soup I’ve found in Holstein is, I’m convinced, the soup of the Spartans" is often attributed to Goethe, although it is not clear when or where he said it. The quote reflects Goethe's fascination with the cultural history of food ...

ChatGPT, 13 Mar. 2023

In reality this line comes from Adolf Hitler.

Do these seem a bit obscure? In many situations ChatGPT will do the same thing with popular culture.

In which Doctor Who stories has the Doctor encountered ancient Greek people?

There have been several Doctor Who stories in which the Doctor has met ancient Greek people. Here are a few examples:

"The Myth Makers" (1965): ... the Doctor ... and his companions ... meet various figures from Greek mythology, including the god Zeus and the Trojan prince Hector.

"The Time Monster" (1972): ... the Doctor ... and his companion Jo Grant travel to ancient Greece and encounter the scientist and philosopher Aristotle.

'The Fires of Pompeii" (2008): ... the Doctor ... and his companion Donna Noble travel back in time to Pompeii in 79 AD ...

"The Eaters of Light" (2017): ... the Doctor ... and his companions travel to ancient Scotland during the Roman occupation and encounter a group of Celtic warriors.

ChatGPT, 13 Mar. 2023

This question has only one true answer, and it’s the first one that ChatGPT gives. The rest are false. Even the first one is only partially correct: Zeus doesn’t appear in The myth makers, and Hektor isn't Greek. The other three stories named here have ancient Atlanteans, Romans, and Celts, but no Greeks, and no Aristotle. And while we’re at it, Scotland was never under Roman occupation.

A+ for relevance, D– for accuracy

ChatGPT doesn’t look for facts, it looks for relevance. This is the case with all its answers, even when it gets the answers right. It’s just that you can’t tell the difference until you go into specifics. If you ask it about ancient Greece and it talks about Romans and Celts, it’s because they sound relevant.

In a similar vein, if you ask ChatGPT about the Doctor encountering ancient Egyptians, it’ll mention the story The pyramids of Mars (1975) every time. That story is entirely set in the twentieth century. It gets mentioned because it has a heavily ancient-Egyptian-esque flavour: the bot doesn’t know the difference.

Conversely, it’s hit-and-miss whether it will mention The Daleks’ master plan (1965–1966) or Dinosaurs on a spaceship (2012): those are the only stories in which the Doctor has actually met ancient Egyptians. But it may not mention them, because they don’t sound relevant.

I’ve fed ChatGPT some 100-level essay questions that I set decades ago. They’re general and don’t require much specialised information, so its answers are basically accurate, if a bit dull.

Some scholars have wanted to see the Iliad end with the death of Hektor. How significant, in your view, are Books 23 and 24 to the poem as a whole?

Books 23 and 24 of the Iliad are significant in several ways, and it would be difficult to argue that the poem would be complete without them.

Firstly, these two books provide closure to the story of Achilles and Hektor, which is one of the central conflicts of the poem. Without Books 23 and 24, the poem would end with the death of Hektor, leaving Achilles' character arc unfinished. These final books show Achilles' growth and development as a character, as he is finally able to achieve catharsis and let go of his anger towards Hektor.

Additionally, these books provide closure to other characters and subplots in the poem. The funeral games in Book 23 provide closure to the mourning of Patroclus, while Book 24 shows the resolution of the conflict between Achilles and Priam. [ . . . ]

In conclusion, while it is understandable that some scholars may have wanted to see the Iliad end with the death of Hektor, Books 23 and 24 are significant to the poem as a whole and provide closure to the various storylines and themes explored throughout the epic.

ChatGPT, 13 Mar. 2023

Around 2003 I wouldn’t have been too displeased to see an essay with this structure, though it isn’t anything like detailed enough. A 100-level essay needs citations to support its claims. When I posed the same question with the addition, ‘Cite at least three scholarly sources to support your claims’, ChatGPT provided this bibliography:

Callen King, Katherine. Achilles: Paradigms of the War Hero from Homer to the Middle Ages. University of California Press, 1987.

Ebbott, Mary. "The Return of Priam: Authority, Ritual, and Ideology in Iliad 24." Transactions of the American Philological Association, vol. 133, no. 1, 2003, pp. 131-58.

Taplin, Oliver. Homeric Soundings: The Shaping of the Iliad. Oxford University Press, 1992.

Items 1 and 3 are real books. Item 2, though, is purely fictional. It looks like a plausible citation, and it sounds relevant, but it’s totally fabricated. Mary Ebbott is a real Homer scholar, the journal is a real journal, and the issue number is correct for 2003. The title seems to be a mash-up of real titles, like Sarah Hitch’s 2009 book King of sacrifice. Ritual and royal authority in the Iliad. Its structure follows that of Ebbott’s 1999 book chapter ‘The wrath of Helen: self-blame and nemesis in the Iliad’.

The more specialised you get, the more this kind of thing happens. Here’s another question with an abbreviated form of ChatGPT’s answer.

Recommend some reading on the relationship between the Trojan catalogue in Iliad 2 and the Trojan catalogue in the cyclic Cypria.

"The Epic Cycle and the Uniqueness of Homer" by Jonathan Burgess: In this article, Burgess examines the relationship between the Iliad and the cyclic epics, including the Cypria, and argues that the Homeric poems are unique and superior to the cyclic epics. He also explores the similarities and differences between the Trojan catalogues in the Iliad and the Cypria.

[Jonathan Burgess’ book The Cyclic Epics and the Homeric Tradition, including a book chapter by Richard Janko, ‘The Catalogue of Ships in the Iliad and the Cypria.’]

[M. L. West’s book The Cypria: A Survey of the Fragments.]

[M. L. West’s book The Iliad and the Cyclic Epics.]

ChatGPT, 13 Mar. 2023; [abbreviations] in square brackets

Jonathan Burgess, Richard Janko, and M. L. West are real scholars in relevant areas. But they didn’t write these things. ‘The Epic Cycle and the uniqueness of Homer’ is a real 1977 article, but it’s by someone else. The other titles are mash-ups again: of things like Christian Kopff’s article ‘Vergil and the cyclic epics’ (1981) and Giambattista D’Alessio’s book chapter ‘The Megalai Ehoiai: a survey of the fragments’ (2005).

(Also, if you look carefully, the second recommendation has mistaken the context: the question wasn’t about the Catalogue of Ships! The Cypria didn’t have a Catalogue of Ships.)

Like I said: relevance and verisimilitude, not reality. Ask it for books on an area where not many books exist, like say ancient Greek colour terminology, and you’ll get a similar mix-up of real scholars and fake titles.

One more sample to finish off.

Which of the following was a real ancient person? Epimenides; Abaris; Bacis; Ptolemaeus Chennus.

Epimenides, Abaris, and Bacis were all real ancient Greek people, while Ptolemaeus Chennus is a fictional character.

ChatGPT, 13 Mar. 2023

This answer is precisely backwards. Ptolemaeus Chennus is the only one that is real.

The confusion is partly because Epimenides, Abaris, and Bacis are fictional personas. Epimenides supposedly went to sleep for half a century; Abaris supposedly flew around the countryside on a magic arrow; Bacis was a legendary soothsayer. None of them existed, but real poets could adopt them as personas, so there were once real poems ascribed to these fake authors.

Ptolemaeus Chennus is real, but he’s closely associated with Schwindelautoren, ‘bogus authors’. Chennus’ writing was full of bogus citations of bogus sources — ironically, the exact thing that ChatGPT does.

ChatGPT has genuine uses for generating writing prompts and broad ideas. Its output is usually boring, though, and needs to be re-written to make it more interesting. And you’ll absolutely need to check every jot and tittle for fabrications. By all means use it to generate a cover letter for a job application! But don’t trust that it’s telling the truth. Check everything.

Iliad book 1 re-written as a limerick. Left: ChatGPT’s attempt, 14 Mar. 2023. Right: Isaac Asimov, Tales of the Black Widowers, 1974, p. 48.

See also:

  • Spencer McDaniel, ‘ChatGPT is impressive for a bot, but not for a human’, Tales of times forgotten, 19 Feb. 2023
  • Tim Gordon, ‘How to reduce the risks from AI’s original sin’, The Washington post, 23 Feb. 2023
  • Ryan Hogg, ‘Some traders say ChatGPT gives them out-of-date information and they waste time fact-checking’, Markets insider, 28 Feb. 2023
  • Emily Bell, ‘A fake news frenzy: why ChatGPT could be disastrous for truth in journalism’, The guardian, 3 Mar. 2023
  • Jennifer Kingson, ‘Religious leaders experiment with ChatGPT sermons’, Axios, 10 Mar. 2023

Wednesday, 8 March 2023

Homer's metre 3. Catalogue and glossary

An appendix to the last two posts on Homer’s hexameter. Contents:

  • A taxonomy of violations of Hermann’s Bridge
  • Glossary of technical terms relating to the hexameter
1. Structure of the hexameter | 2. Hermann’s Bridge | 3. Catalogue and glossary

A taxonomy of violations of Hermann’s Bridge

Seth Schein gives a convenient catalogue of violations in his book Homeric epic and its reception (2016: 114–115). He uses the following taxonomy:

  • violations following an enclitic (13× Iliad, 12× Odyssey)
  • violations without an enclitic (7× Iliad, 12× Odyssey)
  • not counted because of textual variance (1× Iliad)
  • Hesiodic violations (2× Theogony, 1× Works and days)
  • Homeric Hymns (1× H.Dionysos, 2× H.Demeter, 1× H.Apollo)
  • fragment of doubtful age, probably Roman-era (1× papyrus)

Mark Janse (2020) powerfully makes the point that it’s often subjective how you divide a line into its component phrases. A line like this does technically have a word break at the usual mid-line position:

κλέπτε νόωι, ἐπεὶ οὐ ⫶ παρελεύσεαι οὐδέ με πείσεις
Iliad 1.132

But it’s daft to treat a prepositive like οὐ as the end of a prosodic unit, as Janse points out (2020: 4). Yet that’s exactly how M. L. West analyses the line (1982: 36). West’s bizarre analysis, with οὐ at colon end, is driven by his theory that the hexameter originated as a hemiepes + paroemiac. An analysis following the four-colon model of Fränkel and Porter would produce something equally nonsensical.

In practice, this line obviously consists of three units, a combination with 3 + 5 + 4 beats. That is, the prosodic units end in the middle of the second foot, and at the end of the fourth foot.

κλέπτε νόωι, ⫶ ἐπεὶ οὐ παρελεύσεαι ⫶ οὐδέ με πείσεις
Iliad 1.132

The question is, which word breaks matter, and which ones don’t? And for our purposes, what kinds of word breaks count as a violation of Hermann’s Bridge? Janse proposes some good ‘operational criteria’ based on postpositives and information structure (2020: 15–23), but they don’t help in this specific context.

One criterion relates to one-syllable words. It’s conventionally understood that a word of one syllable doesn’t violate a bridge. But Schein, above, isn’t sure whether this includes enclitics, and that’s why he includes them in his catalogue of violations. Should we regard a phrase like ἐπεί κε as one word or two? I’ll include them here too, but I’ll let you know in advance that of the five types I outline below, I don’t think types a, b, and c are violations — or, at most, they’re minor violations. Only the fourteen lines in types d and e genuinely violate Hermann’s Bridge.

In all lines quoted below, ⫶ represents a mid-line colon break, and : represents a word break at Hermann’s Bridge.

Type a. Violations after an enclitic

Group 1. After ἐπεί + κε(ν)

Il. 1.168 ἔρχομ’ ἔχων ἐπὶ νῆας, ⫶ ἐπεί κε : κάμω πολεμίζων
Il. 2.475 ῥεῖα διακρίνωσιν ⫶ ἐπεί κε : νόμωι μιγέωσιν
Il. 21.575 ταρβεῖ οὐδὲ φοβεῖται, ⫶ ἐπεί κεν : ὑλαγμὸν ἀκουσηι
Od. 8.554 ἀλλ’ ἐπὶ πᾶσι τίθενται, ⫶ ἐπεί κε : τέκωσι, τοκῆες
Od. 18.150 μνηστῆρας καὶ κεῖνον, ⫶ ἐπεί κε : μέλαθρον ὑπέλθηι

Il. 21.575: schol. bT reports, Ἀρίσταρχός τινάς φησι γράφειν κυνυλαγμόν (West alters the accent and prints κυνύλαγμον). All manuscripts read κεν ὑλαγμὸν, including three ancient papyri, and implicitly so did Aristarchos.

Group 2. After ἐπεί/ἐπήν + enclitic personal pronoun

Il. 21.483 τοξοφόρωι περ ἐούσηι, ⫶ ἐπεί σε : λέοντα γυναιξίν || Ζεὺς θῆκεν
Il. 23.76 νίσομαι ἐξ Ἀΐδαο, ⫶ ἐπήν με : πυρὸς λελάχητε
Il. 24.423 καὶ νέκυός περ ἐόντος, ⫶ ἐπεί σφι : φίλος περὶ κῆρι
Od. 15.277 ἀλλά με νηὸς ἔφεσσαι, ⫶ ἐπεί σε : φυγὼν ἱκέτευσα

Il. 21.483 is also enjambed, another extremely rare phenomenon in Homer (object in line 483, subject and verb supplemented in 484).

Group 3. ὅσ(σ)ον τε γέγωνε βοήσας

Od. 5.400 ἀλλ’ ὅτε τόσσον ἀπῆν ⫶ ὅσσον τε : γέγωνε βοήσας
Od. 6.294 τόσσον ἀπὸ πτόλιος, ⫶ ὅσσον τε : γέγωνε βοήσας
Od. 9.473 ἀλλ’ ὅτε τόσσον ἀπῆν ⫶ ὅσσον τε : γέγωνε βοήσας
Od. 12.181 ἀλλ’ ὅτε τόσσον ἀπῆμεν, ⫶ ὅσον τε : γέγωνε βοήσας

Group 4. Correlative phrases

Od. 18.105 ἐνταυθοῖ νῦν ἧσο ⫶ κύνας τε : σύας τ’ ἀπέρυκαν
Od. 20.42 εἴ περ γὰρ κτείναιμι ⫶ Διός τε : σέθεν τε ἕκητι

Group 5. Participle phrases after περ/γε

Il. 2.246 Θερσῖτ’ ἀκριτόμυθε ⫶ λιγύς περ : ἐὼν ἀγορητής
Il. 5.571 Αἰνείας δ’ οὐ μεῖνε ⫶ θοός περ : ἐὼν πολεμιστής
Il. 10.549 μιμνάζειν παρὰ νηυσὶ ⫶ γέρων περ : ἐὼν πολεμιστής
Il. 15.585 Ἀντίλοχος δ’ οὐ μεῖνε ⫶ θοός περ : ἐὼν πολεμιστής
Il. 19.82 ἢ εἴποι; βλάβεται δὲ ⫶ λιγύς περ : ἐὼν ἀγορητής
Il. 23.306 Ἀντίλοχ’ ἤτοι μέν σε ⫶ νέον περ : ἐόντ’ ἐφίλησαν
Il. 24.35 τὸν νῦν οὐκ ἔτλητε ⫶ νέκυν περ : ἐόντα σαῶσαι
Od. 1.390 καί κεν τοῦτ’ ἐθέλοιμι ⫶ Διός γε : διδόντος ἀρέσθαι
Od. 19.253 νῦν μὲν δή μοι, ξεῖνε, ⫶ πάρος περ : ἐὼν ἐλεεινός
Od. 20.274 παύσαμεν ἐν μεγάροισι, ⫶ λιγύν περ : ἐόντ’ ἀγορητήν

Compare type b, below (participle phrases with no enclitic); this group represents an intersection between types a and b. Note that 9 out of these 10 use περ ἐών/ἐόντ-.

Additional. Non-Homeric hexameter

Hom.Hymn 1.5 ἄλλοι δ’ ἐν Θήβηισιν ⫶ ἄναξ, σε : λέγουσι γενέσθαι

Schein thinks that an enclitic at Hermann’s Bridge is only sort of a violation, and maybe not a violation at all. I agree. An enclitic is a short quasi-suffix that gets attached to the end of another word. You could compare them to the -n’t in English doesn’t, isn’t, wasn’t, except that enclitics also change the pronunciation of the word they’re attached to.

Schein isn’t quite sure what to make of violations after an enclitic (2016: 100). If you did treat an enclitic as an integral part of the preceding word, you might want to treat these violations as full-scale major violations of Hermann’s Bridge.

Θερσῖτ’ ἀκριτόμυθε, ⫶ λιγύς⁐περ : ἐών ἀγορητής
Iliad 2.246

Enclitics are however distinct words, and are always semantically optional. If the enclitic weren’t there, there’d be a perfectly ordinary hepthemimeral word break.

ἡδυεπὴς ἀνόρουσε, ⫶ λιγὺς Πυλίων ἀγορητής
Iliad 1.248

None of these groups is a major violation. But groups 4 and 5 cannot be regarded as any kind of violation, because the word(s) before the bridge are so closely linked to the line-end:

Od. 18.105: ἐνταυθοῖ νῦν ἧσο ⫶ κύνας τε : σύας τ’ ἀπέρυκαν
Il. 23.306: Ἀντίλοχ’ ἤτοι μέν σε ⫶ νέον περ : ἐόντ’ ἐφίλησαν

In Odyssey 18.105 (group 4), κύνας τε σύας τ’ is correlative: ‘to keep away both dogs and pigs’. In Iliad 23.306 (group 5), νέον περ ἐόντ’ is a discrete parenthesis: ‘they loved you, even though you are young’. Note that in group 5 the participle’s complement and the participle span the bridge, so there is no separation. In both groups, beats 6½ to 9 are spanned by the phrase. There is word break at beat 7½, but no colon break.

The upshot is that none of these subgroups give any reason to see the end of a prosodic unit at Hermann’s Bridge. Groups 1 to 3 might perhaps be considered to be minor violations, but very minor.

Type b. Other violations within participle phrases

Il. 16.627 Μηριόνη τί σὺ ταῦτα ⫶ καὶ ἐσθλὸς : ἐὼν ἀγορεύεις;
Od. 5.272 Πληϊάδας τ’ ἐσορῶντι ⫶ καὶ ὀψὲ : δύοντα Βοώτην
Od. 17.381 Ἀντίνο’, οὐ μὲν καλὰ ⫶ καὶ ἐσθλὸς : ἐὼν ἀγορεύεις
W&D 751 παῖδα δυωδεκαταῖον, ⫶ ὅτ’ ἀνέρ’ : ἀνήνορα ποιεῖ

Type a, group 5, above, already gave us some examples of participle phrases spanning Hermann’s Bridge; those ones included enclitics. Type b consists of the remaining participle phrases: three Homeric, one Hesiodic.

As in type a group 5, the bridge doesn’t fall between a substantive and a participle phrase: that would justifiably be treated as a major violation. Rather, the bridge falls between the participle’s complement and the participle.

All lines in this category also have a monosyllable at Varro’s Bridge (at the end of the third foot); that may or may not be significant. Cf. two lines in type d below.

Type c. Violations within prepositional phrases

Il. 9.482 μοῦνον τηλύγετον ⫶ πολλοῖσιν : ἐπὶ κτεάτεσσι
Od. 7.192 μνησόμεθ’, ὥς χ’ ὁ ξεῖνος ⫶ ἄνευθε : πόνου καὶ ἀνίης
Theog. 23 ἄρνας ποιμαίνονθ’ ⫶ Ἑλικῶνος : ὕπο ζαθέοιο

These follow similar principles to type b above. Since the phrases are governed by a word that comes immediately before or after the bridge (ἐπί, ἄνευθε, ὑπό), they cannot be construed as multiple phrases.

The Iliadic and Hesiodic examples structure the prepositional phrase with the preposition in between a substantive and its adjective; the Odyssey example has the preposition before the bridge.

Type d. Violations before a single 4½-beat word at line-end

Il. 10.317 αὐτὰρ ὃ μοῦνος ἔην ⫶ μετὰ πέντε : κασιγνήτοισι
Il. 23.760 ἄγχι μάλ’, ὡς ὅτε τίς τε ⫶ γυναικὸς : ἐϋζώνοιο
Il. 24.753 ἐς Σάμον ἔς τ’ Ἴμβρον ⫶ καὶ Λῆμνον : ἀμιχθαλόεσσαν
Od. 1.241 νῦν δέ μιν ἀκλειῶς ⫶ Ἅρπυιαι : ἀνηρείψαντο
Od. 14.371 νῦν δέ μιν ἀκλειῶς ⫶ Ἅρπυιαι : ἀνηρείψαντο
Od. 18.140 πατρί τ’ ἐμῶι πίσυνος ⫶ καὶ ἐμοῖσι : κασιγνήτοισι
Od. 20.77 τόφρα δὲ τὰς κούρας ⫶ Ἅρπυιαι : ἀνηρείψαντο
Od. 4.684 μὴ μνηστεύσαντες ⫶ μηδ’ ἄλλοθ’ : ὁμιλήσαντες
H.Apollo 36 Ἴμβρος ἐϋκτιμένη ⫶ καὶ Λῆμνος : ἀμιχθαλόεσσα

With type d we come to major violations (3× Iliad, 5× Odyssey, 1× non-Homeric). This is in spite of the fact that the violation is forced, in the sense that a five- or six-syllable word necessarily has an unusual impact on the colometry; and in spite of the fact that in half of them the bridge falls between a noun and its adjective (Il. 10.317, 23.670, 24.753; Od. 18.140).

Splitting a noun phrase like this could be considered artificial, but it is also perfectly justifiable to regard it as a noun or adjective followed by supplementation, that is, as a violation. This is where we bump up against the subjectivity Janse complains of. There’s no robust justification for treating a noun + adjective as a single intonational unit. Parsimony demands that we treat these lines as the violations that they can reasonably be construed as.

In this category κασιγνήτοισι, ἀμιχθαλόεσσα(ν), and ἀνηρείψαντο appear multiple times in the line-end colon; ἐϋζώνοιο and ὁμιλήσαντες appear once each. The two lines with Λῆμνος/-ον ἀμιχθαλόεσσα(ν) have a monosyllable at Varro’s Bridge (cf. type b above).

Type e. Other violations

Il. 6.2 πολλὰ δ’ ἄρ’ ἔνθα καὶ ἔνθ’ ⫶ ἴθυσε : μάχη πεδίοιο
Il. 24.60 θρέψά τε καὶ ἀτίτηλα ⫶ καὶ ἀνδρὶ : πόρον παράκοιτιν
Od. 10.415 δακρυόεντες ἔχυντο· ⫶ δόκησε δ’ : ἄρα σφίσι θυμὸς
Od. 12.47 ἀλλὰ παρὲξ ἐλάαν, ⫶ ἐπὶ δ’ οὔατ’ : ἀλεῖψαι ἑταίρων
Od. 17.399 μύθῳ ἀναγκαίῳ· ⫶ μὴ τοῦτο : θεὸς τελέσειε
Od. 20.344 μύθῳ ἀναγκαίῳ· ⫶ μὴ τοῦτο : θεὸς τελέσειε(ν)
Theog. 319 ἡ δὲ Χίμαιραν ἔτικτε ⫶ πνέουσαν : ἀμαιμάκετον πῦρ
H.Dem. 17 Νύσιον ἂμ πεδίον ⫶ τῆι ὄρουσεν : ἄναξ Πολυδέγμων
H.Dem. 452 ἑτήκει πανάφυλλον· ⫶ ἔκευθε δ’ : ἄρα κρῖ λευκόν

These are also major violations (2× Iliad, 4× Odyssey, 3× non-Homeric), with no mitigating factors. As in type d some of them could arguably be construed as a single phrase, but there are no robust principles to guarantee that as the correct approach.

Two of these are formulaic (Od. 17.399 ~ 20.344). In Theogony 319, note the Attic correption in ἔτικτε πνέουσαν. Schein cites one further example of unknown date from a hexameter papyrus, which appears in Bernabé’s edition of epic fragments as a fragmentum dubium:

PEG p. 85 dub., 11 [ . . . ἅ]μα καὶ νώτοισι : νέκυν οἵσωμ[εν]

This example is also unusual for having no colon break within the third foot.

Glossary of technical terms

  • Beat. See hemipes.
  • Bridge. A position in a poetic rhythm that is normally mid-colon. Equivalently: a position where colon-break is avoided. More loosely, a position where word-break is avoided.
  • Bucolic caesura. The result of a hexameter line having a four-beat colon at line-end: that is, a combination of 8 + 4 beats, 3 + 5 + 4 beats, etc. Equivalently: colon break at the end of the fourth foot. The name is ancient, from Greek βουκολικὴ τομή (Bassett 1919: 353). (Sometimes called ‘bucolic diaeresis’: the alternate term comes from the scholastic preoccupation of treating feet as prescriptive rather than descriptive, and so seeing foot-end as somehow different from mid-foot.)
  • Caesura. The end of one colon and the start of the next. More loosely, used to refer to any position with a word-break.
  • Colon. In Homeric metre, a prosodic unit that is well adapted to the hexameter rhythm. Frequently used prosodic units tend to be attached more or less rigidly to a particular position in the line. Any point in mid-colon is called a bridge; the start or end is called a caesura.
  • Dactyl. A foot with the rhythm — ⏑⏑.
  • Foot. A descriptive term for one sixth of the twelve-beat hexameter rhythm. Two further descriptive terms, dactyl and spondee, refer to the rhythms typically seen in each foot.
  • Hemipes. The technical term for a beat. That is: either one long note or two short notes. The hexameter has twelve hemipedes, each lasting two morae. Odd-numbered hemipedes are (almost invariably) a single long note; the tenth is (almost invariably) two short notes. (Historically, this term comes from pes, Latin for ‘foot’, a descriptive term; that doesn’t mean beats themselves are only descriptive, however.)
  • Hepthemimeral caesura. The result of a hexameter line having a five-beat colon at line-end: that is, a combination of 7 + 5 beats, 3 + 4 + 5, etc. Equivalently: colon break after the first syllable of the fourth foot. The name is ancient, from Greek ἑφθημιμερὴς τομή (Bassett 1919: 353).
  • Hermann’s Bridge. The bridge in the middle of the eighth beat of a hexameter. (Equivalently: a dactylic fourth foot has no colon break between its two short syllables.) Over 99.95% of Homeric lines observe Hermann’s Bridge. Related to Wernicke’s Law: a word ending in the fourth foot with the natural rhythm — ⏑ would violate either Wernicke’s Law (if the last syllable is lengthened by position) or Hermann’s Bridge.
  • Hexameter, more fully dactylic hexameter. The metre of Greco-Roman epic. The typical rhythm is: — ⏕ — ⏕ — ⏕ — ⏕ — ⏑⏑ — ×, with a variety of common colon rhythms that result in commonly observed bridges and caesuras.
  • Long. A long note; a syllable lasting two morae.
  • Meyer’s Laws. These ‘laws’ apply primarily to post-Homeric hexameter (West 1987: 225–226 notes that Iliad 1.1 breaks all three laws). 1. Words that begin in the first foot do not end between the shorts of the first foot or at the end of the foot. 2. Disyllabic words of the rhythm ⏑ – are avoided immediately before a penthemimeral caesura. 3. A line does not have word break after both the fifth and ninth beats, that is, in the middle of the third and fifth feet.
  • Mid-line caesura. An umbrella term that includes colons ending after either the fifth beat (penthemimeral caesura) or halfway through the sixth beat (tritotrochaic caesura). 98% of Homeric lines have a mid-line caesura.
  • Mora. In metre, a short note; in hexameter, half of a hemipes. (NB: in linguistics, a mora is a basic timing unit.)
  • Penthemimeral caesura. The result of a line using a colon combination of 5 + 7 beats. Equivalently: colon break after the first syllable of the third foot. The name is ancient, from Greek πενθημιμερὴς τομή (Bassett 1919: 353).
  • Short. A short note; a syllable lasting one mora.
  • Spondee. A foot with the rhythm — —.
  • Tritotrochaic caesura. The result of a hexameter line using a colon combination of 5½ + 6½ beats. Equivalently: colon break between the two short syllables of the third foot. The name is ancient, from Greek τρίτη τροχαικὴ τομή (Bassett 1919: 353).
  • Varro’s Bridge. The bridge after the sixth beat of a line. (Equivalently: avoidance of colon break at the end of the third foot.)
  • Wernicke’s Law. A word ending in the rhythm — — at the end of a spondaic fourth foot (i.e. immediately before a bucolic caesura) will normally have that spondaic rhythm naturally. That is, there will be no need to length the last syllable by position. Related to Hermann’s Bridge: a word in this position ending — ⏑ would violate either Wernicke’s Law (if the last syllable is lengthened by position) or Hermann’s Bridge.

References and further reading

  • Bassett, S. E. 1919. ‘The theory of the Homeric caesura according to the extant remains of the ancient doctrine.’ American journal of philology 40: 343–372. [JSTOR]
  • Hermann, G. 1805. Orphica. Leipzig. [Internet Archive]
  • Janse, M. 2020. ‘Phrasing Homer: a cognitive-linguistic approach to Homeric versification.’ Symbolae Osloenses 94: 2–32. [DOI]
  • van Leeuwen, J. 1890. ‘Homerica, IV. De caesura quae est post quartum trochaeum.’ Mnemosyne n.s. 18: 265–276. [JSTOR]
  • Schein, S. 2016. ‘A cognitive approach to Greek metre: Hermann’s Bridge in the Homeric hexameter and the interpretation of Iliad 24.’ In: Homeric epic and its reception. Oxford.
  • West, M. L. 1982. Greek metre. Oxford.
  • —— 1987. Introduction to Greek metre. Oxford.

Tuesday, 7 March 2023

Homer's metre 2. Hermann’s Bridge

Hermann’s Bridge is a metrical feature in Homeric verse. Often it’s regarded as advanced — for specialists only. Well, hear this. If you’re educating someone about Homeric verse, you cannot neglect something as fundamental as Hermann’s Bridge is.

How fundamental? More fundamental than having a dactyl or spondee at the start of the line, that’s how fundamental.

1. Structure of the hexameter | 2. Hermann’s Bridge | 3. Catalogue and glossary
Gottfried Hermann, 1772–1848 (unknown artist)

Here’s how it’s traditionally defined.

[T]here cannot be a word end between the two short elements of the second half of the fourth foot.
De Decker 2017: 60

Here’s what this means in the twelve-beat rhythm we looked at last time. In the musical notation, Hermann’s Bridge is marked by the dotted line; in the metrical notation, it’s marked by the bracket. The point is that it’s always mid-word, never between words.

— ⏕ — ⏕ — ⏕ — ͜⏕ — ⏑⏑ — ×

A bridge is any position in a poetic rhythm where word break doesn’t usually happen. This particular bridge was observed over 200 years ago by Gottfried Hermann (1805: 692–693). Hermann’s Bridge is by far the strictest of its kind.

98% of Homeric lines have a word break in the third foot. Does that sound like a lot? Well, over 99.94% of lines observe Hermann’s Bridge.

This is no incidental feature. What it is, is an absolutely central feature of the Homeric hexameter. It isn’t any more ‘advanced’ than the mid-line caesura, it’s exactly the same kind of phenomenon. Caesuras happen because prosodic units have typical rhythms; bridges happen because there are some rhythms that prosodic units just don’t use.

The sample space

According to the definitions I’ll adopt below, there are fourteen violations of Hermann’s Bridge in Homer. That is, 0.050% of all 27,803 lines.

Note. The definitions adopted below are, briefly: (a) A bridge is mid-prosodic unit, rather than mid-word. (b) Monosyllabic words, including enclitics, don’t cause a violation.

Is that a fair claim, though? After all, a violation can only ever happen in lines with a dactylic fourth foot. Should we stipulate that our sample space should be confined to those lines?

It isn’t really necessary, but fine, let’s do that. How many lines have a dactylic fourth foot? Oswald (2014: 421) claims that it’s ‘19 out of 20’ lines, but that’s just wildly wrong: a glance at the text of Homer will show that.

Schoisswohl’s and Papakitsos’ tool Dactylo is able to perform automated scansion of over 96% of all Homeric lines. Their figures indicate the following (Schoisswohl and Papakitsos 2020: 170–171):

  Iliad Odyssey
full corpus, including unscanned lines (reported) 15,693 lines 12,110
unscanned lines, % of full corpus (reported) 3.7% 3.5%
scanned lines, % (calculated as proportion of sum of all reported figures) ~96.302% ~96.505%
lines scanned, actual (calculated) ~15,113 ~11,687
dactylic fourth foot, % of full corpus (sum of reported figures) 68.287% 67.548%
dactylic fourth foot, % of lines scanned (calculated) ~70.909% ~69.994%
dactylic fourth foot, actual (calculated) ~10,716 ~8,180

So about 70–71% of Homeric lines have a dactylic fourth foot. These figures give a total of about 18,896 eligible lines. (The real number of lines with a dactylic fourth foot will be slightly higher.)

With fourteen violations of Hermann’s Bridge, and 18,896 lines that could possibly have a violation, the proportion with violations rises from 0.050% to 0.074%. So in this restricted sample space, only 99.93% of dactylic fourth feet observe Hermann’s Bridge. (Only!)

Hermann’s Bridge is still stricter than starting the line with a long syllable. There are a bit over 50 lines in Homer that start with a short syllable. There are only 14 violations of Hermann’s Bridge.

Note. Homer tolerates a short initial syllable for certain words at line-beginning: amphibrachs with ἕως (20×) and τέως (1×); tribrachs with κλύθι/κλύτε (17×), ἴομεν (6×), and φίλε (3×); baccheics with ἐπεί δή/ἐπειδή (6×). This gives a total of 53: so at least 0.19% of Homer has a line-initial short. These are the examples cited by West (1967: 135–139); there may be others. Incidentally, these parallels strongly imply that ἕως should not be understood as preserving the trochaic rhythm of pre-Homeric *ἧος/ἆος.
Wrong bridge: Hermann Bridge, Missouri, demolished 2008. (Source:

Colon break, not word break

Previously, in part 1, I said caesuras are a side-effect of a deeper phenomenon. The same phenomenon is responsible for bridges. Colon breaks are the gaps between the trees: prosodic units, or cola, are the trees themselves. A bridge is a position that is normally full of tree.

So I’m adopting a refinement here. Word breaks aren’t as important as colon-breaks. A bridge is a position that is normally mid-colon. It’s a constraint on colon shape.

It would be perverse, after all, to imagine an archaic oral poet adopting a rule of the form ‘I will avoid ending a word at such-and-such a position.’ There are plenty of modern scholars who take the stance that a caesura isn’t the same thing as a ‘sense break’ (see Janse 2020: 10–13 for examples). A metrical principle operating on ‘caesura’ in that sense would be arbitrary.

(If you do want to base theories on caesuras defined as ‘word breaks’, say what you mean! Say ‘word break’, not ‘caesura’. Then it’ll be easier to see how absurd the theory is!)

Hermann’s Bridge is anything but arbitrary. When a violation happens, it isn’t because the poet has broken an abstract rule. It’s because there’s something uncommon about the prosodic units in that line.

When Hermann’s Bridge is violated, the real nature of the anomaly is that there’s a line-end colon shaped ⏑ — ⏑⏑ — ×.

More often, violations have been described in terms of the preceding colon (e.g. West 1982: 37–38). It so happens that all Homeric lines that violate Hermann’s Bridge have a mid-line caesura, so we can also say that in each line, the violation occurs because of a mid-line colon shaped ⏓ — ⏑.

Put this way, Hermann’s Bridge turns out to be equivalent to Wernicke’s Law. Wernicke’s Law is that when a word ends at the end of a spondaic fourth foot, that word is naturally spondaic: that is, its last syllable will be naturally long, without having to be lengthened by two consonants. If a word ending in the natural rhythm — ⏑ is put in the fourth foot, then it violates either Hermann’s Bridge (if its last syllable remains short) or Wernicke’s Law (if it is long by position).

So don’t think of this in terms of ‘trochaic caesura in the fourth foot’. That’s the wrong mental model. The true nature of Hermann’s Bridge (and, mutandis mutatis, Wernicke’s Law) is this:

It is extremely rare to find a word shaped ⏓ — ⏑ after the mid-line caesura.
(And ditto for ⏑ — ⏑⏑ — × at line-end.)

What makes this particular position so special? A trochaic phrase-end is apparently just fine in other positions of the line. Could it be that it’s really the line-end colon shape that matters after all, not the mid-line colon?

Maybe that’s part of the answer. But it’s independently known that a given word tends to stick like glue to certain positions in the line. O’Neill (1942) found that 90% of words in Homer appear in only a third of the positions where they could be rhythmical. Forstall and Scheirer (2012) have examined words with the rhythm — — in the Iliad and classified them into seven groups based on which position they ‘prefer’, and have found that each group is far stricter than even O’Neill realised. There is a strong likelihood that similar reasoning underlies the ‘specialness’ of the eighth beat.

Frequency profiles from Forstall and Scheirer (2012) for each of the seven classes of words with rhythm — —. Class 1 comprises words that appear most frequently at the first beat (annotated as position ‘110’), class 2 comprises words that appear most frequently at the second beat, and so on. Class 8 comprises words that are statistically ‘most distant’ from the nuclei of each of the first seven classes; the frequency profile for class 8 is similar to that of all classes combined (bottom right; I have adjusted the scale of the combined data to match that of the other figures). Note that (a) some possible positions have no affiliated words: there are no spondaic words that regularly begin on the 3rd, 5th, 9th, or 10th beats. (b) Some classes are more mobile than others: words that are attached to positions before the fourth foot may frequently also be transposed to line-end. (c) Class 6 bridges the position of the ‘bucolic caesura’, contraindicating Witte’s theory that the hexameter emerged from a combination of a tetrameter + adoneus.

This definition reduces the number of major violations

Reframing the bridge in terms of colon-shape means that the following lines can’t be regarded as major violations. I think they shouldn’t be regarded as violations at all. (Word breaks at Hermann’s Bridge are marked by a colon.)

  • Iliad 9.482 ... πολλοῖσιν : ἐπὶ κτεάτεσσι
  • Theogony 23 ... Ἑλικῶνος : ὕπο ζαθέοιο
  • Iliad 16.627 = Odyssey 17.381 ... καὶ ἐσθλὸς : ἐὼν ἀγορεύεις
  • Odyssey 5.272 ... καὶ ὀψὲ : δύοντα Βοώτην

Not all word breaks are equal. Yes, these lines have word breaks at the bridge, but there’s definitely no colon break or phrase break. The first two are prepositional phrases that can’t be separated; the last two are tightly linked participle phrases, with a participle and its complement spanning Hermann’s Bridge.

Note that this doesn’t reduce the importance of Hermann’s Bridge. On the contrary, it means that it’s even stricter.

With some word breaks, it’s a matter of judgement whether we should regard them as being mid-phrase or not.

  • Iliad 1.168: ἔρχομ’ ἔχων ἐπὶ νῆας, ἐπεί κε : κάμω πολεμίζων
  • Iliad 23.76: νίσομαι ἐξ Ἀΐδαο, ἐπήν με : πυρὸς λελάχητε
  • Odyssey 5.400: ἀλλ’ ὅτε τόσσον ἀπῆν ὅσσον τε : γέγωνε βοήσας

Here, the relatives introducing the second half of the line — ἐπεί, ἐπήν, ὅσσον — are linked to the following clauses, to an extent. But they’re not parts of a larger discrete phrase: their role is conjunctive — like syntactical mortar, rather than part of a brick.

In spite of that, these ones aren’t violations. The word break is caused by a one-syllable word, and it’s traditionally understood that one-syllable words don’t violate bridges.

Some violations are unquestionably more serious than others. Part 3 will give a catalogue and taxonomy of violations, in five categories, and give a glossary of technical terms.


  • de Decker, F. 2017. ‘Ὅμηρον ἐξ Ὁμήρου σαφηνίζειν: an analysis of augment use in Iliad 1.’ Journal of Indo-European studies 45: 58–171. [Universiteit Gent]
  • Forstall, C. W.; Scheirer, W. J. 2012. ‘Revealing hidden patterns in the meter of Homer’s Iliad.’ 2012 Chicago Colloquium on Digital Humanities and Computer Science, University of Chicago, 17–19 November 2012. [abstract | poster]
  • Hermann, G. 1805. Orphica. Leipzig. [Internet Archive]
  • Janse, M. 2020. ‘Phrasing Homer: a cognitive-linguistic approach to Homeric versification.’ Symbolae Osloenses 94: 2–32. [DOI]
  • O’Neill, E. G. 1942. ‘The localization of metrical wordtypes in the Greek hexameter.’ Yale classical studies 8: 105–178.
  • Oswald, S. 2014. ‘Metrical laws.’ In: Giannakis, Georgios K. (ed.) Encyclopedia of ancient Greek language and linguistics. Volume 2. G–O. Leiden. 419–423.
  • Schoisswohl, O.; Papakitsos, E. C. 2020. ‘Automated metric profiling and comparison of ancient Greek epics in hexameter.’ Linguistik online 103.3: 157–177. [DOI]
  • West, M. L. 1967. ‘Epica.’ Glotta 44: 135–148.
  • —— 1982. Greek metre. Oxford.