Saturday 21 May 2022

How to read an app crit

All ancient and mediaeval texts have textual variants. That’s because they’re transmitted in manuscripts, and all manuscripts contain scribal errors. No scribe is immune. Even if a text exists in only one manuscript, it’s often possible to infer that it contains errors.

This is what the app crit is for: the apparatus criticus (‘critical apparatus’). The app crit is the chunk of gibberish at the bottom of every page in a modern critical edition. The app crit is a meticulous record of textual variants, scholarly suspicions, and other annotations to the text.

This is an introduction to deciphering the app crit. We’ll look at examples from four ancient and mediaeval texts, in four languages. They’re arranged in ascending order of difficulty.

1. Old High German: the Hildebrandslied

The Hildebrandslied is a fragmentary 8th/9th century poem in which the hero Hildebrand unwittingly encounters his son Hadubrant in combat. Here are the opening lines, with text and app crit as they appear in the edition by Wilhelm Braune, revised by Karl Helm in 1952.

The app crit at the bottom is in German: fair enough, for a German poem. The entries are separated by a large horizontal gap. Each entry gives line number; text as printed; and further information, depending on context. Where a word from the text is quoted, it’s followed by the source for that variant: in this example, the source is always the manuscript, because there’s only one manuscript of the Hildebrandslied.

Text in roman type is used for the readings. Italics are used for the editor’s own annotations. This practice is fairly standard and widespread: we’ll see it again in examples 2 and 3, below.

Because the Hildebrandslied survives in only one manuscript, the variations in the app crit are modern editors’ alterations, not different readings in different manuscripts. The first entry, for line 3 ‘Hiltibrant’, reads:

Statt des n hat die Hs. h (Hiltibraht). So auch 7. 14. 30. 36. 45.

Instead of n the MS has h (Hiltibraht). Similarly in (lines) 7, 14, 30, 36, 45.

Hs. is short for Handschrift (‘manuscript’). In English, Latin, and French the standard abbreviation is ‘MS’, for manuscript, manu scriptum, or manuscrit.

This entry indicates that the editor has normalised the manuscript spelling Hiltibraht to Hiltibrant every time it appears. But the manuscript is very consistent: which spelling is more authentic? Hard to say, without expertise in Old High German linguistics. Maybe you disagree with the alteration, maybe you agree: the point of the app crit is to give you enough information to consider it for yourself.

The next three entries are also spelling normalisations. The manuscript has ringa (line 6), wer (9), and welihhes (11). The editor’s knowledge of Old High German leads them to add an extra h to the start of each word. The last entry, line 13 mir, is a more radical alteration by the editor: that’s a grammar thing, not a spelling thing.

One thing this app crit does not comment on — and it ought to — is the string of dots in lines 10–11. By convention, a string of dots indicates a lacuna, a gap in the text. The manuscript doesn’t have a gap, but a modern editor has judged that there’s a chunk missing. Here it’s because of the syntax. Hildebrand is making a speech: the first part is in indirect speech (‘he asked in a few words who his father was among the men in the people’), but from eddo hwelihhes onwards it switches to direct speech, quoting his exact words (‘Which lineage do you come from? Tell me the one thing and I’ll know the other ...’).

Every edition of the Hildebrandslied does the same thing here, and since we’re talking about it, I’ll say that I don’t agree with it. Slipping from indirect to direct speech may be a solecism in 19th century prescriptive grammar, but that doesn’t mean it’s wrong for 8th/9th century poetry. Moreover, there’s alliteration in the half-lines on either side of the supposed lacuna, exactly as there should be in German alliterative verse: fireo – folche – hwelihhes is a legitimate alliteration. (For the record, I disagree with the lacunas marked later on in the poem too.)

2. Old Norse: the Vǫluspá 

The Vǫluspá, ‘prophecy of the seeress’, is the most famous poem in the elder Edda, mainly because of its account of Ragnarok. Here are the first two stanzas, with text, translation, and app crit from Ursula Dronke’s 1997 edition.

This app crit is in English, but it’s also denser: there are multiple manuscripts, and that means textual variants. As in the Hildebrandslied, we get line number, printed text, then a variant followed by the source for that variant; and any other relevant information, as needed.

The first entry, ‘1/2 helgar] so H; om. R’, unpacks as follows:

  • ‘1/2': stanza 1, line 2.
  • ‘helgar]’: text as printed.
  • so H’: short for ‘this is what manuscript H has here’.
  • om. R’: ‘manuscript R omits this word’

The second entry, for stanza 1 line 4, indicates that the editor has chosen the spelling Heimdallar from manuscript H, rather than Heimdalar from manuscript R. And so on. The last two entries, for 2/3 þá and 2/6 iviðiur, have an extra comment: ‘See MS. R corrections 1’ and ‘2’. These are cross-references to an explanatory section, following the poem at page 88. They’re places where the scribe wrote the wrong word and then corrected it. (There are tidier ways to report a scribal correction.)

What about ‘H’ and ‘R’: what are they, how are you meant to know what they are, or how to track them down? Dronke’s edition isn’t generous in explaining these. You’d be excused for trying to find them in her list of abbreviations on page xiv — but that list doesn’t include manuscripts.

Instead, Dronke gives a paragraph-by-paragraph description of the surviving manuscripts on page xi, in the book’s general introduction, with the abbreviations buried in the middle of each paragraph. She gives a separate, longer, account following the poem, at pages 61–62. She doesn’t tell us which libraries the manuscripts are in or their callmarks, and she doesn’t give the folio numbers for which pages of the manuscript contain the poem.

Dronke hasn’t made things easy. She could have made this information more convenient, useful, and complete. I have to say, I’m not impressed.

The best practice is to give a list of manuscript abbreviations at the start of the text, with the manuscript’s location, library, callmark, page numbers in the manuscript, and the date when the manuscript was made. If I were doing that for this edition, it would look like this:


Codex Regius: Reykjavik, Árni Magnússon Institute GKS 2365 4to, ff. 1r–5r (ca. 1270)
Hauksbók: Reykjavik, Árni Magnússon Institute AM 544 4to, ff. 20r–21r (early 14th cent.)
portions quoted in Snorri Sturluson, Gylfaginning
text of Snorri in Codex Regius: Reykjavik, Árni Magnússon Institute GKS 2367 4to (ca. 1325)
text of Snorri in Codex Trajectinus: Utrecht, Universiteitsbibliotheek Traj 1374ˣ (Tˣ) (ca. 1595; derived from a copy dating to ca. 1250–1300)
text of Snorri in Codex Upsaliensis: Uppsala, Universitetsbibliotek DG 11 (U) (ca. 1300–1325)
text of Snorri in Codex Wormianus: Copenhagen, Arnamagnæan Institute AM 242 fol. (ca. 1350)

(The excerpt shown above only cites R and H. The other manuscripts pop up in later parts of the poem.)

3. Latin: Statius, Thebaid 

Statius’ Thebaid is a twelve-book epic about the mythical war of the Seven against Thebes, written in the 80s–90s CE. Here’s an excerpt from the 1972 edition of book 10 by R. D. Williams.

Once again the app crit gives line number, the text printed and its source, then variants and their sources. Other annotations are in italics. Williams additionally uses bold type for the manuscript abbreviations, which I like. He gives a simple and easily accessible list of manuscript abbreviations on the page facing the first page of the text, headed sigla (‘abbreviations’), including the callmark and approximate date of each manuscript.

Things are getting more complicated, though. First, the manuscript list includes 15 manuscripts. Second, Williams’ app crit is in Latin. That makes sense, for a Latin poem, but it does have the knock-on effect that the library names in the manuscript list are given in Latin too. Even for an experienced reader, they can be impenetrable. One of them is actually wrong.

If a manuscript is called Codex Parisinus with a catalogue number, you may be able to guess that means it’s in the Bibliothèque Nationale in Paris. But others, like Codex Matritensis, Codex Guelferbytanus, and Codex Mediceus, are harder. Matritensis doesn’t look much like ‘Madrid’ (which is what it means). Guelferbytanus looks even less like Wolfenbüttel, and it’s extra hard because Wolfenbüttel isn’t exactly a famous name. And Mediceus doesn’t even refer to a place: it refers to a specific collection of manuscripts at the Biblioteca Laurenziana in Florence.

The fact is, these designations are intended for specialists who already know what the manuscripts collections are and where they are. Things would be easier if we were given city names in a modern language, and library names, even if Latin is used for the callmark.

Fortunately, the American scholar Ryan Baumann has made a list of Latin library names used in manuscript lists, and has released it for free here.

Another problem is that Williams’ list of manuscripts is mostly just copied from Klotz’s 1908 edition, with a couple of additions. As a result he records one manuscript, N, as being in the Phillipps Collection in Cheltenham (Codex Cheltoniensis). But that collection hasn’t existed since the early 1900s. The manucript was purchased in 1925, and is now in Dublin in the Chester Beatty Library, manuscript number 76.

The app crit itself is also more complex than the previous ones:

One abbreviation for lots of manuscripts. The manuscript list includes a special abbreviation, ω. This means ‘a reading found in manuscripts other than P’ (consensus codicum praeter P). It’s a group of manuscripts, not a single manuscript.

Lower-case letters, Greek letters. Two manuscript abbreviations are lower-case (t, r), and two are designated by Greek letters (δ, Θ). Williams didn’t invent these abbreviations, but he should explain inconsistencies like that. The normal convention is that a lower-case letter represents a derivative manuscript, where we also have the manuscript it was copied from; and a Greek letter represents either a group of manuscripts (like ω, above), or a lost manuscript that was the ancestor of some surviving manuscripts (a ‘hyparchetype’).

The obelus symbol. The symbol † appears in the app crit, but not in the main text. Normally in a modern edition † indicates a corruption, a place where the editor knows the text is wrong, but hasn’t been able to work out what the correct text was. Sometimes it’s jokingly called a ‘dagger of despair’. But that isn’t what it means here. Here it indicates that the scribe wrote a word, then wrote † above the line, along with a variant. It’d be nice if the editor explained this.

4. Ancient Greek: the ‘Homeric’ Hymn to Aphrodite 

The Hymn to Aphrodite is a 7th century BCE narrative poem about Aphrodite’s love affair with Anchises. Here’s the opening, in Filippo Càssola’s standard edition of the Hymns.

Càssola’s manuscript list is at the start of the collection of Hymns. But it’s pretty threadbare: he gives the library names (in Latin) and a catalogue number, but no locations, and no dates. He doesn’t give a detailed description of the manuscripts in his introduction to the book. By 21st century standards this is really slack.

Out of the app crits we’ve looked at, this one is by far the most esoteric. That’s partly because it’s in Latin. There’s no good reason to use Latin, other than to mark Greek literature as ‘belonging’ with Latin literature, ring-fencing them both and creating a gulf between them and ancient Asian literature. For the record, there is no gulf. For the Hymns, Hittite and Levantine poetry are much more important parallels than anything in Latin. (Editions of Akkadian, Ugaritic, Hebrew, and Sanskrit poetry regularly use English for the app crit; for Hittite, either German or English.)

The fact that Càasola’s introduction is in Italian rubs salt in the wound. This edition requires you to know three languages — two of them totally unrelated to the language of the poem itself. The only value of this combo is as a barrier to entry. It’s a great big sign saying ‘Hittitologists keep out’. It’s certainly not for anyone’s convenience.

Many Greek app crits use Latin, but mostly they stick to conventional expressions. That means you can decode the app crit even if you’re not a latinist. Another American scholar, Karl Maurer, has provided a list of common Latin terminology here. That would suffice for the Statius in example 3, above. It partly covers Càssola’s Latin. But not much of it.

Càssola’s basic format is familiar — line numbers, text as printed and source, variants and their sources — but he also cites suggestions made by modern critics (in line 4, διειπετέας comes from Wilhelm Schulze’s 1892 book Quaestiones epicae; the full title is on page lxxvi). One of them (Abel, cited for line 6) doesn’t appear in Càssola’s bibliography. And two sources, ‘Aldina¹’ and ‘Chalcondyles’ (cited for line 10), aren’t modern critics, but early modern editions published in the 15th and 16 centuries. You need to know all of this off the top of your head to use this app crit. Definitely not user-friendly.

Worse still, Càssola’s Latin is much harder than it needs to be. There’s no way past it: to read Càssola’s annotations, you need to know Latin, and you need to know it well.

Lines 1–151: ‘om. Π foliis avulsis’. (Notice that Càssola doesn’t put his annotations in italics, as in examples 1 to 3.) Maurer’s cheatsheet covers om.: it means all these lines are omitted in manuscript Π (cod. Parisinus suppl. 1095). But for foliis avulsis you’ll have to brush up on your Latin ablative absolutes. This bit means ‘because the pages have been torn out’.

Line 6: πᾶσι δὲ ἔργα is a correction suggested by two modern scholars, Hoffmann and Flach. After that we hit a wall of abbreviations, with no punctuation to help the reader follow the structure of the annotation. What it means is this: πᾶσι δ’ ἔργα is the variant given in six manuscripts (M, At, D, B, Γ, and V), while πᾶσιν δ’ ἔργα, with an extra letter, appears in seven others (A, Q, P, and x, where x represents the group E, T, L, and Π).

Lines 10–11 (written ‘10–1’): ‘usque ad πόλεμοί τε et ab καὶ ἀγλαὰ in unum conflarunt ET’. This is Càssola being a mean-spirited bastard. First, conflarunt is a high-faluting version of the verb form conflaverunt, so you don’t just need to know Latin, you need to be familiar with literary Latin. The note as a whole means: ‘Manuscripts E and T have joined together the text up to πόλεμοί τε, and from καὶ ἀγλαὰ onwards.’ Or, to put it another way, ‘the words ἅδον ... μάχαι τε are missing in E and T.‘ But why use a simple om., when you could use usque ad ... et ab ... in unum conflarunt? Mustn’t make it too easy for the proles, I guess.

Final thoughts

It’s easy to criticise. But it’s also pretty easy to provide clear information and to use punctuation marks. I have the utmost respect for the critical skills of all these editors, but where they’ve been thoughtless, I resent that.

The point of scholarship, the point of an app crit, is to make information easily accessible. Examples 2 to 4 do an uneven job of that. Càssola, in particular, has gone out of his way to make things accessible only for an inner circle of experienced scholars. It’s the very definition of ‘esoteric’.

There are harder app crits out there. But the very hardest ones — the Nestle-Aland edition of the New Testament, and M. L. West’s editions of Homer — are actually much better than these ones. They look extremely forbidding, because they take up a huge amount of space on the page. It takes a lot of work to read them. But they’re much better thought out, and much more clearly explained.

Their difficulty lies in the fact that there are hundreds of manuscripts for those texts, and that means lots of citations when it comes to variants. But their manuscript lists, and the way they write in the app crit, are crystal clear. West does use Latin, which is very regrettable; but at least he doesn’t mix it up with extra languages. And in his case, Maurer’s cheatsheet will see you through almost every note.


  • Baumann, R. 2020. ‘Latin names of libraries commonly used in the naming of manuscripts.’ [github link]
  • Braune, W.; Helm, K. 1952. Althochdeutsches Lesebuch. 12th edition. Tübingen.
  • Càssola, F. 1975. Inni omerici. Milan.
  • Dronke, U. 1997. The poetic Edda. Volume II. Mythological poems. Oxford.
  • Klotz, A. 1908. P. Papini Stati Thebais. Leipzig. [Internet Archive link]
  • Maurer, K. 2018. ‘Commonest abbreviations, signs, etc. used in the apparatus to a classical text.’ [University of Dallas link]
  • Williams, R. D. 1972. P. Papini Stati Thebaidos liber decimus (Mnemosyne supplement 21). Leiden.

Wednesday 4 May 2022

Who designed the Julian calendar?

The Roman calendar was a mess before the Romans adopted the Julian calendar in 46 BCE. It was ostensibly lunar, but months ranged from 28 days to 31 days, as they still do today, so the months didn’t line up with lunar phases. It had intercalary months to keep it in step with the seasons, but political intrigues resulted in it being nearly three months out of synch.

In 46 BCE, Julius Caesar cut through the political red tape and decreed a fixed calendar based on a 365¼ day cycle. To do this he had to draw on his powers as both dictator and pontifex maximus, or top priest. It was a phenomenal achievement. The calendar no longer even pretended to be lunar, but no one cared. It was the world’s first solar calendar. And that was even better.

Pliny the Elder claims that one of the experts Caesar employed as a consultant was an astronomer named Sosigenes. I’m here to tell you that while the Julian calendar is magnificent, Sosigenes’ role is overblown. Also, we have no idea where Sosigenes came from.

Sosigenes (Hume Cronyn) gives Cleopatra (Elizabeth Taylor) a biology lesson (Cleopatra, 1963). Perhaps she’s intrigued because he’s writing on paper, not papyrus.

We still use a slightly modified form of Caesar’s calendar today. The modification is so slight that no one alive today remembers the last time our calendar behaved differently from the Julian calendar, and hardly any of us will live to see the next time.

The new calendar was designed so that the equinoxes and solstices would fall on the same date every year. The traditional dates shown below are different from the modern ones, because the Julian calendar isn’t perfect. It’s based on a solar year of 365.25 days, but a solar year is actually 365.2422 days. As a result the solstices slip out of synch by one day every 128 years. To fix this, in 1582 the Gregorian calendar was instituted, as a slight revision to the Julian calendar. It was pinned to the equinox and solstice dates as they were in 325 CE, because 325 CE is when the Nicene formula for calculating the date of Easter was finalised.

Ancient authors give different dates for the solstices and equinoxes: the dates shown here are based on Pliny the Elder, and partly coincide with dates and intervals quoted by Columella and Ptolemy. Other authors — including Caesar — put the solstices and equinoxes on other dates: see below.

Ancient astronomers from Hipparchos onwards were aware that the solar year was slightly under 365¼ days. Ptolemy reports on two sets of observations, one made by Hipparchos, the other by himself, which calculated the error to be approximately one day every 300 years: that is, a solar year of 365.2467 days (Almagest 3.1; 204–206 ed. Heiberg). Caesar was unaware of Hipparchos’ observation, or he chose to ignore the discrepancy. Given that the true error is larger than Hipparchos or Ptolemy thought — one day every 128 years — that’s probably just as well.

Sosigenes of ... where, now?

Here’s what Pliny says about Sosigenes (Natural history 18.211–212):

... Caesar the dictator forced individual years back to the cycle of the sun, employing Sosigenes, who was an expert in his science. ... And Sosigenes himself, though more careful than others in his three treatises, did not stop questioning, since he corrected himself ...

Sosigenes appears in one other place, when Pliny cites him for the statement that the planet Mercury never appears more than 22° away from the sun (Natural history 2.39; actually the maximum elongation of Mercury varies between 18° and 28°).

Look up Sosigenes today, and you’ll often find him called ‘Sosigenes of Alexandria’.

But wait. Pause. Rewind. Take a look at Pliny, and let me remind you he’s our only source for Sosigenes. Do you see any mention of Alexandria?

No, you don’t. The idea that Sosigenes was Alexandrian is entirely a product of the modern imagination. I’ve found it in books as far back as the 1700s, so it’s not very recent, but it’s still a modern fiction.

Note. The misinformation doesn’t stop there. Wikipedia plasters fake Alexandrian and Egyptian connections all over the place, including in the article title, but also gives fake transliterations of his name into Greek — yes, his name is Greek in origin, but it isn’t attested anywhere in Greek, and he could for example be a Roman from southern Italy — and gives three totally fake titles for his lost works. A single editor invented these titles and their Greek versions out of thin air in March 2021, at the same time as adding spurious connections to the Antikythera device.

The tradition of calling Sosigenes ‘Alexandrian’ originates in indirect testimony — not about Sosigenes, but about Caesar himself.

Caesar was in Alexandria in 48–47 BCE, first hunting down Pompey, then bringing down Ptolemy XIII and setting up Cleopatra as sole pharaoh of Egypt. One mediaeval source tells us that he took a strong interest in astronomy during wartime —

(Caesar) says that it was in wartime that he focused on the study of astronomy: he put aside all other thoughts in the war. And the outcome proves that he meant this truly, since his book that he wrote about calculation is not inferior to that of Eudoxus.
Scholium on Lucan, cod. Lips. Rep. 1, N. 10 10.185 (p. 781 ed. Weber)
Note. I cannot trace Weber’s source for this scholium. ‘Lips.’ means that the manuscript is or was in Leipzig, but Weber’s edition dates to 1831, and manuscript shelfmarks at Leipzig no longer look anything like this.

And four ancient sources tell us that Caesar’s new calendar was based on ‘Egyptian teaching’.

And later, based on Egyptian teaching, Gaius Caesar appointed that the period (of a year) was 365¼ days, and that some months should have 30 days, others should have 31, and February should have 28. For in antiquity it was reckoned that each month had 30 days, and that 5¼ should be added to the total.
John Lydus, De mensibus 3.5–6 = p. 40,8–41,2 ed. Wuensch
Note. Similarly Appian, Civil war 2.154; Dion Cassius 43.26; Macrobius, Saturnalia 1.14.3, 1.16.39.

So this must be where the idea of Sosigenes being Alexandrian comes from. Even though none of these writers mentions Sosigenes, and even though no ancient writer connects Sosigenes to Egypt in any way.

Obviously that’s no basis for calling him ‘Sosigenes of Alexandria’. It’s a fabrication, and it needs to stop.

But come to that, should we even take them at their word that Caesar’s source of information was ‘Egyptian’?

According to Macrobius, Caesar drew attention to parallels in the Egyptian calendar himself. But the Julian calendar isn’t an Egyptian product in any sense. There are five reasons I say this:

  1. As we’ll see below, one key principle of the new calendar was minimal alterations to the Roman calendar. The names and positions of the months remained the same, as did the key days of the Kalends, Nones, and Ides; the extra days were distributed across the months that had fewer than 31 days; intercalation took place in the same position as in the republican calendar, that is, after 23 February; and care was taken to make sure the positions of Roman religious observances were unaltered. The Egyptian calendar, by contrast, had 12 months of equal length, with Egyptian names and 30 days each, plus 5 epagomenal (extra) days.
  2. Another key principle was the addition of one intercalary day (leap day) every four years. The Egyptian calendar didn’t have this — not until 17 years later, after the fall of the Ptolemies.
  3. The reckoning of a solar year as 365¼ days originated with an astronomer from Anatolia and based in Athens, not Egypt.
  4. Egypt’s calendar had 365 days because of physical reality, not local customs. Egypt didn’t have a monopoly on the fact that a solar year lasts roughly 365 days.
  5. We have fairly extensive documentation of Caesar’s own work on the calendar and observations of seasonal phenomena, and that he wrote a detailed treatise on the subject.

Taking these points into account, the simplest reading is that Caesar and other ancient observers drew attention to Egypt because the Egyptian calendar was already close to the correct value, and not because the new calendar was based on it.

And if you look carefully at John Lydus’ account, above, you’ll see his story is clearly not true. The calendar of ‘antiquity’ that he describes is the Alexandrian calendar after 30 BCE. Caesar can’t have got the idea of a 365¼ day calendar from Egypt, as Lydus claims, because Egypt didn’t have a 365¼ day calendar at the time.

Note. Similarly Theodor Mommsen, writing over 160 years ago; ‘Sosigenes of Alexandria’ should have disappeared from the face of the earth after he wrote (1859: 295 n.22): ‘... scholarly opinion stamped Sosigenes as Alexandrian for lack of evidence. No ancient source is going to contradict my statement: I think unbiased judges will be persuaded that much older and weightier authorities characterise Caesar’s model as the Italian-Eudoxian calendar, and that this rules out the other proposition; that in real terms it is bizarre to bring from abroad what one has long had at home; that no direct borrowing from Egypt has yet been demonstrated in the organisation of the Julian year; and that it is therefore very difficult to understand why we must ‘in any case’ accept that Caesar’s advisers were Alexandrian. The consideration that the name Sosigenes — obviously a standard Greek name, and decidedly rare — also appears on Egyptian papyrus, and that there(?) it is probably derived from the deity Shu ... is so dubious that it suffices to mention it.’

Where did Caesar’s calendar really come from?

The astronomer who measured the solar year as 365¼ days was Kallippos of Kyzikos, who studied at Plato’s Academy and Aristotle’s Lycaeum in Athens in the late 4th century BCE. Among other things, Kallippos determined exact periods between each of the solstices and equinoxes.

Previously Meton had measured a lunisolar cycle of 235 lunar months, corresponding to 19 solar years. Kallippos extended this to a cycle of 912 lunar months plus 28 intercalary months, or 27,759 days, corresponding to 76 solar years — an average of 365¼ days per year.

Note. For Kallippos’ 365¼ day year see Geminus, Phainomena 8.59–60; see further Neugebauer 1975: 615–624.

Meton’s 19-year cycle gave the year an average of 365 5/19 days, that is, 365.2632 days. Kallippos’ year of 365.25 days was an improvement on this. Later, as we saw, Hipparchos improved Kallippos’ calculation still further, to 365.2467 days.

And by the way, observe that Meton, Kallippos, and Hipparchos all lived in Greece, not Egypt. Alexandria has nothing to do with this story.

So, what should we infer: is it that Sosigenes made Kallippos’ work the basis for the Julian calendar? That’s a possible interpretation, except that it’s still missing a key fact.

You see, Caesar himself wrote a detailed treatise called De astris (‘On the stars’), on astronomy, on the length of the year, and containing a calendar with solar dates for numerous seasonal and astronomical phenomena, including solstices and equinoxes.

That is to say, it would appear that the Julian calendar is the result of Julius Caesar’s own research. He didn’t farm out the work to experts, he was the expert. When Pliny cites four schools of thought about measuring the sun’s progress around the ecliptic — the Chaldaean, Egyptian, Greek, and Italian schools — it’s Caesar himself that represents the Italian school.

The De astris doesn’t survive, alas. But the fragments, preserved in other extant sources, are collected in Alfred Klotz’s 1927 Teubner edition, and they strongly suggest that not only was Caesar knowledgeable about astronomy, his work was startlingly carefully thought out in other respects too. Caesar didn’t just lengthen the Roman year to 365¼ days. He had solid, specific reasons for the month lengths he adopted; he made his own observations of the stars and seasonal weather; he put a huge amount of effort into making the new calendar politically acceptable and into avoiding religious upsets; even more, he put careful thought into which days in each month were going to be the extra days.

Here are Caesar’s alterations:

  Republican calendar Days added Julian calendar
January 29 days 19 Jan, 20 Jan 31 days
February 28 bissextus (leap day) 28 or 29
March 31 31
April 29 26 Apr 30
May 31 31
June 29 29 Jun 30
Quinctilis/July 31 31
Sextilis/August 29 29 Aug, 30 Aug 31
September 29 29 Sep 30
October 31 31
November 29 29 Nov 30
December 29 29 Dec, 30 Dec 31
Total 355 (= 12 lunar months of 29½ days) 10¼ 365¼
Note. For the exact dates Caesar added, see Macrobius, Saturnalia 1.14.7–9. Censorinus, De die natali 20.9, corroborates the number of days added to each month; the republican-era Fasti Antiates confirm Macrobius’ figures for months in the republican calendar (Degrassi 1957: 23–41).

In both systems, intercalations — extra days to make the year line up with the seasons — were in February. In the republican system, an intercalary month could be inserted after 23 February, and in the Julian system, every fourth year the 24th of February would last two days, which Caesar called bissextus.

Incidentally, for those who already know something about the Roman calendar, the pre-Julian month lengths are the reason that ‘July, October, March, and May / have Nones the 7th, Ides the 15th day’. It’s because those are the months that had had 31 days all along; the 29-day months had them on the 5th and the 13th, and Caesar didn’t change that. The extra days he added were towards the end of each month, so as to avoid altering the dates of religious observances.

The dates of the solstices and equinoxes

The diagram I gave above is based on Pliny’s dates for the solstices and equinoxes:

(Daylight) increases from midwinter, and is equal to the night at the spring equinox, 90 days and 3 hours later. Then it exceeds the night up to the solstice, 94 days and 12 hours later. * * * up to the autumn equinox. And then, after it is equal to the daylight, the night increases until midwinter, 88 days and 3 hours later.
Pliny, Natural history 18.220

Pliny’s figure for the period between the summer solstice and autumn equinox is missing, but a period of 92.5 days is implied by the other figures and by a 365¼ day year. It so happens that Ptolemy gives two figures that agree with Pliny, including the missing 92.5 day period —

[Hipparchos] assumes that the interval from spring equinox to summer solstice is 94½ days, and that the interval from summer solstice to autumnal equinox is 92½ days ...
Ptolemy, Almagest 3.4 (trans. Toomer)

The only date Pliny pinpoints is the winter solstice, on 25 December (NH 18.221). That implies the rest of the dates used in my diagram, above. Here are some other sets of solstice and equinox dates reported in the 1st and 2nd centuries BCE and CE.

  spring equinox summer solstice autumn equinox winter solstice
Hipparchos 94.5 days after equinox 92.5 days after solstice
Caesar — (25 Mar?) 24 Jun 24 Sep
Varro 90 days after solstice (24 Mar) 45 days after Favorinus = 92 days after equinox (24 Jun) 94 days later (26 Sep) 89 days later (24 Dec)
Hyginus, Columella 25 Mar 24 Sep 25 Dec
Pliny 90.125 days after winter solstice (25 Mar) 94.5 days later (27/28 Jun) 88.125 days before winter solstice (= 92.5 days after summer solstice, i.e. 28 Sep) 25 Dec = 88.125 days later
Ptolemy 22 Mar 140 CE 24/25 Jun 140 CE 26 Sep 139 CE
Notes. Sources: Hipparchos, reported by Ptolemy, Almagest 3.4; Caesar, reported by Pliny, Natural history 18.246, 18.256, 18.312 (in book 1 Pliny cites Caesar’s De astris among his sources for book 18); Varro, Res rustica 1.28; Columella, De re rustica 9.14.1, 9.14.10–11 (citing Hyginus); Pliny, Natural history 18.220–221; Ptolemy, Almagest 3.4.

Parentheses denote information that the text does not state explicitly. In Caesar’s case, Pliny quotes the 25 March date in one sentence, then cites Caesar in the following sentence; it’s only Klotz’s edition that links the two. For Varro, the dates shown here are based on the inference that his date for Favonius (the west wind) coincides with the beginning of spring, which Varro puts on 7 February. See above on the 92.5-day period in Pliny.

Some dates are widely mistranslated and/or misreported. In the Loeb translation of Columella, viii calendas Aprilis is mistranslated as 24 Mar. (for 25 Mar.), and viii calend. Ianuarii as 23 Dec. (for 25 Dec.); in the Loeb of Pliny, viii kal. Ian. is mistranslated as 26 Dec. (for 25 Dec.). In addition, Columella is widely reported as putting the winter solstice on 24 Dec., even by Neugebauer. I cannot tell how these errors have arisen. The text in each case is clear and unambiguous.

Ptolemy’s measurements are a day later than modern reckoning, which gives the dates as 5:27 pm 21 Mar. 140 CE, 3:11 pm 23 Jun. 140 CE, and 10:41 pm 24 Sep. 139 CE (= Terrestrial Time plus 2 hours for the longitude of Alexandria).

There’s a substantial body of scholarship over these dates, but mostly about which coordinate system the ancient authors use for setting the points and divisions of the seasons against the sun’s progress through the zodiac (Neugebauer 1975: 593–600), and on what the above table may have looked like in the republican calendar (Mommsen 1859: 54–79 on the rustic calendar, tabulation at 62).

There is certainly more variation than you might think from looking at Christian traditions about the dates of Easter and Christmas. Christians from the 3rd century onwards consistently used the dates 25 March and 25 December for the spring equinox and winter solstice, as I described last year.

Those are the dates we find in Pliny, Columella, and (so Columella tells us) Hyginus, the most celebrated Roman astronomer of Augustus’ time. It’s striking that in Pliny these dates, which disagree with Caesar, are stuck in between two discussions of Caesar.

NH 18.210–211 Caesar’s solar cycle; Sosigenes’ involvement
NH 18.220–221 Pliny’s solstice and equinox dates (which disagree with Caesar)
NH 18.232 onwards Lengthy catalogue of seasonal and astronomical phenomena, including some of Caesar’s solstice and equinox dates

Pliny’s solstice and equinox dates are of great interest. Given that they partially correspond to what Ptolemy says about Hipparchos, they could be derived from Hipparchos.

Actually I suspect they might be Kallippos’ own dates. Remember that the Julian calendar slips out of synch with the seasons by 1 day every 128 years. As a result, when ancient writers give us calendar dates for solstices, we can estimate when those dates were observed. We compare the quoted dates with the dates as calculated by modern astronomy, and see which period they’re valid for.

We do need to allow leeway. Ancient observers made mistakes measuring the equinoxes and solstices: Ptolemy himself erred by a day in 139–140 CE (see notes to table above). With that in mind, here are the date ranges where the quoted dates are valid, to varying degrees of tolerance.

Source Dates quoted Valid period, dates exactly as quoted Valid period, ±1 day tolerance Valid period, ±2 days tolerance
Caesar 24 Jun, 24 Sep 12 to 167 CE 121 BCE to 287 CE 253 BCE to 407 CE
Varro 24 Mar, 24 June, 26 Sep, 24 Dec no valid period 165 BCE to 51 CE 289 BCE to 179 CE
Hyginus, Columella 25 Mar, 24 Sep, 25 Dec no valid period no valid period 261 to 26 BCE
Pliny 25 Mar, 27/28 Jun, 28 Sep, 25 Dec 429 to 298 BCE 557 to 162 BCE 689 to 26 BCE

Caesar’s and Varro’s dates could plausibly have been observed in their own lifetimes. But in Pliny’s case, that’s quite a stretch. Pliny’s dates look as though they come from observations made much earlier.

It has been suggested that the 25 March/25 December dates could come from Hipparchos (thus Hannah 2005: 151, following a suggestion of Christian Ludwig Ideler in the 1820s). I think the full set of Pliny’s dates points to an earlier origin. And, given that Kallippos, the discoverer of the 365¼ day cycle, lived slap in the middle of the valid date range for Pliny, I’m going to suggest that Kallippos could also be the originator of Pliny’s season lengths and solstice dates.


  • Degrassi, A. 1957. Inscriptiones latinae liberae rei republicae, vol. 1. Florence.
  • Hannah, R. 2005. Greek & Roman calendars. Constructions of time in the classical world. London.
  • Klotz, A. (ed.) 1927. ‘vii. De astris.’ In: C. Iuli Caesaris commentarii, vol. 3. Teubner. 211–229. [Internet Archive]
  • Mommsen, Th. 1859. Die römische Chronologie bis auf Caesar, 2nd ed. Berlin. [Internet Archive]
  • Neugebauer, O. 1975. A history of ancient mathematical astronomy. Berlin/Heidelberg.