Content uploaded by Leo Depuydt
Author content
All content in this area was uploaded by Leo Depuydt on May 22, 2019
Content may be subject to copyright.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months,
Both Before First Visibility of the New Crescent
Leo Depuydt
119
1. Statement of Purpose: First Visibility of the New Crescent Never Served as Marker
of the Beginning of the Lunar Month in Egypt, Greece, or Mesopotamia
1.1. A Prevalent Assumption
Hardly any assumption about the ancient world has been as dominant, or as stubborn,
from time immemorial as the one that ancient months—in as far as they were lunar, which
they mostly were—began with first visibility of the new crescent (short: first crescent vis-
ibility). Strictly speaking, beginning the month with first crescent visibility means—or at
least ought to mean—that daylight of lunar Day 1 immediately follows the evening in
which the new crescent is for the first time sighted. This strict principle is nowhere explic-
itly enunciated in ancient sources and hardly ever in modern publications. According to
the strict understanding of the principle, it should not be possible to begin a lunar month
at any time before the new crescent has been sighted.
In conjuring up the ancient world and picturing daily life in, say, Athens, are we to
imagine, as is now universally done, that the minds of ancient Greeks like Pericles, So-
crates, and Aristotle were anxiously anticipating the first sighting of the thin new crescent
as marker of the beginning of a new month and also of the year’s first month and therefore
of new year?
uite to the contrary, all kinds of evidence scattered over multivaried sources support
the assumption that first visibility nowhere in the ancient world, not in Greece nor any-
where else, marked the beginning of the month. And that includes in all probability Baby-
lonian astronomical texts, that bastion of chronological exactitude, in relation to which
probably no one would now dare to deny that lunar months always began after the new
crescent had been sighted.
Nothing has had a greater influence on the modern interpretation of ancient lunar
months, I believe, than the general awareness of the custom undeniably prevalent in Islam
since the time of the Prophet in the lands where Egyptian and Babylonian civilizations
once flourished to begin months with the sighting of the new crescent. In other words,
daylight of lunar Day 1 begins in the morning that follows the evening in which the new
crescent is first sighted. There is nothing wrong with beginning months with first crescent
visibility. But that is just not how the ancients did it.
I have elsewhere already undertaken provisional efforts to question the role generally
attached to first visibility of the new crescent in the modern study of the ancient world1
Leo Depuydt
120
and have wanted to treat it at greater length for some time, expressing my hopeful anticipa-
tion on no fewer than four occasions.2
1.2. Egypt — Greece — Mesopotamia
The proposition that lunar months begin before first crescent visibility is somewhat estab-
lished when it comes to ancient Egypt. Evidence is adduced below to confirm that Greek
lunar months too began on average before first crescent visibility. The Greek evidence in
fact comes from Egypt, which was home in the Late period to a large immigrant Greek-
speaking population. In addition, it will be argued that Egyptian lunar months began a day
or so before Greek lunar months.
As regards Mesopotamia, first crescent visibility rules absolutely. Kugler, the pioneer-
ing decipherer of much of Babylonian astronomy, summed it up as follows in his Von
Moses bis Paulus after more than two decades of research on the subject: “Das erstmalige
Wiedererscheinen der feinen Sichel am abendlichen Westhimmel ist das Zeichen für den
Anfang des Monats”.3 Then again, in more recent years, it has been noted off and on that
the picture that emerges from the sources is not nearly as neat as Kugler’s terse statement
suggests, for example in relation to the need for actually sighting the crescent to begin a
new month.4
Babylonian astronomical texts are thought to provide the premier evidence of first cres-
cent visibility’s role. But it will be argued below that, in astronomical texts, Babylonian
months might just as well begin with the earliest possible measurable interval between
sunset and moonset after new moon, called NA in Babylonian. A NA-calendar, if the term
is permitted, would be the result of adding strict regularity to a lunar calendar used in soci-
ety at large. The aim would be to organize empirical data in a rigorous manner that is more
suitable to the creation of Babylonian lunar theory. It is true that the interval NA, at least
when it is measured and not estimated or predicted, is one facet of a set of events of which
first crescent visibility is another facet. But it is not because “big” and “green” are two facets
of the phenomenon “big green car” that the mind cannot focus on the facet “green” at the
exclusion of the facet “big”.
As regards texts other than Babylonian astronomical texts, much evidence will be ad-
duced in support of a newly postulated type of ancient lunar calendar. The new calendar
will be called here the new crescent (in)visibility calendar, which must have included a great
measure of ad hoc determinations on whether to make a lunar month 29 days or 30 days
long (see section 10.13). It cannot be said that the months of this calendar begin at first
crescent visibility. They may or they may not. Instead, the contrast between visibility and
invisibility of the new crescent on Day 29 is exploited to determine whether the day that
follows Day 29 of the month will be the last of the present lunar month or the first of the
next lunar month. The aim is not to begin the month with first crescent visibility or with
any other lunar phenomenon for that matter. The aim is to determine how long the pres-
ent lunar month will last, 29 days or 30 days. In works on calendars, the new crescent is
normally associated with visibility. But in the new crescent (in)visibility calendar, both the
visibility and the invisibility of the new crescent play equally important roles. Each has its
own distinct consequence. Visibility on Day 29 produces a month of 29 days. Invisibility
on Day 29 produces a month of 30 days. Importantly, invisibility on Day 29 by no means
guarantees visibility on Day 30. If there is invisibility also on Day 30, then daylight of lunar
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 121
Day 1 begins before first crescent visibility. Accordingly, first crescent visibility is not the
marker. The toggle of (in)visibility on Day 29 is. That being said, there are many indica-
tions in the sources that the new crescent was sighted too early or too late. Such irregularity
must have had a domino effect affecting ensuing lunar months. Strict observation of the
Day 29-rule must therefore often have been impossible.
Along the same lines, it will be argued below (see section 6.7) that, strictly speaking, the
Egyptian and Greek lunar calendars are not old crescent invisibility calendars, but rather
old crescent (in)visibility calendars.
A comprehensive survey of lunar time-reckoning in all nations of the ancient world
remains desirable. But producing such a survey would be no small feat. Then again, it is
advisable, and even indispensable, to securely establish individual points before moving on
to a grand synthesis.
Much of the present paper revolves around two basic calendrical concepts: (1) the be-
ginning of the lunar month; (2) first visibility of the new crescent as marker of the begin-
ning of the lunar month. Before outlining this paper’s line of argument in section 4, it will
be useful to dwell briefly with these two concepts in sections 2 and 3.
2. The Beginning of the Lunar Month
Ancient lunar months began around new moon. New moon, also called conjunction, is the
point in time when the moon is right between the earth and the sun. New moon cannot be
observed because the moon is invisible at the time. Its light is drowned out by the sun that
is right behind it. The exception is when sun, moon, and earth are on the exact same line.
A solar eclipse then takes place. The moon is seen as a black disk passing from right to left
across the sun disk, covering it wholly or partly.
It is clear what one sees of the moon shortly before and shortly after new moon. One
morning roughly 25 to 50 hours before new moon, the old crescent appears for the last
time in the eastern horizon right before sunrise. That is last visibility of the old crescent. Or
short: last crescent visibility. Then, for a period lasting mostly either one and a half or two
and a half days, the moon remains out of sight. Next, one evening roughly 25 to 50 hours
after new moon, and weather permitting, the new crescent can be seen in the western ho-
rizon right after sunset. That is first visibility of the new crescent. Or short: first crescent
visibility.
In order to fix the beginning of a lunar month, a certain daylight period needs to be
picked and assigned the number one or some equivalent designation. Butwhen it comes
to establishing by which methods a certain daylight period was made into daylight of lunar
Day 1 in various ancient nations, a problem arises: nowhere in any ancient source is there an
explicit report as to what exactly was done to determine which daylight is that of lunar Day
1. To my knowledge, no ancient source says more about events relating to the beginning
of the lunar month than the Talmud. A number of scenarios of what happens around new
moon are discussed in detail. Yet, these scenarios are not quite detailed enough to establish
what exactly was done to fix the beginning of the month. One would like to picture—as
if watching a video recording—a specific person making specific decisions and uttering
specific statements. I am not referring to celebrations or sanctifications of the decision, to
which the Talmud makes ample reference, but rather to the precise circumstances of the
Leo Depuydt
122
decision itself as a rational act. The sources do not bring us close enough to that critical
event. What really happened therefore remains the subject of speculation.
From the prominent ancient civilizations of Egypt, Greece, and Mesopotamia, we do
not even have anything close to detailed descriptions such as those in the Talmud. True,
quite a few cuneiform texts refer in one way or another to events that take place around the
turn of the month and somehow relate to fixing the beginning of the month. Moreover,
there are various references to the beginning of the lunar month in classical authors and
rare references in hieroglyphic sources. But all this still leaves us in the dark as to how ex-
actly Day 1 was picked in Egypt, Greece, and Mesopotamia as an act of the free will.
It is generally assumed that observation either of the old crescent or of the new crescent
played some role in determining the beginnings of lunar months in the ancient world. The
old crescent is observed in the morning and the new crescent in the evening. In the case of
the old crescent, the natural thing would seem to be to wait for the morning of first invis-
ibility. The previous morning is then the one of last visibility. In principle, last visibility
itself can only be established after the fact; one cannot know with certainty beforehand
whether the old crescent will or will not be visible the next morning, even if visibility may
be so limited one morning that invisibility the next morning seems all but certain. In the
case of the new crescent, the natural thing would seem to be to wait for the evening of first
visibility. The previous evening is then obviously the one of last invisibility. In principle,
last invisibility itself can only be established after the fact; one cannot know with certainty
beforehand whether the new crescent will or will not be visible the next evening.
Much attention has been paid to the problem of the visibility of the crescent. This
problem is scientific and astronomical in the strict sense. It involves many factors. All agree
that certain decisive factors are forever lost. These factors include local weather conditions
and the location of the observers as well as their state of mind, including focus and atten-
tion span.
However, visibility is just one facet of fixing the beginning of the lunar month. What
was no longer seen one morning or what was again seen one evening needed to be exploited
in order to fix daylight of lunar Day 1. Such exploitation involved specific thoughts, words,
and acts on the part of flesh-and-blood people. It is with those thoughts, words, and acts,
regarding which no explicit evidence survives, that the present paper is concerned.
3. First Visibility of the New Crescent as Marker of the Beginning of the Lunar Month
Strictly speaking, a lunar month can be said to begin with first visibility of the new crescent
only if the daylight period that follows the evening in which the new crescent is first seen is
daylight of lunar Day 1. In other words, the morning of lunar Day 1 ought to immediately
follow the evening of first visibility. Nights were probably not counted in antiquity, except
very rarely in certain technical contexts. Nighttime was just a numberless stretch of dark-
ness and of human inactivity separating numbered episodes of light and of human activity
that begin with dawn and end with dusk. Activities started before dawn or continued after
dusk were annexed to the adjacent daylight period.
This definition of first visibility of the new crescent as marker of the beginning of lu-
nar months may seem slightly cumbrous. But my personal experience in reading works on
calendars and chronology is that more explicitness in defining first principles would help
promote the study of the subject as a mature discipline in its own right. One advantage of
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 123
the above definition as I see it is that it avoids the vexed question of when the day began in
various ancient nations, in the morning, in the evening, at midnight, and so on. The begin-
ning of the day is called its epoch. Accordingly, a day whose beginning falls in the morning
is said to have a morning epoch. This is not the place to address the issue of the epoch of
the day at length. But briefly here (see also section 8), my view on the matter is that for
most people most of the time, the day began in the morning and ended in the evening and
included activities started before dawn and continued after dark. It seems like the most
natural view. In earlier papers I have myself, like most every student of chronology before
me, eagerly embraced the relevance of the concept of the epoch of the day. But I have
now become rather convinced that the epoch may well be a ghost concept, and its study
hence the pursuit of a ghost problem. Even the fact that, in certain Babylonian astronomi-
cal texts, what happens at night is described before what happens during the day does not
necessarily imply an evening epoch (see section 10 below).
Both in ancient sources and in modern writings, one occasionally finds statements to
the effect that the new crescent first appears on lunar Day 1. But such statements often
critically leave unsaid whether the new crescent is first seen in the evening that imme-
diately follows daylight of lunar Day 1 or in the evening that precedes daylight of lunar
Day 1. One possibility that needs to be contemplated is that, in some ancient nation, one
aimed more or less for the new crescent to appear just after the sunset ending daylight of
lunar Day 1. That sunset is after all closer to daylight of lunar Day 1 than the sunset of the
previous evening. However, the result of such a procedure is in effect that daylight of lunar
Day 1, and hence the month itself, begins before first visibility. Again, strictly speaking, it
would seem wise to delimit the concept of beginning lunar months with first visibility of
the new crescent to the practice of having daylight of lunar Day 1 follow first visibility in
the evening, as is the case in the religious Muslim calendar. However, if anyone insists on
describing a calendar in which first crescent visibility falls in the evening following daylight
of lunar Day 1 also as beginning lunar months with first crescent visibility, then it should
at least be made explicitly clear in which evening in relation to daylight of lunar Day 1 the
new crescent was first seen.
4. Outline of the Argument
The ultimate aim of this paper and its capstone is to make a contribution to the theme of
the conference at which an extract of it was read. This capstone constitutes the paper’s final
section, section 11. The conference theme is evoked in the question: What does it mean
to live the lunar calendar? This paper’s line of argument will lead to a slightly different but
related question: What does it mean to live three lunar calendars? Indeed, an attempt is
made below to show that, during a few decades in the third century BCE, no fewer than
three different lunar calendars were operative all at the same time in Egypt: (1) the native
Egyptian lunar calendar; (2) the Greco-Macedonian lunar calendar; and (3) the Hebrew
calendar. In 332 BCE, Alexander had conquered Egypt. In the last three centuries before
the common era, rulers descending from Alexander’s Macedonian general Ptolemy ruled
Egypt as Pharaohs. Most rulers of this dynasty were called Ptolemy. This phase of Egyptian
history is therefore known as the Ptolemaic period.
Naturally, it is not possible to seek an answer to the question as to what it meant to
live with three lunar calendars if there were no three lunar calendars. Much of this paper is
Leo Depuydt
124
therefore devoted to the preliminary effort of proving that there were three distinct lunar
calendars in the earlier third century BCE in Egypt. The existence of the Hebrew calen-
dar hardly requires proof. The calendar must have been used by the Jewish diaspora in
Egypt. But it has not been demonstrated that the native Egyptian lunar calendar and the
Greco-Macedonian lunar calendar differed from one another. It goes without saying that
the names of the months of the two calendars differed. But did the two calendars operate
according to different calendrical mechanisms?
There are six main steps in this paper’s line of argument leading up to the capstone
section 11. They are as follows. The first main step is a review of pertinent past research
pertaining to the Egyptian and Greek lunar calendars (see section 5). There is of course no
lack of references in the literature to the effect that ancient lunar months began with first
crescent visibility. Gathering such references would be fastidious. The search is instead for
references that ancient lunar months did not so begin. It has been known for some decades
now that native Egyptian lunar months simply begin too early for the new crescent to
have become visible before daylight of lunar Day 1. First Ludwig Borchardt in anecdotal
and incipient manner and then more systematically Richard A. Parker (earlier perhaps also
Heinrich Brugsch, but only he) have done much to establish this fact. As there is nothing
new to be said about the fact in question, the evidence will not be systematically revisited
here; still, some of it will receive mention below. The Greek calendar is another matter. To
my knowledge, only one scholar has seriously challenged the view that Greek lunar months
began with first crescent visibility, namely W. Kendrick Pritchett. The aim of this paper’s
step one is to analyze Pritchett’s evolving views regarding the matter. Pritchett refers to
his ideas as a “theory”. The design of the present paper is to go beyond theory and adduce
proof.
The second main step of this paper is an investigation of the core empirical data (see
section 6). The set consists of 32 Julian dates of lunar Day 1 derived from 32 double dates.
The focus is on demonstrating that two key numerical relations apply. First, native Egyp-
tian lunar months began on average roughly a day before Greco-Macedonian lunar months.
Second, both began on average before first visibility of the new crescent. Daylight of Day 1
of Egyptian lunar months began on average roughly half a day before conjunction or new
moon. Daylight of Day 1 of Greek lunar months began on average roughly half a day after
conjunction or new moon. Half a day after conjunction is a point in time that is simply too
soon for the new crescent to have become visible, let alone half a day before conjunction.
Owing to all the complexities characterizing the course of the moon, there was much
fluctuation from month to month in the afore-mentioned distances. However, what mat-
ters here is the averages. There is also much inherent irregularity in how lunar calendars
based on observation of the moon operate. This irregularity is bound to distort the averag-
es somewhat. However, what matters here is that the chances that certain crucial character-
istics of the empirical data adduced below are pure coincidence would appear to be statisti-
cally insignificant. Therefore, the possibility that the data do not support what needs to
be demonstrated can be rejected with high probability. The irregularity also accounts for
the fact that lunar months might on occasion begin after first visibility of the new crescent.
However, what matters here is that, when they do, such a beginning was not intentional. It
cannot be excluded that the ancients sometimes considered it significant that the new cres-
cent often became visible for the first time in the evening following daylight of lunar Day 1.
However, what matters here is that the new crescent played no role in fixing lunar Day 1.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 125
The documentation of the two afore-mentioned numerical relations will need to be
supplemented by an explanation of which calendrical mechanisms could have produced
them. These calendrical mechanisms will be described in detail and historical evidence
that points to their existence will be adduced.
In the third main step, additional evidence pertaining to the native Egyptian lunar cal-
endar is provided (see section 7). Additional evidence pertaining to the Greek lunar calen-
dar follows in step four (see section 8).
Steps two, three and four are devoted to a presentation of the empirical data and a de-
scription of the calendrical mechanisms that presumably produced them. The fifth main
step presents a control test that forms a bridge between the data and the mechanisms (see
section 9). A theoretical test is performed to establish whether, when the mechanisms are
applied to any lunar months at any time, they produce modern data that are similar to the
ancient data, thus corroborating the validity of the ancient data.
Steps two to five concern the lunar calendars of two of what are, judging by the scope
of the surviving sources, the three most prominent ancient civilizations before Rome came
onto the scene. The sixth main step concerns the third, ancient Mesopotamian civilization,
and especially its cultural capital, Babylon (see section 10). In steps two to five, evidence is
adduced to the effect that neither Egyptian nor Greek lunar months began after first cres-
cent visibility. Step six extends this same tenet to the Babylonian lunar calendar. In trying
to knock two hallowed tenets off their pedestals, namely that the day in Babylon began in
the evening and that the month began with first crescent visibility, step six will naturally be
perceived as more radical than the preceding steps.
5. Voice Crying in the Desert: W. Kendrick Pritchett
5.1. Pritchett in 1959
The new crescent has an enduring place in Classicists’ intellectual, and perhaps also ro-
mantic, imagination of the past. This state of affairs has persisted to the present day. One
reads in the most recent survey of what is known about Greek and Roman calendars that,
in Athens, the first month of the year began “on the evening of the first sighting of the new
moon’s crescent following the summer solstice”.5 Yet, in 1959, Pritchett questioned this
fundamental assumption when he wondered whether “the Athenians used some observable
phase other than the thin crescent of the new moon to determine the length of their lunar
mo nt hs”. 6 I am not aware of any other dissenting voices in the history of Classical scholar-
ship besides Pritchett’s. Nor have I searched very systematically for reactions to Pritchett’s
dissension. If one considers only original reasoned arguments that have appeared in print,
Pritchett may well have stood pretty much alone in the last half a century with his view that
the new crescent was not used to fix lunar Day 1 in Greek calendars.
Pritchett first took up the study of the Greek calendars during or soon after World
War II by collaborating with Otto Neugebauer of Brown University on a joint publication
entitled The Calendars of Athens.7 In this work, it is shown that three calendars were used
in ancient Athens: (1) a lunar calendar whose lunar Day 1 was determined by observation
of the moon; (2) a calendar “according to archon” in which the lunar calendar was modi-
fied by adding and subtracting days, but whose year still began on the same new year as the
lunar calendar; (3) a calendar that originally reflected the division of the year according to
Leo Depuydt
126
the prytanies of the boule.
The study of the Greek calendar and related topics such as the sequence of the archons
is of such complexity that it could easily turn into a full-time occupation. As incomplete as
my knowledge of the Athenian calendar may be at this time, I do not hesitate to embrace
Alexander Jones’s assessment that the central thesis of Pritchett’s and Neugebauer’s book
“has on the whole held up well against a steady barrage of rival models”.8 In the half century
that followed his joint publication with Neugebauer, Pritchett wrote regularly about the
ancient Greek calendar.9 His principal opponent in regard to all kinds of facets of ancient
Greek calendars was Benjamin Meritt, a skilled student of epigraphy in his own right. I am
personally quite comfortable with the notion that there was both a winner and a loser in
this debate—and that Pritchett won.
In 1959, influenced by what Parker, also of Brown University, had recently written on
Egyptian lunar months,10 Pritchett suggested that lunar Day 1 of Athenian lunar months
was fixed in time by means of observation of the old crescent in the morning at the begin-
ning of the 29th daylight period of the month. There can be no doubt that Egyptian lunar
months began before first visibility of the new crescent. Some of the empirical evidence to
that effect is repeated below. It was therefore inferred that observation of the old crescent
must somehow have played a role in fixing lunar Day 1, even if there is no explicit state-
ment anywhere in the sources that it did. Yet, to the present day, the notion that ancient
Egyptians were diligently waiting for the new crescent to begin a lunar month, just as all
other inhabitants of the ancient world presumably were, has persisted in the popular imagi-
nation. There is no doubt that, to the religious Muslims in modern Egypt, the new crescent
is everything. The arrival of Ramadan’s new crescent is a much anticipated event. But it is
time that the view became universally established that, to their fellow Egyptians in antiq-
uity, the new crescent meant nothing at all as far as the strict calendrical structure of the
lunar month was concerned.
Pritchett was led to propose that observation of the old crescent may also have played
a role in the Athenian calendar because of the specific way in which days are named at the
end of the lunar month (see below). Accordingly, he suggested that old crescent observa-
tion operated as follows at Athens. If the old crescent was no longer visible in the morning
at the beginning of the 29th daylight period of the month, the 29th daylight period that
immediately followed became the last daylight period of the month, the next daylight pe-
riod became that of lunar Day 1, and the month had only 29 days. If the old crescent was
still visible that same morning, the 29th daylight period became the penultimate daylight
period of the month, the next daylight period became the 30th of the month, and the
month had 30 days. That way it was known either one or two days in advance when day-
light of lunar Day 1 would begin.
It is to be assumed that there were occasional irregularities in a manmade product such
as an observational lunar calendar. These irregularities presumably required ad hoc adjust-
ments. Therefore, when it comes to the empirical data presented below, it will be above all
the averages that count to reveal the nature of the Greek lunar calendar.
Parker’s Egyptian lunar calendar, which had earlier also been mostly Ludwig Bor-
chardt’s, differed from Pritchett’s Athenian lunar calendar of 1959. In both calendars, lu-
nar Day 1 was fixed by means of observation of the old crescent. But in Parker’s Egyptian
lunar calendar, old crescent observation took place in the morning at the beginning of the
daylight period that follows the 29th daylight period of the month—not in the morning at
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 127
the beginning of the 29th daylight period of the month as in Pritchett’s Athenian lunar
calendar of 1959. Simply put, old crescent observation took place after 28 days in Athens
and after 29 days in Egypt.
In Parker’s Egyptian lunar calendar, if the old crescent was no longer visible, the day-
light period that follows the 29th daylight period of the month became daylight of lunar
Day 1 and the month had 29 days. There was then no advance notice of the start of the new
lunar month. If the old crescent was still visible, the daylight period that follows the 29th
daylight period of the month became daylight of lunar Day 30, the next daylight period
became lunar Day 1 of the following month, and the month had 30 days.
It inevitably follows from the mechanisms described above that the morning of first
invisibility of the old crescent on average fell at the beginning of daylight of lunar Day 1
in the Egyptian lunar calendar but at the beginning of daylight of the last day of the lunar
month, either the 29th or the 30th, in the Athenian lunar calendar. In other words, the
Egyptian lunar calendar began on average a day earlier than the Athenian lunar calendar.
At the same time, the same procedures stipulate that the morning of old crescent observa-
tion is the 28th daylight period of the month in the Athenian lunar calendar but the day
after the 29th daylight period of the month in the Egyptian lunar calendar. In other words,
the morning of old crescent observation is a day farther removed from lunar Day 1 in the
Egyptian lunar calendar than it is from lunar Day 1 in the Athenian calendar.
On the one hand, the Athenian lunar month on average begins a day later than the
Egyptian lunar month. On the other hand, the morning of old crescent observation in the
next month is one day less removed from lunar Day 1 in the Athenian lunar calendar than
it is in the Egyptian lunar calendar. Consequently, the morning of old crescent observa-
tion will on average fall in the same morning in both calendars. Old crescent observation
will then again produce the one-day interval between the beginning of the Athenian lunar
month and the beginning of the Egyptian lunar month. One lunar month later, old cres-
cent visibility will again fall in the same morning in both calendars, and so on in perpetuity.
Accordingly, if the two calendars are used in the same locale, they will be synchronized—
with one running on average a day behind the other. Pritchett’s statement that “the day of
new crescent visibility . . . is the first day of the month, not the second as in Egypt”11 clearly
implies that Athenian lunar months began a day later than Egyptian lunar months. It is a
relation that will be confirmed by actual empirical evidence adduced below.
The crucial question remains: What led Pritchett to postulate that the mechanism used
to determine the beginnings of lunar months in the morning of old lunar observation was
not the same in Athens as in Egypt ? Pritchett took note of the fact that, in 29-day Athenian
lunar months, the name of the day that was omitted was the name of Day 29 in a 30-day
lunar month. In other words, the last day of the lunar month had the same name in both
29-day and 30-day lunar months. No one had ever considered the possibility that this pe-
culiar property of Greek calendars might be relevant to how lunar Day 1 is fixed by means
of observation of the new moon. As Pritchett phrases it, “[t]his terminology is used at the
end of the [Athenian] months, and it has never received discussion in connection with an
observation calendar”.12 From the “terminology” in question, Pritchett implies that “[b]y
the end of the 28th day the official in charge of the calendar would have to decide whether
the 29th day of the month was [the last-but-one day or the last day of the month]”.13
Strictly speaking, by the internal logic of Pritchett’s lunar calendar of 1959, one ought
to read “by the middle of the 28th day” instead of “by the end of the 28th day” in the
Leo Depuydt
128
statement just cited. The day lasted from evening to evening in Pritchett’s calendar. Old
crescent observation naturally falls in the morning and therefore in the middle of a day. In
Pritchett’s calendar of 1959, the task at hand was to infer from old crescent observation
which day was going to begin in the evening that followed, the last-but-one or the last
one. But again, there is no need to bring the issue of when the day began into the discus-
sion. One can strictly operate with successively numbered or named daylight periods that
include any extensions to before dawn and to after sunset. As the time of almost all human
activity, daylight is most of what matters. Pritchett somewhere calls daylight a “business”
day.14 In sum, Pritchett’s above cited statement is here reinterpreted as stating that, in the
morning of old crescent observation, it needed to be established which day the immedi-
ately following daylight period would be.
Pritchett does not fully explicate the logic that causes old crescent observation, along
with the concomitant choice of name for the immediately following daylight period, to
take place when it does. What is that logic? The first step is to realize that Athenian and
other Greek lunar months can end in one of two ways, as follows: (1) (Day 29) name A,
(Day 30) name B; (2) (Day 29) name B. The second step is the observation that there are
two options in naming Day 29, name A and name B. Options inevitably imply a choice.
And a choice cannot be made later than the time when the options take effect. Since the
options undeniably take effect in the morning at the beginning of the 29th daylight period,
that morning is the latest possible time for making the choice.
Pritchett’s Athenian lunar calendar of 1959 might be called an old crescent calendar.
But it would appear that the new crescent was also heeded in some sense. That is because
Pritchett assumes that the decision on Day 28 was designed so that “the day of new crescent
visibility . . . [would be] the first day of the month”.15 By new crescent visibility, Pritchett
apparently means that first visibility of the new crescent immediately follows—rather than
precedes, as one strictly speaking expects in the case of a first crescent visibility calendar—
daylight of lunar Day 1. In that sense, the lunar calendar proposed by Pritchett in 1959
heeded both the old crescent and the new crescent.
Pritchett otherwise also assumed in 1959 that the day began in the evening in Athens.
In other words, his 1959 calendar had an evening epoch. However, when the day begins
plays no role in the line of argument presented in this paper.
In the end, Pritchett does not seem to have been fully convinced of what he wrote in
1959. In the entry “Calendars” in the second edition of the Oxford Classical Dictionary,16
to which he contributed a description of Greek calendars probably submitted in 1964–
1966,17 it is laconically noted that lunar Day 1 was “determined presumably by observation
of the first visibility of the new moon after conjunction”.18 This statement clearly contra-
dicts what he wrote in 1959. Indeed, by 1970, Pritchett’s partial about-face of 1964–1966
appears to have become a full one.
5.2. Pritchett in 1970
In his monograph entitled The Choiseul Marble, Pritchett makes a proposal19 that is “an
alternative explanation to that proposed [in Pritchett (1959)]”.20 Whereas he assumed in
1959 that both the old crescent and the new crescent played a role in fixing lunar Day 1, he
returns in 1970 to the universally accepted view that, if the Athenian lunar calendar oper-
ated by observation of the moon, only the new crescent could have played a role. Whereas
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 129
he assumed in 1959 that the day began in the evening, he now believes that it began in
the morning.21 But once again, when the day began will be considered irrelevant in what
follows; in a sense, Pritchett’s switch from assuming an evening beginning and ending to
assuming a morning beginning and ending is a step closer to the definition of the natural
day as beginning in the morning and ending in the evening in that at least one of the two
limits overlaps.22
Pritchett’s lunar calendar of 1970 was a first visibility calendar in the strictest sense, as
defined above. That is, daylight of lunar Day 1 followed first visibility of the new crescent
in the evening before. What one does in a first visibility calendar such as the religious
Muslim calendar is to watch in the evenings close to new moon until one first spots the
new crescent. When the crescent is spotted, the daylight beginning the next morning be-
comes daylight of lunar Day 1. In Pritchett’s Athenian lunar calendar of 1970, one does
something that has the exact same effect. The reason that the mechanism is different is
that, as was noted above, there are two options for naming Day 29 in the Athenian lunar
calendar. The naming of the 29th daylight therefore needs to involve a choice that is made
before the 29th daylight itself. In Pritchett’s Athenian lunar calendar of 1959, the choice
was made at old crescent observation. Since the old crescent plays no role in Pritchett’s cal-
endar of 1970, the choice inevitably needs to be made at new crescent observation, which
takes place in the evening. In Pritchett’s calendar of 1959, the morning of old crescent
observation begins daylight of Day 29. In his calendar of 1970, the evening of new crescent
observation ends daylight of Day 29. In old crescent observation, visibility precedes invis-
ibility. In new crescent observation, the opposite is the case. Therefore, in old crescent
observation, visibility delays the end of the lunar month by a day. In new crescent visibility,
visibility expedites the end of lunar month by a day. If the new crescent is visible, the im-
mediately preceding daylight period is given the name that the last day of the month has in
both 29-day and 30-day Athenian lunar months and the next daylight is that of Day 1. If
the new crescent is invisible, the immediately preceding daylight period is given the name
that Day 29 has in 30-day lunar months and one waits a day hoping that the new crescent
will be visible the next evening. But anyway, what is seen the next morning is not all that
relevant anymore because lunar months are never longer than 30 days.
It follows that the interval between the beginning of the Egyptian lunar month and the
Athenian lunar month is no longer one day, as it is in case of the 1959 calendar, but rather
two to three days.
Pritchett was aware that one disadvantage of his calendar of 1970 is that daylight of
Day 29 was not named until the evening that immediately follows it.23 How could Athe-
nians spend a day without knowing which day it was?
An even more problematic characteristic of his calendar of 1970 is that its months be-
gin one to two days after those of the 1959 calendar. Such a late beginning is simply contra-
dicted by empirical evidence presented below and all else that is known about the Athenian
and other Greek lunar calendars, much of it summarized later by Pritchett himself.24
Finally, one of the names of the last day of the month in both 29-day and 30-day calen-
dars is vη κα vέα “old and new”. In his Life of Solon, at 25, Plutarch writes that the “old”
portion of that day belongs to the expiring month and the “new” portion to the beginning
month. But what divides the two portions? In 1970, Pritchett assumed it was “the visibil-
ity of the new crescent by the evening light”.25 Later, in 1982, he took it to be the “synodic
conjunction”, that is, the moment when the moon is right in front of the sun and therefore
Leo Depuydt
130
invisible except at solar eclipses; conjunction precedes first visibility by very roughly a day
on average. The two assumptions of 1970 and 1982 directly contradict one another. But in
1982, Pritchett adduced abundant evidence that the ancient Greeks themselves assumed
that conjunction separated the two parts of vη κα vέα.
5.3. Pritchett in 1982
In 1970, Pritchett had radically reversed his position of 1959 regarding the beginning of
the Athenian lunar month, concluding that “the picture was quite clear”.26 But in 1982,
he made a second radical reversal by returning more or less to his position of 1959, except
for the fact that he now assumed that the day began in the morning, as he already had in
1970, and not in the evening.27 These two radical reversals make it easy to lose confidence
in Pritchett’s discussions concerning how ancient Athenians and Greeks in general deter-
mined the beginning of the lunar month.28
Then again, the treatment of 1982 is by far the longest of the three and presents signifi-
cant new evidence. Pritchett adduces an impressive lineup of ancient authors who all state
as a matter of course that the Greek lunar months lasted from conjunction to conjunction
and that the last day of the month is the day of conjunction. There is not a peep in any
of these sources about the first visibility of the new crescent. Importantly, Pritchett ad-
duces certain considerations that, in lunar months whose beginning is determined by old
crescent observation in the morning that begins the 29th daylight period of the month,
conjunction will indeed on average take place on the last day of the lunar month. Empirical
evidence of this fact will be adduced below.
The amount of convincing detail in Pritchett (1982) and the coherent picture it offers
do much to favour the view that Pritchett (1970) was a transitory aberration. In my mind,
Pritchett emerges as someone whose expertise with calendars, which was inspired by Otto
Neugebauer and Richard A. Parker of Brown University, led him to look in one direction
when everyone else was and had always been looking in the opposite direction. Rowing
upstream into a heavy countercurrent, he apparently needed some time to get to what he
was looking for. The fact that it did take some time and included an episode of self doubt
is best viewed as evidence of how difficult it is, and still may prove to be, to dethrone the
new crescent definitively from its lofty perch atop the modern imagination of the ancient
world.
Pritchett was born in 1909, retired from the University of California at Berkeley in
1976, and died at age 98 in 2007. In 1982, when he finally arrived at where he wanted to
be in regard to the beginning of the Athenian lunar month, he was well into retirement
and into his seventies. However, an Internet obituary reporting that he worked 10 hours a
day seven days a week for 30 years after retirement suggests that he was still very much in
his prime in 1982. In fact, in 2001, when he was in his early nineties, he published a mono-
graph on the subject of Athenian calendars that “purports to be an evaluation of the criti-
cisms which were brought against Calendars of Athens published with the collaboration
of Otto Neugebauer in 1947”. After 54 years, Pritchett’s lifelong study of Greek calendars
had come full circle.
In the end, Pritchett deserves great merit for relating the specific way lunar days are
named at the end of the Athenian lunar month to the way in which the beginning of the
month was determined. It was a seminal insight. In light of the fact that the present paper
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 131
revolves around how the Greek lunar calendar and the Egyptian lunar calendar relate to one
another, it is interesting to note that Pritchett came to his understanding of the Athenian
calendar with the help of what he had learned first about the Egyptian lunar calendar.
When this investigation was well underway and some notion had been formed about
the difference between the Egyptian lunar calendar and the Greek lunar calendar (espe-
cially in light of the fact that both the Greek name of the last day of the lunar month, vη
κα vέα “old and new”, and the Egyptian name of the first day of the lunar month, psπdntyw,29
apparently refer to day of conjunction), I came upon the following statement by Pritchett:
“If we advance the [Julian] dates by one [day], the Greek [lunar] calendar becomes a rep-
lica of the Egyptian lunar calendar”.30 This is more or less the same as stating that Greek
lunar months begin a day later than Egyptian lunar months. It was encouraging to find
oneself in good company. Pritchett offers no hard empirical data in support of his state-
ment, even if he gathers many useful supportive indications from various sources. Accord-
ingly, he describes the statement cited above as a “theory”.31 The aim of what follows is to
present empirical data in support of this theory.
6. Core Empirical Data: Modern Dates of Lunar Day 1 Derived from Double Dates
6.1. The Irrelevance of Most Ancient Lunar Dates to the Present Hypothesis
Two sets of data are being sought. The first set ought to allow one to establish when Egyp-
tian lunar months begin. The second set ought to allow one to establish when Greek lunar
months begin. Once the two sets of data have been secured, the Egyptian beginning and
the Greek beginning can be compared with one another.
There is no lack of Egyptian and Greek lunar month and day dates in ancient sources.
In proportion to the totality of the sources that have survived, there are bound to be fewer
Egyptian than Greek lunar dates because the Egyptian lunar calendar was restricted mainly
to the religious sphere. In Egypt, events outside the confines of life in the temple were as
a rule dated according to the so-called civil calendar, which is not lunar but consists of 12
months of 30 days with five added days for a total of 365.
Many Egyptian and Greek lunar dates have survived from many centuries of history.
But of hardly any of these dates do we know the exact equivalent date in the modern com-
mon calendar now used worldwide, the so-called Julian or Julian-Gregorian calendar. For
the sake of simplicity, I will call the Julian date the modern date. Needless to say, there were
no Julian dates before 45 BCE, when that calendar was instituted. The modern calendar is
simply extended back into the past to before 45 BCE in order to conveniently date events
according to a single standard.
It is often possible to determine the modern equivalent of an ancient lunar date to within
a margin of two to three days. But that is not good enough for the purpose of establishing
when exactly lunar months begin. Exact dates are needed. As it happens, on rare occasions,
the exact modern equivalent of an ancient lunar date can be established indirectly. Two
cases are as follows. First, a lunar date may date an astronomical event whose modern date
can be obtained independently from computations. That modern date naturally also coin-
cides with the lunar date. Second, a lunar date may be equated in a document with a date by
another ancient calendar whose modern date is known. That modern equivalent also coin-
cides with the lunar date. Two dates equated with one another are called a double date.
Leo Depuydt
132
6.2. Double Dates
The focus of what follows will be on a set of double dates, some including an Egyptian
lunar date and others a Greek lunar date. The lunar dates are all from Egypt, including
all the Greek dates. After Alexander’s conquest of Egypt in 332 BCE, Greek had become
an Egyptian language and the Greco-Macedonian calendar, including the Macedonian
month names, were imported into Egypt. For the purpose of comparison, it is a fortunate
circumstance that both sets were found at about the same longitude. Lunar months begin
at different times at different longitudes.
In all double dates, the other date is an Egyptian civil date about whose modern equiva-
lent there is no doubt. This set of double dates will be deemed sufficient to confirm the
theory in whose support they are adduced. Still, some related dates and other additional
evidence will be adduced as well below (see sections 7 and 8).
6.3. How to Derive a Modern Date of Lunar Day 1 from Double Dates
If the modern date of an ancient lunar date is known, then the modern date of daylight
of Day 1 of the ancient lunar month in question is known as well. For example, in one
Egyptian lunar date that is part of a double date (see below), an Egyptian lunar Day 15 is
equated in a document with an Egyptian civil date. Daylight of the civil date is known to
fall on 19 Oct 559 BCE. Daylight of lunar Day 15 is therefore also daylight of 19 Oct 559
BCE. If daylight of lunar Day 15 is daylight of 19 October, then daylight of lunar Day 1
falls 14 days earlier and coincides with daylight of 5 October.
Once the modern date of lunar Day 1 is determined, it can be established where lunar
Day 1 falls in relation to the astronomical lunar cycle that passes from new moon to wax-
ing moon to full moon to waning moon and back to new moon. The relation between the
calendrical lunar month and the astronomical lunar cycle can be expressed by measuring
the interval between a fixed point in time in the calendrical lunar months and a fixed point
in time in the astronomical cycle. When several such intervals have been measured, an av-
erage interval can be calculated. When an average interval has been obtained both for a set
of Egyptian lunar dates and a set of Greek lunar dates, the two averages can be compared.
The fixed point in time in the calendrical lunar month chosen here is 6:00 a.m., the
average time of sunrise, in the morning that begins daylight of lunar Day 1. Another fixed
point in the calendrical day could equally well have been chosen, for example, noon of
lunar Day 1. The real time of sunrise has not been chosen because that would involve the
prior assumption that the changing time of sunrise somehow played a role in the relation
between the astronomical lunar cycle and the calendrical lunar month, whatever that role
may be. Logically speaking, one cannot make that assumption before making the compari-
son. That would be an instance of circular reasoning.
The fixed point in time in the astronomical lunar cycle chosen here is new moon or
conjunction. Various programs available on the Internet provide the times of conjunction
to within minutes. But as it happens, Goldstine’s times published in 1973 will still do for
the purpose of historical investigations and they will be used here.32 One could conceiv-
ably choose another point in the astronomical lunar cycle for the purpose of the initial
comparison, for example the last visibility of the old crescent or the first visibility of the
new crescent. The old crescent is last seen in the morning about one to two days before
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 133
conjunction. Visibility needs to be distinguished from sighting. It is not because the moon
could be seen that it actually was. However, modern computations of crescent visibility are
not as accurate as those of conjunction. It is not always possible to establish with very high
probability in which morning the old crescent could last be seen or in which evening the
new crescent could first be seen. Conjunction is therefore preferred here to last crescent
visibility as a fixed point of reference. Still, after the initial comparison, the relation of the
empirical data to visibility or invisibility of the old or new crescent will be examined as
well.
It is distinctly possible that principles used to determine the beginnings of lunar months
were not always strictly applied. Lax application of the rules would produce irregularities
in the data. But what matters, in the first instance, is the average interval.
In the example mentioned above, daylight of 5 October of 559 BCE is daylight of lunar
Day 1. New moon or conjunction occurred at 2:11 a.m. on 6 October 559 BCE. This is
Goldstine’s time for Babylon,33 reduced by 47 minutes to reflect the location of Assuan,
whose longitude is about that of Edfu where the date was found. The distance between
6:00 a.m. on 5 October and 2:11 a.m. on 6 October is 20 hours and 11 minutes. The de-
sign of what follows is to obtain two sets of such intervals, one set pertaining to Egyptian
lunar dates and the other to Greek lunar dates, and to produce two averages.
Once the modern date of Day 1 of an ancient lunar month is obtained, its relation to
the morning of last crescent visibility and the evening of first crescent visibility can be
established. In the example cited above, daylight of 5 October of 559 BCE is daylight of
lunar Day 1. The morning of October 4 was most probably the last morning in which the
old crescent could still be seen.34 Consequently, daylight of lunar Day 1 begins in the morn-
ing in which the old crescent is for the first time invisible.
6.4. The Known Modern Dates of Lunar Day 1 Derived from Double Dates (28)
One reads in Genesis 18 that the Lord promised to spare Sodom if ten righteous men
could be found. But no ten were found. In the case of instances of modern dates of lunar
Day 1 derived from double dates consisting of an Egyptian or Greek lunar date and a civil
date, I am relieved to note that at least ten do survive. But not a whole lot more. Exactly
28 are known to me. This is not much for two to three thousand years of the combined
histories of Egypt and Greece. Perhaps other double dates will surface at some point.35
The double dates from which the 28 instances of lunar Day 1 have been derived have been
well-known for some time and there is on the whole not much controversy regarding their
interpretation. What minor problems the dates pose will be discussed below. I believe these
28 to be sufficient in number to yield results that are statistically significant.
As was noted before, in double dates, two dates are equated with one another. One of
the two dates is a civil date, whose modern equivalent is known with certainty in the period
of Egyptian history to which the double dates belong. The other date is lunar. Naturally,
the double dates containing an Egyptian lunar date are written in Egyptian and the double
dates containing a Greek date are written in Greek.
In eight of the 28 modern dates of lunar Day 1 derived from double dates, the lunar
date is Egyptian. In 20 instances, the lunar date is Greek. Further below, the eight Egyptian
dates will be supplemented by 12 instances of a modern date of lunar Day 1 as derived from
temple service dates.
Leo Depuydt
134
The 28 lunar dates are all from Egypt. That is to be expected in the case of the Eg yptian
lunar dates. But the Greek lunar dates are also from Egypt. They belong to the Macedo-
nian calendar used by the Greek-speaking population of Egypt in Ptolemaic times. The
Greek lunar dates all belong to the third century BCE. In the later third century BCE, the
Macedonian calendar lost its lunar character and was eventually entirely assimilated to the
civil calendar.
6.5. Two Average Time Intervals between Conjunction and 6:00 a.m. of Lunar Day 1 Yielded
by Double Dates, One Egyptian, the Other Greek
The double dates yield 28 specific time intervals that separate conjunction from 6:00 a.m.
in the morning that begins daylight of lunar Day 1. From these 28 specific time intervals,
two average time intervals can be derived: one from the eight specific time intervals per-
taining to the Egyptian lunar calendar; the other from the 20 specific time intervals per-
taining to the Greek lunar calendar.
Details pertaining to the double dates that include an Egyptian lunar date are listed
in table 1, along with what can be derived from them. The specific intervals that separate
conjunction from 6:00 a.m. in the morning of lunar Day 1 are listed in column VI. These
III III IV VVI
Year Civil or
Alexandri-
an Date
Lunar
Date
Modern Date of
Date in Col. I
(Daylight)
Modern
Date of
Lunar Day 1
(Daylight)
Closest
Conjunction
Distance in Hours
from Conjunction
to 6:00 a.m. in
Morning of Lunar
Day 1
1 12 of Amasis II šmw 13 I šmw 15 19 Oct 559 BCE 5 Oct 6 Oct, 2:11 a.m. – 20h 11m
2 28 of Ptolemy VIII IV šmw 18 III šmw 23 10 Sep 142 BCE 19 Aug 17 Aug, 11:29 p.m. + 30h 31m
3 30 of Ptolemy VIII II šmw 9 II šmw 6 2 Jul 140 BCE 27 Jun 27 Jun, 9:10 p.m. – 15h 10m
4 10 of Ptolemy III III šmw 7 Day 6 23 Aug 237 BCE 18 Aug 18 Aug, 1:27 a.m. + 4h 33m
5 10 of Ptolemy IV III šmw 7 Day 6 17 Aug 212 BCE 12 Aug 11 Aug, 5:01 p.m. + 12h 59m
6 6 of Cleopatra VII III šmw 13 Day 5 13 Jul 46 BCE 9 Jul 8 Jul, 5:23 a.m. – 12h 37m
7 1 of Augustus IV prt 21 Day 16 17 Apr 29 BCE 2 Apr 2 Apr, 2:54 p.m. – 8h 54m
8 21 of Augustus III šmw 10 Day 16 4 Jul 9 BCE 19 Jun 19 Jun, 6:03 a.m. – 0h 03m
T 1. Double Dates Consisting of an Egyptian Lunar Date and an Egyptian Civil Date. For
details and bibliographical references pertaining to the sources from which the double dates have
been derived and the rationale for ordering them in the way that they are, see Depuydt (1997a), pp.
161–175. Dates 1, 2, and 3 in column II have a month date and a day date; dates 4 to 8, a day date
only. Dates 1 to 7 in column II are civil dates; date 8, an Alexandrian date. The times for conjunction
are Goldstine’s (1973) for Assuan, except 6, which is for Memphis.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 135
specific intervals yield an average interval of minus 1 hour 06 minutes 30 seconds. In other
words, 6:00 a.m. in the morning that begins daylight of lunar Day 1 falls on average a little
over one hour before conjunction. This means that the previous evening fell on average
about half a day before conjunction. There is therefore no way that the new crescent could
have been seen on average. Further below, the eight specific intervals will be supplemented
by 12 additional specific intervals derived from temple service dates in order to obtain an
average interval derived from, not just eight specific intervals, but 20 (see section 7). The
average derived from 20 intervals will corroborate the average derived from just eight.
The 20 specific intervals pertaining to the Greek lunar calendar are derived from 32
double dates. That means that some intervals are derived from more than one double date.
The 32 double dates are listed by Grzybek.36 Grzybek’s list has been adapted for table 2,
which lists the details regarding the double dates and what can be derived from them.
Grzybek was aware of more double dates than those listed in table 2. But he assumed
that, in the dates he does not list, the lunar date may well have been artificially derived from
the Egyptian civil date by being given the same day number or a day number that is 7 or
T 2 (following page). Double Dates Consisting of a Greek Lunar Date and an Egyptian Civil
Date. For details and bibliographical references pertaining to the sources from which the double
dates have been derived, see Grzybek (1990), pp. 135–137. Columns I and II follow Grzybek. The
dates in IV may differ from Grzybek’s, primarily because he assumes that certain letters were written
between dawn and sunrise and therefore had a day date that is one lower than letters written after
sunrise. I consider a change in day date at sunrise highly improbable (see Depuydt (2002), p. 474, re-
ferring to the insightful but largely forgotten study by Bilfinger (1888)). The regnal years of Ptolemy
II Philadelphos are Macedonian regnal years. Nos. 14 to 18 belong in time after number 24. This is
because Grzybek’s numbering of the double dates runs from Dios to Dios, Dios being Month 1 of
the Macedonian year, whereas the regnal year in his view began on 27 Dystros (Grzybek (1990), pp.
157–169). The order of the Macedonian months is as follows: Dios, Apellaios, Audnaios, Peritios,
Dystros, Xandikos, Artemisios, Daisios, Panemos, Loios, Gorpiaios, and Hyperberetaios. In nos. 2,
27, and 31, the Macedonian dates stand between parentheses, not because they are absent from the
text, but because they may be artificial. In each of the three double dates, the Macedonian day date
is seven less than the Egyptian day date. It has been argued that seven may sometimes have been
mechanically subtracted without heeding the lunar cycle (cf. Grzybek (1990), pp. 151–154). Grzy-
bek likewise assumes the existence of mechanical subtraction of 10 (Grzybek (1990), 152). The
conjunctions in column V are Goldstine’s (1973) for Babylon adjusted to Alexandria by subtracting
58 minutes.
Notes to the table:
* The year is 252 BCE
** “36” is the year date in the edition of the papyrus, P. Hib I 77. Grzybek ((1990), p. 154 note 93)
emends to “30”, following F. Uebel. Uebel’s emendation is accepted here. As Grzybek suggests, a dark
spot or speck erroneously read as “6” may have followed “30” and an inspection of the original manu-
script could clear up the matter. He also assumes (Grzybek (1990), p. 154, note 93) that the docu-
ment was written between dawn and sunrise and that the day date changed from 23 to 24 at sunrise.
Yet, later (p. 155), he refers to the date as “an error or false reading of the scribe”. In any event, I accept
“23” at face value and consider a change of day date at sunrise highly unlikely (see subscript above).
Leo Depuydt
136
III III IV VVI
Year of
Ptolemy
II Phila-
delphos
Civil Date Lunar Date Modern Date of Date
in Col. I (Daylight)
Modern Date
of Lunar Day I
(Daylight)
Closest
Conjunction
Distance in hours
from Conjunc-
tion to 6:00 a.m.
in Morning of
Lunar Day 1
1. 22 Epeiph 12 Loios 19 4 Sep 264 BCE (1) 17 Aug 16 Aug, 6:21 p.m. + 11h 39m
2. 29 Pharmouthi 30 (Artemisios 23) 22 Jun 257 BCE (2) 31 May 1 Jun, 10:57 a.m. – 28h 57m
3. 29 Thoth 9 Hyperberetaios 8 3 Nov 257 BCE (3) 27 Oct 26 Oct 9:27 a.m. + 20h 33m
4. 29 Thoth 13 Hyberberetaios 12 7 Nov 257 BCE same as 3 same as 3 same as 3
5. 29 Thoth 21 Hyperberetaios 20 15 Nov 257 BCE same as 3 same as 3 same as 3
6. 29 Thoth 24 Hyperberetaios 23 18 Nov 257 BCE same as 3 same as 3 same as 3
7. 29 Choiak 4 Audnaios 4 27 Jan 256 BCE (4) 24 Jan 23 Jan, 1:57 p.m. + 16h 03m
8. 29 Choiak 24 Audnaios 24 16 Feb 256 BCE same as 7 same as 7 same as 7
9. 29 Tybi 10 Peritios 10 4 Mar 256 BCE (5) 23 Feb 22 Feb 8:11 a.m. + 21h 49m
10. 29 Tybi 11 Peritios 11 5 Mar 256 BCE same as 9 same as 9 same as 9
11. 30 Pachons 9 Artemisios 10 1 Jul 256 BCE (6) 22 Jun 20 Jun 9:55 a.m. + 44h 05m
12. 30 Mesore 13 Loios 16 3 Oct 256 B CE (7) 18 Sep 16 Sep 10:44 a.m. + 43h 16m
13. 30 Choiak 10 Apellaios 21 2 Feb 255 BCE (8) 13 Jan 12 Jan 2:49 p.m. + 15h 11m
14. 31 Phamenoth 27 Dystros 20 20 May 254 BCE (9) 1 May 30 Apr 9:49 a.m. + 20h 11m
15. 31 Phamenoth 29 Dystros 22 22 May 254 BCE same as 14 same as 14 same as 14
16. 31 Phamenoth 30 Dystros 23 23 May 254 BCE same as 14 same as 14 same as 14
17. 31 Phamenoth 30 Dystros 23 23 May 254 BCE same as 14 same as 14 same as 14
18. 31 Phamenoth 30 Dystros 23 23 May 254 BCE same as 14 same as 14 same as 14
19. 31 Pharmouthi 4 Xandikos 15 27 May 255 BCE (10) 13 May 11 May 8:28 a.m. + 45h 32m
20. 31 Pachons 18 Daisios 2 10 Jul 255 BCE (11) 9 Jul 9 Jul 7:39 a.m. – 1h 39m
21. 31 Pachons 30 Daisios 14 22 Jul 255 BCE same as 20 same as 20 same as 20
22. 31 Payni 2 Daisios 16 24 Jul 255 BCE same as 20 same as 20 same as 20
23. 31 Payni 11 Daisios 25 2 Aug 255 BCE same as 20 same as 20 same as 20
24. 31 Phamenoth 6 Peritios embol. 28 29 Apr 254 BCE (12) 2 Apr 31 Mar 6:25 p.m. + 35h 25m
25. 32 Mesore 1 Panemos 26 21 Sept 254 BCE (13) 27 Aug 26 Aug 4:31 p.m. + 13h 29m
26. 33 Payni 14 Daisios 20 4 Aug 253 BCE (14)16 Jul 16 Jul 8:50 a.m. – 2h 50m
27. 34 Hathyr 29 (Dios 22) 21 Jan 251 BCE (15) 31 Dec* 30 De c 5:49 a.m. + 24h 11m
28. 34 Phamenoth 3 Peritios 28 25 Apr 251 BCE (16) 29 Mar 28 Mar 10:08 a.m. + 19h 52m
29. 35 Epeiph 30 Panemos 28 19 Sep 251 BCE (17) 23 Aug 22 Aug 5:07 p.m. + 12h 53m
30. 36** Pachons 22 Artemisios 23 14 Jul 256 BCE (18) 22 Jun 20 Jun 9:55 a.m. + 44h 05m
31. 37 Phaophi 16 (Hyperberetaios 9) 8 Dec 249 BCE (19) 30 Nov 26 Nov 6:44 p.m. + 83h 16m
32. 37 Choiak 21 Apellaios 17 11 Feb 248 BCE (20) 26 Jan 25 Jan 9:07 a.m. + 20h 53m
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 137
10 removed from the civil day number.37 The artificial character of the lunar date of such
double dates can sometimes apparently be confirmed by the fact that the lunar date does
not accord with the lunar cycle. Whatever may be of Grzybek’s proposal, the dates he does
not list have not been considered here.
The specific intervals that separate conjunction from 6:00 a.m. in the morning of lunar
Day 1 are listed in column VI of table 2. They yield an average interval of plus 22 hours
56 minutes 51 seconds. In other words, 6:00 a.m. in the morning of lunar Day 1 falls on
average a little under 23 hours after conjunction. Accordingly, the previous evening falls on
average roughly about ten hours after conjunction. That is on average too soon after con-
junction for sighting of the new crescent to have become possible. The age of the moon,
that is, the time from conjunction, needs to be on average very roughly 24 hours.
6.6. A Comparison of the Egyptian and Greek Average Time Intervals
A simple comparison of the two averages reveals that the Egyptian lunar months in ques-
tion on average begin about 24 hours 4 minutes 21 seconds (1h 06m 30s before conjunction
+ about 22h 56m 51s after conjunction) before the beginning of Greek lunar months. The
number of the lunar dates is not very high. But the difference between the set of Egyptian
dates and the set of Greek dates is unmistakable, it would appear.
In table 3 below, spatial distribution is used to evoke the difference between the Egyp-
tian set and the Greek set. Each instance of the letter E represents an Egyptian lunar date;
each instance of G, a Greek lunar date. The position of the letter indicates where 6:00 a.m.
of the morning that begins daylight of lunar day 1 is located in relation to conjunction.
from – 30h to – 20h: E G
from – 20h to – 10h: E E
from – 10h to 0h: E E G G
—————— conjunction ——————
from 0h to + 10h: E
from + 10h to + 20h: E G G G G G G
from + 20h to + 30h: GG G G G
from + 30h to + 40h: E G
from + 40h to + 50h: G G G G
more than 80h: G
T 3. Locations of 6:00 a.m. of Lunar Day 1 in relation to Conjunction (E = Egyptian lunar
date; G = Greek lunar date).
Another way of evoking the sharp difference between the Egyptian set and the Greek
set is in relation to a certain point of time before or after conjunction. In no Egyptian date
does 6:00 a.m. in the morning of lunar Day 1 fall later than 35 hours after conjunction. By
contrast, it does so in six, or 30%, of the Greek dates. Furthermore, in only one Egyptian
date, or 12½%, does 6:00 a.m. in the morning of lunar Day 1 fall later than 13 hours after
conjunction. But it does so in no fewer than 15, or 75%, of the Greek lunar dates.
Leo Depuydt
138
In selecting the 20 double dates, Grzybek made certain assumptions that can be seen
as weakening their validity. But none of these assumptions is so outrageously unreasonable
that calculating averages by taking his choices at face value did not seem worthwhile. Still,
it remains a fact that the dates are not entirely without problems. There are three types of
problems and the problems affect six of the 20 modern dates of lunar Day 1 (for the sequen-
tial numbers, see column IV in table 2), with two types of problems affecting one of the six.
First, two of these six dates are the result of emendation. The day date is emended in one
(no. 14)38 and the year date in another (no. 18).39 Second, one of the six dates is what may
be called an egregious outlier (no. 19). In it, the lunar month begins on the fourth day after
conjunction, untypically very late. Third, in four of the six dates (nos. 2, 9, 15, and 19), the
difference between the day number of the lunar date and the day number of the civil date is
7. There are instances of double dates in later Ptolemaic times in which the lunar dates have
by all appearance lost their connection with the moon and the difference between the two
day dates is also 7. In Grzybek’s view, already mentioned above, there is therefore reason to
suspect that, in those later double dates, the lunar date was artificially differentiated from
the civil date by subtracting or adding 7. As it happens, in one of the dates in which the dif-
ference between the two day dates is 7 (no. 2), the lunar month begins uncharacteristically
early; in another, uncharacteristically late (no. 19). It seems therefore tempting to discard
all four lunar dates involved as evidence because they may be artificial. Then again, lunar
dates from the reign of Ptolemy II Philadelphos otherwise generally retain their connec-
tion with the lunar cycle. And it cannot be denied that there must have been cases in which
the civil day number and the lunar day number were seven apart.
It will be wise to obtain additional average intervals for the Greek lunar dates by dis-
regarding, say, only the outlier, only the emended date, all six of the slightly problematic
dates, and other kinds of selections from the problematic dates. It appears that, however
one may play the numbers, the shortest average interval, obtained by omitting just the
outlier and the date in which the year is emended, is still plus 18h 25m 20s. The difference
between the Egyptian and the Greek average intervals is then still plus 19h 31m 50s
(1h 06m 30s + 18h 25m 20s). If one throws out all six of the slightly problematic dates, the
average interval in the case of the Greek lunar dates is about plus 22h 47m 13s.
There may be yet other ways of playing the numbers involving yet other specific selec-
tions of data based on certain assumptions. But I do not see how the distinctive gap of
roughly a day between the Egyptian lunar dates and the Greek lunar dates could be elimi-
nated by any thinkable kind of selection.40
One more interesting, and perhaps legitimate, way of comparing the Egyptian and
Greek lunar dates is as follows. Each set of dates has one outlier. One Greek lunar date
(no. 10 in column IV in table 2) begins more than 80 hours after conjunction. Even if the
date was bona fide, special circumstances may have applied, such as bad weather. But the
important consideration is as follows. Such a date cannot be typical of any rule-determined
way of beginning the lunar month. It is the only one of the 20 Greek dates regarding which
this assessment is possible. It is therefore justified to omit it. The resulting average interval
is about plus 19h 46m 22s. One Egyptian lunar date (no. 2 in table 1) is also something of
an outlier. If one omits it, the average interval drops to about minus 5h 37m 34s. Disregard-
ing the two outliers, the gap between the two average intervals is then about 25h 23m 56s,
about a day.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 139
6.7. The Egyptian and Greek Lunar Calendars as, Strictly Speaking, Old Crescent (In)vis-
ibility Calendars
In what precedes, old crescent invisibility has been described as a key ingredient of Egyp-
tian and Greek lunar calendars. And to a great extent, it is. But strictly speaking, there is
more to the story. It is clearly not the case that, in either calendar, it is established that the
old crescent is invisible. Rather, it is determined whether it is still visible or not. Its invis-
ibility leads to a certain course of action and so does its visibility. In other words, both
invisibility and visibility play a role and they do so as a kind of a toggle. What is more, if the
old crescent is still visible at the time in question, it does not necessarily mean that it will
be invisible in the next evening. There is too much irregularity in the Egyptian and Greek
lunar months, in spite of the fact that certain principles seem to be followed in determining
the beginning of the lunar month.
Along the same lines, there is every reason to believe that a new crescent (in)visibility
calendar was used in Mesopotamia (see section 10.13). The nomenclature of the final days
of the Greek months otherwise seems to guarantee that the old crescent is watched in the
Greek world and not, as in Mesopotamia, the new crescent.41 Naturally, the extant evi-
dence for Greek lunar calendars covers only part of the Greek world. Likewise, the extant
evidence for Mesopotamian lunar calendars covers only part of the Mesopotamian world.
The best that can be done is to extrapolate from this evidence. If different mechanisms, or
even if the old crescent sometimes played a role in Mesopotamia and the new crescent in
the Greek world, we may well never learn anything about that in the absence of evidence.
6.8. Excursus 1: A Statistical Analysis
What are the chances that the distribution of Egyptian lunar dates and Greek lunar dates
described above is completely random? One way in which statisticians answer this type
of question is by trying to quantify what the chances are that the null hypothesis needs to
be rejected. According to the null hypothesis, the said distribution is random. The higher
the chances that the null hypothesis needs to be rejected, the smaller the chances that the
research hypothesis—according to which the distribution is not random—is wrong. Basic
statistical theory includes the z-test and t-test, in which two numbers z and t are deter-
mined by using formulas and then looked up in tables to find a corresponding p-value
between 0.00 and 1.00 that expresses how probable it is that a distribution is random.
Subtracting that number from 1 naturally yields the probability that the distribution is not
random. For example, if a distribution has a probability of 0.99 or 99% of being random,
the probability that it is not random is 0.01 (1 – 0.99) or 1%.
In the winter and spring of 2010, David Sheffield, an undergraduate physics major at
Brown University (class of ’11), took a tutorial with me on calendars and chronology of
the ancient world. When the subject of the present paper came up, he volunteered to per-
form the z-test and the t-test and produced probabilities of less than 1% that the above
distribution is random, noting that probabilities of less than 5% are generally considered
significant and probabilities of less than 1% highly significant. But he also cautioned that
the low number of data may affect the degree of probability and that additional analysis of
the statistical kind remains desirable.
Leo Depuydt
140
At the very least, it needs to be said that statistical considerations do not undermine the
value of the empirical data derived from double dates in their capacity as evidence. It seems
to me that they rather strengthen it.
6.9. Excursus 2: How Do Individual Modern Dates of Lunar Day 1 Relate to First Invisibil-
ity of the Old Crescent?
As has been noted above, when it comes to the average time interval between conjunc-
tion and 6:00 a.m. of the morning that begins daylight of lunar Day, there is a distinct
difference between the Egyptian lunar calendar and the Greek lunar calendar. Greek lunar
months appear to begin on average roughly a day later than Egyptian lunar months. In the
footsteps of Pritchett, the difference was explained as follows. It was assumed that ancient
Egyptians in principle began lunar Day 1 right away in the morning when the old crescent
was no longer visible. At the same time, it was assumed that, that very same morning, an-
cient Athenians in principle decided instead that daylight of lunar Day 1 would begin the
next morning, a day later. The one-day delay in the Athenian calendar inevitably follows
from the fact that ancient Athenians gave the same name to the last day of both 29-day and
30-day lunar months. There is no trace of a similar procedure in the surviving day names
of the native Egyptian lunar calendar. In 29-day months, Athenians did not use the name
that Day 29 had in 30-day months. Lunar day 29 thus was named differently in 29-day and
30-day months. Consequently, it was necessary to decide what to name Day 29 at the latest
by the morning that began the 29th period of daylight of the month.
The following crucial question has remained unanswered: Does the morning in which
the old crescent is for the first time invisible begin daylight of lunar Day 1 in the Egyptian
lunar calendar, on the one hand, and daylight of the last day of the month, either the 29th
or the 30th, in the Greek lunar calendar, on the other hand? The date of the morning of
first invisibility of the old crescent can be computed with much probability. However, in-
visibility can be marginal. It then seems advisable to propose two dates, one more probable,
one less probable, for the morning of first invisibility in order to achieve something like
very high probability. In such cases, it is scientifically impossible to date first invisibility to
one single date with very high probability. In addition, historically speaking, even if the old
crescent could no longer be seen, certain circumstances may have prevented watchers from
establishing whether it was or was not visible. Such circumstances, when they applied, will
forever remain unknown.
In what follows, I use the dates for last visibility of the old crescent yielded for the
location of Cairo (30°00' N and 31°17' E) and for a visibility arc of 11°30' by a program
created by Lange and Swerdlow42 as well as the dates of first invisibility of the old crescent
computed by Peter J. Huber for “a location near Memphis (30° E, 30° N)”.43 Naturally, last
visibility falls a day before first invisibility. One is therefore readily derived from the other.
Lange’s and Swerdlow’s program produces a single date for the morning of last visibility of
the old crescent. On the other hand, Huber gave a second possible date of first invisibility
of the old crescent in instances in which invisibility is marginal, that is, in three of the eight
instances of Day 1 of an Egyptian lunar month listed in table 1, namely nos. 1, 2, and 4.
Let us first consider the eight dates of lunar Day 1 according to the Egyptian lunar
calendar. If the calendrical mechanism described above were flawlessly applied, one would
expect the eight modern dates of Day 1 of an Egyptian lunar month listed in table 1 to be
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 141
the date of the morning of first invisibility of the old crescent. Is this so? Yes, but only in
five out of eight instances, or 62.5%, according to the Lange-Swerdlow dates (nos. 1, 3, 4,
7, and 8) and only in four out of eight instances according to Huber’s primary date (nos. 1,
3, 7, and 8). Then again, in no. 4, Huber offers the Lange-Swerdlow date as an alternative
date of lower probability. In the three other instances, the lunar month twice begins a day
later (nos. 5 and 6) and once two days later (no. 2) according to both the Lange-Swerdlow
dates and the Huber dates. However, Huber offers a date that is only one day later as an
alternative for no. 2. Incidentally, his third alternative date is a day before first invisibility
for no. 1.
In sum, computations indicate that the following picture has a certain undeniable prob-
ability of being true: the lunar month begins in the morning of first invisibility in five
instances and one day later in three instances. In other words, the score is not perfect. The
Egyptian lunar dates begin a little later than one might expect from a perfect execution of
the calendrical mechanism, three days in eight instances, or 0.375 days on average. There
is every reason to assume that it is possible that the calendrical mechanism was not flaw-
lessly applied. Conditions for watching out for invisibility may have been marginal or even
entirely wanting. It cannot be excluded that the inability to make a decision whether the
day should be 29 days or 30 days long resulted in choosing 30 over 29 as the length of the
day because 30 is the ideal length of the month. Such a mind set would result in a calen-
dar running slightly later than one in which the afore-mentioned calendrical mechanism
was perfectly applied. At the next turn of the month, first invisibility of the old crescent
would then tend to occur earlier than it otherwise would have, perhaps even before the
morning that begins the daylight period that follows the 29th daylight period. The natural
choice would then obviously be to make the month 29 days long, thus compensating for a
month that may have been longer than it otherwise should be. Nothing is easier to assume
the distinct possibility of such scenarios. But in the end, we will never know every detail
about what happened at the end of a lunar month in terms of deciding the beginning of
the next.
It will also never be known whether fixing the beginning of the lunar month might on
occasion in any way have been influenced by trying to have the new crescent be visible in
the evening that follows daylight of lunar Day 2, called Abd in Egyptian. There is evidence
that the Egyptians at least sometimes assumed that the new crescent would be visible that
evening.44 But then, the name of lunar Day 3, mspr, is perhaps derived from spr “arrive”;
Parker therefore considered it possible that the name refers to the occasional arrival of
the new crescent on that day.45 Someone who carefully observed the change in distance
between the moon and the sun, on average a little over 12° per day, and who also had some
idea of how far the moon needed to be removed from the sun to be visible might perhaps
have been able to estimate in which evening the new crescent was most likely to be vis-
ible for the first time and consequently give advice as to when to begin the lunar month
to make sure that the new crescent would be visible in the evening following daylight of
Abd. Any such effort would cause the beginning of the lunar month to fall later than a
beginning determined by the calendrical mechanism described above. That is because the
interval between the morning of first invisibility of the old crescent and the evening of first
visibility of the new crescent is one and a half days in about 54.18% of the cases and two
and a half days in about 44.30% of the cases.46 In the latter 44.30% of the cases, the lunar
month would need to begin one day later than first invisibility of the old crescent in the
Leo Depuydt
142
morning, that is, one day later than a beginning determined by the calendrical mechanism
described above. Visibility in the evening following daylight of Abd is possible according
to a somewhat meager four of Huber’s dates (nos. 3, 4, 7, and 8), of which one (no. 3) is
the primary date of two possible dates, and also according to four of the Lange–Swerdlow
dates. In other words, there is no recognizable influence from visibility of the new crescent
in the evening following daylight of Abd.
It will also never be known whether aiming to have conjunction fall on psπdntyw might
have played a role. Conjunction is an invisible event, except at solar eclipses. Still, anyone
keenly observing the moon approaching the sun by a certain amount every day might have
some notion of the day on which the moon would join the sun. But as it happens, if day-
light of psπdntyw always begins in the morning of first invisibility of the old crescent, 6:00
a.m. of that morning will on average fall about half a day before conjunction (see below).
Lunar Day 1 will therefore typically be the day on which the moon joins the sun and also
a day on which the moon is invisible both in the morning before sunrise and the evening
after sunset.
Let us next consider the 20 dates of lunar Day 1 according to the Greek lunar calendar.
The 20 modern dates of Day 1 of a Greek lunar month yielded by the 32 modern double
dates listed in table 2 are as follows (years are BCE): (1) 17 Aug 264; (2) 21 May 257; (3)
27 Oct 257; (4) 24 Jan 256; (5) 23 Feb 256; (6) 22 Jun 256; (7) 18 Sep 256; (8) 13 Jan 255;
(9) 1 May 254; (10) 13 May 255; (11) 9 Jul 255; (12) 2 Apr 254; (13) 27 Aug 254; (14)
16 Jul 253; (15) 31 Dec 252; (16) 29 Mar 251; (17) 23 Aug 251; (18) 22 Jun 256; (19) 30
Nov 249; and (20) 26 Jan 248. If the calendrical mechanism described above were flaw-
lessly applied, one would expect these 20 dates to be the date of the morning that follows one
day after the morning of first invisibility of the old crescent. Is this so? Yes, but only in eight
out of 20 instances, or 40%, according to the Lange-Swerdlow dates and Huber’s primary
dates (nos. 1, 3, 4, 5, 8, 13, 15, and 17).
In 11 of the other 12 dates, the Lange-Swerdlow dates and Huber’s primary dates are
the same. Six of these 12 dates (nos. 6, 7, 9, 16, 18, and 20) fall two days after the morning
of first invisibility, or one day too late to accord with the calendrical mechanism described
above. One (no. 10) falls three days after the morning of first invisibility, or two days too
late to accord with the calendrical mechanism. One (no. 19) falls four days after the morn-
ing of first invisibility, or three days too late to accord with the mechanism. Two (nos. 11
and 14) are the dates of the morning of first invisibility itself and therefore fall one day too
early to accord. And one (no. 2) falls one day before first invisibility, or two days too early
to accord.
In one of the 13 dates (no. 12), the Lange-Swerdlow date and Huber’s primary date dif-
fer. The Lange-Swerdlow falls two days after the morning of first invisibility, or one day too
late to accord with the calendrical mechanism. Huber’s primary date falls three days after
the morning of first invisibility, or two days too late to accord. However, Huber’s second-
ary date is the same as the Lange-Swerdlow date.
The fact that only eight of the 20 dates accord with the postulated calendrical mecha-
nism at first sight does not seem to bode well for this paper’s research hypothesis, even if
these eight dates still constitute the most frequent case, edging out the six cases in which
the lunar month begins a day later than the calendrical mechanism requires. However, the
picture changes significantly as soon as one does two things. I believe that neither of these
two things can be interpreted as manipulating the data. The first thing is to take Huber’s
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 143
secondary dates into consideration. The second thing is to consider what has been said
above about the problems that affect six of the 20 dates.
First, Huber’s secondary dates. There are five. In four of them (nos. 5, 11, 14, and 15),
first invisibility happens a day earlier. In one of them (no. 12), it happens a day later. Hu-
ber’s secondary dates may be less probable than his primary dates. However, both ulti-
mately exhibit a certain probability and both therefore deserve to be considered as distinct
possibilities. It has been noted above that, according to Huber’s primary date, two dates
(nos. 11 and 14) are those of the morning of first invisibility itself and therefore fall one
day too early to accord with the calendrical mechanism. As it happens, according to Hu-
ber’s secondary date, the dates fall a day later and therefore do accord. The number of dates
that accord hence rises to 10 out of 20. Moreover, one date that falls two days too late (no.
12) falls only one day too late according to the secondary date. The following optimal
picture therefore has a certain probability of being true. Besides the 10 dates that accord
(nos. 1, 3, 4, 5, 8, 11, 13, 14, 15, and 17), seven fall one day too late (nos. 6, 7, 9, 12, 16, 18,
and 20); one (no. 2), two days too early; one (no. 10), two days too late; and one (no. 19),
three days too late.
The second thing is to consider what has been said above about the problems that affect
six of the 20 dates (nos. 2, 9, 14, 15, 18, and 19). For example, the date that is two days too
early (no. 2) and the date that is three days too late (no. 19) are either much too early or
much too late by any measure. It is not clear what caused these deviations. If one eliminates
these two from consideration, the following picture emerges: 10 dates accord (nos. 1, 3, 4,
5, 8, 11, 13, 14, 15, and 17); seven fall one day too late (nos. 6, 7, 9, 12, 16, 18, and 20);
and one (no. 10), two days too late. If one eliminates all of the six problematic dates from
consideration, the following picture emerges. Eight dates, or about 57.1%, accord (nos. 1,
3, 4, 5, 8, 11, 13, and 17); five, or about 35.7% fall one day too late (nos. 6, 7, 12, 16, and
20); and one (no. 10), two days too late. There is again no compulsion to assume that the
calendrical mechanism was flawlessly applied. Bad conditions for watching the old cres-
cent might well have produced 30-day lunar months when a 29-day lunar month would
have accorded better with a strict application of the calendrical mechanism.
Could attempts to have first visibility of the new crescent fall in the evening following
daylight of lunar Day 1 have played a role? According to 12 of Huber’s dates (nos. 1, 3, 4, 5,
8, 9, 12, 13, 15, 16, 17, and 20), of which two are secondary dates (nos. 1 and 12), visibility
at that time is a possibility. If one eliminates the six dates affected by problems (see above),
visibility is possible in 10 dates (nos. 1, 3, 4, 5, 8, 12, 13, 16, 17, and 20) out of fourteen, or
71.4%. In three of the four others (nos. 6, 7, and 10), visibility was possible the day before;
in one (no. 11), the day after.
It was occasionally assumed in ancient Greece that conjunction fell on the last day of
the lunar month.47 Could aiming to have conjunction fall on that day by following the
regression of the moon in relation to the sun in the days before conjunction have played a
role in fixing the beginning of the lunar month? Possibly. But as it happens, if the calendri-
cal mechanism described above was flawlessly applied, 6:00 a.m. of the morning of the last
day would on average fall about half a day before conjunction (see below). Conjunction
would therefore typically fall on the last day of the month. Even if the fact that conjunction
tends to fall on the last day of the month followed unintentionally from the application of
said calendrical mechanism, at least some ancients may have viewed that fact as a welcome
consequence.
Leo Depuydt
144
In six out of 20 dates (nos. 6, 7, 10, 12, 18, and 19), sighting the new crescent in the
evening before daylight of lunar Day 1 is possible. But the number is not sufficiently high
to justify that the Greek calendar operated by first visibility of the new crescent as is now
universally assumed.
7. More Modern Dates of Day 1 of Egyptian Lunar Months
So far, eight modern equivalents of Day 1 of an Egyptian lunar month have been sub-
jected to examination in order to establish when in relation to the lunar cycle Egyptian
calendrical months began. The sample is admittedly rather small. Additional data seem
desirable. Among other data relevant to establishing when Egyptian lunar months began
is an interesting set of 32 complete or incomplete temple service dates of Ptolemaic or Ro-
man times recently assembled and studied in detail by Bennett.48 A temple service date is a
day number signifying the position of the day in question in a specific term of service in a
temple. The term of service was called wrš in Egyptian. For example, a temple service date
may identify a certain day as Day 12 of the wrš.
Temple service dates are not Egyptian lunar dates in the strict sense and they make no
explicit reference to the Egyptian lunar calendar. But since the terms of service in question
began on a certain day at the beginning of the lunar month and lasted a lunar month,
temple service dates are no doubt lunar in character. A full understanding of the Egyp-
tian lunar calendar therefore requires an analysis and correct understanding of the related
temple service dates.
It is not at once clear whether the temple service dates can be adduced as evidence
in support of the theory of the relation between Egyptian lunar calendar and the Greek
lunar calendar adopted and defended in this paper. The principal problem is that there is
some uncertainty as to whether the temple service began on lunar Day 1, called psπdntyw
in Egyptian, or on lunar Day 2, called Abd in Egyptian. Two facts for which there is some
evidence are as follows. First, on the one hand, computation indicates that the beginnings
of the temple service terms accord well with the day that follows the day of first invisibility
of the old crescent.49 Second, on the other hand, there is fairly good evidence, including the
eight lunar dates derived from double dates above, that Egyptian lunar months began a day
earlier with first invisibility.50 These two facts can be reconciled in one of two ways. Either
the temple service begins on Day 2. Or the temple service dates are evidence of a second
lunar calendar beginning on Abd . The second explanation seems unlikely. First, some of
the lunar dates derived from double dates are also found in temples and yet their months
begin on psπdntyw. It therefore seems improbable that two lunar calendars whose months
had different beginnings were operative in temples. And second, Luft has produced valid
arguments that the temple service began on Abd in the Middle Kingdom.51 Why would the
beginning have been different in later times? In sum, the first explanation is to be preferred
and in fact will be in what follows.
Bennett analyzes 32 modern dates of lunar Day 1 derived from temple service dates.52
Of those 32, five are described as “complete” and 20 as “incomplete”. Seven more dates are
those that Bennett considers sufficiently certain among all the dates that can be derived
from evidence found at Dime.53 Only the five “complete” dates and the seven sufficiently
certain dates from Dime are considered here. They are listed in table 4. Conjunction
falls on average 11 hours 13 minutes 45 seconds after 6:00 a.m. in the morning at the
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 145
beginning of daylight of Day 1. Clearly, the lunar month begins on average at least a day
earlier than the beginnings of the lunar month derived from Greek documents listed in
table 2. Furthermore, in 10 cases out of 12, daylight of lunar Day 1 begins in the morning
of the most probable date for first invisibility of the old crescent. All these empirical data
accord well with the research hypothesis of the present paper.
In the modern dates of Day 1 of Egyptian lunar months listed in table 1, conjunction
falls on average 1h 06m 30s after 6:00 a.m. in the morning that begins daylight of lunar
Day 1. This is 10h 7m 15s later than the average interval derived from the modern dates
of Day 1 of Egyptian lunar months in table 3. This gap seems significant. Then again, of
the 20 Egyptian dates listed in tables 1 and 4, no. 2 in table 1 is significantly irregular. If
just this one date is omitted from consideration, the 10-hour gap between the average in-
terval derived from the dates in table 1 and the average interval derived from the dates in
table 4 is roughly cut in half. I see therefore no reason to assume that different calendrical
mechanisms produced the dates of table 1, on the one hand, and those of table 4, on the
other hand. The average interval derived from all 20 dates in tables 1 and 4 is minus 7h
10m 51s.
III III IV V
Modern Date of
Lunar Day 2 (=
Service Day)
Modern Date of
Lunar Day 1 (Day-
light)
Closest Conjunc-
tion (Daylight)
Distance in
Hours from
Conjunction
to 6:00 a.m.
in Morning of
Lunar Day 1
Morning of
First Invis-
ibility of the
Old Crescent
1. Bennett no. 1 24 Dec 56 B CE 23 Dec 56 B CE 23 Dec, 11:17 a.m. – 5h 17m 23 Dec
2. Bennett no. 2 22 Jan 55 BCE 21 Jan 55 BCE 22 Jan, 2:16 a.m. – 20h 16m 21 Jan
3. Bennett no. 3 29 Aug 48 BCE 28 Aug 48 BCE 28 Aug, 5:30 a.m. + 0h 30m 28 Aug
4. Bennett no. 4 3 Feb 37 BCE 2 Feb 37 BCE 2 Feb, 10:31 a.m. – 4h 31m 2 Feb
5. Bennett no. 5 13 Apr 66 CE 12 Ap 66 CE 13 Apr, 9:52 a.m. – 25h 52m 12 Apr
6. Bennett no. 26 7 Feb 24 BCE 6 Feb 24 BCE 7 Feb, 1:24 a.m. – 19h 24m 6 Febr
7. Bennett no. 27 8 Mar 24 BCE 7 Mar 24 BCE 8 Mar, 4:33 p.m. – 32h 33m 7 Mar
8. Bennett no. 28 15 Nov 68 CE 14 Nov 68 CE 13 Nov, 8:20 p.m. + 9h 40m 13 Nov
9. Bennett no. 29 14 Dec 68 CE 13 Dec 68 CE 13 Dec, 11:45 a.m. – 5h 45m 13 Dec
10. Bennett no. 30 20 Mar 90 CE 19 Mar 90 CE 20 Mar, 1:59 a.m. – 19h 59m 19 Mar
11. Bennett no. 31 19 Apr 90 CE 18 Apr 90 CE 18 Apr, 3:50 p.m. – 9h 50m 18 Apr
12. Bennett no. 32 9 Apr 91 CE 8 Apr 91 CE 8 Apr, 7:28 a.m. – 1h 28m 7 Apr
T 4. More Modern Dates of Lunar Day 1 of Egyptian Lunar Months. For details and biblio-
graphical references pertaining to the sources from which the modern dates of lunar Day 1 have been
derived, see Bennett (2008). The times for conjunction are Goldstine’s (1973) for Babylon, adjusted
for Memphis by subtracting 53 minutes.
Leo Depuydt
146
In table 5 below, spatial distribution is used to evoke the difference between lunar Day
1 according to the Egyptian lunar calendar and lunar Day 1 according to the Greek lunar
calendar, as in table 3, but now including the temple service dates. That means that 20
Egyptian dates are now compared to 20 Greek dates. As in table 3, each instance of the
letter E represents an Egyptian lunar date; each instance of G, a Greek lunar date. The
Egyptian dates derived from temple service dates are represented by Es, rather than by just
E. The position of the letter indicates where 6:00 a.m. of the morning that begins daylight
of lunar day 1 is located in relation to conjunction. David Sheffield notes that, based on the
z-test, it is less than 0.0001% probable that this distribution is pure coincidence.54
from – 40h to – 30h: Es
from – 30h to – 20h: E Es G
from – 20h to – 10h: E E Es Es Es
from – 10h to 0h: E E Es Es Es Es Es G G
—————— conjunction ——————
from 0h to + 10h: E E Es Es
from + 10h to + 20h: E G G G G G G
from + 20h to + 30h: G G G G G
from + 30h to + 40h: E G
from + 40h to + 50h: G G G G
more than 80h: G
T 5. Locations of 6:00 a.m. of Lunar Day 1 in relation to Conjunction (E = Egyptian lunar
date; Es = Eg yptian lunar temple service date; G = Greek lunar date).
8. More Modern Dates of Day 1 of Greek Lunar Months
There is additional evidence that pertains to how the beginning of ancient Greek lunar
months was determined, but not much. This evidence includes a number of modern dates
of lunar Day 1 that can with some probability be derived from the extant sources. Most
prominent among them are seven month and day dates of astronomical events found in
Ptolemy’s Almagest. The dates are according to a lunar calendar whose month names are
Greek. In four of the dates, the month names are Athenian; in three dates, Macedonian.
Ptolemy provides the lunar date’s equivalent in the Egyptian civil calendar. Since the mod-
ern date of the Egyptian civil date is known, so automatically are the modern date of the
lunar month and day date and also the modern date of lunar Day 1 of the month in ques-
tion. It is then possible to establish how the beginning of the month relates to conjunction
and to lunar visibility and invisibility. The seven derivations are presented in table 6. What
is in italics is actually in the text.
Owing to certain complications, the value of the seven dates as evidence is mixed. For
example, not everyone associates the seven instances of lunar Day 1 with the same mod-
ern dates, partly in consequence of differences of opinion as to when the day begins in
antiquity.55 In fact, three of the seven dates are in all probability to be disqualified at once
as evidence of the Greek lunar calendar. The Macedonian lunar month names in nos. 1,
2, and 3 in table 6 are in all probability Greek in name only. The three dates are said to
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 147
III III IV VVI VII
Location
in the
Almagest
“Greek”
Lunar Date
Egyptian
Date
Equated with
Lunar Date
in II
Modern
Date of the
Egyptian
Date in III
Date of
Daylight
of Lunar
Day 1
Closest
Conjunction
Date of First Invisibility
of the Old Crescent
(FIOC) or First
Visibility of the New
Crescent (FVNC)
1. IX 7.10 5 Apellaios
at dawn
(Babylo-
nian!)
Thoth (night
of ) the 27th
to the 28th
night of 18
to 19 Nov
245 BCE
(dawn)
15 Nov 13 Nov, 1:22 a.m.
(Babylon!)
evening of 14 Nov
(FVNC)
2. IX 7.9 14 Dios
at dawn
(Babylo-
nian!)
Thoth (night
of ) the 9th to
the 10th
night of 29
to 30 Oct
237 BCE
(dawn)
17 Oct 15 Oct, 10:25 p.m.
(Babylon!)
evening of 16 Oct
(FVNC)
3. XI 7 5 Xanthikos
in the
evening
(Babylonian
month!)
14 Tybi 1 Mar
229 BCE
(evening)
26 Feb 24 Feb, 11:17 a.m.
(Babylon!)
evening of 25 Feb
(FVNC)
4. VII 3 25 Poseideon 16 Phaophi 20 Dec
295 BCE
26 Nov 26 Nov, 8:31 a.m.
(Alexandria)
morning of 26 Nov
(FIOC)
evening of 27 Nov
(FVNC)
5. VII 3 15
Elaphebo-
lion
5 Tybi 9 Mar
294 BCE
23 Feb 23 Feb, 2:47 a.m.
(Alexandria)
morning of 21 Jan
(FIOC)
evening of 23 Jan
(FVNC)
6. VII 3 8 Antheste-
rion
29 Athyr 29 Jan
283 BCE
22 Jan 22 Jan, 11:51 a.m.
(Alexandria)
morning of 21 Jan
(FIOC)
evening of 23 Jan
(FVNC)
7. VII 3 25 Pyanep-
sion
7 Thoth 8 Nov
283 BCE
15 Oct 14 Oct, 2:02p.m.
(Alexandria)
morning of 14 Oct
(FIOC)
evening of 16 Oct
(FVNC)
T 6. Seven Modern Dates of Lunar Day 1 Derived from Ptolemy’s Almagest. Text in italics is in
the Greek text of the Almagest. In dating certain night-time events, Ptolemy uses so-called “double
dates” of the type “Thoth (night of ) the 9th to the 10th” (Almagest IX 7.9). There is more than one
interpretation of what exactly Ptolemy means by a double date. But, in any event, double dates never
leave any doubt about which night Ptolemy is referring to.
Leo Depuydt
148
be “according to the Chaldaean calendar”. The calendar of the dates in nos. 1, 2, and 3 is
therefore presumably the Babylonian calendar whose month names have been replaced
by Macedonian month names; after Alexander’s conquest, the use of Macedonian month
names spread to much of his empire. As it happens, the lunar months of dates nos. 1, 2 and
3 begin one or two days later than the Greek lunar months found in double dates discussed
above—at least according to the specific assumptions according to which their beginnings
were obtained (see below)—and so do lunar months in Babylonian astronomical texts. As
to establishing the modern date of daylight of lunar Day 1, a detailed discussion exceeds
the scope of the present paper and it is not clear thatthere is a certain solution. According
to one scenario, the day numbers 5, 14, and 5 of the lunar dates 5 Apellaios, 14 Dios, and
5 Xanthikos were found in Babylonian astronomical texts, but they were accompanied
by the equivalent Babylonian lunar month names. Babylonian astronomy was thriving in
the third and second centuries BCE. The three day numbers were somehow transmitted
to Ptolemy in the second century CE. In the translation from Babylonian to Greek, the
Babylonian month names were replaced by Macedonian month names. In Babylonian as-
tronomical reports, the description of what happens at night precedes the description of
what happened in the daylight period with the same day number. Accordingly, daylight
of 5 Apellaios, 14 Dios, and 5 Xanthikos would be daylight of 19 November, 30 October,
and 2 March.56
But new evidence contradicts this theoretical scenario in one respect. A Babylonian
astronomical tablet reveals that the Babylonian name of the Xanthikos at hand was Add-
aru, that this Addaru began in the evening of 25 February 229 BCE, and that daylight of
1 Addaru was 26 February (Jones (2006), p. 269; I owe this reference to a personal e-mail
communication by Chris Bennett of December 14, 2011). Ptolemy’s Egyptian civil date
leaves no doubt that the Xanthikos observation took place in the evening of 1 March 229
BCE, which is the evening of 6 Addaru in Babylonian astronomical texts. Yet, Ptolemy
dates the observation to lunar 5 Xanthikos; he must have found the date in an earlier source.
Jones (2006), p. 269 observes that “the observation report should actually correspond to
February 29”. Bennett (2011), p. 34 suspects a “conversion error”. But he also considers it
possible that “the conversion is correct”, stating,
If so, the two calendars cannot be identical, although to all appearances they are closely related.
For example, the ‘Chaldean calendar’ might have been a schematic Greek astronomical calendar.
Alternately, the ‘Chaldean’ dates can be simply reconciled mathematically with both the Babylonian
calendar and the Egyptian dates for the recorded observations of Mercury and Saturn by supposing
that they used a dawn epoch, i.e. that a ‘Chaldean’ date began at dawn on the corresponding Baby-
lonian date. (p. 35)
In any event, it is now certain that, in the date 5 Xanthikos, the month can be Babylo-
nian but the day number cannot.
I believe that the difference in lunar day date can be accounted for as follows. In Ptole-
my’s chronological system, the evening following daylight of Day x is always the evening of
Day x, and not the evening of Day x + 1 as it is in Babylonian astronomical texts. In other
words, the day date does not change at sunset as it does in Babylonian astronomy. Anyone
converting Babylonian dates of observations into Egyptian civil dates must have known
which Babylonian daylight day numbers corresponded to which Egyptian daylight day
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 149
numbers and must also have been used to systematically decreasing the day number by one
for evening events. This procedure could easily have been applied, perhaps automatically
so, to lunar Addaru when converting it into Macedonian Xanthikos. In other words, there
can have been no doubt at the time of conversion that daylight of 5 Addaru was daylight
of Egyptian civil 14 Tybi and that the Babylonian and Egyptian dates of the observation
made in the evening immediately following this daylight period were 6 Addaru and 14
Tybi. The lunar day number changed but the Egyptian civil day number did not. It would
have been more than tempting to leave the day date unchanged at sunset in the lunar date
as it is in the Egyptian date. Furthermore, it is highly improbable that the day date changed
at sunset anywhere outside the highly technical context of Babylonian astronomy. Chang-
ing 6 Xanthikos into 5 Xanthikos cannot cause confusion because the lunar date does not
date the observation. The Egyptian civil date does.
The dates for daylight of Day 1 in nos. 1, 2, and 3 in table 6 have been obtained on the
reasonable assumptions that the day numbers of the three lunar dates and the day number
of the Egyptian civil dates refer to the same daylight periods and that day numbers did not
change at sunset in the lunar dates as they surely did not in the Egyptian civil dates. Con-
sequently, the dates of daylight of 5 Apellaios, 14 Dios, and 5 Xanthikos are 19 November,
30 October, and 1 March, and the dates of daylight of 1 Apellaios, 1 Dios, and 1 Xanthikos
are 15 November, 17 October, and 26 February.
As suggested elsewhere in this article, I consider the epoch to be a ghost concept. Even
for astronomers like Ptolemy, the day basically began in the morning and ended in the
evening and extensions of activity to before sunrise or dawn and to after dusk or sunset
were included. Nighttime was in principle a numberless stretch of darkness. Accordingly,
dating nighttime events was always a problem. Ptolemy’s use of double dates, as in “(in the
night) from the 5th to the 6th”, was one way of avoiding all ambiguity as to which night
was meant. While avoiding ambiguity was the design of double dates, their linguistic ex-
pression suggests that the night was itself not numbered. The “5th” and the “6th” in the
expression above may well mainly refer to daylight periods.
I do not believe that, in actual calendrical practice, there was ever any focus at any time
in antiquity on a single point in time returning once every 24-hour cycle and serving as
the end of one 24-hour cycle and the beginning of another 24-hour cycle, a so-called ep-
och. Ancient epochs owe their existence largely to ancient reports on the beginning of the
day by mostly Latin authors, including Censorinus, Gellius, Pliny, and Varro—with Varro
firmly at the origin of them all. It seems to have satisfied Varro’s sense of orderliness or de-
light in exotic detail to assign different beginnings of the day to different nations. I believe
that, in doing so, he created a pseudo-concept. True epochs came into existence only later
with the advent of midnight as the beginning and end point of a 24-hour system. In the
confines of astronomy, a noon epoch was also used to fit all the events of a single night
conveniently into the same day. But the concept of the epoch should not be projected back
into the ancient past, it appears to me. True, in Babylonian astronomy, nighttime precedes
daylight with the same number. But does that have to mean anything more than just that?
The four other lunar dates are Greek, in the sense that they were recorded by the Greek-
speaking Timocharis in Greek-speaking Alexandria. It is again assumed that the day num-
bers of the lunar dates and the day numbers of the Egyptian civil dates refer to the same
daylight and that day numbers did not change at sunset in the lunar dates as they surely
did not in the Egyptian civil dates. Accordingly, two of the four lunar months begin in
Leo Depuydt
150
the morning of first invisibility of the old crescent, which according to what has been said
above accords better with the Egyptian lunar calendar than with the Greek lunar calendar.
Two of the four lunar months begin in the morning following the morning of first invis-
ibility of the old crescent, which accords better with the Greek lunar calendar. It is not fully
clear what exactly to make of this. In any event, the four dates provide additional evidence
that daylight of Day 1 of Greek lunar months did not begin in the morning after the eve-
ning of first visibility of the new crescent.
Three more possible modern dates of daylight of Day 1 of Greek lunar months are as
follows. First, there is good evidence that the modern date of the first daylight period of
the first Callippic cycle is 28 June 330 BCE.57 The morning of first invisibility of the old
crescent is 27 June. Daylight of lunar Day 1 therefore begins in the morning that follows
the morning of first invisibility of the old crescent, as is common in the Greek lunar dates
derived from double dates studied above. Second, reports survive that Meton observed the
summer solstice of 432 BCE on 13 Skirophorion.58 The solstice occurred in the morning
of 28 June. If Meton observed the solstice on the correct day, which seems distinctly pos-
sible,59 then daylight of 1 Skirophorion is 16 June. The morning of first invisibility of the
old crescent is 16 June. This lunar date could therefore serve as evidence that Greek lunar
months begin before first visibility of the new crescent.
The third date concerns the decisive battle at Gaugamela, in which Alexander defeated
Darius III, and Greece turned the tables on Persia after two centuries of strife. Accord-
ing to the best possible chronological information, namely Babylonian astronomical texts,
the battle was fought in the morning of Day 24 of the Babylonian lunar month Ululu.60
But according to Plutarch (Life of Camillus 9.15), the battle took place on Day 26 of the
Athenian lunar month Boedromion. The battle was fought far from Greece. But then, one
of the two armies waging the battle right there and then was Greek and its soldiers would
know what day of the month it was according to a Greek calendar. It was a glorious day
that they would want to remember long after. If the date is accepted as historical, the Greek
lunar month began two days earlier than the Babylonian astronomical lunar month. This
is altogether normal. According to computations I owe to Peter J. Huber,61 such a two-day
interval ought to occur on average in about 44.30% of the cases. But a one-day interval is
also normal. It is expected to occur in about 54.18% of the cases.
The Babylonian date leaves no doubt that the battle was fought during daylight of 1
October 331 BCE. Daylight of Day 1 of Boedromion therefore falls on 6 September of
that year. The morning of first invisibility of the old crescent was 6 September at Mosul.
But visibility in the morning of 5 September seems to have been low. In any event, the
month could not have begun with first crescent visibility.
It is true that the view that first crescent visibility meant everything to the ancient
Greeks still dominates. Still, there is a certain awareness out there, which I have not tried to
document at great length, that the little that can be know about when Greek lunar months
begin, especially as it is derived from astronomical texts and as it has been evidenced above
by four lunar dates in Ptolemy’s Almagest and by the beginning of the first Callippic cycle,
points in a quite different direction. Among earlier testimonies of this same awareness is
Epping’s in his Astronomisches aus Babylon, a milestone in the study of ancient astronomy.
Epping writes that, “bei den Griechen”, the beginning of the month was determined “nach
dem mittleren Neumond”.62 Ideler, the greatest student of chronology of the nineteenth
century, observes about Greek lunar months that “ihr Anfang in der Regel dem ersten Tage
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 151
nach der Conjunction entsprach, wo sich das Mondlicht zuerst zu zeigen pflegt, ob es gleich
[modern obgleich es] nach der jedesmaligen Lage der Ekliptik auch wol erst am zweiten
oder dritten Tage nach der Conjunction sichtbar werden kann, wie Geminus richtig be-
merkt”.63
Modern dates of lunar Day 1 provide direct empirical evidence relating to the begin-
ning of ancient Greek lunar months. These dates leave no doubt that Greek lunar months
began before first crescent visibility. But there are two other types of evidence that indi-
rectly support the same notion. These two types cannot be reviewed in detail here.
The first type of evidence consists of ancient testimonies that, in the Greek lunar cal-
endar, the last day of the month, alternatively called vη κα vέα and τριακά, was the day of
conjunction, whereas, in the Egyptian lunar calendar, it was the first day, called psπdntyw.
Much of the evidence can be found gathered elsewhere.64
In fact, conjunction seems to have been viewed on occasion as a point in time heralding
the beginning of the month. The last day of Greek lunar months and the first day of Egyp-
tian lunar months sit astride that point in time. In that sense at least, the two belong not
only to the end of the previous month but also to the beginning of the following month.
They are “straddle” days, as it were. That would explain why Hesiod, in his Works and
Days, at 768, began his calendar with τριακά, as Pritchett observes, and not with lunar Day
1.65 That could also explain why, as J. F. uack proposes,66 wrš designated at the same time
the last day of the temple service and psπdntyw or lunar Day 1. Both τριακά and wrš were
interpreted as straddling the point in time when the moon joins the sun as marker of the
beginning of the month and hence had dual status as both an end and a beginning.67
The second type of evidence concerns the fact that the last day of 29-day and 30-day
lunar months had the same name. For example, a papyrus kept at Cornell University dat-
ing to the mid third century BCE contains a record of the amounts of lamp oil to be dis-
tributed every day for the two Macedonian lunar months Apellaios and Audnaios.68 The
editors note that, in the second month, “[t]he entry for the 29th is lacking”.69 Day “30” (λ)
therefore immediately follows Day “28” (λη). But evidently, as Pritchett first noted, what
happened instead is that the second month had 29 days and the first had 30.70 In a long
and at times heated debate that has lasted decades, some have defended the possibility that
a day name at the beginning of the last third of the month could be omitted instead. But
Pritchett always maintained that no such omission ever took place and I confidently follow
him in this regard.
9. A Test as Bridge between the Data and the Calendrical Mechanism
According to the empirical data pertaining to the Greco-Macedonian calendar presented
above, 6:00 a.m. in the morning that begins daylight of lunar Day 1 falls on average some-
where roughly between 17 and 25 hours, that is, about a day or a little less, after con-
junction. That means that the evening preceding daylight of lunar Day 1 falls on average
roughly only half a day or less after conjunction. No one doubts that an evening falling
at such a time generally occurs too soon for the new crescent to have been visible in it.
Accordingly, visibility of the new crescent cannot have determined the beginning of the
Greek lunar months in question. At the same time, no one would doubt that daylight of
lunar Day 1 generally falls too late for the morning that begins it to have been the morning
of first invisibility of the old crescent.
Leo Depuydt
152
In the footsteps of Pritchett, it was suggested that a peculiar calendrical mechanism
could account for the distance between 6:00 a.m. in the morning that begins daylight of lu-
nar Day 1 and conjunction and therefore also for the specific beginnings of the lunar months
in question, namely on average about a day later than Egyptian lunar months. According to
this calendrical mechanism, the morning of daylight of lunar Day 1 falls two days or 48
hours after the morning of last crescent visibility.
The question arises: What kind of average interval between 6:00 a.m. of Day 1 and
conjunction does the calendrical mechanism in question produce if it is rigorously ap-
plied? And how do these beginnings compare to those of the actual Greek lunar months
examined above?
It appears that there is no great difficulty in obtaining an ideal average interval. The
morning of last crescent visibility can be computed with fairly high probability. In fact,
one could even perform a test by using actual modern day observations. In the present case,
I have taken the average of the ages of the moon—that is, the distance in time from true
conjunction—in the morning of last visibility of the old crescent over a period of 18 years,
namely the years 1900 CE–1917 CE, or roughly one Saros cycle, for the location of Cairo,
using the program created by Lange and Swerdlow.71 After one Saros cycle, many proper-
ties of the course of the moon come full circle. This circumstance should make the average
more representative.
As average moon age I obtained about minus 35h 04m 07s, say minus 35 hours. The
specific intervals are between sunrise and conjunction. The average interval is therefore
between average sunrise, or 6:00 a.m., and conjunction. If the afore-mentioned calendri-
cal mechanism is rigorously applied, there are 48 hours from 6:00 a.m. in the morning of
last visibility of the old crescent to 6:00 a.m. in the morning of lunar Day 1. At the same
time, there are only about 35 hours from 6:00 a.m. in the morning of last visibility to
conjunction. It may be concluded that 6:00 a.m. in the morning of lunar Day 1 falls on
average about 13 hours (48–35) after conjunction. That average interval is fairly close to
the average interval of 17 to 25 hours derived from actual dates. What matters most is that
both average intervals occupy the same position in relation to three points in time in the
lunar month. First, both averages fall well after conjunction, between half a day and a day.
Second, they fall too early for first visibility of the new crescent to play a role. Third, they
fall too late for daylight of lunar Day 1 to begin immediately in the morning of first invis-
ibility of the old crescent.
It should be realized that the 13-hour interval involves an ideal application of the Greek
lunar calendar mechanism whereas an interval such as 17 to 25 hours is derived from actual
lunar dates. There is every reason to believe that methods of determining the beginnings of
lunar months were not always rigorously applied in actuality. Lack of rigor ought not have
been too much of an obstacle. After all, lunar months are always either 29 or 30 days long,
except in Rome, where they appear to have been either 29 or 31 days long.
If the beginning of the month strayed a little too far from new moon, it should have
been easy to restore the synchronism of the month with the lunar cycle by a specific choice
of either 29 or 30 as length of the next one or two months. There must also have been ob-
stacles to a precise application of the rule. Weather conditions may have made observation
impossible. Or someone might have neglected to observe the moon or made an error of
observation.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 153
10. First Visibility of the New Crescent in Mesopotamia: No Marker of the Month’s
Beginning
10.1. In Egypt and Greece, No; but also in Mesopotamia?
The three most prominent hubs of civilization in the west in the centuries before the rise of
Rome are Egypt, Greece, and Mesopotamia, as is obvious from the sheer number of extant
sources.
Evidence presented in the preceding sections shows that both Egyptian and Greek lu-
nar months on the whole began just too early for the new crescent to have been visible
in the evening immediately preceding daylight of lunar Day 1, with Greek lunar months
beginning about a day later than Egyptian lunar months. In other words, first visibility of
the new crescent was not used in principle to mark the beginning of the month. The design
of the present section is to argue that the same may well have been the case in ancient West
Asia. It may be time to question basic assumptions as to how the beginning of the lunar
month was determined in ancient West Asia and abandon centuries old conceptions.
A distinction applies between, on the one hand, watching the moon in all its phases
including the new crescent and, on the other hand, using the new crescent to determine
which daylight period is that of lunar Day 1. There is no lack of evidence that the moon
was watched in Mesopotomia. Many reports to this effect have survived.72 But to my
knowledge, nowhere is it stated explicitly in any source either that lunar months began
when the new crescent was first sighted or that the daylight period immediately following
that evening was daylight of lunar Day 1. Watching the overall behavior moon around new
moon, including the new crescent, could have served as a guarantee that the beginning of
the lunar month would not stray too far from new moon so that lunar months and lunar
cycles from new moon to full moon and back to new moon would mostly overlap with one
another. But that is not quite the same as using the first visibility of the new crescent to
determine lunar Day 1.
10.2. The Lunar Day 1 Immediately Following Alexander the Great’s Death
On June 11, 323 BCE, at 3:00 p.m.–4:00 p.m., or very close to that hour, Alexander the
Great died in Babylon.73 Babylonian astronomical texts leave no doubt that he died on the
last day of the month according to the Babylonian calendar, or that daylight of the next
day was daylight of lunar Day 1.74 If the beginning of the new Babylonian month was de-
termined by first visibility of the new crescent, then the new crescent ought to have been
for the first time visible just a few hours after Alexander’s death. That same evening, the
moon rose at 7:52 p.m., 50 minutes after sunset. However, computation reveals that the
new crescent could hardly, if at all, be seen that evening.
Lange and Swerdlow give 12 June as date of the evening of first visibility.75 They use a
visibility arc (“the altitude of the lower limb of the moon plus one third of the distance be-
tween the centers of moon and sun”) of 11.3° as lower limit for possible visibility. In their
opinion, “[t]his appears to work as well as any other method—no method is perfect—in
distinguishing visible from invisible; a few first visibilities have been seen at lower values
and a few not seen at higher values”.76 But it may be useful to test the limits by lowering the
visibility arc to below Lange’s and Swerdlow’s lower limit. In fact, when the arc is lowered
Leo Depuydt
154
from 10.66° to 10.65°, their program switches to June 11 as date of the evening of first
visibility. The phase of the moon—expressed as the percentage of the moon disk that is
illuminated—would be only 0.7% in the evening of June 11. The age of the moon—that
is, the distance in time from conjunction to the sunset immediately preceding first visibil-
ity—would be plus 15h 13m.77
The fact that visibility of the new crescent seems almost impossible in the evening that
follows Alexander’s death by a couple of hours presses the question: Did or did not the
month begin in Babylon with first visibility of the new crescent? A more general version of
this question is as follows: Did or did not the month begin anywhere in ancient West Asia
with first crescent visibility?
A number of general observations about the evidence are in order. They are presented
in the following sections. Together these observations constitute a line of argument favour-
ing the notion that the beginnings of lunar months in Mesopotamia were not narrowly
determined by first visibility of the new crescent.
10.3. Two Ways of Establishing the Relation of First Visibility of the New Crescent to Lunar
Day 1
There is no lack of ancient West Asian lunar dates. In fact, there is an abundance of them.
But only in the case of relatively few of these dates can it be established when exactly first
visibility of the new crescent occurred in relation to daylight of Day 1. There are basically
two ways in which the location of first crescent visibility in relation to lunar Day 1 can be
established: (1) Either a text explicitly states on what day of the month, as signified by a
day number, the moon was first seen again (for the sources transmitting such information,
see sections 10.11 and 10.13 below). (2) Or the lunar date and its corresponding lunar
Day 1 can be dated somehow in the modern Julian calendar (for the sources in which such
lunar dates are found, see sections 10.4–10 and 10.12 below). In other words, the ancient
lunar date is absolutely dated. It is now possible to compute with reasonably high prob-
ability where exactly first crescent visibility fell in relation to any Julian date in antiquity.
The same automatically also applies to any ancient lunar date whose Julian equivalent is
known.
Among the sources transmitting lunar dates whose Julian equivalent can be known, it
seems appropriate to distinguish between astronomical texts (see sections 10.4–10) and
non-astronomical texts (see section 10.12). The astronomical texts provide by far the most
such lunar dates. It is not clear to which extent the calendrical techniques used in astro-
nomical texts made an impact beyond the narrow confines of the temples in Babylon and
Uruk where the astronomers plied their trade. Babylonian astronomy was a highly sophis-
ticated intellectual art practiced by a secretive clan of astronomers. There is evidence that
Babylonian astronomers jealously guarded their science.78 Still, it is difficult to see how,
in Babylon and Uruk in the later first millennium BCE, astronomers could have used day
dates that differed from those used by the cities’ populations at large. Moreover, Babylon
was the cultural capital of Mesopotamia. It is therefore reasonable to assume that its cal-
endar was used outside its city walls. There is a small amount of evidence that calendrical
information was sent from major cultic centers.79 Then again, it seems out of the ques-
tion that the highly sophisticated calendrical techniques of Babylonian astronomy were
applied in communities all over West Asia. How many communities in the vast territory of
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 155
West Asia were anywhere close to a center of astronomy anyhow? Furthermore, the rules in
question could not have played a role before the time when they were invented in the first
millennium BCE
What is wrong with the assumption that, in much of West Asia most of the time, the
beginning of the lunar month was often determined by certain officials with the sole vague
requirement that lunar Day 1 stray not too far from new moon? Keeping it close should
have been easy by making specific choices of 29 or 30 as the length of the lunar month in
days. As a result, lunar Day 1 would oscillate around new moon. But such oscillation did
not have to cause dysfunction. What is wrong with the assumption that, in much of West
Asia most of the time, nothing was probably more common than for one of two months
associated with the same lunar cycle in two different cities to last 29 days and the other 30
days? And what is wrong with the assumption that, in much of West Asia most of the time,
nothing was probably more common than for two months associated with the same lunar
cycle in two different cities to begin one, two, or three days apart, probably rarely more?
Conversely, even if the calendrical techniques of Babylonian astronomy were not wide-
spread, they still might reflect practices prevalent over the centuries in Mesopotamian
communities at large.
10.4. The Beginning of the Month in Babylonian Astronomical Texts: The Recent Study of
the Subject
Just in the last couple of decades, our knowledge of Babylonian astronomy has advanced
considerably. One can almost speak of a Renaissance in the field. These advances have also
benefited our understanding of the beginning of lunar months. Even so, it has become ever
clearer that much still remains to be done when it comes to establishing how the sophisti-
cated Babylonian theories of the third and second centuries BCE were constructed out of
raw empirical data in earlier centuries. This stage of Babylonian astronomy is now called
the Intermediate stage, to distinguish it both from the more primitive astronomy of the
second and early first millennia BCE and the advanced theories of the third and second
centuries BCE.
It should be clear right at the outset that none of all this progress is contested in any
essential way in what follows. The present focus is on the relation between first visibility
of the new crescent and the beginning of the lunar month. The line of argument that is de-
veloped below about this relation is seen as somehow complementary to other statements
on the same subject.
A brief outline of recent work on the beginning of the lunar month is as follows. The
selection of pertinent studies cited below should lead to most everything else that is rel-
evant to the matter.
Owing in great part to efforts by Brack-Bernsen mainly relating to the astronomical
facet of the matter and by Hunger mainly relating to the philological facet of the matter,
it is now certain that Babylonian astronomers constructed rules to determine the begin-
ning of the lunar month beforehand and also what these rules are.80 Steele has established
that, “in an overwhelming number of cases”, different types of Babylonian of astronomical
texts “really did agree” on “the beginning and length of Babylonian months”.81 He con-
cludes from this “that during the Seleucid and Parthian periods the day of the beginning
of the month was always determined in advance”.82 Stern has devoted a detailed study to
Leo Depuydt
156
the relation between first crescent visibility of the new crescent and the beginning of the
new month as evidenced in the astronomical Diaries.83 The Diaries are day-by-day records
of what was observed in the nighttime and daytime skies. They hold much if not most of
the ultimate empirical foundation of Babylonian astronomical theories. Other important
observations of recent date on the beginning of the lunar month are found in studies by
Huber and Steele84 and by Britton.85 A recent survey by Steele appeared in The Oxford
Handbook of Cuneiform Culture.86
10.5. The Beginning of the Month and First Visibility of the New Crescent in Babylonian
Astronomical Texts
As to the beginning of the month in Babylonian astronomy, one has the impression that
the new crescent should have been generally visible in the evening preceding daylight of
the corresponding lunar Day 1. That would seem to confirm the notion that the daylight
period immediately following the evening of first visibility of the new crescent was daylight
of lunar Day 1.
Then again, the score is not perfect. Take the astronomical Diaries, in which what hap-
pens in the sky is reported day by day. It has long been known that there are cases in which
the lunar month appears to begin a little too early for the new crescent to have been vis-
ible already in the evening preceding daylight of lunar Day 1.87 What is happening here?
Sweeping these cases under the rug does not seem advisable.
It is also quite often stated in the Diaries that the new crescent was not seen in the
evening immediately preceding daylight of lunar Day 1 or sometimes also that one did not
even care to look out for it. Obstacles such as mist and clouds are often cited as the reason.
In regard to such cases, it is generally assumed that the possibility of visibility circumstanc-
es permitting was predicted.
10.6. The Time Interval Called NA in Babylonian Astronomical Texts
On the whole, sighting the new crescent is not nearly as prominent as one may have ex-
pected it to be if it was indeed the defining principle in determining the beginning of the
month. Thus, nowhere is it stated explicitly that it had that function. But instead of visibil-
ity, there is something else, related to first crescent visibility yet also distinct, that features
much more prominently in astronomical texts than first crescent visibility. It is the time
interval between sunset and moonset, called NA in Babylonian. NA is as a rule given at the
beginning of every month in the Diaries. What is NA?
When the moon reappears soon after new moon after an absence of mostly one and a
half to two and a half days, the following is seen. First the sun sets below the western hori-
zon. Then the thin lunar crescent becomes visible above the western horizon about above
where the sun has just set. Soon after, the thin crescent sets itself below the western hori-
zon. The interval between the time when the sun cuts the horizon on its downward trajec-
tory and the time when the moon does so in its wake is roughly one to two hours. It is this
time interval that is called NA and is measured in UŠ. One UŠ lasts about four minutes.
In recent decades, it has become abundantly clear that the interval NA and other inter-
vals like it served as fundamental and critically important raw empirical data for Babylo-
nian lunar theory. One principal aim of Babylonian astronomy was to describe the course
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 157
of the moon in all its complexity. Particularly helpful in this regard was the careful descrip-
tion of how the moon moves in relation to the sun. Every day the moon falls behind, as it
were, in relation to the sun by on average about 12 degrees. The sun and the moon are like
two runners racing across the sky from the eastern horizon to the western horizon with the
sun moving faster and catching up with the moon about every 29.5 days at what is called
new moon. To describe this movement, the need is for empirical data.
Among phenomena pertaining to the courses of moon and sun that readily present
themselves to observation are six time intervals between a horizon crossing of the sun and
a horizon crossing of the moon, that is, between the sun cutting eastern or western hori-
zon by rising or setting and the moon cutting either horizon by rising or setting. These six
intervals can easily be measured and Babylonian astronomers most eagerly and diligently
measured them. They are now called the Lunar Six (the name is due to Abraham Sachs).
Two of these six intervals fall around new moon when sun and moon are close to one
another at the same horizon. One is measured when the moon is for the last time seen ris-
ing before the sun rises at the end of the month and the other when the moon is for the first
time seen setting before the sun sets at the beginning of the month. The latter is called NA,
as was noted above. Four of the six intervals fall close to full moon. The first is measured
when the moon is seen setting for the last time before the sun rises, the second when the
moon is seen setting for the first time after the sun rises, the third when the moon is seen
rising for the last time before the sun sets, and the fourth when the moon is seen rising for
the first time after the sun sets.
The present concern is exclusively with NA as an indispensable component of Babylo-
nian lunar theory.
10.7. Estimating or Predicting NA
In the Babylonian astronomical Diaries, it is frequently stated that the moon was not seen
or that one did not even look in the evening preceding daylight of lunar Day 1. Yet, the
length of NA is still as a rule listed. These cases are so numerous and so well-known that it
seems superfluous to adduce any here as evidence. It must be assumed that, in such cases,
NA was estimated or predicted.
Rules making it possible to determine NA by prediction have indeed come to light (see
section 10.4). It is not clear to what extent exactly these rules were applied. According to
one of these rules, NA should not be smaller than 10°; according to another, not smaller
than 12°.88 Then again, it is possible to find instances in which NA is smaller than 10° in
the Diaries.89
Before rules had been designed or when and if existing rules were not applied, no so-
phisticated theory was necessarily needed to predict NA. Indeed, the following scenario
cannot be dismissed out of hand as impossible. In the days preceding the one and a half to
two and a half day period that the moon is not visible, someone carefully observing the sky
could easily establish roughly how much the moon moves in relation to the sun in one day
and roughly estimate where the moon would be in relation to the sun even during the days
in which it cannot be seen. The amount by which the moon moves in relation to the sun
each day ranges from about 10°46' to about 14°21', for an average of about 12°11'. But the
amount does not change abruptly by large increments or diminutions from one day to the
next. One could therefore possibly measure the amount accurately in the days before new
Leo Depuydt
158
moon and reliably project the moon’s progression forward for a couple of days. Since the
crescent is observed in the morning in the days before new moon but in the evening in the
days following new moon, an amount corresponding to a lunar movement of a little more
than half a day would need to be entered into the estimate beyond a number of full days.
If NA was estimated or predicted, there is the intriguing possibility that it did not mat-
ter to Babylonian astronomers if NA became too small for visibility of the new crescent, as
long as it remained positive. NA cannot drop so low that it becomes negative, that is, that
moonset precedes sunset. In that case, astronomers would not try to identify the evening
of first crescent visibility but rather the evening when moonset for the first time follows
sunset and no longer precedes it. A negative NA would upset the empirical foundation of
Babylonian lunar theory. But it seems as if a positive NA that was too small for visibility
would not. It seems moot to speculate what Babylonian astronomers could have thought
of a negative NA because negative numbers entered the realm of mathematics only centu-
ries later.
10.8. The Interval Called NA and the First Visibility of the New Crescent
As phenomena, NA and first crescent visibility are related but also distinct. It is critically
important to the present line of argument to establish what sets the two apart and what
unites them. NA, at least when it is measured and not estimated or predicted, and first
crescent visibility are best seen as two distinct facets of a single larger phenomenon. In this
case, the single larger phenomenon is the evening of first crescent visibility. One facet is
the fact that the light of the moon reaches the eyes of observers, as an event. Another facet
is the interval of time between subset and moonset that evening. In the same way, the fact
that it rains and exactly how long it rains are two facets of a single event.
As two facets of a single larger phenomenon, NA and first crescent visibility are inextri-
cably connected. However, there is no such necessary connection in the minds of behold-
ers of the two facets. It is altogether possible for the mind to select one facet for attention
at the exclusion of the other. For example, one can measure NA without attributing any
significance or function to first crescent visibility.
In sum, the fact that NA and first crescent visibility are connected to one another in
reality as two facets of a single larger phenomenon does not necessarily mean that there is
any connection between the two in the sense that selecting one for attention necessarily
implies also paying attention on the other.
10.9. A Universal Assumption regarding First Crescent Visibility in Babylonian Astronomical
Te x t s
It is now universally accepted, or so it would seem, that the lunar month began with first
crescent visibility in Babylonian astronomical texts. What is more, it seems generally ac-
cepted that Babylonian astronomical texts offer the best proof that the lunar month began
with first crescent visibility throughout the towns and cities of Mesopotamia, or at least,
that that was the intent, even if certain circumstances caused deviations.
Logically speaking, an alternative assumption concerning astronomical texts cannot
be dismissed out of hand. Clearly, the interval called NA mattered a lot to Babylonian
astronomers. It is also the first significant empirical datum of the lunar cycle. It therefore
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 159
naturally belongs at the very beginning of the account of the events of a month. Further-
more, NA is an evening event. Accordingly, if one begins the month with NA, it is neces-
sary to begin the month in the evening. Also, if one begins the month with NA, one can
hardly give the first night of the month the same day number as the immediately preceding
daylight period, either 29 or 30. It is only natural to begin the month with the number 1.
Accordingly, nighttime periods precede daylight periods with the same day number. If the
month began with NA, then Babylonian astronomers made the existing calendar much
more rigorous and were able to impose it on the rest of Babylon and maybe beyond.
It is true that NA and first crescent visibility are two facets of a single larger phenom-
enon. But as was suggested in section 10.8, it is possible to pay attention to one facet at the
exclusion of the other.
Did the lunar month in Babylonian astronomical texts begin with NA or first crescent
visibility? Or perhaps even both at the same time? It is difficult to see what could clinch
the matter. The instances in which the month begins too early for visibility to be possible
while NA remains positive may be viewed as an argument in favour of NA. One thing
seems certain. Beginning the month with measured NA, let alone predicted NA, could
hardly reflect a practice followed in society at large. It seems much too theoretical and too
rigorous. It is therefore not clear what Babylonian astronomical texts tell us about calendri-
cal practices at large. Consequently, the other evidence gains in importance. There are two
main types (see 10.3): reports as to on what the day the moon was first seen (see 10.11);
lunar dates whose equivalent in the Julian calendar is known (10.12).
But first, a note on the beginning of the day in Babylon is in order.
10.10. The Beginning of the Day in the City of Babylon
It is not clear to what extent, if at all, beginning the day in the evening was observed outside
the temple in Babylon where the astronomers were performing their duties. I doubt that
a Babylonian asked to join someone for dinner in the evening of lunar Day 5 would show
up in the evening that immediately follows daylight of Day 4. Likewise, no one invited to
dinner in modern Jerusalem in the evening of “Day 2” (yom sheni), that is, Monday, would
show up Sunday evening, which follows daylight of “Day 1” (yom rishon), just because
holidays and the Sabbath begin in the evening. The evening beginning as a Jewish or Mus-
lim custom is limited to religious practice, just as the evening beginning in Babylon may
well have been limited to astronomical practice. For most people most of the time, the day
must have begun in the morning and ended in the evening and any extensions of activity to
before dawn or sunrise and to after dusk or sunset were included. Nights were numberless
episodes of inactivity.
10.11. Reports as to on Which Day the Moon Was First Seen
Letters written by Assyrian and Babylonian scholars90 and astrological reports to Assyr-
ian kings91 abound with the conditional clauses “if the moon becomes visible on Day 30”
and “if the moon becomes visible on Day 1”.92 On the whole, visibility on Day 30 seems
to be something bad; visibility on Day 1, something good. The nature of these cuneiform
sources is such that there is every reason to believe that they reflect great care in observing
the night sky. These sources are among the best we have in terms of diligent observation
Leo Depuydt
160
outside of Babylonian astronomical and certain astrological texts.
It is tempting to interpret the visibility on Day 30 and the visibility on Day 1 mentioned
above along the lines of the structure of Babylonian astronomical texts, more specifically
the Diaries. I have the impression that this interpretation is widely accepted, even if mostly
tacitly or by the absence of an alternative explanation.
According to this interpretation, visibility on Day 30 means that the new crescent be-
comes visible for the first time at the beginning of nighttime of Day 30, which precedes
daytime of Day 30. As in Babylonian astronomical texts, Day 30 is in this case a designa-
tion of Day 1 of a lunar month that immediately follows a lunar month of 29 days. Lunar
days are either 29 days or 30 days long. But the standard length was considered to be 30
days. Therefore, either a lunar month ended after 29 days and the first day of the following
lunar month was called Day 30, with the next day being called Day 2. Or a lunar month
ended after 30 days and the first day was called Day 1.
According to this same interpretation, visibility on Day 1 means that the new crescent
becomes visible for the first time at the beginning of nighttime of Day 1, which precedes
daytime of Day 1.
Considering how often the conditional clauses “if the moon becomes visible on Day
30” and “if the moon becomes visible on Day 1” are attested, one might assume that day-
light of lunar Day 1 as a rule immediately followed the evening in which the new crescent
was first seen. Upon closer inspection, however, there is much that contradicts this as-
sumption (see below). In the end, I believe it cannot even be positively excluded that first
visibility on Day 30 or Day 1 means that the new crescent became visible in the evening
immediately following daylight of Day 30 or Day 1. In other words, it is not certain that,
outside astronomical texts, the day number changed at sunset. Extensions of the workday
to before sunrise and to after sunset would then receive the same day number as the day-
light period that they are abutting.
It should first be pointed out that the afore-mentioned clauses are conditional clauses.
It is not stated that the moon was in fact seen on Day 30 or Day 1. Indeed, one might ask,
why attach special significance to the appearance of the new crescent on those days if the
whole point was that it became as a rule first visible on those days?
It is not difficult to find evidence in the letters and reports in question that the moon
became visible on days other than Day 30 or Day 1. What is more, once the beginning of
the lunar month drifted away from first crescent visibility, and lunar months being either
29 days or 30 days long, it may not have been easy to bring daylight of Day 1 back in line
with first crescent visibility, if such was the intent. Therefore if one month does not begin
with first crescent visibility, others may not have either. A selection of statements to this
effect is as follows. A more in-depth study of what is said about the moon around the turn
of the month in West Asian documents from the last three millennia BCE remains desir-
able.
In one astrological report, one finds the following statement: “If the moon at its appear-
ance is visible early, the month will bring worry”.93 There does seem to be a sense that there
was an ideal time for the moon to appear and that its appearance could therefore be early
in relation to this standard. In an exorcist’s report, one finds the conditional clause “if the
moon at its appearance becomes visible on Day 28 as if on Day 1”. Apparently, there was an
awareness as to what the moon was supposed to look like on Day 1. But it is not clear which
evening is meant, the one before daylight of Day 1 or the one after daylight of Day 1.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 161
In a letter to an Assyrian king, an exorcist states: “I observed the (crescent of the) moon
on Day 30, but it was high, too high to be (the crescent) of Day 30. Its position was like
that of Day 2”.94 Clearly, the lunar month did not begin with first crescent visibility. In this
case, it began later because the crescent should have been visible the preceding day, circum-
stances permitting.
In general, it is fairly regularly stated that the moon was not seen when one attempted
to sight it. It is superfluous to cite specific instances. It would seem difficult to maintain a
rigid criterion such as beginning the lunar month with earliest possible new crescent vis-
ibility if absence or presence of the crescent could not be evaluated when it needed to be.
What is more, once one month was off kilter, one or more ensuing ones might be too. One
solution, as the best one could do under the circumstances, is to keep the beginning of the
month fairly close to new moon, which cannot have been all that difficult. Still, it would
have been desirable that the new crescent be visible at the beginning of the month, whether
in the evening preceding or in the evening following daylight of lunar Day 1.
An alternative modus operandi that may have been used, though to an unknown ex-
tent, is presented in section 10.13 below. It involves the creation of a new concept in calen-
drics. Among postulated ancient calendars, the old crescent is as a rule associated with
invisibility and the new crescent with visibility in that the beginning of the lunar month
is marked either by the invisibility of the old crescent or the visibility of the new crescent.
But what if both visibility and invisibility were associated with the new crescent? I believe
that much evidence outside Babylonian astronomy strictly speaking can be construed in
favour of a lunar calendar in which the beginning of months was determined by new crescent
(in)visibility.
10.12. Lunar Dates Whose Equivalent in the Julian Calendar Is Known in Non-astronom-
ical Sources
The only sources outside Babylonian astronomical texts that may make it possible to es-
tablish the Julian dates of the Babylonian lunar Day 1 are, as far as I know, Aramaic double
dates from Egypt.
As J. K. Fotheringham was the first and the only ever to observe, the Julian dates of lu-
nar Day 1 fall just a little too early for first crescent visibility to have served as marker of the
beginning of the lunar month.95 Stern more generally notes that “perhaps at Elephantine,
visibility of the new moon was not used as a criterion to determine when the new month
began”, without specifying whether first crescent visibility came too early or too late.96
There are 14 completely preserved double dates.97 The average distance between con-
junction and 6:00 a.m. of Day 1 is about +21h 27m 51s or, without the aberrant no. 3,
+30h 30m 28s. The first average is in tune with that obtained from Greek lunar dates; the
second falls a few hours later. In any event, even in the latter case, the average distance from
conjunction to the evening before daylight of lunar Day 1 is about 18 to 19 hours. This
interval is on average too short for first crescent visibility to serve as marker of the month’s
beginning. Indeed, any interval larger than 18 to 19 hours, say 24 hours, needs to be com-
pensated by one that is shorter, say, 13 to 14 hours, an interval that is clearly too short for
the first crescent to have been seen.
It seems difficult to assume that the Western Asian mercenaries on the Egyptian island
of Elephantine adopted the manner of beginning lunar months used behind the walls of
Leo Depuydt
162
Egyptian temples. The Egyptian lunar calendar was strictly religious and almost secretive.
10.13. A New Ancient Lunar Calendar: The New Crescent (In)visibility Calendar
Among the cuneiform sources that are not strictly astronomical, one finds reports of lunar
observation pertaining to the calendar. They include a set of astrological reports to Assyr-
ian kings98 and a set of letters from Assyrian and Babylonian scholars99 dated to the Neo-
Assyrian period (earlier first millennium BCE). In light of how little has been preserved,
these sources are as good as it gets when it comes to illustrating how the beginning of
lunar months was determined in Mesopotamia outside of astronomical texts. An attempt
is made below to reconstruct the principles according to which the beginning of lunar
months was determined according to these sources. It remains unclear, naturally, to which
extent exactly these rules were used in society at large, be it in the Neo-Assyrian period or
in other epochs of Mesopotamian history.
If the beginning of lunar months was strictly determined by means of first crescent vis-
ibility, the following would need to be typical in the sources at hand: daylight of lunar Day
1 immediately followed the evening in which the new crescent was first seen. There are two
possibilities at this point.
First, if the day began in the evening as it does in Babylonian astronomical texts, the
new crescent would typically first be seen on Day 30 at the end of a 29-day lunar month
or on Day 1 at the end of a 30-day period. In Babylonian astronomical texts, Day 30 is
the designation for the first day of a lunar month that immediately follows a 29-day lunar
month.
Second, alternatively, if human activity taking place before dawn or after sunset was
dated by the same day number as the daylight period it abuts, the new crescent would typi-
cally first be seen either on Day 29 at the end of a 29-day lunar month or on Day 30 at the
end of a 30-day lunar month. The next day would in both cases be Day 1 of the next lunar
month.
Instead, what one finds in the sources is something entirely different. The fundamental
fact is that there is abundant reference to sighting the crescent on Day 29, on Day 30, and
on Day 1, three different days and not two. This cannot be reconciled with what is found
in Babylonian astronomical texts. But what does it mean?
Step One: Sighting on Day 29 as opposed to Sighting on Day 30 and Day 1.—The point
of departure of the present line of argument is a striking difference between the sightings
on Day 29 and the sightings on Day 30 and Day 1. The sightings on Day 29 are actual
sightings as a rule reported in a statement such as “We saw the moon”. By contrast, the
sightings on Day 30 and Day 1 are hypothetical sightings as a rule described by the condi-
tional clauses “if the moon becomes visible on Day 30”100 and “if the moon becomes visible
on Day 1”.101 Visibility on Day 30 seems to be something bad; on Day 1, something good.
Visibility on Day 1 is occasionally predicted, as in “Now, in intercalary Adar, on Day 1 the
moon will become visible”,102 or reported, as in “On Day 1, the moon became visible”,103
but this is rare.
Step Two: The Timing of the Moon Watch.—Step two of the present line of argument
is that there can be no doubt about the following fact. The evening in which one as a rule
actively watched the sky in search of the new crescent is that of Day 29; the new crescent is
either sighted or not sighted at that time.104
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 163
A second, additional, watch may be held on Day 30, as in the following reports: “[We
kept] watch for the moon. On Day 29, there were clouds. [We did not see the moon.]
On the next day, [. . .] it was two days old”;105 “We watched on Day 29. The clouds were
den[se]. We did not see the moon. We watched on Day 30. We saw the moon. It was very
high. The (weather) of Day 29 has to do with it. What is it that the king says?”;106 and “We
kept wa[tch on Day 29]. There were clouds. We did not see the moon. T[od]ay, on Day
30, there were c[lou]ds again. When they di[spersed], we saw [the mo]on. [It] was [(not)
like the] moon of [Day] 29”.107
In one case, a watch on Day 30 alone is reported;108 one assumes, in light of what else is
known, that another watch may well have taken place on the preceding day.
So when it is reported that “They watched the moon. The clouds were dense. The
moon was not seen. Day 30 became long”,109 it may confidently be assumed in light of the
specification “Day 30 became long” (that is, the month had 30 days [see below]) that the
watch took place on Day 29.
Step Three: The Evening of Day 29, the Time of Sighting, as the Evening Following Day-
light of Day 29.—Before trying to reconstruct how the Mesopotamian lunar calendar func-
tioned according to texts other than Babylonian astronomical texts, an important question
needs to be settled. It is clear from the sources that the evening of Day 29 was as a rule the
evening in which a watch was kept to look out for the new crescent. There is also no doubt
that, in Babylonian astronomical texts, the evening of Day 29 immediately follows daylight
of Day 28. The question arises: Does that same evening immediately follow daylight of
Day 28 or daylight of Day 29 in other texts?
It seems somehow natural that day numbers would not change at the moment of sunset
in society at large. Changing the day number at sunset seems only possible in the highly
systematized calendar of Babylonian astronomical texts. But the principal consideration in
favour of assuming that the evening of Day 29 immediately followed daylight of Day 29 is
as follows.
Let us assume that the evening of Day 29 immediately followed daylight of Day 28.
The main problem of a lunar calendar is to determine whether the month will have 29 days
or 30 days. This is the same as determining whether the day following Day 29 will be the
last of the same month or the first of the next month. It seems difficult to make this deci-
sion just after daylight of Day 28. The next daylight period will always be that of Day 29.
There is otherwise no indication in the day-names in Mesopotamia, as there is in the Greek
world, that a decision was made one day ahead of the time, that is, in the evening just after
daylight of Day 28 about the daylight period that is next after daylight of Day 29.
If the evening of Day 29 immediately follows daylight of Day 29, then the evenings of
Days 30 and 1 immediately follow daylight of Days 30 and 1 respectively. Since cuneiform
texts often refer to the possibility of first visibility of the new crescent on Day 1 (see above),
it must be assumed that it was considered altogether possible that the lunar month began
before the new crescent was first seen. Still, it may be considered a good omen that the new
crescent made its first appearance on Day 1. First appearance on Day 1 seems like a good
sign rather than a bad sign according to the sources.
Step Four: A Day-29-Rule.—According to the evidence cited above, no time is any-
where nearly as prominent as a time when a moon watch is kept than the evening of Day
29. It is also clear that the new crescent is either sighted or not sighted at that time. The
best assumption is that the next daylight period is that of the last day of the month, Day
Leo Depuydt
164
30, if the new crescent is sighted and Day 1 of the next month when the new crescent is not
sighted, even if this principle is not explicitly stated as such in the sources. The focus on the
evening of Day 29 suggests the desirability of the Day 29-rule just postulated. In practice,
however, the rule was probably often if not very often not applied and the evidence sup-
ports this assumption (see Step Six below).
Step Five: The Evening of Day 29 as a Systematic Time of Sighting and First Crescent Vis-
ibility on Days 30 and 1.—The evidence cited above suggests that Days 29, 30, and Day 1
are all three days on which sighting of the moon is considered possible if not normal. The
Day 29-Rule described above accords with this impression. The sources leave no doubt
that the new crescent could be sighted on Day 29. But the sources also make it clear that it
could not be sighted at that time. It is a fact that first visibility of the new crescent falls on
the first day after the day of first invisibility of the old crescent in about 55.18% of all cases
and on the second day in 44.30% of all cases; it falls on the same day in 1.04% of all cases
and on the third day in 0.48% of the cases.110 According to the Day 29-rule (see Step Five),
the lunar month has 30 days if the new crescent is invisible in the evening of Day 29. Ac-
cordingly, the moon is seen in about half of all cases in the evening immediately following
daylight of Day 30 and in about half of all cases in the evening immediately following Day
1. Both are normal. In the latter case, the lunar month begins after first crescent visibility.
The fact that the new crescent is very rarely first visible on the third day after first invis-
ibility of the old crescent, only in 0.48% of all cases, seems to be confirmed by the following
statement: “The moon disappeared on Day 27. On Day 28 and Day 29, it stayed inside the
sky. It was seen (again) on Day 30. When (else) should it have been seen? It should stay
inside the sky less than four days. It never stayed four days”.111 Presumably, visibility on Day
30 is interpreted as “staying inside the sky” for four days and this is considered a problem.
The author of the text apparently expected visibility on Day 28 or on Day 29.
Step Six: Fluctuation.—While it seems clear that there is some kind of focus on keeping
the watch on Day 29, and while it is reasonably easy to account for this focus by postulat-
ing a Day 29-rule, and while this Day-29-rule easily accords with the fact that both Day 30
and Day 1 were considered thinkable as the day of first crescent visibility, and while there
was an explicit sense that the old crescent could disappear and the new crescent appear at
an “inappropriate time”112 and by implication also at an appropriate time, one seriously
wonders to what extent any kind of rule was neatly applied. For example, the new crescent
could become visible “on Day 28 as if on Day 1”113 and the new crescent could after all
become visible at an “inappropriate time”.
All in all, it cannot have been all that difficult to keep the beginning of the lunar month
close to new moon. To that aim, astronomers would advise kings in their choices of 29-
day and 30-day months, for example by planning a couple of 30-day months in succession
beforehand if the new crescent seemed to have begun appearing on the whole a little too
early. Historically speaking, there is every reason to believe that the rigorous lunar calendar
of the Babylonian astronomers was somewhat isolated as a phenomenon.
11. The Sociology and Politics of Living Three Lunar Calendars
A principal design of the conference “Living the Lunar Calendar”, at which an extract of
the present paper was read, was to probe the sociopolitical ramifications of life with a lu-
nar calendar. The subject acquires a certain additional complexity if one considers what it
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 165
must have meant to live with more than one lunar calendar. The aim of the present paper
so far has been to demonstrate that there were in fact two lunar calendars in simultaneous
use in Ptolemaic Egypt in the third century BCE. Before considering sociology or politics,
this tenet needed to be demonstrated first. The coexistence of the two lunar calendars was
short-lived, however. The Greco-Macedonian calendar lost its lunar connection later in
the third century BCE. In the end, it was assimilated completely to the Egyptian civil cal-
endar of 12 months of 30 days plus five added days for a total of 365 days. Even when it was
independent, the Greek lunar calendar played only a secondary role, one subordinated to
the civil calendar, even if the Greek lunar date was listed first in double dates in deference
to the awareness of who was really in charge in Egypt.
But two lunar calendars is not where it stops. A third lunar calendar was used in Egypt
by the Jewish diaspora. The Jewish calendar is a descendant of the lunar calendar of Baby-
lonia, to which the Israelites had been exiled in the sixth century BCE.
How was it possible for three lunar calendars to coexist in a single country? If coexis-
tence was the case, three lunar months beginning on three different days may on occasion
have been running alongside one another in Egypt. How was this practicable? The validity
of the lunar dates derived above from double dates as evidence critically depends on the
practicability of lunar calendars existing alongside one another in close vicinity. Indeed,
one might ask: Why would a native Egyptian speaker and a Greek speaker both living in
a single small Egyptian town use two different calendars? If the close coexistence of two
lunar calendars was not practicable, then the numerical data presented and analyzed at
length above must be considered one huge statistical aberration.
There are no sources in which ancient Egyptians explicitly tell us how the lunar calen-
dar affected their lives. The practicability of coexisting lunar calendars therefore will need
to be demonstrated in other ways. The key observation that can serve as point of departure
of such a demonstration is how completely isolated from one another the world of the
Egyptian lunar calendar and the world of the Macedonian-Greek lunar calendar were. The
Egyptian lunar calendar was entirely religious and used exclusively in the somewhat dark
and secretive confines of temple life and hieroglyphic culture. The Greek lunar calendar is
mainly represented in business documents written by townspeople. Egyptian priests and
Greek businessmen hardly talked with one another. In all probability, only very few native
speakers of Greek also spoke Egyptian, and vice versa. The two power blocs perennially
competing with one another in Ptolemaic Egypt were the native Egyptian priesthood and
the Greek-speaking state bureaucracy with a Pharaoh of Macedonian descent at the top.
Both needed to be financed and relied on taxation. The two staked out their respective
territories by signing treaties, such as the Memphis Decree of 196 BCE that is inscribed
in Egyptian and Greek on the Rosetta Stone. The Rosetta Stone is a point of contact be-
tween two communities that largely led separate existences within the borders of a single
country.
An additional question is whether it was possible for the Greek lunar month to begin
on the same day everywhere in Egypt. Even if there was no time to dispatch messengers to
everywhere in Egypt to communicate the beginning of the month, the principles followed
to date a Greek document written in the Fayyum must have been basically the same as
those followed in dating a document written in Greek-speaking Alexandria and different
from those followed behind the thick stone walls of a nearby Egyptian temple enclosure.
Last but not least, there is the Jewish lunar calendar. Like the Egyptian lunar calendar, it
Leo Depuydt
166
must have been 100% religious. Its coexistence with other calendars in modern times easily
serves as an analogy of how it must have coexisted with other calendars in ancient times.
The Jewish calendar is used today all over the world solely to regulate religious festivals.
But for that pillar of Judaism, the celebration and observation of the Sabbath, it is obvi-
ously not needed.
Notes
1. Depuydt (2002), pp. 471–477. Some of what follows has already years before the Jerusalem conference
“Living the Lunar Calendar” been part of papers read at Annual Meetings of the American Oriental Soci-
ety held in March 1997 in Miami, Florida, in March 2002 in Houston, Texas, and in March 2004 in San
Diego, California and entitled “The Beginning(s) of Day and Month in Egypt and the Ancient World”,
“The Day in Antiquity”, and “First Crescent Visibility’s Irrelevance: Additional Evidence, including from
Babylonian Astronomical Texts” respectively. These papers mostly concern the moon. But one often trav-
els or moves to the cities where they were read in search of the sun. I thank Peter J. Huber for performing
critical calculations, not only in relation to the present paper, but also on various other occasions in relation
to investigations on Middle and New Kingdom chronology that have not—and, one hopes, not yet—
come to fruition. I also thank Chris Bennett for reading semifinal and penultimate versions of the present
paper and making several helpful comments, including pointing out a couple of erroneous numbers.
2. Depuydt (1996), p. 42; Depuydt (1997b), p. 127 (at line 18, for “last crescent visibility” read “. . . invis-
ibility”); Depuydt (2007), 76 note 43; and Depuydt (forthcoming), section C.2.
3. Kugler (1922), p. 2 (“The first reappearance of the slim sickle in the western evening sky is the sign for the
beginning of the month”).
4. See, for example, Beaulieu (1993), Britton (2007), p. 115–119, Huber (1982), and Steele (2011), p. 478–
481.
5. Hannah (2005), p. 43.
6. Pritchett (1959), p. 152.
7. Pritchett and Neugebauer (1947).
8. Jones (2005), p. 165 note 2.
9. The five principal contributions are Pritchett (1959), (1970), pp. 39–89, (1982), (1999), and (2001).
10. Parker (1950), pp. 9–23 (“Chapter I: The Beginning of the Egyptian Lunar Month”); Parker (1957), p.
39.
11. Pritchett (1959), p. 154.
12. Pritchett (1959), p. 152.
13. Pritchett (1959), p. 153.
14. Pritchett (1970), p. 73.
15. Pritchett (1959), p. 154.
16. Hammond and Scullard (1970), pp. 192–193.
17. Hammond and Scullard (1970), p. v.
18. Hammond and Scullard (1970), p. 192.
19. Pritchett (1970), pp. 72–73.
20. Pritchett (1970), p. 73.
21. The diagram at Pritchett (1970), p. 72 clearly shows daylight preceding nighttime in the same day. The ex-
pression “at dusk following the completion of the 28th day” makes it seem as if the day ends in the evening;
but morning as the completion of the 28th day also seems possible as an interpretation of this phrase.
22. As noted at the outset of this paper, following in the footsteps of others, I used to consider the problem of
when the day begins important. It is therefore slightly unfortunate that the only time Pritchett cites me, as
far as know, it is to adduce my support of the significance of precisely that problem (Pritchett (2001), p.
95, note 2, referring to Depuydt (1997a), p. 27).
23. Pritchett (1970), p. 73.
24. Pritchett (1982), pp. 260–266.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 167
25. Pritchett (1970), p. 72.
26. Pritchett (1982), p. 72.
27. Pritchett (1982), pp. 260–266.
28. When Pritchett ((1999), p. 88) writes that Pritchett (1982) “correct[s]” Pritchett (1959), pp. 151–154
and Pritchett (1970), pp. 72–73, which are “based on a theory of a day of evening visibility”, two matters
seem to have been confused, namely the beginning of the day and the beginning of the month. Pritchett
(1982) “corrects” Pritchett (1959) in that it is assumed in Pritchett (1982), as it apparently is in Pritchett
(1970), that the day began in the morning whereas it is assumed in Pritchett (1959) that it began in the
evening. Pritchett (1982) “corrects” Pritchett (1970) in that it is assumed in Pritchett (1982), as it is in
Pritchett (1959), that the beginning of the month was determined by watching the old crescent in the
morning whereas it is assumed in Pritchett (1970) that it was determined by watching the new crescent in
the evening.
29. Depuydt (1998).
30. Pritchett (1982), p. 266.
31. Pritchett (1982), p. 266.
32. Goldstine (1973).
33. Goldstine (1973), p. 37.
34. Thus Lange and Swerdlow (2006). Whenever dates of visibility and invisibility phenomena are mentioned
in what follows without explicit reference to a source, the source is Lange and Swerdlow (2006).
35. After reading a semifinal version of this paper, Chris Bennett—who has a monograph in press on the his-
tory of the Macedonian calendar in Egypt for the series Studia Hellenistica—reported that there are only
a handful more, dating to Roman times (personal e-mail communication of October 5, 2010). They have
not been included in this paper. We agreed that they do not appear essential to this paper’s line of argu-
ment. For information about them, I refer to Bennett’s forthcoming study. [This study has now appeared
as Bennett (2011).]
36. Grzybek (1990), pp. 135–137.
37. Grzybek (1990), pp. 135 note 42, 151–155.
38. See Grzybek (1990), p. 137 note 47.
39. See footnote ** in table 2.
40. For example, as part of his comments on a semifinal version of the present paper, Chris Bennett suggested
using “Alexandria-only” dates, 15 according to his count (personal e-mail communication of October 5,
2010). The results do not deviate in any significant way from those obtained in the other selections.
41. See, for example, Pritchett (1959), p. 152.
42. Lange and Swerdlow (2006).
43. Personal e-mail communication of February 11, 2009.
44. See, for example, Parker (1950), p. 12 §§38–39.
45. Parker (1950), p. 13 ¶47.
46. Peter J. Huber, personal e-mail communication of February 11, 2009.
47. Pritchett (1982), pp. 260–261.
48. Bennett (2008). In Depuydt (1997a), pp. 184–186, I styled two temple service dates (nos. 5 and 24 in the
tables in Bennett (2008), pp. 547–551) as “double dates”. In a certain regard, they are. But in the present
paper, I restrict the term “double date” to cases in which the lunar date is a day in the Egyptian lunar month
and not a certain day in a temple service term.
49. Bennett (2008).
50. See also Depuydt (1998).
51. Luft (1992), pp. 189–195, 205–208.
52. See the tables in Bennett (2008), cols. 547–552.
53. Bennett (2008), cols. 551–552 note 82.
54. Personal e-mail communication of October 21, 2010.
55. An important early discussion of the dates is Bilfinger (1888), pp. 77–88 (dates with Macedonian month
names), 147–154 (dates with Athenian month names).
Leo Depuydt
168
56. Hannah (2008), p. 94 somehow obtains 18 November, 30 October, and 1 March as well as 14 November,
16 or 17 October, and 25 February as lunar Day 1, but it is not fully clear to me how.
57. van der Waerden (1960), p. 71; cf. Depuydt (1996), pp. 31–32.
58. Depuydt (1996).
59. Depuydt (1996), pp. 40–42. At p. 41, with note 30, conjunction for Babylon should have been conjunc-
tion for Alexandria. But in this case, the difference does not affect the conclusions drawn.
60. Sachs and Hunger (1988), p. 195.
61. Personal e-mail communication of February 11, 2009.
62. Epping (1889), p. 179.
63. Ideler (1825–1826), vol. 1, p. 279.
64. Se e, for example, Pritchett (1982), pp. 260–266 for the Greek calendar, and Depuydt (1998) for the Egyp -
tian lunar calendar.
65. Pritchett (1982), p. 261 note 53.
66. Bennett (2008), col. 535 note 43 and col. 548, repeating a personal communication by uack cited else-
where.
67. For the related concept of the “straddle” month, a month encompassing a point in time that serves as a
herald of the beginning of the year, in the sense that the first new moon following it is the beginning of
lunar Month 1, see Depuydt (1997), pp. 43, 213–215.
68. Westermann and Kraemer (1926), pp. 1–59 (no. 1).
69. Westermann and Kraemer (1926), p. 22 note 1.
70. Pritchett (1982), p. 256.
71. Lange and Swerdlow (2006). I chose modern dates because, in the version of the program that I down-
loaded, t had been disregarded in computing the age of the moon. However, around 1900 CE, t is zero
or close to zero.
72. See, for example, Hunger (1992), passim and Parpola (1993), passim.
73. Depuydt (1997b) (for errata, see Depuydt (2008), p. 74); Depuydt (2008), pp. 47–51.
74. Depuydt (1997b), pp. 121–124.
75. Lange and Swerdlow (2006).
76. See the section on the moon in the text entitled “Computation visibility phenomena” accompanying the
program Lange and Swerdlow (2006).
77. In a personal e-mail communication of October 9, 2010, Peter J. Huber urged me to consider that the
probability that the first crescent was seen in the evening of 11 June 323 BCE is not entirely negligible.
Naturally, additional assessments of the probability in question remain desirable and would surely be wel-
comed.
78. Brack-Bernsen (2010), p. 278.
79. Beaulieu (1993); Steele (2011), p. 478.
80. See especially Brack-Bernsen (1997), (1999), and (2002), and Brack-Bernsen and Hunger (2002). Brack-
Bernsen (2010) is a survey for a wider audience, with additional observations.
81. Steele (2007). The quote is from Brack-Bernsen (2010), p. 296.
82. Steele (2007), p. 143.
83. Stern (2008).
84. Huber and Steele (2008).
85. Britton (2008).
86. Steele (2011).
87. Such instances are gathered in Stern (2008). The author does otherwise assume that lunar months began
with first crescent visibility in Babylonian astronomical texts.
88. For a summary with references See Stern (2008), p. 37 note 11.
89. See, for example, Sachs and Hunger (1996), pp. 210–211 (tablet BM 45830).
90. Parpola (1993).
91. Hunger (1992).
92. See, for example, the “list of text headings” in Hunger (1992), pp. 369–373.
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 169
93. Hunger (1992), p. 32 no. 53.
94. Parpola (1993), p. 177 no. 225.
95. Depuydt (2002), p. 473.
96. Stern (2000), p. 164.
97. Depuydt (2002), p. 475.
98. Hunger (1992).
99. Parpola (1993).
100 . The following list of instances found in Hunger (1992) should be complete or very nearly complete, but
the difference hardly matters statistically speaking: p. 10 nos. 11–12, p. 11 no. 13, p. 32 no. 53, pp. 35–36
no. 60 (twice), p. 36, no. 61, p. 51 no. 85 (twice), p. 66 no. 107, p. 75 nos. 120–121, p. 90 no. 150, p. 101
no. 171, p. 103 no. 176, p. 105 no. 183, p. 111 nos. 191–193, p. 136 no. 244 (twice), p. 137 no. 246, p. 146
no. 262 (Hunger: “on the 1st day”), p. 146 no. 263, p. 147 nos. 246–265, p. 161 no. 292, p. 170 no. 304,
p. 171 no. 305, p. 180 no. 319, p. 188 no. 331, p. 196 no. 344–345, p. 197 no. 346, p. 204 no. 358, p. 213
no. 375, p. 224 no. 390, p. 225 nos. 391–393, p. 241 no. 424, p. 249 nos. 440–442, p. 264 no. 472, p. 266
no. 478, p. 268 no. 485, p. 274 no. 500, p. 284 no. 512, p. 285 no. 514.
101. The following list of instances found in Hunger (1992) should be complete or very nearly complete, but
the difference hardly matters statistically speaking: p. 8 no. 7, p. 9 no. 9, p. 10 no. 10, p. 20 no. 37, p. 35 no.
57, p. 51 no. 86 (twice), p. 52 no. 87, p. 72 no. 113, p. 74 nos. 116–119, p. 90 nos. 148–149, 98 no. 165,
p. 109 no. 188, p. 110 no. 189, p. 140 no. 251, pp. 140–141 no. 252, p. 143 nos. 256–257, p. 144 no. 258,
p. 145 no. 259, p. 161 nos. 290–291, p. 180 no. 318, p. 187 nos. 329–330, p. 195 no. 342, p. 211 no. 372
(“It becomes visible on Day 1” as a hypothetical phenomenon), p. 212 no. 373, p. 232 no. 409, p. 238 no.
418, p. 239 no. 420, p. 240 nos. 421–422, p. 241 no. 423, p. 249 no. 439, p. 251 no. 446, p. 254 no. 449, p.
256 no. 456, p. 260 no. 463, p. 271 no. 492, p. 274 no. 498, p. 281 no. 505, p. 282 no. 506 (twice), p. 282
no. 507, p. 283 no. 508–510, p. 284 no. 511.
102. Hunger (1992), p. 141 no. 253; also p. 148 no. 267 (twice).
103. Hunger (1992), p. 257 no. 456.
104. In the following list, cases in which the new crescent was visible on Day 29 are marked by “crescent sight-
ed” and cases in which the new crescent was not visible on Day 29 are marked by “crescent not sighted”:
Hunger (1992), p. 45 no. 79 (not sighted, according to Hunger’s plausible reconstruction), p. 75 no. 120
(not sighted), pp. 80–81 nos. 126–129 (sighted), and p. 81 nos. 130–132 (not sighted); Parpola (1993),
p. 105 no. 126 (sighted), p. 109 no. 138 (not sighted), p. 110 no. 139 (not sighted), p. 110 no. 140 (not
sighted), p. 111 no. 141 (not sighted), p. 111 no. 142 (sighted), p. 112 no. 146 (not sighted; Parpola plau-
sibly reconstructs Day 29 as day of the watch). In these 16 watches taking place in the evening of Day 29,
the new crescent was sighted in 6 instances and not sighted in 10 instances.
105. Hunger (1992), p. 45 no. 79.
106. Hunger (1992), p. 75 no. 120.
107. Parpola (1993), p. 112 no. 146.
108. Hunger (1992), p. 82 no. 133.
109. Parpola (1993), p. 112 no. 145.
110. Peter J. Huber, personal e-mail communication of February 11, 2009.
111. Hunger (1992), p.197 no. 346.
112. Hunger (1992), p. 52 no. 88 (probably new crescent), p. 197 no. 346 (old crescent disappears on Day 27),
and p. 219 no. 382 (old crescent disappears on Day 24).
113. Hunger (1992), p. 11 no. 14
References
Beaulieu, P.-A., 1993, “The Impact of Month-lengths on the Neo-Babylonian Cultic Calendar”, Zeitschrift für
Assyriologie und orderasiatische Archäologie 83, 66–87.
Bennett, C., 2008, “Egyptian Lunar Dates and Temple Service Months”, Bibliotheca Orientalis 65, 525–554.
——, 2011, Alexandria and the Moon: An Investigation into the Lunar Macedonian Calendar of Ptolemaic
Leo Depuydt
170
Egypt, Studia Hellenistica 52 (Leuven: Peeters).
Bilfinger, G., 1888, Der bürgerliche Tag: Untersuchungen über den Beginn des Kalendertages im Classischen
Altertum und im Christlichen Mittelalter (Stuttgart: Kohlhammer).
Brack-Bernsen, L., 1997, Zur Entstehung der babylonischen Mondtheorie: Beobachtung und theoretische Berech-
nung on Mondphasen, Boethius 40 (Stuttgart: Franz Steiner Verlag ).
——, 1999, “Goal-Year Tablets: Lunar Data and Predictions”, in N. M. Swerdlow (ed.), Ancient Astronomy and
Celestial Divination (Cambridge, Mass.: MIT Press), 149–177.
——, 2002, “Predictions of Lunar Phenomena in Babylonian Astronomy”, in J. M. Steele and A. Imhausen
(eds.), Under One Sky: Astronomy and Mathematics in the Ancient Near East, Alter Orient und Altes Testa-
ment 297 (Münster: Ugarit-Verlag), 5–19.
——, 2010, “Methods for Understanding and Reconstructing Babylonian Predicting Rules”, in A. Imhausen
and T. Pommerening (eds.), Writings of Early Scholars in the Ancient Near East, Egypt, Rome, and Greece:
Translating Ancient Scientific Texts, Beiträge zur Altertumskunde 286 (Berlin: De Gruyter), 277–297.
——, and Hunger, H., 2002, “TU 11, a Collection of Rules for the Prediction of Lunar Phases and of Month
L en gt hs ”, SCIAMVS 3, 3–90.
Britton, J. P., 2007, “Calendars, Intercalations and Year-lengths in Mesopotamian Astronomy”, in J. M. Steele
(ed.), Calendars and Years: Astronomy and Time in the Ancient Near East (Oxford: Oxbow Books), 115–
132.
——, 2008, “Remarks on Strassmaier 400”, in M. Ross (ed.), From the Banks of the Euphrates: Studies in Honor
of Alice Louise Slotsky (Winona Lake, Indiana: Eisenbrauns), 7–33.
Depuydt, L., 1996, “The Egyptian and Athenian Dates of Meton’s Observation of the Summer Solstice
(–431)”, Ancient Society 27, 27–45. Three erroneous numbers in this article are “27,758¼” (for 27,758¾)
at p. 37 line 20, “3 July” (for 15 July) at p. 43 line 20, and “27,759” (for 55,518) at p. 45 line 20.
——, 1997a, Civil Calendar and Lunar Calendar in Ancient Egypt, Orientalia Lovaniensia Analecta 77 (Leu-
ven: Uitgeverij Peeters and Departement Oosterse Studies).
——, 1997b, “The Time of Death of Alexander the Great: 11 June 323 B.C. (–322), ca. 4:00–5:00 PM”, Die
Welt des Orients 28, 117–135.
——, 1998, “The Hieroglyphic Representation of the Moon’s Absence (Psπdntyw)”, in L. H. Lesko (ed.), An-
cient Egyptian and Mediterranean Studies in Memory of William A. Ward (Providence, Rhode Island: De-
partment of Egyptology), 71–89.
——, 2002, “The Date of Death of Jesus of Nazareth”, Journal of the American Oriental Society 122, 466–
480.
——, 2007. “Calendars and Years in Ancient Egypt: The Soundness of Egyptian and West Asian Chronology
in 1500–500 BC and the Consistency of the Egyptian 365-Day Wandering Year”, in J. M. Steele (ed.),
Calendars and Years: Astronomy and Time in the Ancient Near East (Oxford: Oxbow Books), 35–81.
——, 2008, From Xerxes’ Murder (465) to Arridaios’ Execution (317): Updates to Achaemenid Chronology (In-
cluding Errata in Past Reports), British Archaeological Reports S1887 (Oxford: Archaeopress). A sheet
with addenda and errata is available from the author and may be published somewhere in the near future.
——, forthcoming, “Calendar, Ancient Near East”, in R . S. Bagnall et al. (eds.), Wiley-Blackwell’s Encyclopedia
of Ancient History. The bibliography in this article could not exceed 15 items. I promised to list additional
bibliography in the present article, but have refrained from doing so in light of space constraints.
Epping, J., 1889, Astronomisches aus Babylon, Ergänzungshefte zu den Stimmen aus Maria-Laach 44 (Freiburg:
Herder’sche Verlagsbuchhandlung).
Goldstine, H. H., 1973, New and Full Moons 1001 B.C. to A.D. 1651, Memoirs of the American Philosophical
Society 94 (Philadelphia: American Philosophical Society).
Hammond, N. G. L. and Scullard, H. H., 1970, The Oxford Classical Dictionary (Oxford: At the Clarendon
Press).
Hannah, R., 2005, Greek and Roman Calendars: Constructions of Time in the Classical World (London: Duck-
worth).
Huber, P. J., 1982, Astronomical Dating of Babylon I and Ur III, Occasional Papers on the Near East 1/4 (Mal-
ibu: Undena).
Why Greek Lunar Months Began a Day Later than Egyptian Lunar Months 171
——, and Steele, J. M. (2007), “Babylonian Lunar Six Tablets”, SCIAMVS 8, 3–36.
Hunger, H., 1992, Astrological Reports to Assyrian Kings, State Archives of Assyria 8 (Helsinki: Helsinki Uni-
versity Press).
Ideler, L., 1825–26, Handbuch der mathematischen und technischen Chronologie, aus den Quellen bearbeitet, 2
vols. (Berlin: August Rücker).
Jones, A., 2006, “Ptolemy’s Ancient Planetary Observations”, Annals of Science 63, 255–290.
——, 2007, “On Greek Stellar and Zodiacal Date-Reckoning”, in J. M. Steele (ed.), Calendars and Years: As-
tronomy and Time in the Ancient Near East (Oxford: Oxbow Books), 149–167.
Kugler, F. X ., 1922, Von Moses bis Paulus: Forschungen zur Geschichte Israels nach biblischen und profangeschicht-
lichen insbesondere neuen keilinschriftlichen Quellen (Münster: Aschendorff).
Lange, R. and Swerdlow, N. M., 2006, Version 3.1.0 of the program “Planetary, Lunar and Stellar Visibility”
dated November 20, 2006 and downloaded from www.alcyone.de in early 2009.
Luft, U., 1992, Die chronologische Fixierung des ägyptischen Mittleren Reiches nach dem Tempelarchiv on Il-
lahun, Österreichische Akademie der Wissenschaften, Philosophisch-historische Klasse, Sitzungsberichte
598 (Vienna: Verlag der Österreichischen Akademie der Wissenschaften).
Parker, R. A., 1950, The Calendars of Ancient Egypt, Studies in Ancient Oriental Civilization 26 (Chicago:
University Press).
——, 1957, “The Lunar Dates of Thutmose III and Ramesses II”, Journal of Near Eastern Studies 16, 39–43.
Parpola, S., 1993, Letters from Assyrian and Babylonian Scholars, State Archives of Assyria 10 (Helsinki: Hel-
sinki University Press).
Pritchett, W. K., 1959, “The Athenian Lunar Month”, Classical Philology 54, 151–157.
——, 1970, The Choiseul Marble (Berkeley and Los Angeles: University of California Press).
——, 1982, “The Calendar of the Gibbous Moon”, Zeitschrift für Papyrologie und Epigraphik 49, 243–266.
——, 1999, “Postscript: The Athenian Calendars”, Zeitschrift für Papyrologie und Epigraphik 128, 79–93.
——, 2001, Athenian Calendars and Ekklesias, ΑΡΧΑIΑ ΕΛΛΑΣ: Monographs on Ancient Greek History
and Archaeology 8 (Amsterdam: J.C. Gieben).
——, and Neugebauer, O., 1947,The Calendars of Athens (Cambridge, Mass.: Harvard University Press).
Sachs, A. J. and Hunger, H., 1988, Astronomical Diaries and Related Texts from Babylonia, I: Diaries from 652
B.C. to 262 B.C, Österreichische Akademie der Wissenschaften, Philosophisch-historische Klasse, Denk-
schriften 195 (Vienna: Verlag der Akademie).
——, and Hunger, H., 1996, Astronomical Diaries and Related Texts from Babylonia, III: Diaries from 164
B.C. to 61 B.C, Österreichische Akademie der Wissenschaften, Philosophisch-historische Klasse, Denk-
schriften 247 (Vienna: Verlag der Akademie).
Steele, J. M., 2007, “The Length of the Month in Mesopotamian Calendars of the First Millennium BC”, in
J. M. Steele (ed.), Calendars and Years: Astronomy and Time in the Ancient Near East (Oxford: Oxbow
Books), 133–148.
——, 2011, “Making Sense of Time: Observational and Theoretical Calendars”, in K. Radner and E. Robson
(eds.), The Oxford Handbook of Cuneiform Culture (Oxford: Oxford University Press), 470–485.
Stern, S., 2000, “The Babylonian Calendar at Elephantine”, Zeitschrift für Papyrologie und Epigraphik 130,
159–171.
——, 2008, “The Babylonian Month and the New Moon: Sighting and Prediction”, Journal for the History of
Astronomy 39, 19–42.
van der Waerden, B. L., 1960, “Greek Astronomical Calendars and Their Relation to the Athenian Civil Cal-
endar”, Journal of Hellenic Studies 80, 168–180.
Westermann, W. L and Kraemer, Jr., C. J., 1926, Greek Papyri in the Library of Cornell University (New York:
Columbia University Press).
