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TALANTA XXXVIIII-XXXIX (2006-2007)

THE SOLAR YEAR OF THE COLIGNY CALENDAR
AS AN ANALOGUE OF THE ROMAN SOLAR YEAR
Brent Davis

In this essay, Fotheringham’s suspicion that ‘the Coligny calendar is, like our
Easter calendar, a calendar accommodated to the Julian calendar’ (Rhys and
Fotheringham 1910, 285) is reassessed with Samon as March, in line with the
conclusions of the first in this pair of essays. We find that the resulting relationship between the two calendars is symmetrical and extremely simple, such
that converting dates from one calendar to the other becomes straightforward.
Days marked IVOS are shown to cluster with some precision around dates with
strong traditional associations. In light of these findings, it is suggested that
Fotheringham’s suspicion may have been correct but for his alignment of the
year.
REASSESSING FOTHERINGHAM’S IDEA WITH SAMON AS MARCH

With Samon as March, the Gaulish solar months parallel the Roman months in
length, as shown in the preceding essay, suggesting that Fotheringham may have
been correct in his suspicion that the two calendars existed in a standardised relationship. However, based upon the fact that Samon means ‘summer’, Rhys placed
Samon in June, near the summer solstice (ibid., 210; Rhys 1905, 73).
Let us then reassess Fotheringham’s idea with Samon as March, and do so in the
most straightforward way: by plotting the behaviour of the two calendars against
each other. If the correspondence between the lengths of the solar months does
indicate a standardised relationship between the calendars, then this exercise
should reveal it.

Sequential use of the plate
Some scholars (e.g., Duval and Pinault 1986, 415; Olmsted 1992, 46) believe
that the plate was used sequentially, from left to right in repeated iterations. Others
(e.g. Rhys and Fotheringham 1911, 350; MacNeill 1926, 33; Lainé-Kerjean 1943,
255-6) have suggested that the years on the plate were employed in a simple but
non-sequential pattern. Here, we will examine the behaviour of both patterns of use
against the Roman calendar, beginning with sequential use.

35

Method of sequential use
The solar year on the plate, as shown in the previous essay, contains 366 days,
or 367 if Equos is long. If Equos is given 30 days in (Gaulish) years encompassing a Roman bissextile, and 29 days in other years, as Fotheringham suggested (Fotheringham 1910, 285-6), then this solar year will always amount to
a Roman year and a day, and will advance on the Roman calendar by one day
per year. After 30 years, it will have advanced by 30 days; and at this point,
omitting one 30-day intercalary month should cause the pattern to repeat.
To illustrate, let us take a single day in the Gaulish solar year – say, the first day of
solar Samon – and determine its Roman equivalents over a 30-year period.

Results of sequential use
As shown in the previous essay, the intercalary months indicate the days on which
solar Samon commences in the five ‘plate-years’:
TABLE 1: Days on which solar Samon begins in the five plate-years
Plate-

Start of

year

solar Samon

III

Samon 25

I

II

IV
V

Samon 1

Samon 13
Samon 7

Samon 19

Now let us arbitrarily call March 1, AD 101 ‘Samon 1 of cycle-year 1’, and
observe the behaviour of these five days against the Roman calendar:
TABLE 2: Results of sequential use (cycle-years 1 to 5)
Cycleyear

Start of

Roman

Year II, Samon 13

March 02, 102

solar Samon

1

Year I, Samon 1

4

Year IV, Samon 7

2
3

5

Year III, Samon 25
Year V, Samon 19

Long

equivalent

Equos?

March 03, 103

Y

March 01, 101

March 04, 104

March 05, 105

As can be seen, these five starting-days of solar Samon occur at intervals of a
Roman year and a day, such that the equivalent day of March increments by one
day per year. Making Equos long in bissextile years preserves this pattern.

36

In the second iteration of the plate, the same five days again represent the start
of solar Samon, and continue to mark out a Roman year and a day:
TABLE 3: Results of sequential use (cycle-years 6 to 10)
Cycleyear
6
7

8
9

10

Start of

Roman

Long

Year II, Samon 13

March 07, 107

Y

solar Samon

Year I, Samon 1

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

equivalent

March 06, 106

March 08, 108

March 09, 109

Equos?

March 10, 110

The remaining four iterations continue in the same fashion:
TABLE 4: Results of sequential use (cycle-years 11 to 30)
Cycle-

Start of

Roman

12

Year II, Samon 13

March 12, 112

year
11

13
14

15

16
17

18
19

20

solar Samon

Year I, Samon 1

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

21

Year I, Samon 1

24

Year IV, Samon 7

22

23

25

26

27
28

29

30

equivalent

March 11, 111

March 13, 113

March 14, 114

March 15, 115
March 16, 116

March 17, 117
March 18, 118

March 19, 119

March 20, 120
March 21, 121

Year II, Samon 13

March 22, 122

Year V, Samon 19

March 25, 125

Year III, Samon 25
Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

March 23, 123
March 24, 124

March 26, 126

March 27, 127
March 28, 128

March 29, 129

Long

Equos?
Y

Y

Y

Y

Y

March 30, 130

At this point, omitting ICA at the end of Year 30 will cause the 31st solar Samon
to begin not on March 31, AD 131, but thirty days earlier on March 1, and the
30-year pattern repeats:

37

TABLE 5: Results of sequential use (cycle-years 1 to 5 of next cycle)
Cycleyear
1

2

3

4
5

Start of

Roman

solar Samon

Long

equivalent

Year I, Samon 1

Equos?

March 01, 131

Year II, Samon 13

Y

March 02, 132

Year III, Samon 25

March 03, 133

Year IV, Samon 7

March 04, 134

Year V, Samon 19

March 05, 135

Y

The plate perpetually follows the Roman calendar in this manner, as long as Equos
is given a 30th day only in (Gaulish) years that encompass a Roman bissextile.

Evaluation of results
In this system of use, two things are immediately evident: first, that all five
instances of Equos on the plate will periodically require a 30th day. This would
explain why all surviving ends of Equos show a 30th day: perhaps, as Rhys and
Fotheringham suggested (Rhys/Fotheringham 1911, 358), all five instances of the
month had a 30th day that was used only when needed, just as today’s ecclesiastical calendars always contain an entry for February 29 in the expectation that the
user will know when to employ it. In this context, the numeral CCCLXXXV engraved
into the centre of Year III does not preclude Equos of Year III from containing 29
days, as Orpen felt it did (Orpen 1910, 369): as MacNeill points out, the existence
of this numeral ‘does not imply that the number was invariable’(MacNeill 1926,
28 n.1).
Second, it is evident that for any start of solar Samon, in any cycle, the equivalent day of March is always given by the cycle-year. This makes finding March 1
simple:

TABLE 6: March 1 is always (cycle-year - 1) days before the start of solar Samon
Cycle-

Start of

Roman

Therefore:

2

Year II, Samon 13

March 02, 102

March 01, 102 = Year II, Samon 12

year

1

3

4

5

6
7

8

9

10

solar Samon

Year I, Samon 1

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

equivalent

March 01, 101

March 03, 103

March 04, 104
March 05, 105
March 06, 106

March 07, 107

March 08, 108

March 09, 109
March 10, 110

March 01, 101 = Year I, Samon 1

March 01, 103 = Year III, Samon 23
March 01, 104 = Year IV, Samon 4

March 01, 105 = Year V, Samon 15
March 01, 106 = Year V, ICA 26

March 01, 107 = Year II, Samon 7

March 01, 108 = Year III, Samon 18

March 01, 109 = Year III, Cantlos 28
March 01, 110 = Year V, Samon 10

These five initial days of solar Samon can always be used in this way to locate
March 1 on the plate; all that is necessary is to know the cycle-year.

38

One troubling result
Employing the plate sequentially in this way does create a simple relationship
between the calendars, and it affords a quick way of converting dates from one
calendar to the other. But one result remains troubling: the range over which the
lunar months then wander. Samon, for example, can begin as early as February 7
(in cycle-year 3) and as late as March 26 (in cycle-year 26), a range of no fewer
than 48 days – well over a lunar month and a half. Yet the primary purpose of
intercalary months is to limit this drift. Why would the calendar include not one
but two of them, only to limit it so ineffectively?
Meanwhile, more effective patterns for applying intercalary months had been
known in Europe since the fifth century BC, when Meton published his lunisolar
calendar in Greece (Neugebauer 1957, 7). In Meton’s calendar, the additional
months were applied more awarely so as to restrict the drift to a lunar month or
less, enabling the solar months to continue to begin within their own lunar months
(McCarthy 1993, 207), just as the plate’s own solar months are shown to do in the
previous essay.
Because it minimised drift so effectively, Meton’s calendar was adopted by
astronomers, amongst whom it never lost currency. Ptolemy refers to it in the
Almagest (Samuel 1972, 42-9), and whenever Greek or Roman astronomers of
any subsequent period use a Greek calendar in their work, they use Meton’s (ibid.,
50), such that those who traded ideas with Greek astronomers, or read their writings, could scarcely have remained ignorant of it.
As this had been the case for centuries before the plate, Rhys and Fotheringham
suspected that the Gaulish calendar might well have been intercalated according
to a pattern like Meton’s. Accordingly, they suggested an effective non-sequential
pattern for operating the calendar in a 19-year cycle (Rhys and Fotheringham
1911, 349-50). Lainé-Kerjean (1943, 255-6) proposed an equally-effective pattern for a 30-year cycle, in line with Pliny’s attestation in Naturalis Historia
(XVI. 250) that Gaulish druids marked a cycle of this length.

Non-sequential use of the plate
It would help resolve the issue if such a non-sequential intercalation pattern could
be shown to arise from the plate itself – and in fact, just such a pattern is naturally created by requiring that March begin within Samon. In generating this pattern,
we will again follow Fotheringham’s suggestion that Equos be given 30 days in
(Gaulish) years encompassing a Roman bissextile, and 29 days in other years
(Fotheringham 1910, 285-6). But this time, instead of paying no heed to the relationship between Samon and March, we will require that March 1 remain within
Samon. We will find that the intercalation pattern arises directly from this requirement, and that it produces interesting results.

Method
Divide the 30 days of Samon into five equal spans of six days. For the moment,
let us call these six-day spans ‘hexads’:

39

!
SAMON:

1

"!

hexad 1
2

3

4

5

6

7

hexad 2
8

"!

hexad 3

"!

hexad 4

"!

hexad 5

"

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Fig. 1. Samon divided into five spans of six days.

As before, we take March 1, AD 101 to be Samon 1 of cycle-year 1:
!
SAMON:

1

"!

hexad 1
2

3

4

5

6

7

hexad 2
8

"!

hexad 3

"!

hexad 4

"!

hexad 5

"

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

#
March 1, 101AD (cycle-year 1)

Fig. 2. Location of March 1 within Samon (cycle-year 1).

There is no bissextile in the coming year, so both Equos and February will be
short, and the solar and lunar years will therefore contain 365 days and 354 days,
respectively. As the solar year is 11 days longer than the lunar year, March 1, AD
102 will fall 11 days later in Samon, on day 12; and in the same way, March 1,
AD 103 will fall on day 23:
!
SAMON:

1

"!

hexad 1
2

3

4

5

6

7

hexad 2
8

#
March 1, 101AD (cycle-year 1)

"!

hexad 3

"!

hexad 4

"!

hexad 5

"

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

#
March 1, 102AD (cycle-year 2)

#
March 1, 103AD (cycle-year 3)

Fig. 3. Location of March 1 within Samon (cycle-years 1 to 3).

Let us tabulate these days against the hexads in which they occur:

TABLE 7: Location of March 1 within Samon (cycle-years 1 to 3)
Cycle-year

March 1 is...

Within...

3 (103)

Samon 23

hexad 4

1 (101)

2 (102)

Samon 1

Samon 12

hexad 1

hexad 2

The year following March 1, AD 103 contains a bissextile; but because
February and Equos will be lengthened in tandem, the pattern will remain
undisturbed, and March 1, AD 104 will again fall 11 days later – on ‘day 34’,
outside Samon. This, however, is the very situation we expect the intercalary
months to prevent; so we note that one of them must intervene somewhere
between the Samons of cycle-years 3 and 4, with the result that March 1, AD
104 will actually fall 30 days earlier, on Samon 4:

40

!
SAMON:

1

"!

hexad 1
2

3

4

5

6

7

hexad 2
8

"!

hexad 3

"!

hexad 4

"!

hexad 5

"

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

#
March 1, 104AD (cycle-year 4)

Fig. 4. Location of March 1 within Samon (cycle-year 4).

We will tabulate this fourth entry as follows, so as to show the insertion of an
intercalary month between the third and fourth Samons:
TABLE 8: Location of March 1 within Samon (cycle-years 1 to 4)
Cycle-year

1 (101)

March 1 is...

Within...

Samon 23

hexad 4

Samon 1

2 (102)

hexad 1

Samon 12

3 (103)

hexad 2

Intercalation

4 (104)

Samon 4

hexad 1

So then: the signal to intercalate is arising entirely from the requirement that
March 1 remain within Samon.
If we continue in this way, adding 11 days each year (then subtracting 30 if the
result exceeds 30) so as to ensure that March 1 remains within Samon, we find
that the pattern completes after 30 years:
Table 9, see next page.

One step remains: to express ‘hexad’ as something more meaningful; and in
fact, there is a natural correlation between hexads and plate-years. Earlier, Table
1 listed the days on which solar Samon commences in the five plate-years:
Samon 1, 13, 25, 7, and 19, respectively. Notice that each of the hexads in
Samon is headed by one of these five days:
!

"!

hexad 1

hexad 2

"!

hexad 3

"!

hexad 4

"!

hexad 5

"

Fig. 5. Each hexad begins with one of the days listed in Table 1.

SAMON:

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

41

TABLE 9: Location of March 1 within Samon (cycle-years 1 to 30)
Cycle-year
1 (101)

March 1 is...

Within...

Cycle-year

Samon 23

hexad 4

18 (118)

Samon 1

2 (102)

hexad 1

Samon 12

3 (103)

hexad 2

Intercalation

4 (104)

Samon 4

5 (105)

hexad 1

Samon 15

6 (106)

hexad 3

Samon 26

hexad 5

Intercalation

7 (107)

Samon 7

8 (108)

hexad 2

Samon 18

9 (109)

hexad 3

Samon 29

hexad 5

Intercalation

10 (110)

Samon 10

11 (111)

hexad 2

Samon 21

hexad 4

Intercalation

12 (112)

Samon 2

13 (113)

hexad 1

Samon 13

14 (114)

hexad 3

Samon 24

hexad 4

Intercalation

15 (115)

Samon 5

16 (116)

hexad 1

Samon 16

hexad 3

17 (117)

19 (119)

20 (120)
21 (121)

22 (122)

23 (123)
24 (124)

25 (125)

26 (126)

27 (127)

28 (128)
29 (129)

30 (130)

1 (131)

March 1 is...

Within...

Samon 8

hexad 2

Samon 27

Intercalation
Samon 19
Samon 30

Intercalation
Samon 11

Samon 22

Intercalation
Samon 3

Samon 14

Samon 25

Intercalation
Samon 6

Samon 17
Samon 28

Intercalation
Samon 9

Samon 20

Intercalation
Samon 1

hexad 5

hexad 4

hexad 5
hexad 2

hexad 4

hexad 1
hexad 3

hexad 5

hexad 1

hexad 3

hexad 5
hexad 2

hexad 4

hexad 1

By analogy, let us use the list in Table 1 to associate each hexad with a plateyear:
!
SAMON:

1

!

"!

hexad 1
2

3

4

year 1

5

6

7

"!

hexad 2
8

"!

hexad 3

"!

hexad 4

"!

hexad 5

"

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

year IV

"!

year II

Fig. 6. Hexads associated with plate-years.

"!

year V

"!

year III

"

We can now substitute ‘plate-years’ for ‘hexads’ in Table 9. The result is Table 10:
Table 10, see opposite page.

42

TABLE 10: Location of March 1 within Samon (cycle-years 1 to 30), with
plate-year substituted for hexad
March 1 is...

Cycle-year

1 (101)

Samon 1

2 (102)

Samon 12

3 (103)

Samon 23
Samon 4

5 (105)

Samon 26

Samon 10

Samon 21
Samon 2

13 (113)
14 (114)

Samon 24

Intercalation

15 (115)

Samon 5

16 (116)

Samon 3

Year II

Samon 25

Year III

Intercalation

Samon 6

Year I

Samon 17

28 (128)

1 (131)

Year I

Samon 14

27 (127)

Year II

Year V

Intercalation

26 (126)

29 (129)

Year IV

Samon 22

25 (125)

Year II

Samon 28

Year III

Intercalation

30 (130)

Year I

Samon 16

Samon 11

24 (124)

Year V

Year III

Intercalation

23 (123)

Year II

Year V

Samon 30

22 (122)

Year I

Samon 13

Samon 19

21 (121)

Year V

Year III

Intercalation

20 (120)

Year IV

Intercalation

12 (112)

Year IV

Year III

Intercalation

11 (111)

Samon 8

Samon 27

19 (119)

Year II

Samon 29

10 (110)

18 (118)

Year IV

Samon 18

9 (109)

Year V

Year III

Samon 7

8 (108)

Within...

Year II

Intercalation

7 (107)

March 1 is...

17 (117)

Year I

Samon 15

6 (106)

Cycle-year

Year IV

Intercalation

4 (104)

Within...

Year I

Samon 9

Year IV

Samon 1

Year I

Samon 20

Year V

Intercalation

Notice that, without our intending it, the intercalary months are all occuring
where they should on the plate – that is, only after the Samons of Years III and
V. We can therefore identify the intercalary months:
Table 11, see page 44.

The series of plate-years may appear irregular, but it is not. To illustrate, here
again are the 30 years of the cycle, together with the corresponding plate-years
from the table above (now shown in Arabic numerals):
Cycle-year:
Plate-year:

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1

4

5

1

2

3

4

2

3

4

5

1

2

Fig. 7. Cycle-years against plate-years.

5

1

2

3

4

5

3

4

5

1

2

3

1

2

3

4

The sequence of plate-years seems haphazard only until we depict it as shown
in Fig. 8:

43

5

TABLE 11: Location of March 1 within Samon (cycle-years 1 to 30), with intercalary months identified
Cycle year
1 (101)

2 (102)
3 (103)

4 (104)

5 (105)

6 (106)
7 (107)

8 (108)

9 (109)

10 (110)

11 (111)

12 (112)

13 (113)

14 (114)

15 (115)
16 (116)

March 1 is...
Samon 1

Samon 12

Samon 23

Within...

Year I

Year IV

Year V

ICA

Samon 4

Year I

Samon 15

Year II

Samon 26

Year III

ICB

Samon 7

Year IV

Samon 18

Year II

Samon 29
ICB

Samon 10
ICA

Samon 2

Samon 13

Samon 5

Samon 8

Year IV

21 (121)

Samon 11

19 (119)

20 (120)

22 (122)

23 (123)

26 (126)

25 (125)

Samon 27
ICB

Samon 19
Samon 30
ICB

Samon 22
ICA

Samon 3

Year III
Year V

Year III

Year IV
Year V

Year I

Samon 14

Year II

Samon 6

Year I

Samon 25
ICB

Year III

27 (127)

Samon 17

Year V

29 (129)

Samon 9

Year IV

Year II

1 (131)

Samon 1

Year I

Year I

Samon 16

18 (118)

Year V

Year II

ICA

Within...

24 (124)

Year I

Samon 24

March 1 is...

Year III

Year IV

Samon 21

Cycle year

17 (117)

28 (128)

30 (130)

Samon 28
ICB

Samon 20
ICA

Year II

Year III
Year V

Cycle-year
1

2 3 4 5 6 7

8 9 10 11 12 13

14 15 16 17 18 19

20 21 22 23 24 25

26 27 28 29 30

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Plate-year

Fig. 8. Cycle-years against plate-years (full pattern).
F

That is: we are now viewing the 30 years of the cycle as consisting of eight
sequential iterations of the plate, as shown by the bold borders; but with five
pairs of years omitted at regular intervals, as shown by the shading. This creates a simple, invariable pattern of use: the plate is employed sequentially for
six years, then two years are passed over, then six years are used, two are passed
over, and so on.
This, then, is the intercalation pattern that naturally arises from the sole requirement that March 1 remains within Samon. During these 30 years, March 1
occurs once on each of the 30 days of Samon, but never outside it. Meanwhile,
11 intercalary months are called for at the points shown in Table 11.
Interestingly, Lainé-Kerjean (1943, 255-6) noted that the most astronomically

44

accurate 30-year solution for this calendar would be produced by inserting
intercalary months at alternating 2.5- and 3-year intervals, in this fashion:
A (2.5y) B (3y)

B (2.5y) A (3y)
!

A (2.5y) B (3y)

B (2.5y) A (3y)

A (2.5y) B (3y)

B (2.5y)

Fig. 9. Lainé-Kerjean’s 30-year intercalation pattern.

This series is in fact identical to the one we have generated: Table 11 begins at
the point indicated by the arrow.

Results for first cycle
Using this new intercalation pattern, let us again plot the behaviour of the two
calendars against each other. As before, March 1, AD 101 is taken as Samon 1
of cycle-year 1:
TABLE 12: Results of non-sequential use (cycle-year 1)
Cycle- Start of
year solar Samon
1
Year I, Samon 1

Roman
equivalent
Mar 01, 101

Roman
usage
k.mar.

Long ICM? Lunar
Equos?
year
354

Days to next
solar Samon
354+6 = 360

That is: in cycle-year 1, the plate-year is I, and solar Samon begins on Samon
1; the Roman equivalent is March 1, AD 101, which in Roman usage is ‘k.mar.’
(the kalends of March). The ensuing year does not contain a bissextile, so
Equos will contain 29 days; and there is no intercalary month this year, so this
plate-year will contain 354 days.
The far-right column shows the number of days until the next start of solar
Samon. We know from Table 11 that in cycle-year 2, the plate-year will be IV;
and Table 1 shows that in plate-year IV, solar Samon begins on Samon 7; and
as Samon 7 is six days later than Samon 1, the far-right column indicates that it
will be 354 + 6 = 360 days until the next start of solar Samon. Adding these 360
days to the date produces the next row:
TABLE 13: Results of non-sequential use (cycle-years 1 and 2)
Cycleyear
1
2

Start of
solar Samon
Year I, Samon 1
Year IV, Samon 7

Roman
equivalent
Mar 01, 101
Feb 24, 102

Roman Long ICM? Lunar
usage
Equos?
year
k.mar.
354
vi k.mar.
354

Days to next
solar Samon
354+6 = 360
354+12= 366

In the same way, Table 11 indicates that in cycle-year 3, the plate-year will be
V; and Table 1 shows that in plate-year V, solar Samon begins on Samon 19;

45

and as Samon 19 is twelve days later than Samon 7, the far-right column indicates that it will be 354 + 12 = 366 days to the start of the next solar Samon.
Adding these 366 days to the date produces the third row:
TABLE 14: Results of non-sequential use (cycle-years 1 to 3)
Cycleyear

1

2

3

Start of

solar Samon

Year I, Samon 1

Year IV, Samon 7

Year V, Samon 19

Roman

Roman

Feb 24, 102

vi k.mar.

equivalent

Mar 01, 101
Feb 25, 103

usage

k.mar.

v k.mar.

Long

Equos?
Y

ICM?

Y

Lunar

year

354
354

385

Days to next

solar Samon

354+6 = 360

354+12= 366

385–18= 367

Cycle-year 3 will include a Roman bissextile at its end, in that February 24 of
AD 104 will be doubled; and so cycle-year 3 will also include a 30-day Equos.
In addition, as the plate-year is V, there will be an instance of ICA at the end of
the year; so this calendar year will contain 355 + 30 = 385 days.
For cycle-year 4, however, Tables 11 and 1 show that the plate-year will again
be I, and that solar Samon again begins on Samon 1. This is eighteen days earlier than Samon 19; so to produce the fourth row, we add 385 - 18 = 367 days...
and so on.
Continuing in this way for the entire cycle produces Table 15 (see p. 47):

In the penultimate column, it is apparent that the calendar years variously contain 354, 355, 384, or 385 days; but these year-lengths are entirely dictated by
the structures of the two calendars as they operate against each other.
In the final column, the starting-days of solar Samon mark out rough intervals
of a solar year. Were it not for the bissextiles, these intervals would form a
repeating pattern consisting of one year of 360 days, followed by five of 366
days, for an average of 365. The four-yearly bissextiles increase this average by
0.25 day to 365.25, the average length of the Roman calendar year.
Meanwhile, in the fourth column, a simple and regular pattern of Roman equivalents has been generated. As shown by the horizontal lines, the 30 years fall
into five ‘hexads’, much as the 30 days of Samon did. In the first year of each
hexad, solar Samon begins on k.mar.; in the second year, it begins on vi k.mar.;
then, in each subsequent year, solar Samon begins one day later in the Roman
calendar, until it again begins on k.mar. in the first year of the next hexad. The
only variation occurs in cycle-years 8 and 20, when it happens to begin on vi
k.mar. in a bissextile year. This is the day that is doubled to produce the bissextile, and so in these years, solar Samon begins on the second ‘vi k.mar.’– that
is, on ‘vi2 k.mar.’, the day after the bissextile day.
Notice that solar Samon - and therefore the calendar’s solar year as a whole - can
never begin earlier than vi k.mar. The significance of this date is that it is the first

46

TABLE 15: Results of non-sequential use (cycle-years 1 to 30)
Cycle-

Start of

Roman

Roman

2

Year IV, Samon 7

Feb 24, 102

vi k.mar.

year
1
3
4
5

solar Samon

Year I, Samon 1

Year V, Samon 19
Year I, Samon 1

Year II, Samon 13

6

Year III, Samon 25

9

Year III, Samon 25

7

8

10
11

12

13
14
15
16
17

18

19

20

21
22
23
24

Year IV, Samon 7

Year II, Samon 13
Year IV, Samon 7

Year V, Samon 19
Year I, Samon 1

Year II, Samon 13
Year V, Samon 19
Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Feb 27, 105

Feb 28, 106

Mar 01, 107

Feb 242, 108

Year I, Samon 1

Year II, Samon 13
Year I, Samon 1

Year II, Samon 13

Year IV, Samon 7

Year V, Samon 19

usage

k.mar.

v k.mar.

iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

Feb 25, 109

vi2 k.mar.
v k.mar.

Feb 28, 112

ii k.mar.

Feb 26, 110
Feb 27, 111

Mar 01, 113

iv k.mar.

iii k.mar.
k.mar.

Feb 24, 114

vi k.mar.

Feb 27, 117

iii k.mar.

Feb 25, 115
Feb 26, 116

Feb 28, 118

Feb 26, 122

Year III, Samon 25

30

Feb 26, 104

Year V, Samon 19

Year IV, Samon 7

28

29

Feb 25, 103

Mar 01, 119

Year III, Samon 25

Year III, Samon 25

27

Mar 01, 101

Year V, Samon 19

25

26

equivalent

Feb 242, 120

v k.mar.

iv k.mar.
ii k.mar.
k.mar.

Feb 25, 121

vi2 k.mar.
v k.mar.

Feb 28, 124

ii k.mar.

Feb 27, 123

Mar 01, 125
Feb 24, 126
Feb 25, 127

Feb 26, 128

Feb 27, 129
Feb 28, 130

iv k.mar.

iii k.mar.
k.mar.

vi k.mar.
v k.mar.

iv k.mar.

iii k.mar.
ii k.mar.

Long

Equos?
Y

Y

Y

Y

Y

Y

Y

ICM?

Y
Y
Y

Y

Y
Y
Y
Y
Y
Y

Y

Lunar

Days to next

year

solar Samon

385

385–18= 367

354
354
354

354+6 = 360

354+12= 366
354+12= 366

354

354+12= 366

354

354+12= 366

384

355

384
354

385

354
354
384
355
354

384

354

355
384
354
384
355

384–18= 366
355+6= 361

384–18= 366

354+12= 366
385–18= 367

354+12= 366
354+6= 360

384–18= 366

355+12= 367
354+12= 366
384–18= 366

354+12= 366
355+ 6= 361

384–18= 366

354+12= 366
384–18= 366

355+12= 367

354

354+12= 366

355

355+12= 367

384
354

384

354
384

384–24= 360

354+12= 366
384–18= 366

354+12= 366
384–18= 366

day after Terminalis (vii k.mar.), the traditional end of the Roman year; and so we
can see that the calendar’s solar year is being constrained never to begin earlier than
the traditional start of the Roman year. This seems unlikely to be pure concidence,
and tends to support the idea that Samon is indeed the equivalent of Roman March.

Results for subsequent cycles
Because Equos and February are lengthened in tandem, the bissextile never disturbs the relationship between the calendars; and so the initial day of solar
Samon produces the same pattern of Roman equivalents no matter where the

47

TABLE 16: Results of non-sequential use (entire second cycle, and cycle-years
1 to 8 of third cycle)
Cycleyear

Start of

solar Samon

1

Year I, Samon 1

4

Year I, Samon 1

2

3

5
6
7

8
9

10
11

12

13

14

15

16
17
18
19

20
21
22
23

24
25

26

27

28

29

30
1

2

3

4

5

6

7

8

48

Year IV, Samon 7

Year V, Samon 19

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19
Year I, Samon 1

Year II, Samon 13
Year V, Samon 19
Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19
Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year V, Samon 19
Year I, Samon 1

Year IV, Samon 7

Year V, Samon 19
Year I, Samon 1

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year II, Samon 13

Roman

equivalent

Mar 01, 131

Feb 242, 132
Feb 25, 133

Feb 26, 134
Feb 27, 135
Feb 28, 136

Mar 01, 137
Feb 24, 138
Feb 25, 139
Feb 26, 140
Feb 27, 141

Feb 28, 142

Mar 01, 143

Feb 242, 144
Feb 25, 145
Feb 26, 146
Feb 27, 147
Feb 28, 148

Mar 01, 149
Feb 24, 150
Feb 25, 151
Feb 26, 152

Feb 27, 153
Feb 28, 154

Mar 01, 155

Feb 242, 156
Feb 25, 157

Feb 26, 158

Feb 27, 159

Feb 28, 160

Mar 01, 161
Feb 24, 162

Feb 25, 163

Feb 26, 164

Feb 27, 165

Feb 28, 166

Mar 01, 167

Feb 242, 168

Roman
usage

k.mar.

vi2 k.mar.
v k.mar.
iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi k.mar.
v k.mar.

iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi2 k.mar.
v k.mar.
iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi k.mar.
v k.mar.

iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi2 k.mar.
v k.mar.
iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi k.mar.
v k.mar.

iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi2 k.mar.

Long

Equos?
Y

ICM?

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y
Y
Y
Y

Y
Y
Y

Lunar

year

Days to next

solar Samon

355

355+6=361

354

354+12= 366

354

384

355
384

354
354
385
354

384

354

355

384
354
354
385
354

354
384
355
384

354
354

385

354
354

384

355

384

354

354

385

354

354

384

355

354

354+12=366

384–18= 366

355+12= 367
384–18= 366
354+6= 360

354+12= 366
385–18= 367

354+12= 366
384–18= 366

354+12= 366
355+6= 361

384–18= 366

354+12= 366
354+12= 366
385–18= 367

354+12= 366
354+6= 360

384–18= 366

355+12= 367
384–18= 366

354+12= 366
354+12= 366
385–24= 361

354+12= 366
354+12= 366
384–18= 366

355+12= 367
384–18= 366
354+6= 360

354+12= 366
385–18= 367

354+12= 366

354+12= 366
384–18= 366
355+6= 361

354+12= 366

bissextiles occur. This means that all 30-year cycles produce the same result.
To illustrate this, we need only look at the next 30-year cycle (see Table 16 on
p. 48):

In the second 30-year cycle, the bissextiles are displaced by two years from
their positions in the first cycle, creating a different sequence of year-lengths;
yet the pattern of Roman-style equivalents remains unchanged.
The first few years of the third cycle are also shown, to demonstrate that, as 60
is evenly divisible by 4, the bissextiles now occupy the same locations as in the
first cycle. So then, the full pattern actually encompasses a pair of 30-year
cycles; but the pattern of Roman equivalents remains the same throughout.
In fact, as the location of the bissextiles never affects the pattern of Roman
equivalents, we could just as well begin the first 30-year cycle in AD 102, or in
any other year, rather than in AD 101:
TABLE 17: Results of non-sequential use (cycle-years 1 to 10 of first cycle, if
cycle begins in AD 102)
Cycleyear

1
2

3
4

5

6

Start of

solar Samon

Roman

Roman

Feb 24, 103

vi k.mar.

equivalent

Year I, Samon 1

Mar 01, 102

Year I, Samon 1

Feb 26, 105

Year IV, Samon 7

Year V, Samon 19

Year II, Samon 13

Year III, Samon 25

Feb 25, 104

Feb 27, 106

Feb 28, 107

7

Year IV, Samon 7

Mar 01, 108

10

Year IV, Samon 7

Feb 26, 111

8
9

Year II, Samon 13

Year III, Samon 25

Feb 24, 109

Feb 25, 110

usage

k.mar.

v k.mar.

iv k.mar.

iii k.mar.

ii k.mar.

k.mar.

vi k.mar.

v k.mar.

iv k.mar.

Long

Equos?
Y

Y

Y

ICM? Lunar
year

Y

354

355
384

354

354

Days to next

solar Samon

354+6= 360

355+12= 367
384–18= 366

354+12= 366

354+12= 366

Y

385

385–18= 367

Y

384

384–18= 366

354
354

355

354+6= 360

354+12= 366

355+12= 367

Just the first ten years are shown, but it is clear that although the sequence of
year-lengths is yet again different, the Roman equivalents remain unchanged.
The same is true of the second cycle (see Table 18 on p. 50):

49

TABLE 18: Results of non-sequential use (cycle-years 1 to 10 of second cycle,
if first cycle begins in AD 102)
Cycleyear

Start of

solar Samon

Roman

usage

Feb 25, 134

v k.mar.

1

Year I, Samon 1

Mar 01, 132

4

Year I, Samon 1

Feb 26, 135

2
3

5
6
7

8
9

10

Year IV, Samon 7

Year V, Samon 19

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Roman

equivalent

Feb 24, 133

Feb 27, 136
Feb 28, 137

Mar 01, 138
Feb 24, 139
Feb 25, 140
Feb 26, 141

k.mar.

vi k.mar.

iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi k.mar.
v k.mar.

iv k.mar.

Long

Equos?

Y

Y

ICM? Lunar
year

Y
Y
Y

Days to next

solar Samon

354

354+6= 360

355

355+12= 367

354
384

354
384

354
355
384
354

354+12= 366
384–18= 366

354+12= 366
384–18= 366
354+6= 360

355+12= 367
384–18= 366

354+12= 366

...and the third as well, which (as before) is a duplicate of the first:

TABLE 19: Results of non-sequential use (cycle-years 1 to 10 of third cycle, if
first cycle begins in AD 102)
Cycle-

year

Start of

solar Samon

Roman

usage

Feb 25, 164

v k.mar.

1

Year I, Samon 1

Mar 01, 162

4

Year I, Samon 1

Feb 26, 165

2
3

5
6
7

8

Year IV, Samon 7

Year V, Samon 19

Year II, Samon 13

Year III, Samon 25
Year IV, Samon 7

Year II, Samon 13

Roman

equivalent

Feb 24, 163

Feb 27, 166
Feb 28, 167

Mar 01, 168
Feb 24, 169

k.mar.

vi k.mar.

iv k.mar.

iii k.mar.
ii k.mar.
k.mar.

vi k.mar.

Long

Equos?
Y

Y

ICM? Lunar
year

Y
Y

Days to next

solar Samon

354

354+6= 360

354

354+12= 366

355
384

354
385

354
354

355+12= 367
384–18= 366

354+12= 366
385–18= 367
354+6= 360

354+12= 366

So then, it is also immaterial which year is designated as the start of the first 30year cycle: the pattern of Roman equivalents will always be the same, and will
remain the same for all subsequent cycles.

Evaluation of results
In this non-sequential method of use, all five instances of Equos on the plate
again periodically require a 30th day; and as before, this could explain why all
surviving ends of Equos contain a 30th day. Furthermore, the degree of wander
is now as small as the calendar’s complexity suggests it ought to be. Table 15
shows that Samon can begin as early as February 1 (in cycle-years 9 and 20)
and as late as March 1 (in cycle-year 1) – a range of no more than 29 days, a
result as good as Meton’s.

50

The consequent relationship between Samon and March is so symmetrical and
simple that dates can be converted from one to the other quite easily, even if one
knows only the current cycle-year. For example: say that the current cycle-year
is 16. The calendars can then be coordinated in three simple steps:

Step 1: From the cycle year, locate the current year on the plate:
Add 4 to the cycle-year, divide the result by 6, and discard any remainder.
Double the result, add the cycle-year, and subtract 5 until the number
is 5 or less.
(Formula A)
Example: For cycle-year 16, the result is 2 – that is, plate-year II.
Step 2: From the plate-year, determine the day of Samon on which solar Samon
begins:
Subtract 1 from the plate-year, multiply the result by 12, and add 1.
If greater than 30, subtract 30.
(Formula B)
Example: For Year II, the result is 13 – that is, solar Samon begins on
Samon 13.
Step 3: From the day of Samon on which solar Samon begins, determine the
equivalent day of the kalends of March:
From 32, subtract the cycle-year, then subtract 6 until the number is 6
or less.
(Formula C)
Example: For cycle-year 16, the result is 4 - that is, Samon 13 = iv k.mar.

So then: knowing only that it is cycle-year 16, one can use these three simple
formulae to determine that in this year, Samon 13 coincides with iv k.mar. in
the Roman calendar. As Table 15 shows, these results match the ones derived
earlier for cycle-year 16, using the much more cumbersome method of counting days.

Behaviour of other months
Furthermore: as solar Samon and March both contain 31 days, the same simple
relationship occurs between solar Duman and April:
TABLE 20: Results of non-sequential use (cycle-years 1 to 7): Samon and
Duman
Cycle- Plate-

Start of

Roman

Roman

Start of

Roman

Roman

2

Samon 7

Feb 24, 102

vi k.mar.

Duman 8

Mar 27, 102

vi k.apr.

year

year

3

V

1
4
5
6

7

I

IV

solar Samon
Samon 1

Samon 19

equivalent

Mar 01, 101
Feb 25, 103

usage

k.mar.

v k.mar.

solar Duman
Duman 2

Duman 20

equivalent

Apr 01, 101

Mar 28, 103

usage
k.apr.

v k.apr.

I

Samon 1

Feb 26, 104

iv k.mar.

Duman 2

Mar 29, 104

iv k.apr.

IV

Samon 7

Mar 01, 107

k.mar.

Duman 8

Apr 01, 107

k.apr.

II

III

Samon 13
Samon 25

Feb 27, 105
Feb 28, 106

iii k.mar.
ii k.mar.

Duman 14

Duman 26

Mar 30, 105

Mar 31, 106

iii k.apr.
ii k.apr.

51

Plate-

year

I
V

IV

II

I

IV

III

Start of

solar Samon

Samon 1
Samon 19

Samon 7

Samon 13

Samon 1

Samon 7

Samon 25

Roman

equivalent

Mar 01, 101
Feb 25, 103

Feb 24, 102

Feb 27, 105

Feb 26, 104

Mar 01, 107

Feb 28, 106

Roman

usage

k.mar.
v k.mar.

vi k.mar.
iii k.mar.

iv k.mar.

k.mar.

ii k.mar.

Start of

Duman 2

solar Duman

Duman 20

Duman 8

Duman 14

Duman 2

Duman 8

Duman 26

Roman

equivalent

Apr 01, 101

Mar 28, 103

Mar 27, 102

Mar 30, 105

Mar 29, 104

Apr 01, 107

Mar 31, 106

Start of

solar Anagant

Anagant 4

Anagant 10

Roman

equivalent

Jun 01, 101

May 27, 102

Roman

usage

k.iun.

vi k.iun.

Start of

solar Ogron

Ogron 5

Ogron 11

Roman

equivalent

Jul 01, 101

Jun 26, 102

Roman

equivalent

May 01, 101

Start of

solar Rivros
Rivros 3

Roman

k.apr.

usage

Apr 26, 102
Rivros 15

Rivros 3

Rivros 9

Rivros 27

Start of

solar Cutius
Cutios 6

Cutios 12

Roman

equivalent

Jul 27, 102

Aug 01, 101

May 01, 107

Apr 30, 106

Apr 29, 105

Apr 28, 104

Apr 27, 103

Rivros 9
v k.apr.

iii k.apr.

iv k.apr.

k.apr.

ii k.apr.

Roman

usage

k.iul.

vi k.iul.

Rivros 21

vi k.apr.

TABLE 21: Results of non-sequential use (cycle-years 1 to 7): Samon, Duman and Rivros
Cycle-

year

1
3

2

5

4

7

6

Plate-

IV

I

year

TABLE 22: Results of non-sequential use (cycle-years 1 to 7): Anagant, Ogron and Cutios

Cycle-

year

1

2

Jul 28, 103

Roman
k.mai.

usage

v k.mai.

vi k.mai.

iii k.mai.

iv k.mai.

k.mai.

ii k.mai.

Roman
usage

k.aug.

vi k.aug.
v k.aug.

iv k.aug.

Cutios 24

Jul 29, 104

v k.iul.

Cutios 6

Jun 27, 103

iv k.iul.

Ogron 23

Jun 28, 104

v k.iun.

Ogron 5

May 28, 103

iv k.iun.

Anagant 22

May 29, 104

V

Anagant 4

3
I

ii k.aug.

iii k.aug.

4

k.aug.

Jul 31, 106

Jul 30, 105

Aug 01, 107

Cutios 30

Cutios 18

Cutios 12

ii k.iul.

iii k.iul.
k.iul.

Jun 30, 106

Jun 29, 105

Jul 01, 107

Ogron 29

Ogron 17

Ogron 11

ii k.iun.

iii k.iun.
k.iun.

May 31, 106

May 30, 105

Jun 01, 107

Anagant 28

Anagant 16

Anagant 10

III

II

IV

6

5
7

52

Just the first seven years of the cycle are shown, but the point is clear: solar
Duman and April produce the same pattern of equivalents in Roman usage as
do solar Samon and March.
In the same way, solar Duman is the same length as April, so the same pattern
is also reproduced between solar Rivros and May:
21: Results of non-sequential use (cycle-years 1 to 7): Samon, Duman
and Rivros, see opposite page.

TABLE

Clearly, each subsequent Gaulish solar month will form this same pattern
against its Roman counterpart as long as they both contain the same number of
days, which we find is the case for the next six months of the year:

TABLE 22: Results of non-sequential use (cycle-years 1 to 7): Anagant, Ogron
and Cutios, see opposite page.

TABLE 23: Results of non-sequential use (cycle-years 1 to 7): Giamon, Simivi
and Equos, see next page.

The pattern has now remained the same through the first nine months of the
year. The final three months contain a difference:

TABLE 24: Results of non-sequential use (cycle-years 1 to 7): Elembiu, Edrin
and Cantlos, see next page.

Here we see the regular perturbation caused by the inequality between Equos
and November – namely: with respect to the Roman calendar, (a) solar Elembiu
always begins one day late in years containing a long Equos, whereas (b) solar
Edrin and Cantlos always begin one day early in years containing a short
Equos. The inequality between February and Cantlos, however, does not cause
a further perturbation, but rather corrects the first one, such that the relationship
between March and Samon remains constant.

Universal ‘conversion formulae’
So then, the same pattern of Roman equivalents is reproduced in all but the final
three months; and in these final three months, the pattern is perturbed in a simple and regular way. This means that the three-step conversion process can be
recast as a universal one, useful for any month, in any year of any cycle.
Suppose, for example, that it is now cycle-year 28, and that we want to coordinate the month of Giamon against the Roman calendar. We already know that
Giamon roughly corresponds to September:

53

Plate-

Start of

solar Giamon

Roman

equivalent

Roman

equivalent

Dec 01, 101

Nov 26, 102
Nov 28, 103

Nov 28, 104

Nov 29, 105
Nov 30, 106
Dec 02, 107

Roman

usage

usage

k.dec.

Start of

solar Simivi

solar Edrin

Edrin 11

Edrin 17
iv k.dec.

Edrin 17

Edrin 5

Edrin 11

Edrin 29

vi k.dec.

Edrin 23

iv k.dec.
iii k.dec.

ii k.dec.

iv non. dec.

Roman

equivalent

Roman

usage

Start of

solar Equos
Equos 9

Roman

equivalent

Nov 01, 101

usage

Roman
k.nov.

vi k.nov.

i k.oct.

usage

ii k.ian.

vii k.ian.
v k.ian.

Equos 9

Equos 15

Equos 3

solar Cantlos

Start of

Cantlos 12

Oct 29, 104

Nov 01, 107

Oct 31, 106

equivalent

Roman

Jan 31, 102

Jan 26, 103

iv k.nov.

k.nov.

ii k.nov.

Roman
usage

ii k.feb.

vii k.feb.
v k.feb.

v k.feb.
Jan 28, 105

Jan 28, 104
Cantlos 12

iii k.feb.

iv k.feb.

k.feb.

Jan 30, 107

Jan 29, 106

Feb 01, 108

Cantlos 6

Cantlos 24
Cantlos 18

ICA 1

Cantlos 18

v k.nov.

Oct 27, 102

i k.oct.

equivalent

Dec 31, 101

Dec 26, 102

Dec 28, 103

Dec 28, 104

v k.ian.
Dec 29, 105

iv k.ian.

k.ian.

Dec 30, 106

iii k.ian.
Jan 01, 108

Oct 28, 103

Equos 15

Oct 01, 101

Start of

solar Elembiu

Elembiu 10

Elembiu 16

Elembiu 28

Elembiu 10

Elembiu 22

Elembiu 4

Elembiu 16

Equos 27

vi k.oct.
v k.oct.

iv k.oct.
Oct 01, 107

Roman

ii k.oct.

Roman

Sep 30, 106

Sep 27, 103

Sep 26, 102

Simivi 8

Simivi 26

Simivi 14

k.sep.

v k.sep.

vi k.sep.

Sep 01, 101
Aug 28, 103

Aug 27, 102

Giamon 7
Giamon 25

Giamon 13

I

year

TABLE 23: Results of non-sequential use (cycle-years 1 to 7): Giamon, Simivi and Equos
Cycleyear
1
IV

V

2

Sep 28, 104
Simivi 20

iii k.nov.

Simivi 8

iii k.sep.

Simivi 14

Simivi 2

k.sep.

ii k.sep.

Oct 30, 105

iv k.sep.

Aug 30, 105

Sep 01, 107

Aug 31, 106

Equos 21

Aug 29, 104

Giamon 19

Giamon 13

Giamon 1

Start of

iii k.oct.

Giamon 7

IV

Roman

Sep 29, 105

I

3
5
7

II
III

4
6

Plate-

IV

III

II

I

V

IV

I

year

TABLE 24: Results of non-sequential use (cycle-years 1 to 7): Elembiu, Edrin and Cantlos
Cycleyear
1
2
3
4
5
6
7

54

TABLE 25: Basic correspondence between Gaulish and Roman months
Gaulish

Roman

Gaulish

Roman

Samon

March

Giamon

September

Anagant

June

Elembiu

December

Duman
Rivros
Ogron

Cutios

April
May

July

August

Simivi

Equos

Edrin

Cantlos

October

November

January

February

... but how exactly does Giamon correspond to September in cycle-year 28?

In the following solution, Formula A has remained the same; but Formulae B
and C have been altered so that they will work for any month:

Step 1: From the cycle year, locate the current year on the plate:
Add 4 to the cycle-year, divide the result by 6, and discard any remainder.
Double the result, add the cycle-year, and subtract 5 until the number
is 5 or less.
(Formula A)
Example: For cycle-year 28, the result is 3 – that is, plate-year III.
Step 2: From the plate-year, determine the day of Giamon on which solar
Giamon begins:
Subtract 1 from the plate-year, multiply the result by 12, and add the
month number.
If greater than 30, subtract 30.
(Formula B)
Example: Giamon is the 7th month, so its month-number is 7; and so
for Year III, the result is 1 - that is, solar Giamon begins on Giamon 1.
Step 3: From the day of Giamon on which solar Giamon begins, determine the
equivalent day of the kalends of September:
From 32, subtract the cycle-year, then subtract 6 until the number is 6
or less.
If the month is after Elembiu, add 1; and if it is after long Equos, subtract 1.
(Formula C)
Example: For cycle-year 28, the result is 4 - that is, Giamon 1 = iv k.sep.

The existence of such simple (yet perpetual) rules for conversion demonstrates
the simplicity of the relationship between the calendars that results from equating Samon with March. As has been demonstrated, this simplicity is due largely to the one-to-one correspondence between the Gaulish and Roman monthlengths, if Samon is equated with March; and so not surprisingly, equating
Samon with any other Roman month produces conversion-rules that are
markedly more complex. If the calendar was at all used in Gallo-Roman administration, then, the equating of Samon with March recommends itself as producing by far the simplest system to administer.

55

Sam 26 - Dum 4

Year II

ICA 26 - Sam 4

Year I

TABLE 26: Nine sets of IVOS days in each plate-year

Set

1

Year III

Year IV

Can 26 - Sam 4
Dum 13 - 20

Riv 26 - Ana 3

Dum 26 - Riv 3

Sam 26 - Dum 4
Riv 13 - 20

Ogr 28 - 30; Cut 28 - Gia 3

Riv 26 - Ana 3

Riv 13 - 20

Cut 28 - ICB 3

Dum 26 - Riv 3

Dum 13 - 20
Cut 28 - Gia 9

3

2
Ogr 28 - Cut 3

Equ 26 - Ele 5

7

5

4

Sim 27 - Equ 4

Can 28 - Sam 3

Ele 1 - 3

Edr 1 - 3

Ele 1 - 3

Ele 25

Year V

Riv 13 - 20

Sam 26 - Dum 4
Riv 26 - Ana 3

Sim 9

Cut 28 - Gia 3

Equ 26 - Ele 5
Edr 25

Edr 1 - 3

Can 28 - ICA 3

The waning moon, from just after full to just after last quarter

The waxing moon, from early crescent to just after first quarter

The set then marks:

Edr 25

Edr 1 - 3

Sim 9

Equ 26 - Ele 5

Edr 28 - Can 3

Edr 25

Age of moon of

(day 1 = new moon)

Gia 9

Sim 27 - Equ 4
Can 28 - Sam 3

Ele 25

Sim 9

6
Edr 28 -30; Can 28 - Sam 3

8

Gia 9

9
Days

days 1 (or 2) - 9

the next waxing moon, from early crescent to just after first quarter

The early crescent of one waxing moon, then

The waxing moon, from early crescent to just after first quarter

The new moon

The first-quarter moon, and the day before and after it

The waxing moon, from early crescent to just after first quarter

The full moon

The early crescent of one waxing moon, then

The waxing moon, from early crescent to just after first quarter

The waxing moon, from early crescent to just after first quarter

days 18 - 25

days 3 (or 4) - 8

days 3 - 5, then

days 3 (or 4) - 8

day 30

days 6 - 8

day 14

days 3 - 8

days 1 (or 2) - 8

days 13 - 20

days 3 - 5, then

day 28 - day 3

day 26 - day 3

days 28-30, then
day 28-day 3

the next waxing moon, from early crescent to just after first quarter
days 2 - 9 (or 10)

day 9

day 25

day 1 - 3

day 28 - day 3

day 28 - day 3

day 28 -30, then

days 3 - 8
day 26 (or 27) - day 4 (or 5)

day 26 - day 4

Gaulish month

TABLE 27: Lunar phases marked by sets of IVOS days

Set

1

2

3

4 (normal)

4 (interrupted)

5

6
7

8

9 (normal)

9 (interrupted)

56

RESULTING PLACEMENT OF SETS OF DAYS MARKED IVOS

In attempting to demonstrate some of the patterns produced by equating Samon
with March, I have so far concentrated on the larger structures of the calendar
(years and months); little has been said about individual days and groups of
days, apart from the notations within the intercalary months. Space does not
permit a thorough analysis of the host of smaller elements contained in the calendar. But having developed this hypothesis, it would be interesting to examine
at least one of these smaller structures in detail, simply to see whether the
hypothesis and the structure illuminate each other. To this end, one of the bestknown of these structures will be examined: the sets of days bearing the notation IVOS.

Pattern of ivos days on the plate
Each plate-year can be said to contain nine sets of days marked IVOS (the meaning of which is unknown). Table 26 shows the pattern in which they occur
across the plate (see p. 56).

The lacunae (marked by shading) require that a certain portion of this pattern
be reconstructed by conflation; but because IVOS days occur mostly in blocks,
portions of most blocks have survived, and so this pattern is actually one of the
best-attested and least-controverted in the calendar. Of the sets in Table 26, all
but the shaded ones are wholly or partially extant, such that no set is entirely
missing from more than two of the five years, and all are wholly or partially
extant in both an ordinary and an intercalated year.
Set 2 is perhaps in the poorest condition, with some attendant uncertainty as to
whether all eight of its days were marked IVOS (Duval and Pinault 1986, 342;
Olmsted 1992, 87-88). But this uncertainty does not extend to the first and last
days of the set; and as we are interested in the placement of the sets as a whole,
not of their individual days, let us include set 2 on the basis of its bounds, and
defer the issue of its contiguity.
As Table 26 shows, these sets occur in a regular pattern across the plate. Each
set is shifted to the previous month during the year following an intercalation –
that is, throughout Year I, and during the latter half of Year III and the first half
of Year IV. The sets are then returned to their normal positions by means of a
simple device. The final set in each shifted period — set 9 of Year I, and set 4
of Year IV – begin in shifted position, but are interrupted after three days, and
then resume on the 28th day of the following month, as in ordinary years. All
subsequent sets then fall in their normal positions, until the next intercalation
shifts them again.

57

Pliny’s sexta luna
In Naturalis Historia (XVI. 250), Pliny states that for Gaulish druids, lunar
months began on ‘the sixth day of the moon, which marks for them the beginning of the months, the years, and the century of thirty years’. There has often
been debate about whether this refers to the sixth sunset after first crescent, or
the sixth sunset after new moon; but for an observer, the former option is
excluded by Pliny’s next phrase: ‘as by this time it has considerable strength,
though not yet at its halfway point.’ The sixth sunset after first crescent often
produces a moon past first-quarter, whereas the sixth sunset after new moon
never does. To illustrate, the following figure shows the average appearance of
the moon at the sixth sunset after new moon to a viewer at the latitude of
Coligny, when that average is taken over a full Metonic cycle of 235 lunar
months:

Fig. 10: Average appearance of moon at Pliny’s sexta luna: 31.5% illumination

This shape fits Pliny’s description, and so in this essay, sexta luna is taken to
mean the sixth sunset after new moon. Beginning months at new moon rather
than at first crescent is not as modern an idea as it is often made out to be: in
Meton’s own calendar, months began at the first sunset after new moon (Samuel
1972, 53), and both Ptolemy’s Almagest (Neugebauer 1957, 191-4; 1975, 98-9)
and the astronomical tablets of the Seleucid era (ibid. 1957, 106-9; 1975, 534)
clearly demonstrate an ability to determine the time of new moon with some
precision.

Lunar phases marked by the sets
If lunar months begin at the sixth sunset after new moon, then new moons must
occur on the 25th day or 26th day of the preceding month, depending on
whether that month contains 29 or 30 days. As Table 26 shows, IVOS sets 1, 3,
4, 6 and 9 all begin on or after the 26th day of the month, and end on or before
the 5th day of the following month - that is, they begin on or just after a new
moon, then proceed to mark the waxing moon, from early crescent to just after
first quarter.
Using the same method, we can deduce the lunar phases marked by each set:
TABLE

58

27: Lunar phases marked by sets of IVOS days, see page 56.

In short: the nine sets of IVOS days mark five waxing moons, one first-quarter
moon, one full moon, one waning moon, and one new moon.

Properties of the new moons that precede the sets
Let us look more closely at the new moons preceding each set. The new moons
preceding the five instances of set 1 listed in Table 26, for example, must occur
on the following days:
TABLE 28: New moons preceding IVOS set 1
New moon:

IVOS set 1:

Year I

ICA 26

ICA 26 - Sam 4

Year II

Sam 26

Sam 26 - Dum 4

Year III
Sam 26

Sam 26 - Dum 4

Year IV
Can 25

Can 26 - Sam 4

Year V

Sam 26

Sam 26 - Dum 4

These new-moon dates fall close to the dates on which solar Samon begins in
each plate year, as shown earlier in Table 1:
TABLE 29: New moons preceding IVOS set 1, and dates on which solar Samon
begins
New moon preceding set 1:
Start of solar Samon:
Difference:

Year I

Year II

Year III

Year IV

Year V

5 days

13 days

1 day

11 days

7 days

ICA 26
Sam 1

Sam 26

Sam 13

Sam 26

Sam 25

Can 25

Sam 7

Sam 26
Sam 19

As can be seen, the new moon preceding set 1 never falls more than 13 days from
the start of solar Samon. In nature, new moons occur no less than 29.5 days apart
– and as 13 days is less than half this amount, it is clear that the new moon leading into set 1 will always be the new moon closest to the start of solar Samon.
In the same way, the other eight sets are associated with new moons occurring
closest to the start of other solar months:
TABLE 30: New moons preceding IVOS sets, and their proximity to solar-month
boundaries, see next page.

In set 8 of Year I, the new moon on Elembiu 25 is shown as 15 days from the
start of solar Edrin – but this is not really an exception, for the start of solar
Elembiu (on Elembiu 10) is also 15 days away. This is the only case in which
a new moon falls equidistant between two solar-month boundaries.
But the two interrupted sets – IV set 4, and I set 9 – do contain exceptions.
Because both sets encompass two adjacent waxing moons, Table 30 lists two
new-moon dates for each, and shows that in both sets, the second new moon
falls closest to the expected solar-month boundary, while the first does not. As
a result, IV Ogron 26 and I Edrin 26 become the two exceptions to the pattern.

59

Year V

Cut 26

5 days

Riv 21

Riv 26

5 days

Dum 20

7 days

Sam 19

Sam 26

Dum 25

12 days

Dum 8

Sam 7

Can 25

Year IV

Sam 26

Year III

Sam 25

Dum 25

11 days
Dum 25

Dum 26
1 day

Riv 9

13 days

Gia 25

5 days

Cut 24
Gia 25

Cut 12

Ogr 26; Cut 26

1 day

16 days; 14 days
5 days

12 days

Equ 15

Ele 25

Ele 16

0 days

Equ 27

Ele 25

1 or 2 days

Ele 28

Edr 26

3 days
Edr 26

9 days

Gia 25

Equ 25 or 26

Gia 13

Equ 25 or 26

10 or 11 days

Ele 25

8 days

Ele 4

Equ 3

7 days

Gia 1

Cut 30

4 days

Riv 27

Sam 26

1 day

TABLE 30: New moons preceding IVOS sets, and their proximity to solar-month boundaries
Sam 26

Year II

ICA 26

Year I

New moon preceding set 1:

Dum 14

13 days

Sam 13

Dum 25

5 days

Sam 1

Sam 26
Dum 2

Edr 26

3 days

Ele 22

4 or 5 days

Equ 21

6 days

Gia 19

8 days

Cut 18

Riv 15

Riv 26

11 days

Gia 7

Cut 6

Ogr 26

Riv 3

Riv 26

6 days

Difference:

Start of solar Duman:

Start of solar Samon:

New moon preceding set 2:
Dum 25

Difference:

New moon preceding set 3:
Start of solar Rivros:

Cut 26

11 days
Cut 26

7 days

ICB 26

Difference:

New moon preceding set 4:

Start of solar Cutios:

Gia 25

10 days

New moon preceding set 5:

Cut 26

Difference:
11 days

Sim 26

Ele 25

14 days

Ele 10

13 days

Equ 9

New moon preceding set 6:

Difference:

Start of solar Equos:

Equ 25 or 26

Start of solar Giamon:

Equ 25 or 26

Equ 25 or 26

Difference:

Sim 26

Ele 25

New moon preceding set 7:

Start of solar Elembiu:

Difference

New moon closest to set 8:

9 days

7 days

5 days

ICA 1

3 days

Edr 29

Can 25

Edr 17

Can 25

Edr 5

Edr 26

9 days

Edr 23

Can 25

3 days

Edr 11

15 days

Start of solar Edrin:

Edr 26; Can 25

Difference:

New moon preceding set 9:

Can 18
10 days

Can 6
1 day

Can 24
16 days; 13 days

Can 12
Difference:

Start of solar Cantlos:

60

These results are summarised in Table 31:
TABLE

31: A summary of Table 30

New moon :
preceding

IVOS set 1

IVOS set 2

IVOS set 3
IVOS set 4

IVOS set 5

IVOS set 6

IVOS set 7

IVOS set 8

IVOS set 9

Year I

ICA 26

Sam 26

Dum 25

Ogr 26

Year II

Sam 26

Dum 25
Riv 26

Equ 25/26

Edr 26

Can 25

Riv 26

Ele 25

Ele 25

Edr 26

Dum 25
Cut 26

Gia 25

Equ 25/26

Sam 26

Cut 26

Cut 26

Sim 26

Year III

Equ 25/26

Can 25

ICB 26
Sim 26
Ele 25

Edr 26

Year IV

Can 25

Sam 26

Dum 25

Ogr 26

Year V

Sam 26

Dum 25

Always the new moon

closest to the start of:

Riv 26

solar Samon

solar Duman
solar Rivros

Cut 26

Cut 26

solar Cutios

Ele 25

Ele 25

solar Elembiu

Gia 25

Equ 25/26
Edr 26

Can 25

Gia 25

Equ 25/26
Edr 26

Can 25

solar Giamon
solar Equos
solar Edrin

solar Cantlos

Again, we can see that only IV Ogron 26 and I Edrin 26 fail to meet the condition shown in the far-right column. However, we find that these two exceptions
are part of a second pattern, which becomes apparent if we expand Table 31 to
include all 62 new-moon dates on the plate:
TABLE 32: The 62 new moons on the plate, and their proximity to solar-month
boundaries, see next page

The horizontal line divides the solar year into two halves at solar Samon and
solar Giamon. The new-moon dates preceding the IVOS sets remain aligned as
before, while the new moons that do not precede IVOS sets are shaded. Notice
that each row contains only those new moons occupying a particular sequential
position within the solar year:

TABLE 33: The 62 new moons on the plate, and their sequential positions in the
solar year, see page 63.

The penultimate column implies a second set of conditions for the sets – that
the five sets marking the waxing moon, for example, must mark the waxing of
the 1st, 3rd and 6th new moons of the summer half of the solar year, and the 3rd
and 6th new moons of the winter half. In this second pattern, the exceptions are
now IV Cutios 26 and I Cantlos 25 – the second new moon of each interrupted
set: both these new moons are not the sixth of the season, but an exceptional
seventh.

61

TABLE
Year I

Year II

Year III

Year IV

Year V

Sam 26

Dum 25

Sim 26

Equ 25/26

Dum 25

Gia 25

Sim 26

Ele 25

Sam 26

Riv 26

Ana 25

Sim 26

Gia 25

Equ 25/26
Edr 26

Ogr 26

Ana 25

Dum 25

Sam 26

Riv 26

Can 25

Dum 25

Sam 26
Riv 26
Ana 25

Ogr 26

Ana 25

Ogr 26

Riv 26

Gia 25

Sim 26
Edr 26

Ogr 26

Ele 25

Ele 25

Edr 26

Equ 25/26

Sim 26

Gia 25

Cut 26
ICB 26

Ele 25

Can 25

Cut 26

Gia 25

Equ 25/26

Can 25

Cut 26

Cut 26
Ele 25

Edr 26

Edr 26

Cut 26

Equ 25/26

Can 25

Ogr 26

Can 25

Ana 25

Sam 26

Riv 26

ICA 26
Dum 25

solar Cantlos

solar Edrin

solar Elembiu

solar Equos

solar Giamon

solar Cutios

solar Rivros

solar Duman

solar Samon

closest to the start of:

Always the new moon

32: The 62 new moons on the plate, and their proximity to solar-month boundaries

New moon:
preceding:
IVOS set 1
IVOS set 2
IVOS set 3
IVOS set 4
IVOS set 5
IVOS set 6
IVOS set 7
IVOS set 8
IVOS set 9

62

TABLE
Year V

Sam 26

Year IV

Year III

Can 25

in solar year:

Position of new moon

1st of solar summer

2nd

Phase of moon
marked by set:

Waning

Waxing

Waxing

Ogr 26

Ana 25

Gia 25

Cut 26

Ogr 26

5th

5th

4th

2nd

1st of solar winter

Edr 26

Ele 25

Sim 26

Gia 25

4th

3rd

Waxing

Ogr 26
ICB 26
Sim 26

Ele 25

Edr 26

Ana 25

6th

Waxing

Gia 25

Gia 25

Equ 25-26

Sim 26

Sim 26

Riv 26

3rd

Waxing

Ana 25

Equ 25-26

6th

Ele 25

New

1st Qtr

Full

Equ 25-26

Can 25

Sam 26

Year II

Sam 26
Dum 25

Year I

ICA 26
Sam 26
Riv 26

33: The 62 new moons on the plate, and their sequential positions in the solar year

New moon

preceding:

IVOS set 1
Dum 25
Cut 26

Dum 25
Riv 26
Ogr 26

Dum 25

Cut 26

Sam 26
Riv 26

IVOS set 2
Dum 25
Cut 26

Ana 25

Cut 26
Sim 26

Can 25

Equ 25-26

Ana 25

IVOS set 3
Ogr 26

Riv 26

IVOS set 4
IVOS set 5

Edr 26

Ele 25

Edr 26

Can 25

Can 25

Ele 25

Edr 26

Gia 25

Equ 25-26

IVOS set 6

IVOS set 7
IVOS set 8
IVOS set 9

63

From Tables 32 and 33, we can now formulate practical definitions that entirely account for the sets:
TABLE 34: Practical definitions of IVOS sets
Set....

1

2

must mark the:

waxing

waning

... of the new moon which is:

1st of the summer half

2nd of the summer half

...nearest the start of solar Duman

1st of the winter half

...nearest the start of solar Giamon

5th of the winter half

...nearest the start of solar Edrin

3

waxing

3rd of the summer half

6

waxing

3rd of the winter half

9

waxing

6th of the winter half

4
5

7

8

waxing

fullness

first quarter
day

... and:

...nearest the start of solar Samon

6th of the summer half
4th of the winter half

...nearest the start of solar Rivros
...nearest the start of solar Cutios

...nearest the start of solar Equos

...nearest the start of solar Elembiu
...nearest the start of solar Cantlos

For each set, then, we have posited a pair of conditions, with the implication
that both conditions must always be met. As Tables 32 and 33 show, a single
new moon satisfies both conditions for each set except the two interrupted ones,
where the two conditions are satisfied separately by adjacent new moons. This
suggests a rationale for the existence of the interrupted sets, which then proceed
to mark both waxing moons with IVOS days.
Finally, an observation about set 2. Table 26 shows that this waning moon is
always followed in six days by the waxing moon of set 3; while Table 34 shows
that set 3 marks the waxing of the closest new moon to the start of solar Rivros;
and so it follows that sets 2 and 3 will always frame this new moon. The implication is that a particularly important new moon is being doubly-marked, with
commemmoration of both the waning moon leading into it, and the waxing
moon leading out of it.

Average Roman dates of the sets
In determining average Roman dates for the sets, the earlier parameters were
retained: March 1, AD 101 was taken as Samon 1 of cycle-year 1; Equos was
given a 30th day only in (Gaulish) years that encompass a Roman bissextile;
and the calendar was intercalated according to the pattern shown in Table 11.
The resulting Roman dates of the sets were then tabulated for two consecutive
30-year periods, from AD 101 to AD 161, so as to include the full pattern of bissextiles. The resulting tables are ponderous, but they are summarised in Table
35:
Set 1, for example, has its earliest occurrence in AD 102, when it falls on
February 14-21; and it has its latest occurrence in AD 113 and AD 143, when it
falls on March 14-22. Taken over the 60 years, the average start- and end-dates
for the set are February 28 and March 7; and the average median is March 4 –

64

Dates and year(s) of

60-year average
start & end

Feb 28 - Mar 7

Dates and year(s) of

latest occurrence

Apr 15 - Apr 22

Sep 26, 107 & 137

Aug 11-16, 113 & 143

May 12-19, 113 & 143

Mar 14-22, 113 & 143

Apr 29-May 6, 113 & 143

Jul 19-24, 126 & 156

Apr 14-20, 102 & 132

Feb 14-21, 102

Apr 1-8, 102 & 132
Jul 18-20 + Aug 17-22, 107 & 137

Aug 29, 126 & 156

Nov 12-21, 107

Jul 30 - Aug 4

60-yr avg median
Mar 4

median

May 1

Apr 18

Sep 12

Aug 2
Sep 12

Jul 15 - Aug 19

Feb 1

Dec 2

Nov 2

Dec 25

Oct 29 - Nov 6

Dec 25

Dec 1 - 3
Feb 11-15, 107

Jan 9, 107

Dec 16-18, 107

Jan 15 - Feb 18

Dec 11, 126 & 156

Nov 17-19, 126 & 156

Jan 18-20 + Feb 17-21, 131

Jan 18-23, 120 & 150

Jan 30 - Feb 3

Jan 12-14 + Feb 11-15, 126 & 156

Oct 15-22, 126 & 156

Apr 28 - May 4

Jul 13-15 + Aug 12-17, 102 & 132

earliest occurrence

TABLE 35: Roman dates of IVOS sets over a 60-year period (AD 101 to AD 161)
Set

1
3

2
4 (all but Year IV)

5

4 (Year IV only)

6

7

8

9 (all but Year I)

9 (Year I only)

65

that is, March 4 is the day around which this set is centred, when its dates are
averaged over the entire 60-year period.
For sets 4 and 9, two entries are given – one for the four normal instances of the
set, and one for the interrupted instance. As can be seen, both normal and interrupted varieties produce the same average median in both cases.
Sets 2, 3, 4, 6, and 9, and the Insular quarter-days
As Table 35 shows, the average medians of sets 3, 4, 6 and 9 coincide with the
four quarter-days of the traditional Insular Celtic year (Hutton 1991, 176),
which is divided into equal halves at May 1 and November 1:

Gaulish solar months:

Sam

TRADITIONAL INSULAR YEAR:

WINTER
Mar
Apr

Roman months:

Dum

Riv

Ana

May

S U M M E R
Jun
Jul
Aug
Sep

Ogr

!!
Sets 2 & 3
BELTINE

Fig. 11. Average median dates of
Celtic quarter-days

Cut

!
Set 4
LUGHNASADH

IVOS

Gia

Sim

Equ

Oct

W I N T E R
Nov
Dec
Jan
Feb

!
Set 6
SAMHAIN

Ele

Edr

Can

!
Set 9
IMBOLC

sets 2, 3, 4, 6 and 9, and the Insular

This was certainly an unexpected result, given that this is a Gaulish calendar.
Nevertheless, Figure 11 clearly indicates the four quarter-days, and further suggests that they were once movable lunisolar feasts, like Easter, and that after
Christianisation, they were simply fixed at their median dates in the Roman calendar.
Set 2 has been included to show that it and set 3 frame the new moon associated with Beltine – or more precisely, they mark the waning moon leading into,
and the waxing moon leading out of, the new moon closest to the start of solar
Rivros, with the result that set 3 is centred on May 1 (the traditional date of
Beltine). The configuration of this double-set – a waning moon followed by a
waxing moon – seems an appropriate symbol of Beltine’s status as the end of
civil winter and the start of summer. Intriguingly, this configuration also evokes
the Insular custom of extinguishing all fires at Beltine, and rekindling them
from a consecrated flame (ibid., 178-9), one of the few Celtic customs that can
confidently be dated to pre-Christian times (ibid., 327).
Muirchú’s seventh-century Life of Patrick describes how the saint defied this
custom by kindling an Easter-Eve fire of his own (ibid., 178), and Dr Hutton
questions the account, pointing out that Easter and Beltine can never coincide.
This is certainly true with Beltine fixed at May 1; but with Beltine as the movable feast represented by sets 2 and 3 in Figure 11, the situation is very different. Table 27 shows that set 2 always begins just after a full moon; and in fact,
in 23 out of every 30 years, this full moon is the next after the equinox – that

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is, it is the paschal full moon. As a result, Easter very often occurs within set 2,
the waning-moon or ‘extinguishment’ set of IVOS days; and this would make
Muirchú’s account plausible.
Meanwhile, Table 35 shows that the average median of set 2 is April 18; and so
if sets 2 and 3 are considered together, the average median for the pair becomes
the midpoint between April 18 and May 1 – that is, April 24/25, now known as
St George’s Day. This association of May Day with St George’s Day seems significant: festivals celebrating the return of greenery were ‘known across the
whole Continent and British Isles and held variously on May Day or St
George’s Day since records begin’ (ibid., 272).
Finally, Table 26 shows that the two intercalary months always begin within
sets 4 and 9; and so Figure 11 implies that the intercalary months must always
begin near what we call Imbolc and Lughnasadh. The data show that this is so:
TABLE 36: Roman dates on which the intercalary months begin (AD 101 - AD 161)
ICA begins:

ICB begins:

Jan 26, 115

Jul 31, 117

Jan 28, 104
Jan 30, 112

Jan 28, 123
Jan 30, 131

Jan 27, 134
Jan 29, 142

Jan 26, 145
Jan 28, 153
Jan 30, 161

Aug 1, 106
Jul 29, 109
Jul 28, 120

Aug 2, 125
Jul 30, 128

Aug 1, 136
Jul 29, 139
Jul 31, 147
Jul 28, 150

Aug 2, 155
Jul 30, 158

It is interesting enough to find the Insular quarter-days appearing in a Gaulish
calendar; but Figure 11 and Table 36 hint that these days may actually have
played an important role in the organisation of the plate itself. This becomes
clearer if we depict the entire arrangement of quarter-days on the plate, as is
done in Figure 12. For lack of Gaulish terms, abbreviations of the Irish ones
have been used; and for contrast, the locations of the solstices and equinoxes
have also been indicated in brackets:
Figure 12, see page 68.

Notice that the double-allotment of vertical space to each intercalary month has
forced the quarter-days into adjacent pairs at the start of each half of the plate
– Imbolc with Beltine on the left, Lughnasadh with Samhain on the right, such
that all four are brought into alignment along the top edge of the plate. In the

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Fig.12. Locations of quarter-days, solstices, and equinoxes on the plate.
Boxes = Gaulish lunar months; shading = Gaulish solar months

left half, all instances of Imbolc, Beltine, the autumn equinox, and the winter
solstice are thereby confined to the upper quadrant, within the vertical compass
of ICA; and Beltine itself occurs exclusively along the top row.
With Imbolc as the centre of the Irish civil winter, and Beltine signifying winter’s end, the upper-left and lower-right quadrants then contain nothing but wintertime markers; and in the same way, the upper-right and lower-left quadrants
contain nothing but markers of summertime. If the plate has a ‘winter half’ and
a ‘summer half’, as has so long been suspected, then perhaps the left half is the
winter one. Importantly, this effect has been produced entirely by the doublelength of the intercalary months – an aspect of the calendar’s layout for which
no practical purpose has ever been suggested.
Finally, Lughnasadh is situated prominently at top-centre, which seems appropriate for a calendar with a provenance so near Lugdunum. By the second century,
August 1 was being celebrated in Gaul as the birthday of Augustus, the occasion
of rites at the Altar of the Three Gauls at Lugdunum. Romanised Gaulish tribal
leaders actually held office as priests of Rome and Augustus; and so attendance
at the Altar on this day became an important symbol of loyalty to Rome
(Cornell/Matthews 1982, 83).

Sets 1 and 7, and the Gaulish solar year
Set 1 simply marks the waxing moon that begins the entire year. Set 7, on the
other hand, marks a first-quarter moon – half dark, half light, a symbol of midpoints; and in fact, this first-quarter moon is always the closest to the start of
solar Elembiu, the midpoint of the winter half of the solar year:

68

Gaulish solar months:
GAULISH SOLAR YEAR:
Roman months:
!
Set 1

Sam

Dum

Mar

S U M M E R
Apr
May
Jun
Jul

Riv

Ana

Ogr

Cut
Aug

Gia

Sim

Edr

Can

Sep

W I N T E R
Oct
Nov
Dec
Jan

Equ

Ele

Feb

!
Set 7

Fig. 13. Average median dates of IVOS sets 1 and 7, and the Gaulish solar year

In terms of the Gaulish solar year, then, these two sets mark the start of summer, and the midpoint of winter.

Set 5, and the sun in Virgo
Around AD 200, the sun was entering the constellation of Virgo on August 24
or 25 each year, and leaving it at the equinox on September 24. Table 35 shows
that set 5, a single IVOS day, marks the full moon between August 29 and
September 26; and so this IVOS day will nearly always mark the full moon
whose light originates from the sun in Virgo. In AD 200 exceptions would have
occurred when this day fell on September 25 or 26; but in 44 BC, when the
Julian calendar was introduced, September 26 was the usual date of the equinox, and so at that time, this IVOS day would always have marked the full moon
reflecting the sun in Virgo. Such an association does make some sense, given
Virgo’s ancient associations with harvest and fertility, and the full moon’s congruent associations with abundance and fertility.

Set 8, and the winter solstice
Table 35 shows that set 8, also a single IVOS day, marks the new moon closest
to December 25. For the Romans, this day was the Imperial Feast of the Birth
of the Unconquered Sun (Hutton 1991, 285), the traditional date of the winter
solstice, and very nearly its actual date in Caesar’s time, when it was occurring
on December 23 or 24. Interestingly, the winter solstice appears to be the only
solstice or equinox associated with any day marked IVOS.

Conclusions
Constraining March 1 within Samon naturally produces a 30-year non-sequential intercalation sequence which, when implemented, causes the Gaulish calendar to create a simple, repeating pattern against the Roman calendar. As a
result, conversion between the calendars becomes straightforward, and sets of
days marked IVOS cluster around meaningful dates, including the four Insular
quarter-days, marking the important boundary between April and May with a
double-set. On the plate, the double-length of the intercalary months brings the
four quarter-days into prominent alignment along the upper edge, constrains all
wintertime and summertime markers into diagonally-opposite quadrants, and
leaves Lughnasadh at top-centre, creating an impression that the quarter-days
were being catered for in the layout of the plate.

69

All these findings arise solely from the requirement that March begin within
Samon, in line with the conclusions of the previous essay; and this strongly suggests that the calendar inscribed on the Coligny artifact represents a native
Gaulish calendar in a standardised relationship to the Julian calendar, a relationship of the type found in surviving hemerologia. This is a sensible result for
a calendar from second-century Gaul; and it implies that Rhys and
Fotheringham’s initial suspicion was in fact correct but for their alignment of
the year.
Acknowledgements
I am very grateful to John Adamsons, Dr Gocha Tsetskhladze, University of
Melbourne, Dr Ronald Hutton, University of Bristol, and Dr Helen Fulton,
University of Sydney, for their encouragement and support during the lengthy
preparation of this pair of essays.
BIBLIOGRAPHY

Cornell, T./J. Matthews 1982: Atlas of the Roman World, Oxford.
Duval, P.M./G. Pinault 1986: Recueil des inscriptions Gauloises, Volume 3: Les calendriers,
Paris.
Hutton, R. 1991: The Pagan Religions of the Ancient British Isles: Their Nature and Legacy,
Oxford.
Lainè-Kerjean, C. 1943: Le calendrier celtique. Zeitschrift für keltische Philologie 23, 249-284.
MacNeill, E. 1926: On the Notation and Chronography of the Calendar of Coligny, Eriu 10, 167.
McCarthy, D. 1993: Easter Principles and a Fifth-Century Lunar Cycle used in the British Isles.
Journal of the History of Astronomy 24, 204-224.
Neugebauer, O. 1957: The Exact Sciences in Antiquity, Providence.
Neugebauer, O. 1975: A History of Ancient Mathematical Astronomy, Berlin.
Olmsted, G. 1992: The Gaulish calendar, Bonn.
Orpen, G. 1910: Notices of Books. Journal of the Royal Society of Antiquaries in Ireland 20,
207-211.
Rhys, J. 1905-6: Celtae and Galli, Proceedings of the British Academy 2, 71-107.
Rhys, J./J.K. Fotheringham 1909-10: The Coligny Calendar, Proceedings of the British
Academy 4, 207-289.
Rhys, J./J.K. Fotheringham 1911-12: The Celtic Inscriptions of Gaul. Proceedings of the
British Academy 5, 339-360.
Samuel, A.E. 1972: Greek and Roman Chronology: Calendars and Years in Classical
Antiquity, Munich.
Thurneysen, R. 1899: Der Kalendar von Coligny. Zeitschrift für keltische Philologie 2, 523544.

Brent Davis
Centre for Classics and Archaeology
School of Historical Studies
University of Melbourne, Australia
b.davis2@pgrad.unimelb.edu.au

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Parole chiave correlate