Dear Calendar People

Eclipses 391 years apart are easy to find on the file obtained from catzeute.htm

Here are two examples jul.dat year m d max(UT) hem type eclipse Saros Inex ---------------------------------------------------------------- 2299231.67 1582 dec 25 4h 5m N central annular 125 47 2442041.13 1973 dec 24 15h 2m N central annular 141 43 2584850.71 2364 dec 24 5h 2m N central annular 157 39 2348960.79 1719 feb 19 6h 52m N central annular 116 69 2491770.48 2110 feb 18 23h 27m N central annular 132 65 2634580.67 2501 feb 19 4h 8m N central total 148 61 Using Doug Zonker's Calendar Converter I get the Islamic dates 403 years apart 25 Dec 1582 = 29 Dhu Al-Qada 990 24 Dec 1973 = 29 Dhu Al-Qada 1393 24 Dec 2364 = 29 Dhu Al-Qada 1796 19 Feb 1719 = 29 Rabi I 1131 18 Feb 2110 = 28 Rabi I 1534 18 Feb 2501 = 28 Rabi I 1937 The case that drew my attention to this was jul.dat year m d max(UT) hem type eclipse Saros Inex ---------------------------------------------------------------- 2416556.74 1904 mar 17 5h 40m N central annular 128 60 2559366.15 2295 mar 16 15h 42m S central annular 144 56 which I got from Sepp yesterday.

The 17 Mar 1904 is the epoch of the Liberalia Triday Calendar invented by Peter Meyer ltc.htm which is fact a solar calendar and a lunar calendar that share a 3-day cycle. The lunar calendar has a 12-month year so 391 solar years is close to 403 lunar years. Do Liberalia Triday Solar Year 391 and Liberalia Triday Lunar year 403 both begin on 16 Mar 2295?

Islamic dates (according to the above mentioned converter page) are 29 Dhu Al-Hijjah 1321 and 28 Dhu Al-Hijjah 1724

Sepp could add the following entry to his numbers page calendarnumbers.htm

391 This number of solar years is very close to 403 12-month lunar years. Furthermore, eclipses are likely to repeat on this cycle. See 32.58.. and 33.58.. . and possibly also

403 This number of 12-month lunar years is very close to 391 solar years. Furthermore, eclipses are likely to repeat on this cycle. See 32.58.. and 33.58.. . I notice in Felix's table that each 391-year cycle increases the Saros number of the eclipse by 16 and decreases its Inex number by 4. Felix says nothing about these Saros and Inex numbers other than give the following reference

VAN DEN BERGH G. - Periodicity and Variation of Solar (and Lunar) eclipses (H.D.Tjeenk Willink & Zoon, Harlem, 1955)

I've figured out that Saros numbers of the eclipse months are such that Each month has the same Saros number as the month 233 months before. Each month has the Saros number 1 greater than that of the month 135 months before mod 223. This causes the eclipses to have a narrow range of Saros numbers that slowly drifts upwards with time.

Each month has a Saros number 38 greater than that of the previous month mod 223. 38*135 = 1 mod 223.

I suspect the Inex numbers use the more accurate 358-month cycle, which I call the Octos.

All these eclipse cycles can be constructed out of a 47 month period of 8 eclipse seasons, which I call a long Unitos and a 41 month period of 7 eclipse seasons, which I call a short Unitos.

From these we get Tritos = 47:41:47 = 135 months = 23 eclipse seasons Saros = 47:41:47:41:47 = 233 months = 38 eclipse seasons Octos = Saros+Tritos = 358 months = 61 eclipse seasons

Metonic cycle = 5 Long Unitoses = 235 months = 40 eclipse seasons

391-year cycle = 13 Octoses + Tritos + Long Unitos = 4836 months = 824 eclipse seasons.

This breaks up into 4 cycles of 1209 months and 206 eclipse seasons lasting 97 3/4 solar years and also 100 3/4 12-month lunar years. It consists of 3 Octoses and a Tritos.

With Sepp's example we get

jul.dat year m d max(UT) hem type eclipse Saros Inex ---------------------------------------------------------------- 2416556.74 1904 mar 17 5h 40m N central annular 128 60 2452258.37 2001 dec 14 20h 51m N central annular 132 59 2487961.20 2099 sep 14 16h 53m N central total 136 58 2523664.24 2197 jun 15 17h 51m N central annular 140 57 2559366.15 2295 mar 16 15h 42m S central annular 144 56 The respective Islamic dates are 29 Dhu Al-Hijjah (month 12) 1321, 28 Ramadan (month 9) 1422, 28 Jumada II (month 6) 1523 29 Rabi I (month 3) 1624 and 28 Dhu Al-Hijjah (month 12) 1724

Have Fun this May!

Karl Palmen

Night 12, Month 7, Yerm 4 - 04(07(12

PS: the 850-month cycle of My Yerm Calendar is 1 month short of 2 Octoses and 1 Tritos

*Since writing the above note, I've found out that the period that I called the Octos is
called an Inex. The two types of Unitos are called
the Hepton (7 eclipse seasons) and the Octon (8 eclipse seasons).
Later the 391-year cycle was found to be the Grattan-Guinness Cycle*.

Dear Charles and Calendar People

Charles has provided us with the Ogam Wheel based on a 13-month solar calendar. I've stated, that it could be modified to work with a 12-month calendar.

While neither disputing that it works well with a 13-month calendar nor disputing that a 13-month calendar was used, this I do not regard as essential to this kind of wheel.

I've come up with triple moon wheel that works with the Gregorian Calendar.

The outer wheel has the years of the Metonic cycle and a Star. The years 1995 to 2013 are positioned clockwise relative to the star as follows:

00: STAR 01: 02: 2008 Au#14 03: 1997 Au#03 04: 05: 2005 Au#11 06: 07: 2013 Au#19 08: 2002 Au#08 09: 10: 2010 Au#16 11: 1999 Au#05 12: 13: 2007 Au#13 14: 1996 Au#02 15: 16: 2004 Au#10 17: 18: 2012 Au#18 19: 2001 Au#07 20: 21: 2009 Au#15 22: 1998 Au#04 23: 24: 2006 Au#12 25: 1995 Au#01 26: 27: 2003 Au#09 28: 2011 Au#17 29: 2000 Au#06The Au# are the Golden numbers as used in the Easter rule ( (Year mod 19)+1).

The middle wheel has 30 phases of the moon as with the Ogam wheel.

The inner wheel has the days of the month running clockwise from 1 to 30 and then a 31 with the 1. It also has months at some of these numbers as follows

11 Dec 12 Nov 13 Oct 14 Sep 15 Aug 16 Jul 17 Jun 18 May 19 Apr Feb 20 Mar JanTo use the wheel, (1) Turn the middle wheel so that the FULL moon is by the YEAR in the outer wheel (2) Turn the inner wheel so that the MONTH is by the STAR in the outer wheel. Then the days of the month indicated in the inner wheel are by their own moon phases in the middle wheel.

For 1900 to 2199, it also gives the correct Pascal Full Moons (if I'm correct). For other centuries, Gregorian corrections can be applied to the years in the outer wheel. The April 19 blip rule ensures that no year can ever occupy the star position (Pascal Moon April 19).

The wheel will do a sacrifice at the end of Feb, Apr, Jun, Sep, Nov and in most years Dec (6 in all). The wheel is simpler than the Ogam wheel, because the sacrifices occupy fixed places in the solar calendar year.

Example: 20 July 2001 For 2001 full moon is at position 19 in outer wheel. July 16 is at the star (position 0). So July 20 is at position 4 on outer wheel, opposite 19, so indicating dark/new moon. Today (July 26) is at position 10, indicating a moon age of 6 (Waxing H-rune)

Karl Palmen

04(10(06

July 26 - Moon age 6

Holly 19 - Waxing H-rune

Dear Calendar People

As I said I would, I've produce a conversion table for Julian to 33-year cycle calendar, which I believe is correct. The conversion factor is added to the Julian Calendar date to get the 33-year cycle date. The table gives conversion factors for the Dee-Cecil calendar, which is a present (until 2016) synchronised with the Gregorian Calendar. For the Dee Calendar add 1 to the conversion factor.

For the purpose of the conversion, all years begin on 1 March, subtract 1 from the year number, for dates in January or February.

The Table 1 gives an approximate conversion factor, which is correct for most years and Table 2 tells you how to correct this approximate conversion factor. The third column of table 1, provides a number to subtract from the year number in before using table 2.

Julian to 33-year cycle (Dee-Cecil)

Table 1 Approximate conversion factor and number to subtract from year Year-Range Conv Subtract -0048 to 0083 -2 0000 0084 to 0215 -1 0132 0216 to 0347 0 0264 0348 to 0479 1 0396 0480 to 0611 2 0528 0612 to 0743 3 0660 0744 to 0875 4 0792 0876 to 1007 5 0924 1008 to 1139 6 1056 1140 to 1271 7 1188 1272 to 1403 8 1320 1404 to 1535 9 1452 1536 to 1667 10 1584 1668 to 1799 11 1716 1800 to 1931 12 1848 1932 to 2063 13 1980 2064 to 2195 14 2112 2196 to 2327 15 2244 Table 2 Correction of approximate conversion factor After subtracting the figure in the third column from the year, the result should be in range of -48 to 83. If it's one of the following, then the conversion factor needs correcting, by -1 if negative or +1 if positive. -46 -45 -42 -41 -38 -37 -34 -33 -29 -25 -21 -17 -13 -09 -05 -01 36 40 44 48 52 56 60 64 68 69 72 73 76 77 80 81

**Caveat:** The conversion factor becomes ambiguous
if it is not equal for the both the Julian date and the corresponding Dee-Cecil date
calculated from it. This is because in such a situation the days counted in
the conversion factor contain a leap day in one calendar only.
One should count the leap day in and only in the larger
of the two differing conversion factors

**Now for some examples:**

30 August 2001 Gregorian is 17 August 2001 in the Julian calendar.

Table 1 gives a conversion factor of 13, subtracting 1980 gives 21, which is not in table 2,

so the correct conversion factor is 13, giving 30 August 2001.

1 September 1979 Gregorian is 19 August 1979 in the Julian Calendar.

Table 1 gives a conversion factor of 13, subtracting 1980 gives -1, which is in table 2 and is negative,

so the correct conversion factor is 13-1 = 12, giving 31 August 1979.

22 September 1789 Gregorian is 11 September 1789 in the Julian Calendar,

Table 1 gives a conversion factor of 11, subtracting 1716 gives 73,
which is in table 2 and is positive,

so the correct conversion factor is 11+1 = 12, giving 23 September 1789.

19 September 1799 Gregorian is 8 September 1799 in the Julian Calendar,

Table 1 gives a conversion factor of 11, subtracting 1716 gives 83,
which is not in table 2,

so the correct conversion factor is 11, giving 19 September 1799.

15 February 1971 Gregorian is 2 February 1971 in the Julian Calendar,

The day is before March 1, so this year is taken be be 1970 for conversion.

Table 1 gives a conversion factor of 13, subtracting 1980 gives -10 (for 1970),
which is not in table 2,

so the correct conversion factor is 13, giving 15 February 1971.

15 February 1972 Gregorian is 2 February 1972 in the Julian Calendar,

The day is before March 1, so this year is taken be be 1971 for conversion.

Table 1 gives a conversion factor of 13, subtracting 1980 gives -9 (for 1971),
which is in table 2 and negative,

so the correct conversion factor is 12, giving 14 February 1972.

Karl Palmen

04(11(12 revised 06(02(20