Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

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Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Karl Palmen

Dear Brij and Calendar People

 

The 128-year cycle one of four possible leap year rules listed in the Wikipedia article

https://en.wikipedia.org/wiki/French_Republican_Calendar#Converting_from_the_Gregorian_Calendar

 

I found

https://fr.wikisource.org/wiki/D%C3%A9cret_de_la_Convention_nationale_portant_sur_la_cr%C3%A9ation_du_calendrier_r%C3%A9publicain which has two September equinoxes reckoned in Paris time (1792 & 1793). When I compared them with GMT in

https://stellafane.org/misc/equinox.html I found that Paris time was around 17 or 18 minutes ahead of GMT at that time of year. Now I can have a go at reckoning how the equinox rule would place the leap years and then which leap years my Franciade preserving amendment would drop.

 

The equinox would occur just after midnight in the first of four consecutive common years and just before midnight in the leap year 4 years later, which is 5 years after the previous leap years.

In GMT this midnight would occur around 23:42 or 23:43.

 

Here I list such years

First of 4 consecutive common years  Leap year 5 years after previous leap year

016: Thu, 24 Sep 1807 00:01:39 GMT   020: Mon, 23 Sep 1811 23:20:07 GMT

049: Tue, 22 Sep 1840 23:52:43 GMT   053: Sun, 22 Sep 1844 22:57:28 GMT

078: Thu, 23 Sep 1869 00:27:43 GMT   082: Mon, 22 Sep 1873 23:35:24 GMT

111: Tue, 23 Sep 1902 23:55:27 GMT   115: Sun, 23 Sep 1906 23:15:23 GMT

140: Thu, 24 Sep 1931 00:23:29 GMT   144: Mon, 23 Sep 1935 23:38:18 GMT

173: Wed, 23 Sep 1964 00:16:51 GMT   177: Sun, 22 Sep 1968 23:26:22 GMT

206: Mon, 22 Sep 1997 23:55:33 GMT   210: Sat, 22 Sep 2001 23:04:30 GMT

235: Wed, 23 Sep 2026 00:04:56 GMT   239: Sun, 22 Sep 2030 23:26:34 GMT

xxx

and so the leap years are

003, …, 015,  020, …, 048,  053, …, 077,  082, …, 110,  

115, …, 139,  144, …, 172,  177, …, 205,  210, …, 234,

239.

where “…” indicates once every 4 years in between, including the two years either side.

 

If the original Franciades are used in the compromise, then the Franciades ending in years 19 & 143 would have no leap year.

 

One thing I notice in my list of equinox times for the leap years five years after previous leap year (2nd column), is that the day of week is about the same and is usually exactly the same in alternate rows. This arises from the close approximation to the 62-year cycle of 15 leap years, which has a whole number of weeks.

Also I deliberately arranged the leap year list so each row has four blocks of leap years four apart,  to how often one would need to drop a leap day, if otherwise every 4th year is a leap year.

It turns out that this is usually 124 years after previous but may be 128 years after previous. This arises from the September equinox tropical year lasting about 365.2420 days.

This suggests that a 124-year cycle would be better than a 128-year cycle for the September equinox. The 124-year cycle is simply two 62-year cycles and so has a whole number of weeks.

 

In a Divide-by-Six calendar, having the additional leap weeks occur once every 90 & 96 years alternately, produces exactly the same mean year (365.24193548… days) as the 62-year or 124-year cycle.

 

Karl

 

15(14(17

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 20 July 2016 20:12
To: [hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 128-year Leap Rule

 

Sirs: 

This appears to me, a recent input, that French Republican calendar after year 20 was to account 'Leap Days omitted once every 128-years' proposed at Wikipedia site. 

Unfortunately, the French calendar lasted only for meare 13-years when the idea of Decimale Time was also 'dispensed with' as a compromise for Empror Napoleon's coronation. 

Please see my works: http://www.brijvij.com/ 

Brij Bhushan VIJ, 

Author, Brij's Modified Gregorian Celendar


Sent from my iPhone


On Jul 20, 2016, at 8:08 AM, Karl Palmen <[hidden email]> wrote:

Dear Calendar People

 

The idea of the Georgian Calendar having the December solstice on one of the first two days of the year leads to the idea of having the September equinox on one of the first two days of the French Republican calendar year.

 

There were two contradictory requirements for the French Republican leap year rule

(1) A leap year occurs once every 4 years, as the fourth and final year of a Franciade.

(2) The first day of the year is the day of the September equinox.

 

One possible compromise I thought of not mentioned in

https://en.wikipedia.org/wiki/French_Republican_Calendar#Converting_from_the_Gregorian_Calendar or

https://en.wikipedia.org/wiki/Franciade and therefore possibly not considered, is:

 

The first day of a Franciade is a day of a September equinox.

 

The September equinox may then occur on either the first or second day of a year, but always the first day of the first year of a Franciade.

A leap day would normally be necessary at the end of a Franciade, to ensure this, but one in every around 32 or 33 Franciades would not have a leap day.

A Franciade has no leap day, only if it continues a long run of years that have the equinox on the first day. The first year of the next Franciade is then the final year of this run.

 

Is this idea new to me or has anyone else suggested it?

 

Karl

 

15(14(16

 

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 19 July 2016 16:34
To: '[hidden email]'; [hidden email]
Subject: RE: Georgian Calendar New Year Solstice

 

Dear Tom and Calendar People

 

I did mean Georgian calendar in the sentence that Tom quoted.

 

The Georgian calendar new year was chosen to occur at the northern winter solstice. The first year of the Gregorian Era was set to begin on December 21, 1755 new style.

 

I decided to check out the timing of the December solstices and found out that the first solstice occurred on Mon, 22 Dec 1755 02:05:40 GMT so would occur on the second day (Monday, St. Peter 2) this year and the following 3 years. Over the course of the 132-year cycle the solstice would drift earlier to the first day (Sunday, St. Peter 1) and then be put back to the second day by a dropped leap day, which occurs once every 132 years.

 

So the calendar places the northern winter solstice on one of the first two days of the year, never drifting back to the previous year for thousands of years and drifting into the third day (Tuesday, St. Peter 3) for the first time on Tue, 22 Dec 2550 00:32:34 GMT in year 796 of the Georgian Era, because the December solstice tropical year is longer than the calendar mean year giving rise to a drift of about one hour later each 132-year cycle.

 

Karl

 

15(14(15

 

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Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Walter J Ziobro
Dear Karl and Calendar People:

I have given some thought about how the French Republican Calendar could be modified for contemporary use.  Some of the ideas that I have considered are:

1. Using the autumnal equinox of 4000 BCE as the epoch, and numbering the years from then as Anno Lucis, like the Freemasons. IMO, the rationalism of the Freemasons and the French Republicans have much in common.  Indeed, it has been speculated the Freemasons had a role in the French Revolution.

2.  Using a 33 year leap day rule, as this would track the equinoxes better.

3.  Breaking up the 5-6 day period at the end of the year, and distributing those days to the astronomically longer months, like the Indian National Calendar, thereby tracking all four equinoxes and solstices more closely.  These 31 day months would form a 5-6 month group that could be shifted every 1600 or 2000 years, as the perihelion and aphelion points precess relative to the cardinal seasonal points. 

-Walter Ziobro




-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Thu, Jul 21, 2016 8:08 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Dear Brij and Calendar People
 
The 128-year cycle one of four possible leap year rules listed in the Wikipedia article
 
I found
https://fr.wikisource.org/wiki/D%C3%A9cret_de_la_Convention_nationale_portant_sur_la_cr%C3%A9ation_du_calendrier_r%C3%A9publicain which has two September equinoxes reckoned in Paris time (1792 & 1793). When I compared them with GMT in
https://stellafane.org/misc/equinox.html I found that Paris time was around 17 or 18 minutes ahead of GMT at that time of year. Now I can have a go at reckoning how the equinox rule would place the leap years and then which leap years my Franciade preserving amendment would drop.
 
The equinox would occur just after midnight in the first of four consecutive common years and just before midnight in the leap year 4 years later, which is 5 years after the previous leap years.
In GMT this midnight would occur around 23:42 or 23:43.
 
Here I list such years
First of 4 consecutive common years  Leap year 5 years after previous leap year
016: Thu, 24 Sep 1807 00:01:39 GMT   020: Mon, 23 Sep 1811 23:20:07 GMT
049: Tue, 22 Sep 1840 23:52:43 GMT   053: Sun, 22 Sep 1844 22:57:28 GMT
078: Thu, 23 Sep 1869 00:27:43 GMT   082: Mon, 22 Sep 1873 23:35:24 GMT
111: Tue, 23 Sep 1902 23:55:27 GMT   115: Sun, 23 Sep 1906 23:15:23 GMT
140: Thu, 24 Sep 1931 00:23:29 GMT   144: Mon, 23 Sep 1935 23:38:18 GMT
173: Wed, 23 Sep 1964 00:16:51 GMT   177: Sun, 22 Sep 1968 23:26:22 GMT
206: Mon, 22 Sep 1997 23:55:33 GMT   210: Sat, 22 Sep 2001 23:04:30 GMT
235: Wed, 23 Sep 2026 00:04:56 GMT   239: Sun, 22 Sep 2030 23:26:34 GMT
xxx
and so the leap years are
003, …, 015,  020, …, 048,  053, …, 077,  082, …, 110,  
115, …, 139,  144, …, 172,  177, …, 205,  210, …, 234,
239.
where “…” indicates once every 4 years in between, including the two years either side.
 
If the original Franciades are used in the compromise, then the Franciades ending in years 19 & 143 would have no leap year.
 
One thing I notice in my list of equinox times for the leap years five years after previous leap year (2nd column), is that the day of week is about the same and is usually exactly the same in alternate rows. This arises from the close approximation to the 62-year cycle of 15 leap years, which has a whole number of weeks.
Also I deliberately arranged the leap year list so each row has four blocks of leap years four apart,  to how often one would need to drop a leap day, if otherwise every 4th year is a leap year.
It turns out that this is usually 124 years after previous but may be 128 years after previous. This arises from the September equinox tropical year lasting about 365.2420 days.
This suggests that a 124-year cycle would be better than a 128-year cycle for the September equinox. The 124-year cycle is simply two 62-year cycles and so has a whole number of weeks.
 
In a Divide-by-Six calendar, having the additional leap weeks occur once every 90 & 96 years alternately, produces exactly the same mean year (365.24193548… days) as the 62-year or 124-year cycle.
 
Karl
 
15(14(17
 
From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 20 July 2016 20:12
To: CALNDR-[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 128-year Leap Rule
 
Sirs: 
This appears to me, a recent input, that French Republican calendar after year 20 was to account 'Leap Days omitted once every 128-years' proposed at Wikipedia site. 
Unfortunately, the French calendar lasted only for meare 13-years when the idea of Decimale Time was also 'dispensed with' as a compromise for Empror Napoleon's coronation. 
Please see my works: http://www.brijvij.com/ 
Brij Bhushan VIJ, 
Author, Brij's Modified Gregorian Celendar

Sent from my iPhone

On Jul 20, 2016, at 8:08 AM, Karl Palmen <[hidden email]> wrote:
Dear Calendar People
 
The idea of the Georgian Calendar having the December solstice on one of the first two days of the year leads to the idea of having the September equinox on one of the first two days of the French Republican calendar year.
 
There were two contradictory requirements for the French Republican leap year rule
(1) A leap year occurs once every 4 years, as the fourth and final year of a Franciade.
(2) The first day of the year is the day of the September equinox.
 
One possible compromise I thought of not mentioned in
https://en.wikipedia.org/wiki/Franciade and therefore possibly not considered, is:
 
The first day of a Franciade is a day of a September equinox.
 
The September equinox may then occur on either the first or second day of a year, but always the first day of the first year of a Franciade.
A leap day would normally be necessary at the end of a Franciade, to ensure this, but one in every around 32 or 33 Franciades would not have a leap day.
A Franciade has no leap day, only if it continues a long run of years that have the equinox on the first day. The first year of the next Franciade is then the final year of this run.
 
Is this idea new to me or has anyone else suggested it?
 
Karl
 
15(14(16
 
 
From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 19 July 2016 16:34
To: '[hidden email]'; [hidden email]
Subject: RE: Georgian Calendar New Year Solstice
 
Dear Tom and Calendar People
 
I did mean Georgian calendar in the sentence that Tom quoted.
 
The Georgian calendar new year was chosen to occur at the northern winter solstice. The first year of the Gregorian Era was set to begin on December 21, 1755 new style.
 
I decided to check out the timing of the December solstices and found out that the first solstice occurred on Mon, 22 Dec 1755 02:05:40 GMT so would occur on the second day (Monday, St. Peter 2) this year and the following 3 years. Over the course of the 132-year cycle the solstice would drift earlier to the first day (Sunday, St. Peter 1) and then be put back to the second day by a dropped leap day, which occurs once every 132 years.
 
So the calendar places the northern winter solstice on one of the first two days of the year, never drifting back to the previous year for thousands of years and drifting into the third day (Tuesday, St. Peter 3) for the first time on Tue, 22 Dec 2550 00:32:34 GMT in year 796 of the Georgian Era, because the December solstice tropical year is longer than the calendar mean year giving rise to a drift of about one hour later each 132-year cycle.
 
Karl
 
15(14(15
 
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Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Karl Palmen

Dear Walter and Calendar People

 

Thank you Walter for your reply. I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 22 July 2016 03:58
To: [hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

 

Dear Karl and Calendar People:

I have given some thought about how the French Republican Calendar could be modified for contemporary use.  Some of the ideas that I have considered are:

1. Using the autumnal equinox of 4000 BCE as the epoch, and numbering the years from then as Anno Lucis, like the Freemasons. IMO, the rationalism of the Freemasons and the French Republicans have much in common.  Indeed, it has been speculated the Freemasons had a role in the French Revolution.

2.  Using a 33 year leap day rule, as this would track the equinoxes better.

KARL REPLES: The Symmetrical 33-year cycle ( 3, 7, 11, 15, 19, 23, 27, 31 )  would fit the leap years that occurred while the calendar was in use. Initially only 4 in 33 years would have different new year days from the equinox-based years (20, 24, 28 & 32), by today (33-year cycle 199-231)  this would have increased to 6 in 33 years (210, 214, 218, 222, 226, 230). This would still be better than any of the 3 arithmetic proposals listed on the Wikipedia page and my compromise.



3.  Breaking up the 5-6 day period at the end of the year, and distributing those days to the astronomically longer months, like the Indian National Calendar, thereby tracking all four equinoxes and solstices more closely.  These 31 day months would form a 5-6 month group that could be shifted every 1600 or 2000 years, as the perihelion and aphelion points precess relative to the cardinal seasonal points. 

KARL REPLIES: Placing the 5-6 day period before the September equinox makes this almost unnecessary. For a year beginning 22 September of a Gregorian year not followed by a leap year, we have

1 Vendémiaire = 22 September

1 Nivôse      = 21 December

1 Germinal    = 21 March

1 Messidor    = 19 June

 

Only the fourth quarter fails to start very near its solstice or equinox day. This suggests splitting the 5 or 6 epagomenal days into two parts. The first part has two days and is inserted at the end of the third quarter and the remainder of 3 or 4 days remains the end of the year. This arrangement can be changed no more than once a millennium as the perihelion moves through the tropical year.

 

The proximity of the September equinox year to the 62-year cycle made me think of a leap-week version of the calendar. There are 12 months of the existing names each with four weeks. Each quarter ends with an extra week and in a leap year a second extra week is added to the end of the year.  It is not clear what day of the French Decade was the day of rest. If it were decadi, then the leap week calendar would start its weeks on Monday, if it were primidi, then the leap week calendar would start its weeks on Sunday.

 

Karl

 

15(14(18

 



-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Thu, Jul 21, 2016 8:08 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Dear Brij and Calendar People

 

The 128-year cycle one of four possible leap year rules listed in the Wikipedia article

 

I found

https://fr.wikisource.org/wiki/D%C3%A9cret_de_la_Convention_nationale_portant_sur_la_cr%C3%A9ation_du_calendrier_r%C3%A9publicain which has two September equinoxes reckoned in Paris time (1792 & 1793). When I compared them with GMT in

https://stellafane.org/misc/equinox.html I found that Paris time was around 17 or 18 minutes ahead of GMT at that time of year. Now I can have a go at reckoning how the equinox rule would place the leap years and then which leap years my Franciade preserving amendment would drop.

 

The equinox would occur just after midnight in the first of four consecutive common years and just before midnight in the leap year 4 years later, which is 5 years after the previous leap years.

In GMT this midnight would occur around 23:42 or 23:43.

 

Here I list such years

First of 4 consecutive common years  Leap year 5 years after previous leap year

016: Thu, 24 Sep 1807 00:01:39 GMT   020: Mon, 23 Sep 1811 23:20:07 GMT

049: Tue, 22 Sep 1840 23:52:43 GMT   053: Sun, 22 Sep 1844 22:57:28 GMT

078: Thu, 23 Sep 1869 00:27:43 GMT   082: Mon, 22 Sep 1873 23:35:24 GMT

111: Tue, 23 Sep 1902 23:55:27 GMT   115: Sun, 23 Sep 1906 23:15:23 GMT

140: Thu, 24 Sep 1931 00:23:29 GMT   144: Mon, 23 Sep 1935 23:38:18 GMT

173: Wed, 23 Sep 1964 00:16:51 GMT   177: Sun, 22 Sep 1968 23:26:22 GMT

206: Mon, 22 Sep 1997 23:55:33 GMT   210: Sat, 22 Sep 2001 23:04:30 GMT

235: Wed, 23 Sep 2026 00:04:56 GMT   239: Sun, 22 Sep 2030 23:26:34 GMT

xxx

and so the leap years are

003, …, 015,  020, …, 048,  053, …, 077,  082, …, 110,  

115, …, 139,  144, …, 172,  177, …, 205,  210, …, 234,

239.

where “…” indicates once every 4 years in between, including the two years either side.

 

If the original Franciades are used in the compromise, then the Franciades ending in years 19 & 143 would have no leap year.

 

One thing I notice in my list of equinox times for the leap years five years after previous leap year (2nd column), is that the day of week is about the same and is usually exactly the same in alternate rows. This arises from the close approximation to the 62-year cycle of 15 leap years, which has a whole number of weeks.

Also I deliberately arranged the leap year list so each row has four blocks of leap years four apart,  to how often one would need to drop a leap day, if otherwise every 4th year is a leap year.

It turns out that this is usually 124 years after previous but may be 128 years after previous. This arises from the September equinox tropical year lasting about 365.2420 days.

This suggests that a 124-year cycle would be better than a 128-year cycle for the September equinox. The 124-year cycle is simply two 62-year cycles and so has a whole number of weeks.

 

In a Divide-by-Six calendar, having the additional leap weeks occur once every 90 & 96 years alternately, produces exactly the same mean year (365.24193548… days) as the 62-year or 124-year cycle.

 

Karl

 

15(14(17

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 20 July 2016 20:12
To: CALNDR-[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 128-year Leap Rule

 

Sirs: 

This appears to me, a recent input, that French Republican calendar after year 20 was to account 'Leap Days omitted once every 128-years' proposed at Wikipedia site. 

Unfortunately, the French calendar lasted only for meare 13-years when the idea of Decimale Time was also 'dispensed with' as a compromise for Empror Napoleon's coronation. 

Please see my works: http://www.brijvij.com/ 

Brij Bhushan VIJ, 

Author, Brij's Modified Gregorian Celendar


Sent from my iPhone


On Jul 20, 2016, at 8:08 AM, Karl Palmen <[hidden email]> wrote:

Dear Calendar People

 

The idea of the Georgian Calendar having the December solstice on one of the first two days of the year leads to the idea of having the September equinox on one of the first two days of the French Republican calendar year.

 

There were two contradictory requirements for the French Republican leap year rule

(1) A leap year occurs once every 4 years, as the fourth and final year of a Franciade.

(2) The first day of the year is the day of the September equinox.

 

One possible compromise I thought of not mentioned in

https://en.wikipedia.org/wiki/Franciade and therefore possibly not considered, is:

 

The first day of a Franciade is a day of a September equinox.

 

The September equinox may then occur on either the first or second day of a year, but always the first day of the first year of a Franciade.

A leap day would normally be necessary at the end of a Franciade, to ensure this, but one in every around 32 or 33 Franciades would not have a leap day.

A Franciade has no leap day, only if it continues a long run of years that have the equinox on the first day. The first year of the next Franciade is then the final year of this run.

 

Is this idea new to me or has anyone else suggested it?

 

Karl

 

15(14(16

 

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Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Karl Palmen
In reply to this post by Karl Palmen

Dear Walter, Irv and Calendar People

 

I said “The proximity of the September equinox year to the 62-year cycle made me think of a leap-week version of the calendar. There are 12 months of the existing names each with four weeks. Each quarter ends with an extra week and in a leap year a second extra week is added to the end of the year. “

 

I thought more about this Leap Week version of the French Republican Calendar. I realise that the months and weeks could begin on Saturday to make use of the Saturday, 22 September 1792 epoch.

 

If the years of the first 62-year cycle were to begin on the nearest Saturday to September equinox day, then each 62-year cycle would have leap years at the

3rd , 9th, 15th, 20th, 26th, 32nd, 37th, 43rd, 48th, 54th, 60th  years. This cycle is symmetrical, except for the two middle years (31st & 32nd).

This is also identical to the last 62 years of Irv’s  293-year cycle for Symmetry454 calendar.

http://individual.utoronto.ca/kalendis/leap/52-293-sym454-leap-years.htm .

 

Karl

 

15(14(21

 

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 22 July 2016 13:02
To: 'East Carolina University Calendar discussion List'
Subject: RE: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

 

Dear Walter and Calendar People

 

Thank you Walter for your reply. I reply below.

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Walter J Ziobro
Sent: 22 July 2016 03:58
To:
[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

 

Dear Karl and Calendar People:

I have given some thought about how the French Republican Calendar could be modified for contemporary use.  Some of the ideas that I have considered are:

1. Using the autumnal equinox of 4000 BCE as the epoch, and numbering the years from then as Anno Lucis, like the Freemasons. IMO, the rationalism of the Freemasons and the French Republicans have much in common.  Indeed, it has been speculated the Freemasons had a role in the French Revolution.

2.  Using a 33 year leap day rule, as this would track the equinoxes better.

KARL REPLES: The Symmetrical 33-year cycle ( 3, 7, 11, 15, 19, 23, 27, 31 )  would fit the leap years that occurred while the calendar was in use. Initially only 4 in 33 years would have different new year days from the equinox-based years (20, 24, 28 & 32), by today (33-year cycle 199-231)  this would have increased to 6 in 33 years (210, 214, 218, 222, 226, 230). This would still be better than any of the 3 arithmetic proposals listed on the Wikipedia page and my compromise.



3.  Breaking up the 5-6 day period at the end of the year, and distributing those days to the astronomically longer months, like the Indian National Calendar, thereby tracking all four equinoxes and solstices more closely.  These 31 day months would form a 5-6 month group that could be shifted every 1600 or 2000 years, as the perihelion and aphelion points precess relative to the cardinal seasonal points. 

KARL REPLIES: Placing the 5-6 day period before the September equinox makes this almost unnecessary. For a year beginning 22 September of a Gregorian year not followed by a leap year, we have

1 Vendémiaire = 22 September

1 Nivôse      = 21 December

1 Germinal    = 21 March

1 Messidor    = 19 June

 

Only the fourth quarter fails to start very near its solstice or equinox day. This suggests splitting the 5 or 6 epagomenal days into two parts. The first part has two days and is inserted at the end of the third quarter and the remainder of 3 or 4 days remains the end of the year. This arrangement can be changed no more than once a millennium as the perihelion moves through the tropical year.

 

The proximity of the September equinox year to the 62-year cycle made me think of a leap-week version of the calendar. There are 12 months of the existing names each with four weeks. Each quarter ends with an extra week and in a leap year a second extra week is added to the end of the year.  It is not clear what day of the French Decade was the day of rest. If it were decadi, then the leap week calendar would start its weeks on Monday, if it were primidi, then the leap week calendar would start its weeks on Sunday.

 

Karl

 

15(14(18

 



-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <
[hidden email]>
To: CALNDR-L <
[hidden email]>
Sent: Thu, Jul 21, 2016 8:08 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Dear Brij and Calendar People

 

The 128-year cycle one of four possible leap year rules listed in the Wikipedia article

 

I found

https://fr.wikisource.org/wiki/D%C3%A9cret_de_la_Convention_nationale_portant_sur_la_cr%C3%A9ation_du_calendrier_r%C3%A9publicain which has two September equinoxes reckoned in Paris time (1792 & 1793). When I compared them with GMT in

https://stellafane.org/misc/equinox.html I found that Paris time was around 17 or 18 minutes ahead of GMT at that time of year. Now I can have a go at reckoning how the equinox rule would place the leap years and then which leap years my Franciade preserving amendment would drop.

 

The equinox would occur just after midnight in the first of four consecutive common years and just before midnight in the leap year 4 years later, which is 5 years after the previous leap years.

In GMT this midnight would occur around 23:42 or 23:43.

 

Here I list such years

First of 4 consecutive common years  Leap year 5 years after previous leap year

016: Thu, 24 Sep 1807 00:01:39 GMT   020: Mon, 23 Sep 1811 23:20:07 GMT

049: Tue, 22 Sep 1840 23:52:43 GMT   053: Sun, 22 Sep 1844 22:57:28 GMT

078: Thu, 23 Sep 1869 00:27:43 GMT   082: Mon, 22 Sep 1873 23:35:24 GMT

111: Tue, 23 Sep 1902 23:55:27 GMT   115: Sun, 23 Sep 1906 23:15:23 GMT

140: Thu, 24 Sep 1931 00:23:29 GMT   144: Mon, 23 Sep 1935 23:38:18 GMT

173: Wed, 23 Sep 1964 00:16:51 GMT   177: Sun, 22 Sep 1968 23:26:22 GMT

206: Mon, 22 Sep 1997 23:55:33 GMT   210: Sat, 22 Sep 2001 23:04:30 GMT

235: Wed, 23 Sep 2026 00:04:56 GMT   239: Sun, 22 Sep 2030 23:26:34 GMT

xxx

and so the leap years are

003, …, 015,  020, …, 048,  053, …, 077,  082, …, 110,  

115, …, 139,  144, …, 172,  177, …, 205,  210, …, 234,

239.

where “…” indicates once every 4 years in between, including the two years either side.

 

If the original Franciades are used in the compromise, then the Franciades ending in years 19 & 143 would have no leap year.

 

One thing I notice in my list of equinox times for the leap years five years after previous leap year (2nd column), is that the day of week is about the same and is usually exactly the same in alternate rows. This arises from the close approximation to the 62-year cycle of 15 leap years, which has a whole number of weeks.

Also I deliberately arranged the leap year list so each row has four blocks of leap years four apart,  to how often one would need to drop a leap day, if otherwise every 4th year is a leap year.

It turns out that this is usually 124 years after previous but may be 128 years after previous. This arises from the September equinox tropical year lasting about 365.2420 days.

This suggests that a 124-year cycle would be better than a 128-year cycle for the September equinox. The 124-year cycle is simply two 62-year cycles and so has a whole number of weeks.

 

In a Divide-by-Six calendar, having the additional leap weeks occur once every 90 & 96 years alternately, produces exactly the same mean year (365.24193548… days) as the 62-year or 124-year cycle.

 

Karl

 

15(14(17

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 20 July 2016 20:12
To: CALNDR-
[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 128-year Leap Rule

 

Sirs: 

This appears to me, a recent input, that French Republican calendar after year 20 was to account 'Leap Days omitted once every 128-years' proposed at Wikipedia site. 

Unfortunately, the French calendar lasted only for meare 13-years when the idea of Decimale Time was also 'dispensed with' as a compromise for Empror Napoleon's coronation. 

Please see my works: http://www.brijvij.com/ 

Brij Bhushan VIJ, 

Author, Brij's Modified Gregorian Celendar


Sent from my iPhone


On Jul 20, 2016, at 8:08 AM, Karl Palmen <
[hidden email]> wrote:

Dear Calendar People

 

The idea of the Georgian Calendar having the December solstice on one of the first two days of the year leads to the idea of having the September equinox on one of the first two days of the French Republican calendar year.

 

There were two contradictory requirements for the French Republican leap year rule

(1) A leap year occurs once every 4 years, as the fourth and final year of a Franciade.

(2) The first day of the year is the day of the September equinox.

 

One possible compromise I thought of not mentioned in

https://en.wikipedia.org/wiki/Franciade and therefore possibly not considered, is:

 

The first day of a Franciade is a day of a September equinox.

 

The September equinox may then occur on either the first or second day of a year, but always the first day of the first year of a Franciade.

A leap day would normally be necessary at the end of a Franciade, to ensure this, but one in every around 32 or 33 Franciades would not have a leap day.

A Franciade has no leap day, only if it continues a long run of years that have the equinox on the first day. The first year of the next Franciade is then the final year of this run.

 

Is this idea new to me or has anyone else suggested it?

 

Karl

 

15(14(16

 

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Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Walter J Ziobro
In reply to this post by Karl Palmen
Dear Karl and Calendar List:

I have been thinking some more about applying a 33 year leap day rule to the French Republican Calendar.  One could either apply the invariable leap day rule of the Dee and Dee-Cecil calendars, and get an average year length of 365.242424..days.

However, I have thought of two variations of the 33 year leap day rule:

1, The 400 year truncated 33-year leap day rule (I have mentioned this idea before). and

2  The 900 year truncated 33- year leap day rule.

The 400 year rule would have twelve periods of 33 years, plus one 4 year olympiad.  It would have exactly as many days in 400 years as the current Gregorian calendar (146.097 days), and have the same average year length of 365.2425 days.

The 900 year rule would have 27 periods of 33 years, plus 9 years with 2 leap days.  It would have 328,718 days, exactly as many as 900 years of the Revised Julian calendar', and like the Revised Julian calendar, have an average length of 365.2422222...
 

4 cycles of the 900 year rule period would have 1,314,872 days. exactly 1 day less than 3600 years of the 400 year rule, or of the Gregorian calendar

I am thinking that the 900 year rule would work nicely with the French Republican calendar, and require very little adjustment of the calendar to the current length of the average tropical year for a long period.  The long month lengths  (of 31 days) could be shifted to the subsequent months on the calendar every 1.800 years, to keep the equinox and solstices close to the commencement of each quarter. This periodic shifting would keep the lengths of the seasonal tropical years close to the actual lengths of each.

-Walter Ziobro 



-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 22, 2016 8:02 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Dear Walter and Calendar People
 
Thank you Walter for your reply. I reply below.
 
From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Walter J Ziobro
Sent: 22 July 2016 03:58
To: CALNDR-[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?
 
Dear Karl and Calendar People:

I have given some thought about how the French Republican Calendar could be modified for contemporary use.  Some of the ideas that I have considered are:

1. Using the autumnal equinox of 4000 BCE as the epoch, and numbering the years from then as Anno Lucis, like the Freemasons. IMO, the rationalism of the Freemasons and the French Republicans have much in common.  Indeed, it has been speculated the Freemasons had a role in the French Revolution.

2.  Using a 33 year leap day rule, as this would track the equinoxes better.
KARL REPLES: The Symmetrical 33-year cycle ( 3, 7, 11, 15, 19, 23, 27, 31 )  would fit the leap years that occurred while the calendar was in use. Initially only 4 in 33 years would have different new year days from the equinox-based years (20, 24, 28 & 32), by today (33-year cycle 199-231)  this would have increased to 6 in 33 years (210, 214, 218, 222, 226, 230). This would still be better than any of the 3 arithmetic proposals listed on the Wikipedia page and my compromise.


3.  Breaking up the 5-6 day period at the end of the year, and distributing those days to the astronomically longer months, like the Indian National Calendar, thereby tracking all four equinoxes and solstices more closely.  These 31 day months would form a 5-6 month group that could be shifted every 1600 or 2000 years, as the perihelion and aphelion points precess relative to the cardinal seasonal points. 
KARL REPLIES: Placing the 5-6 day period before the September equinox makes this almost unnecessary. For a year beginning 22 September of a Gregorian year not followed by a leap year, we have
1 Vendémiaire = 22 September
1 Nivôse      = 21 December
1 Germinal    = 21 March
1 Messidor    = 19 June
 
Only the fourth quarter fails to start very near its solstice or equinox day. This suggests splitting the 5 or 6 epagomenal days into two parts. The first part has two days and is inserted at the end of the third quarter and the remainder of 3 or 4 days remains the end of the year. This arrangement can be changed no more than once a millennium as the perihelion moves through the tropical year.
 
The proximity of the September equinox year to the 62-year cycle made me think of a leap-week version of the calendar. There are 12 months of the existing names each with four weeks. Each quarter ends with an extra week and in a leap year a second extra week is added to the end of the year.  It is not clear what day of the French Decade was the day of rest. If it were decadi, then the leap week calendar would start its weeks on Monday, if it were primidi, then the leap week calendar would start its weeks on Sunday.
 
Karl
 
15(14(18
 


-Walter Ziobro
 
 
 
-----Original Message-----
From: Karl Palmen <[hidden email][hidden email]
>
To: CALNDR-L <[hidden email][hidden email]>
Sent: Thu, Jul 21, 2016 8:08 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?
Dear Brij and Calendar People
 
The 128-year cycle one of four possible leap year rules listed in the Wikipedia article
 
I found
https://fr.wikisource.org/wiki/D%C3%A9cret_de_la_Convention_nationale_portant_sur_la_cr%C3%A9ation_du_calendrier_r%C3%A9publicain which has two September equinoxes reckoned in Paris time (1792 & 1793). When I compared them with GMT in
https://stellafane.org/misc/equinox.html I found that Paris time was around 17 or 18 minutes ahead of GMT at that time of year. Now I can have a go at reckoning how the equinox rule would place the leap years and then which leap years my Franciade preserving amendment would drop.
 
The equinox would occur just after midnight in the first of four consecutive common years and just before midnight in the leap year 4 years later, which is 5 years after the previous leap years.
In GMT this midnight would occur around 23:42 or 23:43.
 
Here I list such years
First of 4 consecutive common years  Leap year 5 years after previous leap year
016: Thu, 24 Sep 1807 00:01:39 GMT   020: Mon, 23 Sep 1811 23:20:07 GMT
049: Tue, 22 Sep 1840 23:52:43 GMT   053: Sun, 22 Sep 1844 22:57:28 GMT
078: Thu, 23 Sep 1869 00:27:43 GMT   082: Mon, 22 Sep 1873 23:35:24 GMT
111: Tue, 23 Sep 1902 23:55:27 GMT   115: Sun, 23 Sep 1906 23:15:23 GMT
140: Thu, 24 Sep 1931 00:23:29 GMT   144: Mon, 23 Sep 1935 23:38:18 GMT
173: Wed, 23 Sep 1964 00:16:51 GMT   177: Sun, 22 Sep 1968 23:26:22 GMT
206: Mon, 22 Sep 1997 23:55:33 GMT   210: Sat, 22 Sep 2001 23:04:30 GMT
235: Wed, 23 Sep 2026 00:04:56 GMT   239: Sun, 22 Sep 2030 23:26:34 GMT
xxx
and so the leap years are
003, …, 015,  020, …, 048,  053, …, 077,  082, …, 110,  
115, …, 139,  144, …, 172,  177, …, 205,  210, …, 234,
239.
where “…” indicates once every 4 years in between, including the two years either side.
 
If the original Franciades are used in the compromise, then the Franciades ending in years 19 & 143 would have no leap year.
 
One thing I notice in my list of equinox times for the leap years five years after previous leap year (2nd column), is that the day of week is about the same and is usually exactly the same in alternate rows. This arises from the close approximation to the 62-year cycle of 15 leap years, which has a whole number of weeks.
Also I deliberately arranged the leap year list so each row has four blocks of leap years four apart,  to how often one would need to drop a leap day, if otherwise every 4th year is a leap year.
It turns out that this is usually 124 years after previous but may be 128 years after previous. This arises from the September equinox tropical year lasting about 365.2420 days.
This suggests that a 124-year cycle would be better than a 128-year cycle for the September equinox. The 124-year cycle is simply two 62-year cycles and so has a whole number of weeks.
 
In a Divide-by-Six calendar, having the additional leap weeks occur once every 90 & 96 years alternately, produces exactly the same mean year (365.24193548… days) as the 62-year or 124-year cycle.
 
Karl
 
15(14(17
 
From: East Carolina University Calendar discussion List [[hidden email][hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 20 July 2016 20:12
To: CALNDR-[hidden email][hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 128-year Leap Rule
 
Sirs: 
This appears to me, a recent input, that French Republican calendar after year 20 was to account 'Leap Days omitted once every 128-years' proposed at Wikipedia site. 
Unfortunately, the French calendar lasted only for meare 13-years when the idea of Decimale Time was also 'dispensed with' as a compromise for Empror Napoleon's coronation. 
Please see my works: http://www.brijvij.com/ 
Brij Bhushan VIJ, 
Author, Brij's Modified Gregorian Celendar

Sent from my iPhone

On Jul 20, 2016, at 8:08 AM, Karl Palmen <[hidden email][hidden email]
> wrote:
Dear Calendar People
 
The idea of the Georgian Calendar having the December solstice on one of the first two days of the year leads to the idea of having the September equinox on one of the first two days of the French Republican calendar year.
 
There were two contradictory requirements for the French Republican leap year rule
(1) A leap year occurs once every 4 years, as the fourth and final year of a Franciade.
(2) The first day of the year is the day of the September equinox.
 
One possible compromise I thought of not mentioned in
https://en.wikipedia.org/wiki/Franciade and therefore possibly not considered, is:
 
The first day of a Franciade is a day of a September equinox.
 
The September equinox may then occur on either the first or second day of a year, but always the first day of the first year of a Franciade.
A leap day would normally be necessary at the end of a Franciade, to ensure this, but one in every around 32 or 33 Franciades would not have a leap day.
A Franciade has no leap day, only if it continues a long run of years that have the equinox on the first day. The first year of the next Franciade is then the final year of this run.
 
Is this idea new to me or has anyone else suggested it?
 
Karl
 
15(14(16
 
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Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Karl Palmen

Dear Walter and Calendar People

 

Thank you Walter for your reply. I reply below:

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 26 July 2016 06:07
To: [hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

 

Dear Karl and Calendar List:

I have been thinking some more about applying a 33 year leap day rule to the French Republican Calendar.  One could either apply the invariable leap day rule of the Dee and Dee-Cecil calendars, and get an average year length of 365.242424..days.

However, I have thought of two variations of the 33 year leap day rule:

1, The 400 year truncated 33-year leap day rule (I have mentioned this idea before). and

2  The 900 year truncated 33- year leap day rule.

The 400 year rule would have twelve periods of 33 years, plus one 4 year olympiad.  It would have exactly as many days in 400 years as the current Gregorian calendar (146.097 days), and have the same average year length of 365.2425 days.

The 900 year rule would have 27 periods of 33 years, plus 9 years with 2 leap days.  It would have 328,718 days, exactly as many as 900 years of the Revised Julian calendar', and like the Revised Julian calendar, have an average length of 365.2422222...

KARL REPLIES: Unlike 1. , 2. does not have the leap years spread as smoothly as possible. Much better than that would be four 33-year cycles with one 4 year Olympiad removed. This is the 128-year cycle with 31 leap years and a mean year of exactly 365.2421875 days. Add one Olympiad to seven 128-year cycles to get a 900-year cycle with the same mean year of 365.242222… days. The leap years of this 900-year cycle would be spread as smoothly as possible.


4 cycles of the 900 year rule period would have 1,314,872 days. exactly 1 day less than 3600 years of the 400 year rule, or of the Gregorian calendar

I am thinking that the 900 year rule would work nicely with the French Republican calendar, and require very little adjustment of the calendar to the current length of the average tropical year for a long period.  The long month lengths  (of 31 days) could be shifted to the subsequent months on the calendar every 1.800 years, to keep the equinox and solstices close to the commencement of each quarter. This periodic shifting would keep the lengths of the seasonal tropical years close to the actual lengths of each.

More accurate to the September equinox year (officially used by the French Republican Calendar) would be the 62-year cycle, which can be obtained by removing one Olympiad from two 33-year cycle. The first 62-year cycle could be fitted to September equinoxes, in which case the leap years would be the

3rd, 7th, 11th, 15th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 53rd, 57th & 61st years.

Then the only year up to year 239 (which starts Sept 2030) to begin on a different day than the September equinox would be year 206, which would begin on Mon 22 Sept 1997, instead of Tue 23 Sept 1997. The cycle as two 33-year cycles with every 4th year leap and an Olympiad removed from the end begins with the 17th year.

Walter also raised the issue of a shifting month calendar, which I’ll deal with in another note.

Karl

15(14(22



-Walter Ziobro 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 22, 2016 8:02 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Dear Walter and Calendar People

 

Thank you Walter for your reply. I reply below.

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Walter J Ziobro
Sent: 22 July 2016 03:58
To: CALNDR-[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

 

Dear Karl and Calendar People:

I have given some thought about how the French Republican Calendar could be modified for contemporary use.  Some of the ideas that I have considered are:

1. Using the autumnal equinox of 4000 BCE as the epoch, and numbering the years from then as Anno Lucis, like the Freemasons. IMO, the rationalism of the Freemasons and the French Republicans have much in common.  Indeed, it has been speculated the Freemasons had a role in the French Revolution.

2.  Using a 33 year leap day rule, as this would track the equinoxes better.

KARL REPLES: The Symmetrical 33-year cycle ( 3, 7, 11, 15, 19, 23, 27, 31 )  would fit the leap years that occurred while the calendar was in use. Initially only 4 in 33 years would have different new year days from the equinox-based years (20, 24, 28 & 32), by today (33-year cycle 199-231)  this would have increased to 6 in 33 years (210, 214, 218, 222, 226, 230). This would still be better than any of the 3 arithmetic proposals listed on the Wikipedia page and my compromise.



3.  Breaking up the 5-6 day period at the end of the year, and distributing those days to the astronomically longer months, like the Indian National Calendar, thereby tracking all four equinoxes and solstices more closely.  These 31 day months would form a 5-6 month group that could be shifted every 1600 or 2000 years, as the perihelion and aphelion points precess relative to the cardinal seasonal points. 

KARL REPLIES: Placing the 5-6 day period before the September equinox makes this almost unnecessary. For a year beginning 22 September of a Gregorian year not followed by a leap year, we have

1 Vendémiaire = 22 September

1 Nivôse      = 21 December

1 Germinal    = 21 March

1 Messidor    = 19 June

 

Only the fourth quarter fails to start very near its solstice or equinox day. This suggests splitting the 5 or 6 epagomenal days into two parts. The first part has two days and is inserted at the end of the third quarter and the remainder of 3 or 4 days remains the end of the year. This arrangement can be changed no more than once a millennium as the perihelion moves through the tropical year.

 

The proximity of the September equinox year to the 62-year cycle made me think of a leap-week version of the calendar. There are 12 months of the existing names each with four weeks. Each quarter ends with an extra week and in a leap year a second extra week is added to the end of the year.  It is not clear what day of the French Decade was the day of rest. If it were decadi, then the leap week calendar would start its weeks on Monday, if it were primidi, then the leap week calendar would start its weeks on Sunday.

 

Karl

 

15(14(18

 



-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]
>
To: CALNDR-L <[hidden email][hidden email]>
Sent: Thu, Jul 21, 2016 8:08 am
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

Dear Brij and Calendar People

 

The 128-year cycle one of four possible leap year rules listed in the Wikipedia article

 

I found

https://fr.wikisource.org/wiki/D%C3%A9cret_de_la_Convention_nationale_portant_sur_la_cr%C3%A9ation_du_calendrier_r%C3%A9publicain which has two September equinoxes reckoned in Paris time (1792 & 1793). When I compared them with GMT in

https://stellafane.org/misc/equinox.html I found that Paris time was around 17 or 18 minutes ahead of GMT at that time of year. Now I can have a go at reckoning how the equinox rule would place the leap years and then which leap years my Franciade preserving amendment would drop.

 

The equinox would occur just after midnight in the first of four consecutive common years and just before midnight in the leap year 4 years later, which is 5 years after the previous leap years.

In GMT this midnight would occur around 23:42 or 23:43.

 

Here I list such years

First of 4 consecutive common years  Leap year 5 years after previous leap year

016: Thu, 24 Sep 1807 00:01:39 GMT   020: Mon, 23 Sep 1811 23:20:07 GMT

049: Tue, 22 Sep 1840 23:52:43 GMT   053: Sun, 22 Sep 1844 22:57:28 GMT

078: Thu, 23 Sep 1869 00:27:43 GMT   082: Mon, 22 Sep 1873 23:35:24 GMT

111: Tue, 23 Sep 1902 23:55:27 GMT   115: Sun, 23 Sep 1906 23:15:23 GMT

140: Thu, 24 Sep 1931 00:23:29 GMT   144: Mon, 23 Sep 1935 23:38:18 GMT

173: Wed, 23 Sep 1964 00:16:51 GMT   177: Sun, 22 Sep 1968 23:26:22 GMT

206: Mon, 22 Sep 1997 23:55:33 GMT   210: Sat, 22 Sep 2001 23:04:30 GMT

235: Wed, 23 Sep 2026 00:04:56 GMT   239: Sun, 22 Sep 2030 23:26:34 GMT

xxx

and so the leap years are

003, …, 015,  020, …, 048,  053, …, 077,  082, …, 110,  

115, …, 139,  144, …, 172,  177, …, 205,  210, …, 234,

239.

where “…” indicates once every 4 years in between, including the two years either side.

 

If the original Franciades are used in the compromise, then the Franciades ending in years 19 & 143 would have no leap year.

 

One thing I notice in my list of equinox times for the leap years five years after previous leap year (2nd column), is that the day of week is about the same and is usually exactly the same in alternate rows. This arises from the close approximation to the 62-year cycle of 15 leap years, which has a whole number of weeks.

Also I deliberately arranged the leap year list so each row has four blocks of leap years four apart,  to how often one would need to drop a leap day, if otherwise every 4th year is a leap year.

It turns out that this is usually 124 years after previous but may be 128 years after previous. This arises from the September equinox tropical year lasting about 365.2420 days.

This suggests that a 124-year cycle would be better than a 128-year cycle for the September equinox. The 124-year cycle is simply two 62-year cycles and so has a whole number of weeks.

 

In a Divide-by-Six calendar, having the additional leap weeks occur once every 90 & 96 years alternately, produces exactly the same mean year (365.24193548… days) as the 62-year or 124-year cycle.

 

Karl

 

15(14(17

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 20 July 2016 20:12
To: CALNDR-[hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 128-year Leap Rule

 

Sirs: 

This appears to me, a recent input, that French Republican calendar after year 20 was to account 'Leap Days omitted once every 128-years' proposed at Wikipedia site. 

Unfortunately, the French calendar lasted only for meare 13-years when the idea of Decimale Time was also 'dispensed with' as a compromise for Empror Napoleon's coronation. 

Please see my works: http://www.brijvij.com/ 

Brij Bhushan VIJ, 

Author, Brij's Modified Gregorian Celendar


Sent from my iPhone


On Jul 20, 2016, at 8:08 AM, Karl Palmen <[hidden email]
> wrote:

Dear Calendar People

 

The idea of the Georgian Calendar having the December solstice on one of the first two days of the year leads to the idea of having the September equinox on one of the first two days of the French Republican calendar year.

 

There were two contradictory requirements for the French Republican leap year rule

(1) A leap year occurs once every 4 years, as the fourth and final year of a Franciade.

(2) The first day of the year is the day of the September equinox.

 

One possible compromise I thought of not mentioned in

https://en.wikipedia.org/wiki/Franciade and therefore possibly not considered, is:

 

The first day of a Franciade is a day of a September equinox.

 

The September equinox may then occur on either the first or second day of a year, but always the first day of the first year of a Franciade.

A leap day would normally be necessary at the end of a Franciade, to ensure this, but one in every around 32 or 33 Franciades would not have a leap day.

A Franciade has no leap day, only if it continues a long run of years that have the equinox on the first day. The first year of the next Franciade is then the final year of this run.

 

Is this idea new to me or has anyone else suggested it?

 

Karl

 

15(14(16