62-year cycle and French Republican Equinox Leap Years RE: ...

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62-year cycle and French Republican Equinox Leap Years RE: ...

Karl Palmen - UKRI STFC

Dear Jamison and Calendar People

 

A 62-year cycle rule was suggested on this list for the French Republican calendar and similar.

 

Here I show that the French Republican calendar with equinox leap year rule almost follows the 62-year cycle. 62 consecutive years nearly always have 15 leap years.

 

003, …, 015,  020, 024, …, 048,  

053, …, 077,  082, 086, …, 110,  

115, …, 139,  144, 148, …, 172, 

177, …, 201, 205   210, …, 234,

239, …, 263, 267,  272, …, 296, 

301, …, 325,  330, 334, …, 358,

363, …, 387, 391,  396, …, 420, 

425, …, 449, 453,  458, …, 482,

487, …, 499.

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

210, …, 234,is an abbreviation of 210, 214, 218, 222, 226, 230, 234,.

The grey years 003 & 499 do not bound their …, periods, which extend outside the range of years 1 to 500.

 

 

To make it follow a 62-year cycle only a few leap years would need changing:

 

003, …, 015,  020, 024, …, 048,  

053, …, 077,  082, 086, …, 110,  

115, …, 139,  144, 148, …, 172, 

177, …, 201,  206, 210, …, 234,

239, …, 263,  268, 272, …, 296, 

301, …, 325,  330, 334, …, 358,

363, …, 387,  392, 396, …, 420, 

425, …, 449,  454, 458, …, 482,

487, …, 499.

 

Only the 4 leap years in red have been changed, each postponed by 1 year so allowing the equinox to occur early in the 2nd day of each of the four red years.

 

The 62-year cycle also has a whole number of weeks.

 

This can be seen in this list:

016: Thu, 24 Sep 1807   020: Mon, 23 Sep 1811

078: Thu, 23 Sep 1869   082: Mon, 22 Sep 1873

140: Thu, 24 Sep 1931   144: Mon, 23 Sep 1935

 

 

Karl

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 29 July 2016 13:34
To: 'East Carolina University Calendar discussion List'
Subject: RE: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

 

Dear Calendar People

 

The converter at http://www.calendarhome.com/calculate/convert-a-date  uses the same code as the Fourmilab converter, but is compact, so saving the user from scrolling. I use it to extend my list of Equinox-based French Republican leap years to the first 500 years.

 

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

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

239, …, 267,  272, …, 296,  301, …, 325,  330, …, 358,

363, …, 391,  396, …, 420,  425, …, 453,  458, …, 482,

487, …, 499.

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

210, …, 234,is an abbreviation of 210, 214, 218, 222, 226, 230, 234,.

The grey years 003 & 499 do not bound their …, periods, which extend outside the range of years 1 to 500.

 

If find that the years in the last column are 124 years apart. Other columns may have intervals of 128 or 120 years. This confirms that the 62-year cycle of 15 leap days is accurate for the September equinox. This doubles to form a 124-year cycle of 30 leap days (= once every 4 years with one dropped).

 

In the Franciade compromise I suggested, each leap year would be postponed to the last year of its Franciade and so from year 1 to 500, the years

19,  143, 271, and 395 would drop a leap day. These four years have two intervals of 124 years and one interval of 128 years.

 

One the way, I found out that year 301 starts on 21 September 2092 and so also year 305 starts on 21 September 2096. There are no other such years until after year 500.

 

 

Karl

 

15(14(25

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 27 July 2016 13:03
To: 'East Carolina University Calendar discussion List'
Subject: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

 

Dear Calendar People

 

I found that the Fourmilab calendar converter

https://www.fourmilab.ch/documents/calendar/  converts the French Republican Calendar according to the equinox rule.

 

I found it fitted with the leap years:

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.

 

which reckoned.

 

The years shown began on the days I expected:

016: Thu, 24 Sep 1807   020: Mon, 23 Sep 1811

049: Tue, 23 Sep 1840   053: Sun, 22 Sep 1844

078: Thu, 23 Sep 1869   082: Mon, 22 Sep 1873

111: Tue, 24 Sep 1902   115: Sun, 23 Sep 1906

140: Thu, 24 Sep 1931   144: Mon, 23 Sep 1935

173: Wed, 23 Sep 1964   177: Sun, 22 Sep 1968

206: Mon, 23 Sep 1997   210: Sat, 22 Sep 2001

235: Wed, 23 Sep 2026   239: Sun, 22 Sep 2030

 

Karl

 

15(14(23

 

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Re: 62-year cycle and French Republican Equinox Leap Years RE: ...

Jamison Painter
This is true enough as it goes, yes.

On Mon, Apr 16, 2018, 6:56 AM Karl Palmen - UKRI STFC <[hidden email]> wrote:

Dear Jamison and Calendar People

 

A 62-year cycle rule was suggested on this list for the French Republican calendar and similar.

 

Here I show that the French Republican calendar with equinox leap year rule almost follows the 62-year cycle. 62 consecutive years nearly always have 15 leap years.

 

003, …, 015,  020, 024, …, 048,  

053, …, 077,  082, 086, …, 110,  

115, …, 139,  144, 148, …, 172, 

177, …, 201, 205   210, …, 234,

239, …, 263, 267,  272, …, 296, 

301, …, 325,  330, 334, …, 358,

363, …, 387, 391,  396, …, 420, 

425, …, 449, 453,  458, …, 482,

487, …, 499.

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

210, …, 234,is an abbreviation of 210, 214, 218, 222, 226, 230, 234,.

The grey years 003 & 499 do not bound their …, periods, which extend outside the range of years 1 to 500.

 

 

To make it follow a 62-year cycle only a few leap years would need changing:

 

003, …, 015,  020, 024, …, 048,  

053, …, 077,  082, 086, …, 110,  

115, …, 139,  144, 148, …, 172, 

177, …, 201,  206, 210, …, 234,

239, …, 263,  268, 272, …, 296, 

301, …, 325,  330, 334, …, 358,

363, …, 387,  392, 396, …, 420, 

425, …, 449,  454, 458, …, 482,

487, …, 499.

 

Only the 4 leap years in red have been changed, each postponed by 1 year so allowing the equinox to occur early in the 2nd day of each of the four red years.

 

The 62-year cycle also has a whole number of weeks.

 

This can be seen in this list:

016: Thu, 24 Sep 1807   020: Mon, 23 Sep 1811

078: Thu, 23 Sep 1869   082: Mon, 22 Sep 1873

140: Thu, 24 Sep 1931   144: Mon, 23 Sep 1935

 

 

Karl

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 29 July 2016 13:34
To: 'East Carolina University Calendar discussion List'
Subject: RE: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

 

Dear Calendar People

 

The converter at http://www.calendarhome.com/calculate/convert-a-date  uses the same code as the Fourmilab converter, but is compact, so saving the user from scrolling. I use it to extend my list of Equinox-based French Republican leap years to the first 500 years.

 

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

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

239, …, 267,  272, …, 296,  301, …, 325,  330, …, 358,

363, …, 391,  396, …, 420,  425, …, 453,  458, …, 482,

487, …, 499.

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

210, …, 234,is an abbreviation of 210, 214, 218, 222, 226, 230, 234,.

The grey years 003 & 499 do not bound their …, periods, which extend outside the range of years 1 to 500.

 

If find that the years in the last column are 124 years apart. Other columns may have intervals of 128 or 120 years. This confirms that the 62-year cycle of 15 leap days is accurate for the September equinox. This doubles to form a 124-year cycle of 30 leap days (= once every 4 years with one dropped).

 

In the Franciade compromise I suggested, each leap year would be postponed to the last year of its Franciade and so from year 1 to 500, the years

19,  143, 271, and 395 would drop a leap day. These four years have two intervals of 124 years and one interval of 128 years.

 

One the way, I found out that year 301 starts on 21 September 2092 and so also year 305 starts on 21 September 2096. There are no other such years until after year 500.

 

 

Karl

 

15(14(25

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 27 July 2016 13:03
To: 'East Carolina University Calendar discussion List'
Subject: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

 

Dear Calendar People

 

I found that the Fourmilab calendar converter

https://www.fourmilab.ch/documents/calendar/  converts the French Republican Calendar according to the equinox rule.

 

I found it fitted with the leap years:

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.

 

which reckoned.

 

The years shown began on the days I expected:

016: Thu, 24 Sep 1807   020: Mon, 23 Sep 1811

049: Tue, 23 Sep 1840   053: Sun, 22 Sep 1844

078: Thu, 23 Sep 1869   082: Mon, 22 Sep 1873

111: Tue, 24 Sep 1902   115: Sun, 23 Sep 1906

140: Thu, 24 Sep 1931   144: Mon, 23 Sep 1935

173: Wed, 23 Sep 1964   177: Sun, 22 Sep 1968

206: Mon, 23 Sep 1997   210: Sat, 22 Sep 2001

235: Wed, 23 Sep 2026   239: Sun, 22 Sep 2030

 

Karl

 

15(14(23