French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

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French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Karl Palmen

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

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 21 July 2016 13:08
To: 'East Carolina University Calendar discussion List'
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

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

 

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Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Brij Bhushan metric VIJ
Karl & calendar people:
This gives me some satisfaction that my inputs, as discussed and placed at my home page: http://www.brijvij.com/ have remained under constant examination and/or review digging 'historic back ground' for Reform of the Gregorian calendar my inputs have possibly been the best so far "using my developed 896-year cycle or the 834-year cycle; along with Divide Six(6) option for placing a Leap week, as also on slight modification of LeapDay Rule from -div4/skip100th/count400th to more appropriate div4/skip128th-years can usefully result in getting Mean Year =365+31/128=365.2421875 days. This does not need any further adjustment like the 4000-th year to set the Astronomic clock in tune with possibly the best calculations so far: at little or No Cost to the Tax-Payer. This becomes the Simplest, Surest and Cheapest ever proposal for the Reform of Gregorian calendar. 
Permit me to assume, sirs, while attempting to dig past history of calendars- my inputs have not been ignored by calendar experts and the World Calendar Organisation - especially when my inputs provide solutions to: (a) Decimalisation of Timeof the HOUR i.e. The Hour-Angle, Radian and the value for Pi; (b) No change to dail face/No reworking for trigonometric & mathematical functions; (c) No change to 7-day week EXCEPT shifting the day of July 31 as February 29 (all years) but keeping 365th day and the LeapDay (366th) if used between June 30th & July 01; (d) Not disturbing the the current
Length of days in each month per Keplers Laws of Plentary bodies - maintaining the 'Fist Rule' as learning aid among all classes of children and the lady at Home; (e) I find NO difficulty in using my worked Phase/or Tithi values linked to 19-years, 896-years or the Cycle of Precession linked to current duration of the Mean Lunar Month.
What more simplicity or ease for the Reform of Gregorian calendar can be 'thought/ incorporated/implemented, is my view?
My profound regards to all calendar experts who have been constant 'critics' of my proposed inputs. I salute them all, being a Soldier fighting for a cause?
Brij Bhushan (metric) VIJ
[hidden email]

Sent from my iPhone

On Jul 27, 2016, at 8:03 AM, Karl Palmen <[hidden email]> wrote:

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

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 21 July 2016 13:08
To: 'East Carolina University Calendar discussion List'
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

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

 

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Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Karl Palmen
In reply to this post by Karl Palmen

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: Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Karl Palmen
In reply to this post by Brij Bhushan metric VIJ

Dear Brij and Calendar People

 

The Wikipedia page https://en.wikipedia.org/wiki/French_Republican_Calendar#Converting_from_the_Gregorian_Calendar mentions a 128-year cycle rule for the calendar.

 

It would drop leap years in years 0, 128, 256 and 384 in the first 500 year while the compromise would have leap years one year earlier and drop leap years in 19, 143, 271 and 395. The dropped leap years for the compromise occur 19, 15, 15 and 11 years later than in the 128-year year cycle.

By a stroke of fortune, conversion between a 128-year cycle based on French republican year numbers and one based on Common Era year numbers would be very simple, because FR year 0 ends in CE year 1792 and 1792=14*128. Therefore every FR year would begin on the same day of every CE year (but not vice versa).

 

 

Brij has made two big errors:

 

Brij’s first big error is that the does not think that the slow change of the duration of the mean tropical year is of consequence to the choice of a leap year rule or that the variation of the length of the tropical depending on its start point is of consequence to the choice of leap year rule.  This is a common error, which has been brought about by the story of the Gregorian reform of the Julian Calendar. Accuracy beyond the Gregorian mean year is a more complicated matter as I show next.

 

Here are some equinoxes and solstices 400 years apart to show their drift with any calendar jitter:

Sat 1615-03-21 00:07  Mon 1615-06-22 01:05   Wed 1615-09-23 12:33  Tue 1615-12-22 02:11

Fri 2015-03-20 22:45  Sun 2015-06-21 16:38   Wed 2015-09-23 08:20  Tue 2015-12-22 04:48

Fri 2415-03-20 21:29  Sun 2415-06-21 07:58   Wed 2415-09-23 02:56  Tue 2415-12-22 06:36

Fri 2815-03-20 20:11  Sat 2815-06-20 23:09   Tue 2815-09-22 20:29  Tue 2815-12-22 07:39

One can see that although the equinoxes and the June solstice are drifting earlier, the December solstice is drifting later. So making the calendar more accurate is not simple and its desirability for a civil calendar is questionable. Therefore, Brij’s priority of making the calendar mean year very near today’s duration of the mean tropical year is mistaken. In particular, it leads to the choice of a non-decimal Divide-by-Six leap week rule rather than a decimal Divide-by-Five leap week rule.

 

Brij’s second error is the belief that a conservative change in the calendar or clock would be significantly cheaper than a radical change. Any change no matter how small would need a lot of organisation to bring it about and so would be expensive. A change must bring big benefit to be worthwhile and so needs to be a radical change, anything else is not worth the cost.

Brij’s reorganisation of the months is conservative and so is his decimalisation of time, which preserves the hour.

 

I think Brij has preserved the hour in his decimal time proposal is that any clock or watch with an hour and minute hand could be continued to be used. However use would be much more complicated, because one would have to multiply by 8 + 1/3 instead of 5 to work out the number of minutes for the minute hand from the hour number. This would make people question the benefit of decimal time and encourage use of digital clocks for which preserving the hour has no cost reduction.

 

Even if time were decimalised, the second would need to be kept unchanged for physics. Changing it would require numerous other units changed including at least two of the Volt, Amp and Watt and so would be very expensive. Keeping the second unchanged for physics would have a benefit for the decimal time, because it would allow the number of seconds in a decimal time unit to be changed occasionally to take account of changes in earth’s rotation rate. The current practice of using the same units for physical time and time of day is not sustainable even with leap seconds.

 

 

A nautical kilometre would be the distance along a meridian in which the latitude changes by one hundredth of a grad, where 400 grads = 360 degrees. For the Paris meridian this would be equal to the original definition of the kilometre. The number of nautical miles in a nautical Kilometre by the original definitions of both is 10,000/(90*60) = 1.815815815815… . Today this has been changed to 1.852.

See https://en.wikipedia.org/wiki/Gradian for more about the grad and

https://en.wikipedia.org/wiki/Nautical_mile about the nautical mile.

 

 

Karl

 

15(15(21

 

From: [hidden email] [mailto:[hidden email]]
Sent: 22 August 2016 17:40
To: Palmen, Karl (STFC,RAL,ISIS); [hidden email]
Subject: Fwd: Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

 

Indeed glad to see a post conecting French Republican calendar with my inputs on 128-year LeapDay compromise getting Mean Year=(365+31/128)=365.2422875 days. 

If the ideas are that old (?), what has been resisting that No Consideration had been given during earlier attempts, say during 1920's.....and later during mid 1950's - to reject attempts in this direction by League of Nations and/or United Nations.

One more point that I observe, where did the French/rest of the intelligentsia fail to bridge "Decimalisation of the HOUR in relation to (Arc-angle) I.e. 'Hour-angle' defy" in arriving at a viable definition for Nautical Kilometre to replace Nautical Mile? Please observe:

24hx100mdx100sd :: 24hx60mx60s can be realized if and only if  'arc-angle' 90*x100'x100" :: 90*60'60" are also merged. This is where the French failed and caused the rejection/failure of French Republican calendar and/or the need for Decimale Time. 

My proposal for the Modified Brij-Gregorian calendar is a step in this direction, to become the Simplest, Surest and Cheapest ever inputs: http://www.brijvij.com/

Regards,

Brij Bushan (metric) VIJ

Monday, 2016 August 22H09:66(decimal)

 

Sent from my iPhone


Begin forwarded message:

From: Brij Bhushan metric VIJ <[hidden email]>
Date: July 27, 2016 at 10:35:20 AM MST
To: East Carolina University Calendar discussion List <[hidden email]>
Cc: "[hidden email]" <[hidden email]>
Subject: Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Karl & calendar people:

This gives me some satisfaction that my inputs, as discussed and placed at my home page: http://www.brijvij.com/ have remained under constant examination and/or review digging 'historic back ground' for Reform of the Gregorian calendar my inputs have possibly been the best so far "using my developed 896-year cycle or the 834-year cycle; along with Divide Six(6) option for placing a Leap week, as also on slight modification of LeapDay Rule from -div4/skip100th/count400th to more appropriate div4/skip128th-years can usefully result in getting Mean Year =365+31/128=365.2421875 days. This does not need any further adjustment like the 4000-th year to set the Astronomic clock in tune with possibly the best calculations so far: at little or No Cost to the Tax-Payer. This becomes the Simplest, Surest and Cheapest ever proposal for the Reform of Gregorian calendar. 

Permit me to assume, sirs, while attempting to dig past history of calendars- my inputs have not been ignored by calendar experts and the World Calendar Organisation - especially when my inputs provide solutions to: (a) Decimalisation of Timeof the HOUR i.e. The Hour-Angle, Radian and the value for Pi; (b) No change to dail face/No reworking for trigonometric & mathematical functions; (c) No change to 7-day week EXCEPT shifting the day of July 31 as February 29 (all years) but keeping 365th day and the LeapDay (366th) if used between June 30th & July 01; (d) Not disturbing the the current

Length of days in each month per Keplers Laws of Plentary bodies - maintaining the 'Fist Rule' as learning aid among all classes of children and the lady at Home; (e) I find NO difficulty in using my worked Phase/or Tithi values linked to 19-years, 896-years or the Cycle of Precession linked to current duration of the Mean Lunar Month.

What more simplicity or ease for the Reform of Gregorian calendar can be 'thought/ incorporated/implemented, is my view?

My profound regards to all calendar experts who have been constant 'critics' of my proposed inputs. I salute them all, being a Soldier fighting for a cause?

Brij Bhushan (metric) VIJ

[hidden email]

Sent from my iPhone


On Jul 27, 2016, at 8:03 AM, Karl Palmen <[hidden email]> wrote:

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

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 21 July 2016 13:08
To: 'East Carolina University Calendar discussion List'
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

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

 

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The Metric Second Re: Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Brij Bhushan metric VIJ
Sirs:
Karl has a reason to question my , 'competence' to Reform the current format of the Gregorian calendar with minimal change(s) per my demonstrated/discussed calculations: http://www.brijvij.com/
This brings me back to my 'original & base contribution' - The Metric Second (1973), wherein also I provided concerns like - the grad (calling this a quadrant of 100 degrees metric) linked to the new time interval: The Metric Second i.e. the metric day having 20x100x100=200000 units, via the duration linked to 'tropical year'. 
My approach to the Nautical Kilometre, had . also been pointed. Obviously, the Nautical Mile worked to 1852 'metre'!
As far as the "Decimalsatiin of Time of the HOUR", I do not see the difficulty expressed in considering the equation of 25 divisions (Decimal minutes/seconds) = 15 divisions (minutes/seconds) in each QUDRANT of 90* and/or 100 grad; for which conversion does not need a 'super calculator' - just mental calculations would bridge: MULTIPLY by 5 & DIVIDE by 3; would suffice without changing the face of "clocks/horological instruments", is my view. Horology instruments only need 100 additional graduations along with present 60 graduations (markings for minutes/seconds).
NEVER has man ever suggested such 'simplicity' to arrive/achieve Decimalisation for TIME of the HOUR, when linked to HOUR-Angle of 15x24=360-degree circle I.e. As the Earth spins in its axis for determination of Local Time, at ZERO cost 'mentally' by a child of STANDRD Five upwards! Where is he difficulty, I wonder?
Whatever happened to French Republican calendar, now, is history!
My regards, sir(s)
Brij B. VIJ ([hidden email])
Tuesday, 2016 August 23H09:56(decimal)

Sent from my iPhone

On Aug 23, 2016, at 5:02 AM, Karl Palmen <[hidden email]> wrote:

Dear Brij and Calendar People

 

The Wikipedia page https://en.wikipedia.org/wiki/French_Republican_Calendar#Converting_from_the_Gregorian_Calendar mentions a 128-year cycle rule for the calendar.

 

It would drop leap years in years 0, 128, 256 and 384 in the first 500 year while the compromise would have leap years one year earlier and drop leap years in 19, 143, 271 and 395. The dropped leap years for the compromise occur 19, 15, 15 and 11 years later than in the 128-year year cycle.

By a stroke of fortune, conversion between a 128-year cycle based on French republican year numbers and one based on Common Era year numbers would be very simple, because FR year 0 ends in CE year 1792 and 1792=14*128. Therefore every FR year would begin on the same day of every CE year (but not vice versa).

 

 

Brij has made two big errors:

 

Brij’s first big error is that the does not think that the slow change of the duration of the mean tropical year is of consequence to the choice of a leap year rule or that the variation of the length of the tropical depending on its start point is of consequence to the choice of leap year rule.  This is a common error, which has been brought about by the story of the Gregorian reform of the Julian Calendar. Accuracy beyond the Gregorian mean year is a more complicated matter as I show next.

 

Here are some equinoxes and solstices 400 years apart to show their drift with any calendar jitter:

Sat 1615-03-21 00:07  Mon 1615-06-22 01:05   Wed 1615-09-23 12:33  Tue 1615-12-22 02:11

Fri 2015-03-20 22:45  Sun 2015-06-21 16:38   Wed 2015-09-23 08:20  Tue 2015-12-22 04:48

Fri 2415-03-20 21:29  Sun 2415-06-21 07:58   Wed 2415-09-23 02:56  Tue 2415-12-22 06:36

Fri 2815-03-20 20:11  Sat 2815-06-20 23:09   Tue 2815-09-22 20:29  Tue 2815-12-22 07:39

One can see that although the equinoxes and the June solstice are drifting earlier, the December solstice is drifting later. So making the calendar more accurate is not simple and its desirability for a civil calendar is questionable. Therefore, Brij’s priority of making the calendar mean year very near today’s duration of the mean tropical year is mistaken. In particular, it leads to the choice of a non-decimal Divide-by-Six leap week rule rather than a decimal Divide-by-Five leap week rule.

 

Brij’s second error is the belief that a conservative change in the calendar or clock would be significantly cheaper than a radical change. Any change no matter how small would need a lot of organisation to bring it about and so would be expensive. A change must bring big benefit to be worthwhile and so needs to be a radical change, anything else is not worth the cost.

Brij’s reorganisation of the months is conservative and so is his decimalisation of time, which preserves the hour.

 

I think Brij has preserved the hour in his decimal time proposal is that any clock or watch with an hour and minute hand could be continued to be used. However use would be much more complicated, because one would have to multiply by 8 + 1/3 instead of 5 to work out the number of minutes for the minute hand from the hour number. This would make people question the benefit of decimal time and encourage use of digital clocks for which preserving the hour has no cost reduction.

 

Even if time were decimalised, the second would need to be kept unchanged for physics. Changing it would require numerous other units changed including at least two of the Volt, Amp and Watt and so would be very expensive. Keeping the second unchanged for physics would have a benefit for the decimal time, because it would allow the number of seconds in a decimal time unit to be changed occasionally to take account of changes in earth’s rotation rate. The current practice of using the same units for physical time and time of day is not sustainable even with leap seconds.

 

 

A nautical kilometre would be the distance along a meridian in which the latitude changes by one hundredth of a grad, where 400 grads = 360 degrees. For the Paris meridian this would be equal to the original definition of the kilometre. The number of nautical miles in a nautical Kilometre by the original definitions of both is 10,000/(90*60) = 1.815815815815… . Today this has been changed to 1.852.

See https://en.wikipedia.org/wiki/Gradian for more about the grad and

https://en.wikipedia.org/wiki/Nautical_mile about the nautical mile.

 

 

Karl

 

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From: [hidden email] [[hidden email]]
Sent: 22 August 2016 17:40
To: Palmen, Karl (STFC,RAL,ISIS); [hidden email]
Subject: Fwd: Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

 

Indeed glad to see a post conecting French Republican calendar with my inputs on 128-year LeapDay compromise getting Mean Year=(365+31/128)=365.2422875 days. 

If the ideas are that old (?), what has been resisting that No Consideration had been given during earlier attempts, say during 1920's.....and later during mid 1950's - to reject attempts in this direction by League of Nations and/or United Nations.

One more point that I observe, where did the French/rest of the intelligentsia fail to bridge "Decimalisation of the HOUR in relation to (Arc-angle) I.e. 'Hour-angle' defy" in arriving at a viable definition for Nautical Kilometre to replace Nautical Mile? Please observe:

24hx100mdx100sd :: 24hx60mx60s can be realized if and only if  'arc-angle' 90*x100'x100" :: 90*60'60" are also merged. This is where the French failed and caused the rejection/failure of French Republican calendar and/or the need for Decimale Time. 

My proposal for the Modified Brij-Gregorian calendar is a step in this direction, to become the Simplest, Surest and Cheapest ever inputs: http://www.brijvij.com/

Regards,

Brij Bushan (metric) VIJ

Monday, 2016 August 22H09:66(decimal)

 

Sent from my iPhone


Begin forwarded message:

From: Brij Bhushan metric VIJ <[hidden email]>
Date: July 27, 2016 at 10:35:20 AM MST
To: East Carolina University Calendar discussion List <[hidden email]>
Cc: "[hidden email]" <[hidden email]>
Subject: Brij Home Page & calculations Re: French Republican Equinox Leap Years RE: French Republican Leap Year Compromise? RE: ...

Karl & calendar people:

This gives me some satisfaction that my inputs, as discussed and placed at my home page: http://www.brijvij.com/ have remained under constant examination and/or review digging 'historic back ground' for Reform of the Gregorian calendar my inputs have possibly been the best so far "using my developed 896-year cycle or the 834-year cycle; along with Divide Six(6) option for placing a Leap week, as also on slight modification of LeapDay Rule from -div4/skip100th/count400th to more appropriate div4/skip128th-years can usefully result in getting Mean Year =365+31/128=365.2421875 days. This does not need any further adjustment like the 4000-th year to set the Astronomic clock in tune with possibly the best calculations so far: at little or No Cost to the Tax-Payer. This becomes the Simplest, Surest and Cheapest ever proposal for the Reform of Gregorian calendar. 

Permit me to assume, sirs, while attempting to dig past history of calendars- my inputs have not been ignored by calendar experts and the World Calendar Organisation - especially when my inputs provide solutions to: (a) Decimalisation of Timeof the HOUR i.e. The Hour-Angle, Radian and the value for Pi; (b) No change to dail face/No reworking for trigonometric & mathematical functions; (c) No change to 7-day week EXCEPT shifting the day of July 31 as February 29 (all years) but keeping 365th day and the LeapDay (366th) if used between June 30th & July 01; (d) Not disturbing the the current

Length of days in each month per Keplers Laws of Plentary bodies - maintaining the 'Fist Rule' as learning aid among all classes of children and the lady at Home; (e) I find NO difficulty in using my worked Phase/or Tithi values linked to 19-years, 896-years or the Cycle of Precession linked to current duration of the Mean Lunar Month.

What more simplicity or ease for the Reform of Gregorian calendar can be 'thought/ incorporated/implemented, is my view?

My profound regards to all calendar experts who have been constant 'critics' of my proposed inputs. I salute them all, being a Soldier fighting for a cause?

Brij Bhushan (metric) VIJ

[hidden email]

Sent from my iPhone


On Jul 27, 2016, at 8:03 AM, Karl Palmen <[hidden email]> wrote:

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

 

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From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 21 July 2016 13:08
To: 'East Carolina University Calendar discussion List'
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

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

 

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