Revision of Two Gear/Two Peg Lunisolar Device

[Brillig]

Dear Karl, Irv and Calendar People,

OK How about this device and operation, which I think is a bit more straightforward.

There is a 235-cog gear with one mark near one of the cogs indicating the start of a year.
There is a 19-cog gear with 19 holes used to contain two pegs.
The two gears interlock and are adjusted relative to each other by rotating the 19-cog gear clockwise.
The pegs consist of one short peg moved rarely, and a long peg moved frequently. The frequently moved one is longer so it can be grasped even when the short peg is in place. That was my reason for the different lengths of pegs earlier, but I didn't mention it.
Each time the small gear is rotated, it is rotated until the smaller peg is closest to the larger gear. One month is considered to have passed at this point. While the small gear is being rotated, the new year mark on the large gear should be observed. If it passes the point where the small peg finally comes to rest during the rotation, then the large peg is moved one hole counterclockwise. If the small peg is occupying that hole already, it is moved to the spot previously occupied by the large peg, whereupon the large peg takes the spot previously occupied by the small peg.

In this way, the tall peg travels counterclockwise around the gear, and the small peg travels clockwise around the same gear.

By rotating the gear until the small peg aligns with the large gear, adjustments are automatically made by 1/19 month.

Victor

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Victor and Calendar People

 

Very clever! Victor uses the small slower moving peg as the new moon mark on the moon wheel!

The pegs are moved once every 19 years once every 18*19=342 years the small page move one place in the direction that the moon wheel rotates, so forcing the sun wheel to turn an extra tooth (as it would do if it slipped against the moon wheel).

 

This is better than my suggested revision involving an annual moving of the pegs and correction by slipping of the sun wheel one tooth against the moon wheel.

However my suggestion can be easily modified to produce a 334-year cycle.

 

Karl

 

10(08(26 till noon

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 20 May 2009 23:35
To: CALNDR-L@...
Subject: Revision of Two Gear/Two Peg Lunisolar Device

 

Dear Karl, Irv and Calendar People,

OK How about this device and operation, which I think is a bit more straightforward.

There is a 235-cog gear with one mark near one of the cogs indicating the start of a year.
There is a 19-cog gear with 19 holes used to contain two pegs.
The two gears interlock and are adjusted relative to each other by rotating the 19-cog gear clockwise.
The pegs consist of one short peg moved rarely, and a long peg moved frequently. The frequently moved one is longer so it can be grasped even when the short peg is in place. That was my reason for the different lengths of pegs earlier, but I didn't mention it.
Each time the small gear is rotated, it is rotated until the smaller peg is closest to the larger gear. One month is considered to have passed at this point. While the small gear is being rotated, the new year mark on the large gear should be observed. If it passes the point where the small peg finally comes to rest during the rotation, then the large peg is moved one hole counterclockwise. If the small peg is occupying that hole already, it is moved to the spot previously occupied by the large peg, whereupon the large peg takes the spot previously occupied by the small peg.

In this way, the tall peg travels counterclockwise around the gear, and the small peg travels clockwise around the same gear.

By rotating the gear until the small peg aligns with the large gear, adjustments are automatically made by 1/19 month.

Victor

---

Scanned by iCritical.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Victor and Calendar People

 

This revision can be modified simply to give a 334-year cycle.

 

Instead of moving the peg(s) every 19 years (when the marked teeth meet), move the peg(s), when the marked tooth of the sun wheel meets the short peg.

This will usually be one every 19 years, but after the small peg has moved, it’ll occur again after just 11 years. This would then give rise to a 334-year cycle.

 

The 11 years have 11 rotations of the sun wheel 11*235=2585 teeth equal to 136 rotations of the moon wheel plus one tooth from the small peg move, which is 136*19+1=2585 teeth.

 

Karl

 

10(08(27

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 20 May 2009 23:35
To: CALNDR-L@...
Subject: Revision of Two Gear/Two Peg Lunisolar Device

 

Dear Karl, Irv and Calendar People,

OK How about this device and operation, which I think is a bit more straightforward.

There is a 235-cog gear with one mark near one of the cogs indicating the start of a year.
There is a 19-cog gear with 19 holes used to contain two pegs.
The two gears interlock and are adjusted relative to each other by rotating the 19-cog gear clockwise.
The pegs consist of one short peg moved rarely, and a long peg moved frequently. The frequently moved one is longer so it can be grasped even when the short peg is in place. That was my reason for the different lengths of pegs earlier, but I didn't mention it.
Each time the small gear is rotated, it is rotated until the smaller peg is closest to the larger gear. One month is considered to have passed at this point. While the small gear is being rotated, the new year mark on the large gear should be observed. If it passes the point where the small peg finally comes to rest during the rotation, then the large peg is moved one hole counterclockwise. If the small peg is occupying that hole already, it is moved to the spot previously occupied by the large peg, whereupon the large peg takes the spot previously occupied by the small peg.

In this way, the tall peg travels counterclockwise around the gear, and the small peg travels clockwise around the same gear.

By rotating the gear until the small peg aligns with the large gear, adjustments are automatically made by 1/19 month.

Victor

---

Scanned by iCritical.

[Karl Palmen]

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Dear Victor and Calendar People

 

Rather than moving the moon wheel one complete revolution at the new moon (or start of lunar calendar month), turn it one tooth at a time throughout the lunar month. This would give a more accurate indication of the season by the sun wheel.

 

I’ve thought of a way of doing this. For the 28 days after a new moon (or start of the lunar calendar month), turn it one tooth each Monday, Tuesday, Thursday, Friday and every other Saturday. Over these 28 days the wheel will turn 18 teeth regardless of what day of the week the 28 days begin. Then at the next new moon turn the wheel by one more tooth to complete its turn and lunar month. If the small peg has moved this month, the wheel is then rotated by two more teeth to complete the lunar month.

 

Karl

 

10(08(27

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 20 May 2009 23:35
To: CALNDR-L@...
Subject: Revision of Two Gear/Two Peg Lunisolar Device

 

Dear Karl, Irv and Calendar People,

OK How about this device and operation, which I think is a bit more straightforward.

There is a 235-cog gear with one mark near one of the cogs indicating the start of a year.
There is a 19-cog gear with 19 holes used to contain two pegs.
The two gears interlock and are adjusted relative to each other by rotating the 19-cog gear clockwise.
The pegs consist of one short peg moved rarely, and a long peg moved frequently. The frequently moved one is longer so it can be grasped even when the short peg is in place. That was my reason for the different lengths of pegs earlier, but I didn't mention it.
Each time the small gear is rotated, it is rotated until the smaller peg is closest to the larger gear. One month is considered to have passed at this point. While the small gear is being rotated, the new year mark on the large gear should be observed. If it passes the point where the small peg finally comes to rest during the rotation, then the large peg is moved one hole counterclockwise. If the small peg is occupying that hole already, it is moved to the spot previously occupied by the large peg, whereupon the large peg takes the spot previously occupied by the small peg.

In this way, the tall peg travels counterclockwise around the gear, and the small peg travels clockwise around the same gear.

By rotating the gear until the small peg aligns with the large gear, adjustments are automatically made by 1/19 month.

Victor

---

Scanned by iCritical.

[Brillig]

Dear Karl and Calendar People,

Another option would be to introduce another gear intended to allow a daily manipulation of the device. A gear with ratio 9:14 would be ideal, producing a month length of 29 5/9 days, which is just slightly too long. The 14-tooth wheel would be moved one tooth per day (moving the 9 tooth wheel 9/14 tooth per day) until the next new moon. Approximately once every 3 years, this gear would need to be slipped one tooth to realign with the new moon. This is far enough apart that visible eclipses could be used for the resetting. Lunar eclipses are more frequent than solar eclipses, so I would suggest the full moon rather than the new moon be used to drive this device.

Victor

On Thu, May 21, 2009 at 7:11 AM, Palmen, KEV (Karl) <karl.palmen@...> wrote:

Dear Victor and Calendar People

 

Rather than moving the moon wheel one complete revolution at the new moon (or start of lunar calendar month), turn it one tooth at a time throughout the lunar month. This would give a more accurate indication of the season by the sun wheel.

 

I’ve thought of a way of doing this. For the 28 days after a new moon (or start of the lunar calendar month), turn it one tooth each Monday, Tuesday, Thursday, Friday and every other Saturday. Over these 28 days the wheel will turn 18 teeth regardless of what day of the week the 28 days begin. Then at the next new moon turn the wheel by one more tooth to complete its turn and lunar month. If the small peg has moved this month, the wheel is then rotated by two more teeth to complete the lunar month.

 

Karl

 

10(08(27

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 20 May 2009 23:35
To: CALNDR-L@...
Subject: Revision of Two Gear/Two Peg Lunisolar Device

 

Dear Karl, Irv and Calendar People,

OK How about this device and operation, which I think is a bit more straightforward.

There is a 235-cog gear with one mark near one of the cogs indicating the start of a year.
There is a 19-cog gear with 19 holes used to contain two pegs.
The two gears interlock and are adjusted relative to each other by rotating the 19-cog gear clockwise.
The pegs consist of one short peg moved rarely, and a long peg moved frequently. The frequently moved one is longer so it can be grasped even when the short peg is in place. That was my reason for the different lengths of pegs earlier, but I didn't mention it.
Each time the small gear is rotated, it is rotated until the smaller peg is closest to the larger gear. One month is considered to have passed at this point. While the small gear is being rotated, the new year mark on the large gear should be observed. If it passes the point where the small peg finally comes to rest during the rotation, then the large peg is moved one hole counterclockwise. If the small peg is occupying that hole already, it is moved to the spot previously occupied by the large peg, whereupon the large peg takes the spot previously occupied by the small peg.

In this way, the tall peg travels counterclockwise around the gear, and the small peg travels clockwise around the same gear.

By rotating the gear until the small peg aligns with the large gear, adjustments are automatically made by 1/19 month.

Victor

---

Scanned by iCritical.

[Tom Peters-6]

Op 21-mei-2009, om 14:00 heeft Palmen, KEV (Karl) het volgende  
geschreven:

> Dear Victor and Calendar People
>
> This revision can be modified simply to give a 334-year cycle.
>
> Instead of moving the peg(s) every 19 years (when the marked teeth  
> meet), move the peg(s), when the marked tooth of the sun wheel  
> meets the short peg.
> This will usually be one every 19 years, but after the small peg  
> has moved, it’ll occur again after just 11 years. This would then  
> give rise to a 334-year cycle.
>
> The 11 years have 11 rotations of the sun wheel 11*235=2585 teeth  
> equal to 136 rotations of the moon wheel plus one tooth from the  
> small peg move, which is 136*19+1=2585 teeth.

Isn't this the traditional saltus lunae, once every 19 years;
and an additional one to correct the Metonic circle by re-syncing the  
Sun and Moon after (17+11) years?

> Karl
>
> 10(08(27
>
> From: East Carolina University Calendar discussion List  
> [mailto:CALNDR-L@...] On Behalf Of Victor Engel
> Sent: 20 May 2009 23:35
> To: CALNDR-L@...
> Subject: Revision of Two Gear/Two Peg Lunisolar Device
>
> Dear Karl, Irv and Calendar People,
>
> OK How about this device and operation, which I think is a bit more  
> straightforward.
>
> There is a 235-cog gear with one mark near one of the cogs  
> indicating the start of a year.
> There is a 19-cog gear with 19 holes used to contain two pegs.
> The two gears interlock and are adjusted relative to each other by  
> rotating the 19-cog gear clockwise.
> The pegs consist of one short peg moved rarely, and a long peg  
> moved frequently. The frequently moved one is longer so it can be  
> grasped even when the short peg is in place. That was my reason for  
> the different lengths of pegs earlier, but I didn't mention it.
> Each time the small gear is rotated, it is rotated until the  
> smaller peg is closest to the larger gear. One month is considered  
> to have passed at this point. While the small gear is being  
> rotated, the new year mark on the large gear should be observed. If  
> it passes the point where the small peg finally comes to rest  
> during the rotation, then the large peg is moved one hole  
> counterclockwise. If the small peg is occupying that hole already,  
> it is moved to the spot previously occupied by the large peg,  
> whereupon the large peg takes the spot previously occupied by the  
> small peg.
>
> In this way, the tall peg travels counterclockwise around the gear,  
> and the small peg travels clockwise around the same gear.
>
> By rotating the gear until the small peg aligns with the large  
> gear, adjustments are automatically made by 1/19 month.
>
> Victor

--
Tom Peters

[Karl Palmen]

Dear Tom and Calendar People

Comments below.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 22 May 2009 09:22
To: CALNDR-L@...
Subject: Re: 334-year cycle from Revision of Two Gear/Two Peg Lunisolar
Device

Op 21-mei-2009, om 14:00 heeft Palmen, KEV (Karl) het volgende  
geschreven:

> Dear Victor and Calendar People
>
> This revision can be modified simply to give a 334-year cycle.
>
> Instead of moving the peg(s) every 19 years (when the marked teeth  
> meet), move the peg(s), when the marked tooth of the sun wheel  
> meets the short peg.
> This will usually be one every 19 years, but after the small peg  
> has moved, it'll occur again after just 11 years. This would then  
> give rise to a 334-year cycle.
>
> The 11 years have 11 rotations of the sun wheel 11*235=2585 teeth  
> equal to 136 rotations of the moon wheel plus one tooth from the  
> small peg move, which is 136*19+1=2585 teeth.

Isn't this the traditional saltus lunae, once every 19 years;
and an additional one to correct the Metonic circle by re-syncing the  
Sun and Moon after (17+11) years?

No. And also the correction would remove a saltus lunae not add it.

For a saltus lunae you need different gear wheels: A moon wheel of 30
teeth and a sun wheel of 371 teeth. The moon wheel is driven one tooth
per day plus an extra tooth in each 29-day lunation. The Saltus lunae is
then the slipping of the moon wheel one tooth against the sun wheel. It
can be implemented by turning the moon wheel 136 times and one tooth
(4081 teeth), which turns the sun wheel exactly 11 times (11*371=4081
teeth).

An arrangement of pegs in 19 holes could be used to time the Saltus
lunae. One possibility is to have a long peg that moves annually and a
short peg that moves once every 12 years in the same direction. Also
both pegs can occupy the same hole. Whenever this happens, we have a
Saltus lunae, but never in a year that the short peg moves. This would
give a 6840-year cycle.

My lunisolar spreadsheets
http://www.the-light.com/cal/kp_Lunisolar_xls.html indicate how many
Saltus lunae any given cycle requires. For the 334-year cycle it is 16.
For an A-year cycle of B leap months, it is 30*B - 11*A.

Karl

10(08(28

--
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[Karl Palmen]

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Dear Brij and Calendar People

 

For the 1730-year cycle Brij calculated and Mean Lunation =29.5307286068  (29^d 12^h 44^m 14^s.95). This is not accurate enough to make the 1730-year cycle worth considering as a lunisolar cycle.

 

The number of years in it is not divisible by six, so it cannot be obtained by a  divide-by-six leap week rule (but 3*1730=5190 year can).

 

Karl

 

10(09(02 till noon

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 22 May 2009 16:46
To: CALNDR-L@...
Subject: 1730-year vs 334-yr cycle RE: 334-year cycle from Revision of Two Gear/Two Peg Lunisolar Device

 

Karl, Tom Peters CC, sir:
My investigation has led me to 1730-year cycle is a combination of my (7*128)+834 =1730-year cycle. 
>> > This will usually be one every 19 years, but after the small peg
> > has moved, it'll occur again after just 11 years. This would then
> > give rise to a 334-year cycle.
334-year cycle can be utilised, with 19-year & 11-year cycles as:  
1. (5*334)+(2*19)+(2*11)  i.e. [334,19, 334,11, 334, 11, 334, 19 & 334] making 1730-years to start the next cycle; and
2. (13*128)+(6*11) i.e. [(2*128), 11, (2*128), 11, (2*128), 11, (2*128), 11, (2*128), 11, (2*128), 11 & 128]-years starting the next cycle.
As pointed earlier, 1730-year cycle, to me appear be the smallest luni-solar cycle, that can utilise 128-year cycle & 334-years cycles fixing "YEAR 0000" which is 15*128 is automatic in continuation. Current year 2009 is 23rd of 3rd 128-year cycle FOR 2nd cycle of 1730-years, making start year at Y1920; as well at 'Year 0000'. The 1730-year cycle has:

1730-yrs/21397.101Ln (631868.988 days);  90267 weeks;             Mean Year=365.2421965318            (365^d 5^h 48^m 45^s.78) and Mean Lunation =29.5307286068  (29^d 12^h 44^m 14^s.95). MY=631869/1730 =7*(52+1/6+56/5190) =365.242196531792 days , can be obtained using div.six(6) plan.

Regards,
Brij Bhushan Vij

(MJD 2454975)/1361+D-152W21-05 (G. Friday, 2009 May 22H11:71 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 [phone]


 

> Date: Fri, 22 May 2009 13:27:26 +0100
> From: karl.palmen@...
> Subject: Re: 334-year cycle from Revision of Two Gear/Two Peg Lunisolar Device
> To: CALNDR-L@...
>
> Dear Tom and Calendar People
>
> Comments below.
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of Tom Peters
> Sent: 22 May 2009 09:22
> To: CALNDR-L@...
> Subject: Re: 334-year cycle from Revision of Two Gear/Two Peg Lunisolar
> Device
>
> Op 21-mei-2009, om 14:00 heeft Palmen, KEV (Karl) het volgende
> geschreven:
>
> > Dear Victor and Calendar People
> >
> > This revision can be modified simply to give a 334-year cycle.
> >
> > Instead of moving the peg(s) every 19 years (when the marked teeth
> > meet), move the peg(s), when the marked tooth of the sun wheel
> > meets the short peg.
> > This will usually be one every 19 years, but after the small peg
> > has moved, it'll occur again after just 11 years. This would then
> > give rise to a 334-year cycle.
> >
> > The 11 years have 11 rotations of the sun wheel 11*235=2585 teeth
> > equal to 136 rotations of the moon wheel plus one tooth from the
> > small peg move, which is 136*19+1=2585 teeth.
>
> Isn't this the traditional saltus lunae, once every 19 years;
> and an additional one to correct the Metonic circle by re-syncing the
> Sun and Moon after (17+11) years?
>
> No. And also the correction would remove a saltus lunae not add it.
>
> For a saltus lunae you need different gear wheels: A moon wheel of 30
> teeth and a sun wheel of 371 teeth. The moon wheel is driven one tooth
> per day plus an extra tooth in each 29-day lunation. The Saltus lunae is
> then the slipping of the moon wheel one tooth against the sun wheel. It
> can be implemented by turning the moon wheel 136 times and one tooth
> (4081 teeth), which turns the sun wheel exactly 11 times (11*371=4081
> teeth).
>
> An arrangement of pegs in 19 holes could be used to time the Saltus
> lunae. One possibility is to have a long peg that moves annually and a
> short peg that moves once every 12 years in the same direction. Also
> both pegs can occupy the same hole. Whenever this happens, we have a
> Saltus lunae, but never in a year that the short peg moves. This would
> give a 6840-year cycle.
>
> My lunisolar spreadsheets
> http://www.the-light.com/cal/kp_Lunisolar_xls.html indicate how many
> Saltus lunae any given cycle requires. For the 334-year cycle it is 16.
> For an A-year cycle of B leap months, it is 30*B - 11*A.
>
> Karl
>
> 10(08(28
>
> --
> Scanned by iCritical.
>

---

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---

Scanned by iCritical.

[MIKE OSSIPOFF]

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Brij--
 
It seems to me that, in one of your posts, you suggested discontinuing the 7-day week in the civil calendar. But people wouldn't stand for that. People would never accept a new civil calendar that doens't have the 7-day week. Religious groups rejected the World Calendar because it tampered with the 7-day week. Seven days is close to the time between new moon, first quarter, full moon and last quarter.
 
Likewise the blank day would be rejected, just as it was when the World Calendar was proposed. Use a leap week instead. Its cyclical drift corresponds to only small average temperature differences, negligible in comparison to daily and annual temperature variations.
 
Also, you described a month system that uses the Roman month names, with slight changes in their lengths. Of course, by my definitions, that's a "modest reform", and I personally would want a "thorough reform". I claim that if we change the month-lengths a little, all we achieve is months that no longer seem appropriate to the old Roman month-names. And I claim that if we change the calendar, then we should get rid of arbitrariness as much as possible, and start over with everything, including starting-date and year-divisions, for a calendar that explicitly refers to the natural year.
 
Mike Ossipoff
 
 
 

---

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[Brillig]

Dear Karl and Calendar People,

I'm not sure if I posted this yet or not, but I have a sketch (drawn
in Google Sketchup) of the device, conceived as a plant hanger.

http://www.pbase.com/victorengel/image/113002829/original

The plant is moved from one hook to the next each day. The
aformentioned pegs are indicated in black and yellow. I've also
thought of coloring the face of the 19-tooth wheel to make the phase
of the moon more obvious. That coloring would move with the short peg.
Additionally, the chain would be made, perhaps of colored glass beads.
The beads would be colored thus (northern hemisphere design -- a plant
hanger is unlikely to change hemispheres):

60 green beads (spring)
60 yellow beads (summer)
58 red beads (fall)
57 blue beads (winter)

These bead numbers should be reasonably accurate to predict the
solstices and equinoxes in the near term. Over the longer term, the
boundaries between the colors may need adjusting by repainting beads,
but the actual bead positions would remain the same since it tracks
the mean tropical year.

Victor

On Thu, May 21, 2009 at 3:35 AM, Palmen, KEV (Karl)
<karl.palmen@...> wrote:

> Dear Victor and Calendar People
>
>
>
> Very clever! Victor uses the small slower moving peg as the new moon mark on
> the moon wheel!
>
> The pegs are moved once every 19 years once every 18*19=342 years the small
> page move one place in the direction that the moon wheel rotates, so forcing
> the sun wheel to turn an extra tooth (as it would do if it slipped against
> the moon wheel).
>
>
>
> This is better than my suggested revision involving an annual moving of the
> pegs and correction by slipping of the sun wheel one tooth against the moon
> wheel.
>
> However my suggestion can be easily modified to produce a 334-year cycle.
>
>
>
> Karl
>
>
>
> 10(08(26 till noon
>
>
>
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of Victor Engel
> Sent: 20 May 2009 23:35
> To: CALNDR-L@...
> Subject: Revision of Two Gear/Two Peg Lunisolar Device
>
>
>
> Dear Karl, Irv and Calendar People,
>
> OK How about this device and operation, which I think is a bit more
> straightforward.
>
> There is a 235-cog gear with one mark near one of the cogs indicating the
> start of a year.
> There is a 19-cog gear with 19 holes used to contain two pegs.
> The two gears interlock and are adjusted relative to each other by rotating
> the 19-cog gear clockwise.
> The pegs consist of one short peg moved rarely, and a long peg moved
> frequently. The frequently moved one is longer so it can be grasped even
> when the short peg is in place. That was my reason for the different lengths
> of pegs earlier, but I didn't mention it.
> Each time the small gear is rotated, it is rotated until the smaller peg is
> closest to the larger gear. One month is considered to have passed at this
> point. While the small gear is being rotated, the new year mark on the large
> gear should be observed. If it passes the point where the small peg finally
> comes to rest during the rotation, then the large peg is moved one hole
> counterclockwise. If the small peg is occupying that hole already, it is
> moved to the spot previously occupied by the large peg, whereupon the large
> peg takes the spot previously occupied by the small peg.
>
> In this way, the tall peg travels counterclockwise around the gear, and the
> small peg travels clockwise around the same gear.
>
> By rotating the gear until the small peg aligns with the large gear,
> adjustments are automatically made by 1/19 month.
>
> Victor
>
> ________________________________
> Scanned by iCritical.
>

[MIKE OSSIPOFF]

 
When talking about calendar reform, I used to only mention a nonfixed World-Calendar, till I decided that it makes no sense to keep the Roman month-names and have April with 31 days and May with 30 days. I know that many would like to rationalize the months a bit, and maybe make the calendar fixed, while keeping the Roman month-names. For tradition. But I suggest to you that such things as a 31-day April and a 30-day May spit in the face of tradition. So then, just discard tradition. Start fresh, from basic principles.
 
I want to start by saying that the Subjective Seasonal Calendar is the best calendar proposal that I know of. That isn't arrogant or presumptuous. Everyone would say that about their favorite anything. That's why it's their favorite.
 
Because, with so many proposals, descriptive names are needed, I'm re-naming "Improved Seasonal" as "Thermal Seasonal".
 
First I'll list the names of my proposals, and then define them, and then comment on their merits.
 
1. Subjective Seasonal Calendar (with fixed and nonfixed versions having slightly different month systems)
2. World Season Calendar (fixed or nonfixed, from Isaac Asimov)
3. Thermal Seasonal Calendar (leapweek-fixed or nonfixed)
4. December Seasonal Calendar (same as above, but starting winter on Dec.1)
5. Roman, December
6. Roman, March (proposed here by victor, already in use for computational purposes)
 
Asimov's World Seasonal Calendar:
 
Fixed. Divides the 364 days into 91-day quarters, numbering their days from 1 to 91. No months. Mean starting date: Winter Solstice of Northern Hemisphere. Asimov used a blank day. I'd substitue a leapweek.
 
Thermal Seasonal Calendar:
 
Same as above, except that:
 
In nonfixed version, the last quarter, Autumn, would have 92 days in normal years. In leapyears, give it 93 days, or give the 2nd quarter 92 days.
 
Middle of the Winter quarter is positioned to follow the average winter solstice of the Norther Hemisphere by a duration equal to an estimate of the average seasonal timelag. I'm using 38 days (1.25 months) as my estimate.
 
Fixed and nonfixed versions could optionally have months, though I claim that the best convenience is achieved when there are no months.
 
Months for fixed version: I suggest 4-week & 5-week months. 454 is popular and acceptable, but I prefer 544, because then the month containing the important Christmas holiday and the winter solstice is honored by more days.
 
Months for nonfixed version: Doesn't really matter, but I suggest 31,30,30  for the same reason as in previous paragraph.
 
December Seasonal Calendar:
 
Same as above, but winter starts on December 1st.
 
Justification: Maybe better winter and summer starting-date is more important than more accurate average timelag.
 
Subjective Seasonal Calendar, nonfixed version:
 
Same as above, but Winter, starting on Dec. 1, has 118 days, extending 28 days into March. Summer, starting on June 1, likewise has 118 days. Spring has 64 days, and Autumn has 65 days, for a total of 365 days. Leapday is added to the end of Autumn or Summer.
 
Justification: Calendar seasons best match our perception of the seasons. Calendar seasons best predict what various times of the year will be like. There's no need to keep the counter-perceptual notion of equal seasons. The transitional periods are perceived by all of us to be shorter than the full summer and winter periods. That's probably true in the tropics too: Most likely, people there don't perceive there to be quarter-year transional periods between the rainy and less-rainy seasons. So the Subjective Seasonal Calendar's seasons would make more sense everywhere than would the assumption of equal seasons.
 
This calendar, though starting summer on June 1, and winter on Dec. 1, retains the 38 day timelag of the Thermal Seasonal Calendar.
 
Subjective Seasonal Calendar, fixed version:
 
Same starting dates for winter and summer. Winter and summer have 17 weeks. Spring and Autumn have 9 weeks, for a total of 52 weeks. Uses leapweek to achieve a fixed calendar.
 
Use of leapweek:
 
Leapweek in fixed calendars would be used at such times so as to minimize the maximum amplitude of the year's cyclical drift with respect to the December solstice, June solstice, or March equinox.
 
Preferably, leapday in nonfixed calendars would be similarly used, though, for nonfixed calendars, the Gregorian leapyear system would be adequate too.
 
Roman, December:
 
Roman months. Year starts Dec. 1.
 
It has good starting dates for summer & winter, but its timelag is too short to well represent the average timelag, and its summer is too short. Therefore it's only a partial improvement over the current Roman Calendar.
 
Roman, March:
 
Roman months. Year starts March 1.
 
Evaluation same as above.
 
Comparing Roman, December and Roman, March:
 
More familiar to start year with December. Roman tradition of starting year with March--And then September, October, November and December are once-again correctly-named. Roman, March is already in use for computational purposes.
 
Mike Ossipoff
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
_________________________________________________________________
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[Brillig]

Dear Karl and Calendar People,

I realize there is a problem with my scheme. First, let me summarize:

* A driver wheel has 14 spokes and 9 teeth. This allows the wheel to
move one spoke a day, completing a revolution in 14 days, conveniently
completing a fortnight -- two weeks. The spokes could have indications
for day of the week.

By virtue of this 9/14 ratio, a 235 link chain intermeshing with the 9
teeth complets one revolution every 235*14/9 = 365.5555 days. That is
considerably too long. Fortunately, so is the month. A 19 tooth wheel
driven by the same chain results in a moon length of 19 * 14/9 =
29.55555 days. That is too long, but close enough that adjustments can
be made at lunar eclipses. Including adjustments at lunar eclipses,
the device follows the synodic lunar period. Given a synodic month of
29.530589 days, the calculated year is thus 29.530589/29.55555 *
365.5555 = 365.2468 days, which is still a bit too long.

The adjustment using the pegs is based on the convenient fact that the
moon is divided into 19 pieces by virtue of the 19 tooth gear. The
amount of time for the error to drift by 1/19 moon is about 18 Metonic
cycles. So the scheme was designed to make an adjustment of one tooth
every 18 Metonic cycles using the short and long pegs I described.

The problem is that the Metonic cycle starting point is identified by
the convergence of the 19 tooth gear and the 235 tooth chain. Since 19
and 235 are relatively prime, the alignment happens once every Metonic
cycle. But the adjustment itself throws a monkey wrench into the
works. After the adjustment, the tooth is no longer aligned with the
chain. The result is that the next Metonic cycle is short counted by
about half. An alternative would be to have a permanent mark on the 19
tooth wheel and have the alignment with the chain always occur with
respect to this mark instead of with the peg.

Victor

On Thu, May 28, 2009 at 3:19 PM, Victor Engel <brillig@...> wrote:

> Dear Karl and Calendar People,
>
> I'm not sure if I posted this yet or not, but I have a sketch (drawn
> in Google Sketchup) of the device, conceived as a plant hanger.
>
> http://www.pbase.com/victorengel/image/113002829/original
>
> The plant is moved from one hook to the next each day. The
> aformentioned pegs are indicated in black and yellow. I've also
> thought of coloring the face of the 19-tooth wheel to make the phase
> of the moon more obvious. That coloring would move with the short peg.
> Additionally, the chain would be made, perhaps of colored glass beads.
> The beads would be colored thus (northern hemisphere design -- a plant
> hanger is unlikely to change hemispheres):
>
> 60 green beads (spring)
> 60 yellow beads (summer)
> 58 red beads (fall)
> 57 blue beads (winter)
>
> These bead numbers should be reasonably accurate to predict the
> solstices and equinoxes in the near term. Over the longer term, the
> boundaries between the colors may need adjusting by repainting beads,
> but the actual bead positions would remain the same since it tracks
> the mean tropical year.
>
> Victor
>
> On Thu, May 21, 2009 at 3:35 AM, Palmen, KEV (Karl)
> <karl.palmen@...> wrote:
>> Dear Victor and Calendar People
>>
>>
>>
>> Very clever! Victor uses the small slower moving peg as the new moon mark on
>> the moon wheel!
>>
>> The pegs are moved once every 19 years once every 18*19=342 years the small
>> page move one place in the direction that the moon wheel rotates, so forcing
>> the sun wheel to turn an extra tooth (as it would do if it slipped against
>> the moon wheel).
>>
>>
>>
>> This is better than my suggested revision involving an annual moving of the
>> pegs and correction by slipping of the sun wheel one tooth against the moon
>> wheel.
>>
>> However my suggestion can be easily modified to produce a 334-year cycle.
>>
>>
>>
>> Karl
>>
>>
>>
>> 10(08(26 till noon
>>
>>
>>
>> From: East Carolina University Calendar discussion List
>> [mailto:CALNDR-L@...] On Behalf Of Victor Engel
>> Sent: 20 May 2009 23:35
>> To: CALNDR-L@...
>> Subject: Revision of Two Gear/Two Peg Lunisolar Device
>>
>>
>>
>> Dear Karl, Irv and Calendar People,
>>
>> OK How about this device and operation, which I think is a bit more
>> straightforward.
>>
>> There is a 235-cog gear with one mark near one of the cogs indicating the
>> start of a year.
>> There is a 19-cog gear with 19 holes used to contain two pegs.
>> The two gears interlock and are adjusted relative to each other by rotating
>> the 19-cog gear clockwise.
>> The pegs consist of one short peg moved rarely, and a long peg moved
>> frequently. The frequently moved one is longer so it can be grasped even
>> when the short peg is in place. That was my reason for the different lengths
>> of pegs earlier, but I didn't mention it.
>> Each time the small gear is rotated, it is rotated until the smaller peg is
>> closest to the larger gear. One month is considered to have passed at this
>> point. While the small gear is being rotated, the new year mark on the large
>> gear should be observed. If it passes the point where the small peg finally
>> comes to rest during the rotation, then the large peg is moved one hole
>> counterclockwise. If the small peg is occupying that hole already, it is
>> moved to the spot previously occupied by the large peg, whereupon the large
>> peg takes the spot previously occupied by the small peg.
>>
>> In this way, the tall peg travels counterclockwise around the gear, and the
>> small peg travels clockwise around the same gear.
>>
>> By rotating the gear until the small peg aligns with the large gear,
>> adjustments are automatically made by 1/19 month.
>>
>> Victor
>>
>> ________________________________
>> Scanned by iCritical.
>>
>

[Karl Palmen]

Dear Victor and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 03 June 2009 21:49
To: CALNDR-L@...
Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device

Dear Karl and Calendar People,

I realize there is a problem with my scheme. First, let me summarize:

* A driver wheel has 14 spokes and 9 teeth. This allows the wheel to
move one spoke a day, completing a revolution in 14 days, conveniently
completing a fortnight -- two weeks. The spokes could have indications
for day of the week.

By virtue of this 9/14 ratio, a 235 link chain intermeshing with the 9
teeth complets one revolution every 235*14/9 = 365.5555 days. That is
considerably too long.

KARL SAYS: The 14/9 ratio is good for only one year. One could use the
moon phase to correct it once a year

I suggested a more accurate ratio of 788/507, which is based on the
31-yerm cycle of 507 lunar months whose number of days is 19*788. The
mean month is 29.530572 days. Any more accurate ratio would have over a
1000 in the numerator.

Also worth considering is a sun wheel with 371 teeth and a moon wheel of
30 teeth. The moon wheel is driven one tooth per day except at the end
of a 29-day lunation (or a month in a given lunar calendar) when the
moon wheel is turned an extra tooth to complete the month. This needs
corrected once every 20 or 21 years on average, by pulling the sun wheel
away from the moon wheel for one day not at the end of a 29-day lunation
so the sun wheel does not turn for that day. The correction is
equivalent to a saltus lunae. If done once every 19 years you get a
19-year cycle.

Karl

10(09(17

--
Scanned by iCritical.

[Brillig]

Dear Karl, and Calendar People,

On Tue, Jun 9, 2009 at 6:54 AM, Palmen, KEV
(Karl)<karl.palmen@...> wrote:

> By virtue of this 9/14 ratio, a 235 link chain intermeshing with the 9
> teeth complets one revolution every 235*14/9 = 365.5555 days. That is
> considerably too long.
>
> KARL SAYS: The 14/9 ratio is good for only one year. One could use the
> moon phase to correct it once a year

The approximation is good for three years, not one. That is long
enough that lunar eclipses can be used to make the correction. The
original concept was to make the device independent of day length,
anyway, so I hesitate to add complexity driven by daily manipulation.

> I suggested a more accurate ratio of 788/507, which is based on the
> 31-yerm cycle of 507 lunar months whose number of days is 19*788. The
> mean month is 29.530572 days. Any more accurate ratio would have over a
> 1000 in the numerator.

Actually, although 788/507 is closer for the month, 129/83 is more
accurate for the year:

235*788/507 = 365.2465
235*129/83 = 365.2410

Victor

[Brillig]

Dear Karl and Calendar People,

On Wed, Jun 3, 2009 at 3:48 PM, Victor Engel<brillig@...> wrote:

>
> The adjustment using the pegs is based on the convenient fact that the
> moon is divided into 19 pieces by virtue of the 19 tooth gear. The
> amount of time for the error to drift by 1/19 moon is about 18 Metonic
> cycles. So the scheme was designed to make an adjustment of one tooth
> every 18 Metonic cycles using the short and long pegs I described.
>
> The problem is that the Metonic cycle starting point is identified by
> the convergence of the 19 tooth gear and the 235 tooth chain. Since 19
> and 235 are relatively prime, the alignment happens once every Metonic
> cycle. But the adjustment itself throws a monkey wrench into the
> works. After the adjustment, the tooth is no longer aligned with the
> chain. The result is that the next Metonic cycle is short counted by
> about half. An alternative would be to have a permanent mark on the 19
> tooth wheel and have the alignment with the chain always occur with
> respect to this mark instead of with the peg.
>

I've decided this is not a problem. I'll have to check my math, but I
think this issue actually increases the accuracy. Normally, an
adjustment is made every 19*235=4465 teeth. However, when the
adjustment is made, the next cycle occurs after only 1880 teeth so
making a mean number of Metonic cycles between adjustments 18 +
1880/4465. This number multiplied by the length of a moon-based
Metonic cycle length is about 127836.4 days. From this we adjust by
one tooth = 14/9 days, resulting in 127834.8 days. To see what year
length this produces, we divide again by 18 + 1880/4465 and then
divide again by 19. The result is a mean year length of 365.2423 days.

Victor

[Brillig]

P.S. If the pegs were rotated the opposite direction, the resulting
mean year length would be 365.24235 days instead of 365.24231 days.
These values are so close as to not really matter which direction the
pegs are rotated, as long as they are rotated consistently.

Victor

On Tue, Jun 9, 2009 at 11:15 AM, Victor Engel<brillig@...> wrote:

> Dear Karl and Calendar People,
>
> On Wed, Jun 3, 2009 at 3:48 PM, Victor Engel<brillig@...> wrote:
>>
>> The adjustment using the pegs is based on the convenient fact that the
>> moon is divided into 19 pieces by virtue of the 19 tooth gear. The
>> amount of time for the error to drift by 1/19 moon is about 18 Metonic
>> cycles. So the scheme was designed to make an adjustment of one tooth
>> every 18 Metonic cycles using the short and long pegs I described.
>>
>> The problem is that the Metonic cycle starting point is identified by
>> the convergence of the 19 tooth gear and the 235 tooth chain. Since 19
>> and 235 are relatively prime, the alignment happens once every Metonic
>> cycle. But the adjustment itself throws a monkey wrench into the
>> works. After the adjustment, the tooth is no longer aligned with the
>> chain. The result is that the next Metonic cycle is short counted by
>> about half. An alternative would be to have a permanent mark on the 19
>> tooth wheel and have the alignment with the chain always occur with
>> respect to this mark instead of with the peg.
>>
>
> I've decided this is not a problem. I'll have to check my math, but I
> think this issue actually increases the accuracy. Normally, an
> adjustment is made every 19*235=4465 teeth. However, when the
> adjustment is made, the next cycle occurs after only 1880 teeth so
> making a mean number of Metonic cycles between adjustments 18 +
> 1880/4465. This number multiplied by the length of a moon-based
> Metonic cycle length is about 127836.4 days. From this we adjust by
> one tooth = 14/9 days, resulting in 127834.8 days. To see what year
> length this produces, we divide again by 18 + 1880/4465 and then
> divide again by 19. The result is a mean year length of 365.2423 days.
>
> Victor
>

[Karl Palmen]

Dear Calendar People

I don't think Victor's calculations are correct here, because he has
overlooked the fact that the adjustment creates one lunation of 20 teeth
instead of the usual 19 teeth. Also I'd expect the adjustment to
truncate a Metonic cycle to 11 years rather than 8 years (1880 teeth) as
stated here. I believe a 334-year cycle would result.

Karl

10(09(17 till noon

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 09 June 2009 17:16
To: CALNDR-L@...
Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device

Dear Karl and Calendar People,

On Wed, Jun 3, 2009 at 3:48 PM, Victor Engel<brillig@...> wrote:

>
> The adjustment using the pegs is based on the convenient fact that the
> moon is divided into 19 pieces by virtue of the 19 tooth gear. The
> amount of time for the error to drift by 1/19 moon is about 18 Metonic
> cycles. So the scheme was designed to make an adjustment of one tooth
> every 18 Metonic cycles using the short and long pegs I described.
>
> The problem is that the Metonic cycle starting point is identified by
> the convergence of the 19 tooth gear and the 235 tooth chain. Since 19
> and 235 are relatively prime, the alignment happens once every Metonic
> cycle. But the adjustment itself throws a monkey wrench into the
> works. After the adjustment, the tooth is no longer aligned with the
> chain. The result is that the next Metonic cycle is short counted by
> about half. An alternative would be to have a permanent mark on the 19
> tooth wheel and have the alignment with the chain always occur with
> respect to this mark instead of with the peg.
>

I've decided this is not a problem. I'll have to check my math, but I
think this issue actually increases the accuracy. Normally, an
adjustment is made every 19*235=4465 teeth. However, when the
adjustment is made, the next cycle occurs after only 1880 teeth so
making a mean number of Metonic cycles between adjustments 18 +
1880/4465. This number multiplied by the length of a moon-based
Metonic cycle length is about 127836.4 days. From this we adjust by
one tooth = 14/9 days, resulting in 127834.8 days. To see what year
length this produces, we divide again by 18 + 1880/4465 and then
divide again by 19. The result is a mean year length of 365.2423 days.

Victor

--
Scanned by iCritical.

[Karl Palmen]

Dear Victor and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 09 June 2009 16:37
To: CALNDR-L@...
Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device

Dear Karl, and Calendar People,

On Tue, Jun 9, 2009 at 6:54 AM, Palmen, KEV
(Karl)<karl.palmen@...> wrote:

> By virtue of this 9/14 ratio, a 235 link chain intermeshing with the 9
> teeth complets one revolution every 235*14/9 = 365.5555 days. That is
> considerably too long.
>
> KARL SAYS: The 14/9 ratio is good for only one year. One could use the
> moon phase to correct it once a year

The approximation is good for three years, not one. That is long
enough that lunar eclipses can be used to make the correction. The
original concept was to make the device independent of day length,
anyway, so I hesitate to add complexity driven by daily manipulation.

> I suggested a more accurate ratio of 788/507, which is based on the
> 31-yerm cycle of 507 lunar months whose number of days is 19*788. The
> mean month is 29.530572 days. Any more accurate ratio would have over
a
> 1000 in the numerator.

Actually, although 788/507 is closer for the month, 129/83 is more
accurate for the year:

235*788/507 = 365.2465
235*129/83 = 365.2410

KARL SAYS:
I realise that if the 19-year cycle were corrected by slipping the
wheels, 788/507 would be appropriate to drive the moon wheel and 129/83
would be appropriate to drive the sun wheel.

If the 19-year cycle were corrected by moving the pegs on the moon wheel
as previously described, then 129/83 would be appropriate to drive
either wheel.


Victor has found a solar calendar cycle whose number of days is a
multiple of 235. The mean year is not sufficiently accurate to have
calendar seasons. Let's look at http://www.the-light.com/cal/VECyc.txt
we see no solar cycle that is a multiple of 235 days, but we do see one
that is a multiple of 47 days, which has a mean year of 365.24251 days.
It has 367 years and 2852 cycles of 47 days so would be implemented by a
gear ratio of 2852/1835. I find that 129/83 is one of the two mixer
ratios for 2852/1835 and the other mixer is 2723/1752. This implies that
any ratio whose mean year is less than that of 2852/1835 (365.24251
days), but more than that of 129/83 (365.2410 day) must have bigger
numbers than either.


However using a fixed drive wheel, would produce considerable lunar
jitter, because of the 20-tooth lunation that occurs on each correction
of the 19-year cycle (adjustment). One could instead use 788/507 for
each 19-tooth lunation and use a faster ratio (e.g. 59/40) for the
20-tooth lunation.

Karl

10(09(18

--
Scanned by iCritical.

[Karl Palmen]

Dear Victor and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 09 June 2009 16:37
To: CALNDR-L@...
Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device

Dear Karl, and Calendar People,

On Tue, Jun 9, 2009 at 6:54 AM, Palmen, KEV
(Karl)<karl.palmen@...> wrote:

> By virtue of this 9/14 ratio, a 235 link chain intermeshing with the 9
> teeth complets one revolution every 235*14/9 = 365.5555 days. That is
> considerably too long.
>
> KARL SAYS: The 14/9 ratio is good for only one year. One could use the
> moon phase to correct it once a year

The approximation is good for three years, not one.

KARL SAYS: Yes if you are prepared to accept an additional jitter of
almost 1 day.
Three years have 705 teeth, which would take 1096 2/3 days driven at
14/9. Three years of 365.2424 days would last 1095.7272 days, which is
0.93946666.. days different.

Karl

10(09(18
--
Scanned by iCritical.

[Brillig]

Dear Karl,

There are two adjustments to the moon wheel and two corresponding
reference points on it. It may be helpful to look at the illustration
at

http://www.pbase.com/victorengel/image/113002829/original

for what follows. Note that the moon wheel at the top is colored light
and dark. This coloration indicates the phase of the moon. It is fixed
to the wheel and does not move with the pegs. This wheel is adjusted
to coincide with lunar eclipses by observation. I figure a maximum of
one tooth adjustment is required for this adjustment each time an
adjustment is required, given the frequency of observable lunar
eclipses. That the lunation indicator is fixed to the wheel means that
a lunation is 19 teeth, by definition.

The other adjustment is computational and is done using the pegs. The
short peg is used as the reference to determine the start of the year.

Whether the adjustment is 1880 teeth or 2585 teeth depends only on
which direction the pegs are rotated.

Victor

On Wed, Jun 10, 2009 at 4:37 AM, Palmen, KEV
(Karl)<karl.palmen@...> wrote:

> Dear Calendar People
>
> I don't think Victor's calculations are correct here, because he has
> overlooked the fact that the adjustment creates one lunation of 20 teeth
> instead of the usual 19 teeth. Also I'd expect the adjustment to
> truncate a Metonic cycle to 11 years rather than 8 years (1880 teeth) as
> stated here. I believe a 334-year cycle would result.
>
> Karl
>
> 10(09(17 till noon
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of Victor Engel
> Sent: 09 June 2009 17:16
> To: CALNDR-L@...
> Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device
>
> Dear Karl and Calendar People,
>
> On Wed, Jun 3, 2009 at 3:48 PM, Victor Engel<brillig@...> wrote:
>>
>> The adjustment using the pegs is based on the convenient fact that the
>> moon is divided into 19 pieces by virtue of the 19 tooth gear. The
>> amount of time for the error to drift by 1/19 moon is about 18 Metonic
>> cycles. So the scheme was designed to make an adjustment of one tooth
>> every 18 Metonic cycles using the short and long pegs I described.
>>
>> The problem is that the Metonic cycle starting point is identified by
>> the convergence of the 19 tooth gear and the 235 tooth chain. Since 19
>> and 235 are relatively prime, the alignment happens once every Metonic
>> cycle. But the adjustment itself throws a monkey wrench into the
>> works. After the adjustment, the tooth is no longer aligned with the
>> chain. The result is that the next Metonic cycle is short counted by
>> about half. An alternative would be to have a permanent mark on the 19
>> tooth wheel and have the alignment with the chain always occur with
>> respect to this mark instead of with the peg.
>>
>
> I've decided this is not a problem. I'll have to check my math, but I
> think this issue actually increases the accuracy. Normally, an
> adjustment is made every 19*235=4465 teeth. However, when the
> adjustment is made, the next cycle occurs after only 1880 teeth so
> making a mean number of Metonic cycles between adjustments 18 +
> 1880/4465. This number multiplied by the length of a moon-based
> Metonic cycle length is about 127836.4 days. From this we adjust by
> one tooth = 14/9 days, resulting in 127834.8 days. To see what year
> length this produces, we divide again by 18 + 1880/4465 and then
> divide again by 19. The result is a mean year length of 365.2423 days.
>
> Victor
>
> --
> Scanned by iCritical.
>
>