Revision of Two Gear/Two Peg Lunisolar Device

[Karl Palmen]

Dear Victor and Calendar People

The Gear system that Victor is referring may be different to the system
I was referring to.

We have a 19-tooth moon wheel, a 235-tooth sun-chain (which could also
be a wheel) and a 9-tooth wheel with 14 hooks on it.

I don't understand Victor's references to adjustments at all. He needs
to be precise about which adjustments he is referring to. I prefer to
call them corrections and refer to what the correction is correcting.


-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 10 June 2009 14:34
To: CALNDR-L@...
Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device

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.

KARL SAYS: This statement is contradicted by a statement on the web page
referred to in the URL, which is "A new lunation starts each time the
small peg arrives at the same spot."

If the statement on the web page is correct and the statement in the
note is not correct, then a lunation has 20 teeth whenever the 19-year
cycle is corrected and so what I stated is still valid.

If his statement in the note is correct and the statement on the web
page is not correct, then I don't see how the pegs correct the 19-year
cycle.

Karl

10(09(18


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.
>
>

--
Scanned by iCritical.

[Brillig]

Dear Karl and Calendar People,

I guess this idea is evolving. I will post another update after I get
my ducks in a row.

Victor

On Wed, Jun 10, 2009 at 9:06 AM, Palmen, KEV
(Karl)<karl.palmen@...> wrote:

> Dear Victor and Calendar People
>
> The Gear system that Victor is referring may be different to the system
> I was referring to.
>
> We have a 19-tooth moon wheel, a 235-tooth sun-chain (which could also
> be a wheel) and a 9-tooth wheel with 14 hooks on it.
>
> I don't understand Victor's references to adjustments at all. He needs
> to be precise about which adjustments he is referring to. I prefer to
> call them corrections and refer to what the correction is correcting.
>
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of Victor Engel
> Sent: 10 June 2009 14:34
> To: CALNDR-L@...
> Subject: Re: Revision of Two Gear/Two Peg Lunisolar Device
>
> 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.
>
> KARL SAYS: This statement is contradicted by a statement on the web page
> referred to in the URL, which is "A new lunation starts each time the
> small peg arrives at the same spot."
>
> If the statement on the web page is correct and the statement in the
> note is not correct, then a lunation has 20 teeth whenever the 19-year
> cycle is corrected and so what I stated is still valid.
>
> If his statement in the note is correct and the statement on the web
> page is not correct, then I don't see how the pegs correct the 19-year
> cycle.
>
> Karl
>
> 10(09(18
>
>
> 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.
>>
>>
>
> --
> Scanned by iCritical.
>
>