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« Return to Thread: Revision of Two Gear/Two Peg Lunisolar Device
Re: 334-year cycle from Revision of Two Gear/Two Peg Lunisolar Device
by Karl Palmen
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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.
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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