I tried postings replies to both Frank & Favio in one post, & it didn’t
work. Neither reply posted. So now I’m starting over, postings them
sseparately. This reply is to Frank, & my reply to Favio will immediately
subsequently be posted. I hope that these replies will post this time.
Hi Frank—
.
Thanks for your reply. At first I thought that you were posting to point
out my error, & it’s a relief that that isn’t so. Here’s what my error was:
.
I said that the ecliptic-month of Libra will start (in our Pacific
Daylight-Savings time here) on September 23rd, some minutes after 3 a.m. I
made that error because I was looking at October instead of September.
.
So, the time that I reported was the day of the month & the time of day at
which the ecliptic month of Scorpio starts in October.
.
The correct time of the beginning of the ecliptic-month of Libra this year
is September 22nd, at 6:04 p.m., in our Pacific Daylight Savings Time.
.
That’s September 23rd, at 1:04 a.m. in UTC. …or 01:04 in 24-hour time.
.
I’m replying inline so that I don’t miss any comments that I mean to reply
to:
.
[quote]
you say nothing about how this calendar
relates to sundials.
[/quote]
.
I mentioned that the FRC approximates the ecliptic-months, so I didn’t
completely leave that out.
.
I agree with your description of a sundial’s declination-lines.
.
…7 of them if you just want to demarcate the 12 ecliptic-months.
.
…except that, often or usually, the old sundials labeled the
ecliptic-months by their _symbols_ rather than their names. …as will my
next sundial.
.
[quote]
7. Now, just for a moment, we do something
VERY SILLY. We replace the labels with
the names of the Gregorian months. So,
replace the label CAPRICORN with the
label JANUARY so on.
[/quote]
.
I would never do that.
.
For one thing:
.
I prefer demarcating & labeling the ecliptic months, because:
.
1. Calendars tell you the Roman month, & so why not let the sundial tell
you the ecliptic-month.
.
2. Telling the ecliptic-month is more accurate, because of course the
relation between ecliptic-months & Roman months varies from year to year.
.
For another thing:
.
If someone would rather that the sundial give Roman months instead of
ecliptic-months, then the sundial should give them the Roman months as
accurately as possible !!!
.
The Roman months could be useful to someone who wanted to orient a portable
window-sill dial or portable window-table dial by rotating it till it tells
the right date. Though I myself prefer ecliptic-months for that purpose
too, probably a lot of people would rather just use the Roman months. So,
if you tell Roman months, then tell them as accurately as possible.
.
[quote]
8. Notice that for about two-thirds of
JANUARY the sun really is in CAPRICORN
so this silly sundial actually gives
the correct Gregorian month about 67%
of the year.
[/quote]
.
Not good enough, especially if someone is using it to orient a portable
table dial or windowsill dial.
.
[quote]
9. NOW for the clever bit. Without changing
ANY detail of the specification of the
Gregorian Calendar (which you clearly
want to keep) you follow the precedent
set by your hero Pope Gregory III…
[/quote]
.
First, I doubt that he called himself Gregory, or that others did in those
days.
.
His name was Gregorius.
.
Secondly, Pope Gregorius & his astronomers accomplished something important
& distinctly-desirable, when they re-set the Julian calendar to its
original relation to the Solar ecliptic-longitude
.
…& additionally improved the leapyear-rule to make it stay that way.
.
(no arithmetical rule will do that perfectly, but the Gregorian
leapyear-does an excellent job.
.
Though, ideally, I prefer my own yearstart rule , which maximizes both
accuracy & simplicity, the Gregorian leapyear-rule is undeniably good
enough.)
.
I should add that I never call it the “Gregorian Calendar”. It’s the
Julian Calendar, with the Gregorian re-alignment with the original Julian
Calendar. I don’t call it “the Julian Calendar”, because “Julian Calendar”
is always used for referring to the drifting & drifted Julian Calendar,
used until the Gregorian reform.
.
I usually call it the Roman Calendar, or sometimes the Roman-Gregorian
Calendar. I guess it could also be called the Julian Calendar with
Gregorian restored seasonal-alignment.
.
I don’t agree that your proposed displacement of the Julian months is
acceptably small. Even the proposed leapweek fixed-calendars only have 3.5
days max error. 10 days displacement would be significant, unprecedented &
excessive.
.
After all, fixing a cumulative-drift of that magnitude was the reason why
the Gregorian reform was deemed necessary. When Summer’s reliably
consistent warm weather starts 10 days after the Summer-Solstice, we
definitely notice that it didn’t start at the solstice.
.
[quote]
12. This way, our 12 spaces really can be
labelled JANUARY to DECEMBER and the
sundial gives the correct Gregorian
month over 90% of the time.
[/quote]
.
Not good enough.
.
[quote]
It is
almost impossible to estimate the date
to better than two or three days close
to the solstices so this calendar would
be quite usable.
[/quote]
.
But you’re talking about a 10-day displacement, not a 3-day displacement. The
leapweek fixed-calendars’ 3.5 day max displacement is barely acceptable. …&
only because it allows a fixed calendar without blank-days.
.
[quote]
The adjusted Gregorian Calendar is very
nearly the same as the Republican Calendar.
[/quote]
.
Yes, FRC approximates the ecliptic-months. I agree with that.
.
The Indian National Calendar, & the Persian Calendar …specifically the
Solar Hiji Calendar…do so with better accuracy, due to their accounting for
our varying speed in orbit & distance from the Sun.
.
[quote]
The main differences are:
1. They made every month 30 days.
2. They changed the rules for leap years.
The first change is not very important but
it is easier to teach children that EVERY
month is 30 days.
[/quote]
.
…but that brings a big problem: What do you do with the extra days that
you’re leaving out? Blank-days? That makes the calendar harder for
children & everyone else too.
.
…even aside from the matter of accuracy.
.
[quote]
The second change IS important because, by
insisting that every year begins on the
day of the September equinox, you don't
get wild swings in the dates of the starts
of the atarts of the astronomical months.
[/quote]
.
Well, with an maximally-accurate arithmetical-approximation yearstart rule,
like the one that I suggested in my reply about the Roman
Vernal-Equinox-start calendar, the swings aren’t very wild. The max error
is half a day.
.
[quote]
With the current Gregorian Calendar, the
September Equinox can be on any of the
dates 21, 22, 23 and 24 September and that
is just at the longitude of France.
[/quote]
.
Reckoning of calendar-displacement ignores local time-differences due to
longitude..
.
The Gregorian leapyear’s shortest jitter-cycle has a max error-contribution
of half a day.
.
The Gregtorian leapyear-rule’s max unidirectional-displacement during its
entire 400-year leapyear-cycle is a number of days equal to 2 plus some
fraction. Yes, that’s more than twice that of my minimum-displacement
yearstart rule, but it still isn’t bad.
.
The Gregorian leapyear rule has a very low mean unidirectional drift-rate.
…more than my yearstart rule, but still not problematic.
.
[quote[
The Republican Calendar ensures that the
September Equinox is ALWAYS on the first
day of the first month of the year.
[/quote]
.
Yes, that makes it a fraction of a day more accurate than the best
arithmetical approximations to the Equinox (or a solstice if such is
desired). But that’s just a fraction of a day.
.
I don’t criticize the use of the actual astronomical equinox or solstice.
For one thing it’s a fraction of a day more accurate. For another thing,
it’s simpler to state, because there’s no need to mention an
approximation-fule.
.
I’d say that using the actual astronomical equinox or solstice would be
fine. The approximations have been popular for convenience.
.
>From what I’ve heard, your FRC calendars are beautifully-illustsrated.
That’s an important part of a calendar’s merit. But I wouldn’t like the
blank-days.
.
During this waning-half of the year, I reckon the time of year by the
ecliptic-months (Scorpio starts in about 2 days) rather than the Roman
months. …because the ecliptic-months more meaningfully tell us where we
are in the seasonal-year, during this half of the year.
.
Whenever I report, at a Pagan forum, when the next ecliptic month is about
to begin, I always tell what the FRC calls (its approximation to) that
ecliptic-month.
.
Wishing you a good year.
.
Wishing you good new ecliptic-month of Scorpio, the month before
Sagittarius, the run-up to the Solstice upturn.
.
Wishing you a good Celtic New-Year, at Samhain
.
Ecliptic-Month Virgo, degree 28
.
Michael
On Tue, Sep 20, 2022 at 4:44 AM Frank King <f...@cl.cam.ac.uk> wrote:
> Dear Michael,
>
> I agree with much of what you say about the
> French Republican Calendar but, importantly,
> you say nothing about how this calendar
> relates to sundials. Let me explain in
> simple steps:
>
> 1. Sketch an outline vertical sundial with
> seven declination curves and a single
> hour line, at 12 noon.
>
> 2. The seven curves mark the boundaries of
> six regions. Note each region is divided
> into two parts by the 12 noon hour line.
>
> 3. We have 12 spaces. Now write the label
> CAPRICORN in the top left space. This
> is the first astronomical month after
> the winter solstice.
>
> 4. In the five spaces underneath, you write
> the names AQUARIUS to GEMINI.
>
> 5. On the right hand side you start at the
> bottom and work up with the names CANCER
> to SAGITTARIUS at the top.
>
> 6. This sundial will now tell you which
> astronomical month you are in. Of
> course you need to know whether the
> solar declination is increasing or
> decreasing but everyone who reads
> this mailing list will know that :-)
>
> 7. Now, just for a moment, we do something
> VERY SILLY. We replace the labels with
> the names of the Gregorian months. So,
> replace the label CAPRICORN with the
> label JANUARY so on.
>
> 8. Notice that for about two-thirds of
> JANUARY the sun really is in CAPRICORN
> so this silly sundial actually gives
> the correct Gregorian month about 67%
> of the year.
>
> 9. NOW for the clever bit. Without changing
> ANY detail of the specification of the
> Gregorian Calendar (which you clearly
> want to keep) you follow the precedent
> set by your hero Pope Gregory III. Just
> once, you cut 10 days from the year. We
> could do this anywhere but let's cut
> 10 days from March. JUST ONCE!
>
> 10. We now find the March Equinox is right
> at the end of March so APRIL almost
> exactly coincides with ARIES.
>
> 11. We find that each Gregorian month now
> almost (but not quite) overlaps the
> corresponding astronomical month.
>
> 12. This way, our 12 spaces really can be
> labelled JANUARY to DECEMBER and the
> sundial gives the correct Gregorian
> month over 90% of the time.
>
> This makes life MUCH EASIER for sundial
> designers who want their sundials to tell
> the date, at least approximately. It is
> almost impossible to estimate the date
> to better than two or three days close
> to the solstices so this calendar would
> be quite usable.
>
> OK. Now for the bit you won't like...
>
> The adjusted Gregorian Calendar is very
> nearly the same as the Republican Calendar.
> The main differences are:
>
> 1. They made every month 30 days.
>
> 2. They changed the rules for leap years.
>
> The first change is not very important but
> it is easier to teach children that EVERY
> month is 30 days.
>
> The second change IS important because, by
> insisting that every year begins on the
> day of the September equinox, you don't
> get wild swings in the dates of the starts
> of the atarts of the astronomical months.
> With the current Gregorian Calendar, the
> September Equinox can be on any of the
> dates 21, 22, 23 and 24 September and that
> is just at the longitude of France.
>
> The Republican Calendar ensures that the
> September Equinox is ALWAYS on the first
> day of the first month of the year in
> France. If you change longitude then
> it will never drift more than a day
> either side.
>
> Suggestion:
>
> Why don't you order one of these calendars
> (English or Italian edition) then:
>
> LIVE WITH IT FOR A YEAR and, this
> time next year, you can tell us all
> how you got on with it :-)
>
> You might even enjoy the pictures and the
> way the months work out.
>
> As others have said: this calendar is
> GREAT FUN.
>
> Have a good year!
>
> Frank
>
> Frank King
> Cambridge, U.K.
>
>
>
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