Why was Pope Gregory's adjustment 10 days not 8 days?

[Karl Palmen]

Dear Moongazer and Calendar people

Moongazer said:
"I think that either way,
Gregory would have had to adjust the calendar by 10 days to restore
things
to the way they were at the time of the first council of Nicaea."

Actually it would have to be adjusted 9 days to make the Gregorian
Calendar the same as the Julian calendar if extrapolated back to the
council of Nicea. If the Gregorian calendar were adopted then without
any days being missed out, then nine additional leap days would have
been missed (500, 600, 700, 900, 1000, 1100, 1300, 1400, 1500) and so it
would be a day behind the actual Gregorian calendar (as if adjusted by 9
days).

However it is curious that year 325 is exactly half way between year
250, which is in the middle of the period in which the Gregorian
calendar would match the Julian calendar and year 400, which is in the
middle of the period in which the Gregorian calendar would be one day
ahead of the Julian calendar. This suggests a equal choice between 9 and
10 days (9.5).

In the 1257 years between 325 and 1582, the Gregorian mean year would
have drift 1257*(3/400) = xxx days with respect to the Julian mean year
9.4275 days, suggesting that 9 is slightly better than 10. Note that the
creators of the Gregorian Calendar regarded their mean year of 365.2425
days as very accurate and so would assume no drift of the equinox
relative to the mean year since Nicea.

However the March equinoxes did drift a little relative to the Gregorian
mean year, but not as much as Moongazer reckoned. He used the figure of
365.2419 days as the mean interval between March equinoxes, which is
incorrect (see other notes). A more accurate figure is 365.24235 days
allowing for the effect of precession on the unequal intervals between
the equinoxes and solstices. This gives a March equinox drift of
(0.00015)*1257 = 0.18855 days relative to the mean Gregorian year. When
added to the 9.4275 days raises it above 9.5 days to give 9.61605 days
so favouring 10 days, but not as decisively as Moongazer had reckoned.

Karl

10(08(11


-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Moongazer
Sent: 02 May 2009 12:18
To: CALNDR-L@...
Subject: Re: Why was Pope Gregory's adjustment 10 days not 8 days?

Wow! I find it amazing and exciting how a question based on nothing more
than
a dyslexic transcription error has engendered so much discussion about
other
matters surrounding the subject of my original question. Thanks, Karl
for
pointing out my error. I can now correct it in my article.

Your answer also explains so much more. (Like why the maths hadn't been
a
problem for me earlier. In my previous writings on this subject, from
which
my recent article was drawn, I had written the date of Nicaea
correctly.)

It also clarifies why March 21 is mentioned in so many sources in
connection
with Nicaea. Until now, I had thought that the authors were simply a day
out
in their assumptions as to when the equinox occurred in 325, but your
little
bit of history about the council using the Ptolemyean date, makes it
clear
that the authors were not mistaken, they were simply reporting the date
that
had been selected by the council.

However, your characterization of the 10 days as a compromise doesn't
seem
right to me. Side-stepping the ensuing debate here as to whether March
20 or
21 was the correct date of the equinox in 325, I think that either way,
Gregory would have had to adjust the calendar by 10 days to restore
things
to the way they were at the time of the first council of Nicaea. For as
far
as Gregory was concerned, his hands were tied. Constantine's council of
325
had subsequently come to be regarded as the first ecumenical council of
the
Christian church and its decisions were held to be unalterable. If not
for
that, Gregory would have had a much simpler adjustment open to him. He
could
simply have severed the nexus with a specific calendar date altogether
and
linked Easter to the actual equinox instead. For the council was in
error in
linking Easter to any Julian date on the assumption that that was the
permanent date of the equinox. But Gregory could not correct that error,
and
if so, neither could he correct their choice of date, even if it were
found
to be wrong.

So, in 1582, to restore things to the way they were 1257 years earlier
in
325, we have: 365.25 - 365.2419 = 0.00781 days per year, and 1257 *
0.00781
= 9.81717, which, rounded, is 10 days. This is the way we would work it
out
now using our present estimation of the tropical year length. In
Gregory's
time what happened historically is that in 1576, Luigi Lilio Ghiraldi,
better known as Aloysius Lilius, a physician of Naples, while working on
a
scheme for a new calendar, found that the equinox of that year occurred
on
March 11, 10 days earlier than March 21. Aloysius Lilius died before he
could inform the authorities of his work, but his brother Antonio
submitted
it to Pope Gregory, who appointed commissioners to check Aloysius's work
and
to frame the new calendar's rules, and they completed their work some
time
before early 1581. (This information comes from Rev S. B. Burnaby's
Elements
of the Jewish and Mohammadan Calendars ... and Explanatory Notes on the
Julian and Gregorian Calendars, London, 1901.)

It seems clear that to this day the Church is stuck with
http://en.wikipedia.org/wiki/Equinox "March 21 as their assumed
ecclesiastical equinox" .

In the first lunation whose 14th day occurs on or after that date, that
14th
day is called the Paschal full moon and Easter is the Sunday following
that
"full moon".
That lunation is not an astronomical lunation but an artificially
computed
calendric-lunation, whose method of calculation was not specified at
Nicaea
but was entrusted (at first) to the Bishop of Alexandria. Although there
have been changes to both the process and the computus itself, the
Church's
official definition of the date of the March equinox for the purpose of
fixing the date of Easter remains March 21.

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