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From: af%sei.ucl.ac.be@CUNYVM.CUNY.EDU ("Alain FONTAINE ", Postmaster - NAD)
Newsgroups: comp.protocols.time.ntp
Subject: Re:  NTP and leap seconds
Message-ID: <901114.101833.+0100.af@sei.ucl.ac.be>
Date: 14 Nov 90 09:18:33 GMT
References: <Mills@udel.edu>
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On Tue, 13 Nov 90 21:23:47 GMT you said:
>But, I can find no explanation why the Gregorian calendar stuffs
>two days relative to the Julian calendar.

A long story... The roman (actually a greek) astronomer Sosigen(us)(os)
devised the rules of the julian calendar, and started it so as to have
the spring equinox on march 25.

In 325, a concilium was held in Nicee. One important subject was the
definitive determination of easter. It was decided to base this determination
on the spring equinox, which was *observed* on march 21. It should have been
on march 25, but was not for two reasons : first, in three centuries, the
julian calendar rules had caused a three day error ; second, Sosigenus had
made (at least) a one day error in his observations. In 325, the systematic
error in the julian calendar was not yet recognized, and so it was believed
that  1- Sosigenus had made a four day error and 2- the spring equinox would
happen on march 21 forever.

And, of course, the equinox continued to happen earlier and earlier. In 1582,
after careful computations by Clavius and others, Pope Gregory XIII edicted
his well known reform. The new rules were much more accurate, and a
discontinuity was introduced to correct the errors of the past. But, since
the date of easter was the main concern, the correction was made to bring
back the equinox to the same date as in 325. Since, in 1582, the equinox had
been observed on march 11, ten days were removed (purely arithmetic rules lead
to a result of 9, but one should remember that, while calendars use integer
number of days, astronomical events happen at different times in the day
and so 'rounding' errors are introduced).

So it does not make sense to try to give an interpretation to the final 'two
days difference'.                                        /AF

BONUS SECTION. Two little programs for julian day number computations.
(Note : these programs take into account the date of adoption of the
gregorian reform in England and Sweden, which is september 2, 1752).

/* compute year month and day ; valid for jday>=0
   input : jday ; output : year month day */
x = jday+306
if jday>2361221 then x = x+10+(jday-2268983)*4 div 146097*3 div 4
y = x mod 36525*4
z = y mod 1461 div 4*5+2
day = z mod 153 div 5+1
month = (z div 153+2) mod 12+1
year = x div 36525*100+y div 1461-4713+(month<3)


/* compute julian day number at noon ; valid for year>=-4712
   input : year month day ; output : jday */
x = year-(month<3)
jday = (x+4713)*365+(x+4716) div 4+((month+9) mod 12*153+2) div 5+day-307
if(year>1752)or((year=1752)and((month>9)or((month=9)and(day>2))))
then jday = jday-(x div 100*3-5) div 4