From: bath@dw3f.ess.harris.com (Kenneth Bath)
Subject: Re:   Why is it?
Date: Thu, 21 Jan 1993 16:43:18 GMT
Reply-To: bath@dw3f.ess.harris.com (Kenneth Bath)
Organization: Harris Semiconductor, Melbourne  FL

|>Can't answer on Passover; Easter is actually tied to an old ecclesiastical
|>formula which does not always compute the actual first full moon.  I've
|>long been interested in the actual formula; I've only been able to obtain
|>tables of the golden numbers (out thousands of years!).  A VMS DCL procedure
|>for computing the date of Easter for the current set of golden numbers is
|>appended.

Thank you for your reply to my posted questions.  In reply to your
desire for a formula for computing the date of Easter, the following
method was devised in 1876 and appeared in "Butcher's Ecclesiastical
Calendar".  It is valid, without exception, for all years of the
Gregorian calendar (years after 1583).  It makes use of integer
quotients and remainders.

Divide          by      Quotient        Remainder
the year        19         -                a
the year        100        b                c
    b           4          d                e
   b+8          25         f                -
  b-f+1         3          g                -
19a+b-d-g+15    30         -                h
    c           4          i                k
32+2e+2i-h-k    7          -                L
a+11h+22L       451        m                -
h+L-7m+114      31         n                p

n = number of month (3 = March; 4 = April)
p+1 = day of the month of Easter Sunday

Why does this work?  I've tried to analyse it and see some astronomical
periods in it (19 years of the Metonic lunar cycle, leap years, etc.), 
but I don't fully understand it.  (It is easy to write code for, though).

In the Julian calendar, the date of Easter is as follows:

Divide          by      Quotient        Remainder
the year        4          -                a
the year        7          -                b
the year        19         -                c
19c+15          30         -                d
2a+4b-d+34      7          -                e
d+e+114         31         f                g

f = number of the month (3 = March; 4 = April)
g+1 = day of the month of Easter Sunday

To check this, Easter was on April 12 in 179, 711, and 1243.

The history of controversy surrounding the date of Easter is quite long
dating all the way back to dicussions between Polycarp and Anicetas in
A.D. 158. (By extension, all the way back to St. John since Polycarp
knew John.)  The rules were laid down at the Council of Nice in A.D. 325:

1. That everywhere the great feast of Easter should be observed upon
one and the same day; and that not the day of the Jewish passover, 
but, as had been generally observed, upon the Sunday afterwards.

2. That the 21st day of March shall be accouned the vernal equinox.

3. That the full moon happening upon or next after the 21st of March
shall be taken for the full moon of Nisan, the Jewish month of which
the 14th day is Passover.

4. That the Lord's day next following that full moon be Easter day.

5. But if the full moon happen upon a Sunday, Easter day shall be
the Sunday after.

The problem, of course, is that if you use the astronomical full moon
for requirement 3, you may violate requirement 1.  That is where the
concept of "Golden Numbers" and the artificial paschal moon came from.

Thanks again for your information.

Ken Bath
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