This is a less involved method to calculate the day of the week
    for dates on Julian calendars from 1.iii.IV and as far into the
    future as workable using standard four-function calculators and
    certain mobile phones via a simplified formula requiring fewer
    key-clicks than any previous method not relying on tables.


Given:

Day.Month.Year as a Date on a Julian Calendar (starting with
 01.march.0004 as the earliest Date to be converted);
   &
 YLLD as the 'Year in which the Last Leap Day occurred' before the
 given Date for calendar years beginning on or before January 1st
 (starting at Year IV, so that YLLD is a positive multiple of 4);
   or
 Y2MB as the 'Year 2 Months Before' a given (historical Julian) Date,
 whereby YLLD/4 = Integer(Y2MB/4);

a standard four-function calculator can convert the given Date into a
day of the week after completing the 3 steps below with less than 3
dozen key-clicks (or at most 3 dozen using RPN & algebraic ones).


STEP 1. Calculate MonthIndex:

        Month * 2.56 + 93

 and then drop the fraction, and the hundreds digit, if any,
 e.g. 123.72 becomes 23, to get a MonthIndex less than 100.


STEP 2. Apply the simplified formula for converting the Date:

       (YLLD/4 + Year + MonthIndex + Day) / 7

   2.a. Calculate YLLD/4:

        Divide Y2MB by 4

   If the result has a fraction, re-enter just the integer portion.
   (This in effect is identical to applying Hans' older formula of
   1990's vintage. If one knows YLLD, one can divide that instead.)

   2.b. Continue with the remainder of the formula.


STEP 3. Apply Hans' keypad mapping:

 Take the first digit after the decimal point (if none, use 0)
 and map that to a day using the following patterns:

  +-----+-----+-----+                    +-----+-----+-----+
  | Fri | Sat |     |                    |  1  |  2  |  3  |
  |  7  |  8  |  9  |                    | Mon | Tue |     |
  +-----+-----+-----+                    +-----+-----+-----+
  | Wed | Thu |     |                    |  4  |  5  |  6  |
  |  4  |  5  |  6  |                    | Wed | Thu |     |
  +-----+-----+-----+                    +-----+-----+-----+
  | Mon | Tue |     |                    |  7  |  8  |  9  |
  |  1  |  2  |  3  |                    | Fri | Sat |     |
  +-----+-----+-----+                    +-----+-----+-----+
  | Sun |                                      |  0  |
  |  0  |                                      | Sun |
  +-----+                                      +-----+

(This is equivalent to assigning days to remainders of divisions by 7
 as for:  Sun=0  Mon=1  Tue=2  Wed=3  Thu=4  Fri=5  Sat=6.)

 The use of a value of 4 for YLLD in Hans' Method remains valid, even if
 IV A.D. was not a leap year as claimed by some historians, if it is used
 just for dates after February IV A.D. whereby the value of 4 for YLLD is a
 boundary condition for valid conversions on later (historical Julian) dates.
 If IV A.D. is a leap year, Hans' Method is historically correct for Julian
 dates as far back as 1.iii.N by allowing, as do astronomers, a value of 0
 for YLLD, as well as Julian year 'N'--the improvised Roman numeral for 0.

EXAMPLE N.  January 30th, 1649  Y2MB = 1648

  2.56 + 93 =  95.56 (MonthIndex = 95)
  1648 / 4  = 412 (no need to re-enter)
               + 1649 + 95 + 30
  Divide by 7 = 312.285714...
  first decimal  =  2  Day of Week = Tue


EXAMPLE I.  February 8th, 1587  Y2MB = 1586

  2 * 2.56 + 93 = 98.12 (MonthIndex = 98)
  1586 / 4 = 396.5
             396 + 1587 + 98 + 8
  Divide by 7 = 298.428571...
  first decimal  =  4  Day of Week = Wed


EXAMPLE II.  June 15th, 1215  Y2MB = 1215

  6 * 2.56 + 93 = 108.36 (MonthIndex = 8)
  1215 / 4 = 303.75
             303 + 1215 + 8 + 15
  Divide by 7 = 220.142857...
  first decimal  =  1  Day of Week = Mon


EXAMPLE III.  October 13th, 1307  Y2MB = 1307

  10 * 2.56 + 93 = 118.6 (MonthIndex = 18)
  1307 / 4 = 326.75
             326 + 1307 + 18 + 13
  Divide by 7 = 237.714285...
  first decimal  =  7  Day of Week = Fri


EXAMPLE IV.  December 12th, 287  Y2MB = 287

  12 * 2.56 + 93 = 123.72 (MonthIndex = 23)
  287 / 4 = 71.75
            71 + 287 + 23 + 12
  Divide by 7 = 56.142857...
  first decimal =  1  Day of Week = Mon


Q. What significant events occurred on the dates above?


 With just 2 modifications, Hans' method is adaptable to Old Style years too,
 such that it still is easy to do with standard calculators, if not mentally,
 for the recent English usage of Old Style as below. (For the usage of 'Old
 Style' applicable to Marian Era of Pisa: dates before January 1st in such a
 calendar year must use a flag of 92 in Step 1; and only YLLD is to be used
 in Step 2; both modifications likewise apply to the Anglican calendar year.
 Examples are left to the Reader as an exercise. The month-numbers remain
 defined in terms of the historical calendar in each case.)


                  MODIFICATIONS FOR THE LATE OLD STYLE YEAR

1. YLLD & Y2MB are replaced by YLDM, 'Year on the Last Day of the Month'.

2. Because of its initial overlap with the historical year, a flag of 93 is
   to apply till December 31st. From January 1st, a flag of 94 applies till
   the end of the Old Style year on March 24th (and similarly applies for a
   Byzantine year till its end on August 31st, for which YLDM is to be
   replaced by 8 + Y6MB.)


EXAMPLE V.  January 30th, 1648  YLDM = 1648

  2.56 + 94 =  96.56 (MonthIndex = 96)
  1648 / 4  = 412 (no need to re-enter)
               + 1648 + 96 + 30
  Divide by 7 = 312.285714...
  first decimal  =  2  Day of Week = Tue


EXAMPLE VI.  February 8th, 1586  YLDM = 1586

  2 * 2.56 + 94 = 99.12 (MonthIndex = 99)
  1586 / 4  =  396.5
               396 + 1586 + 99 + 8
  Divide by 7 = 298.428571...
  first decimal  =  4  Day of Week = Wed


EXAMPLE VII.  March 15th, 1751  YLDM = 1752

  3 * 2.56 + 94 = 101.68  (MonthIndex = 1)
  1752 / 4 =  438 (no need to re-enter)
               + 1751 + 1 + 15
  Divide by 7 = 315.
  first decimal  =  0  Day of Week = Sun


EXAMPLE IIX.  March 25th, 1752  YLDM = 1752

  3 * 2.56 + 93 = 100.68 (MonthIndex = 0)
  1752 / 4 =  438 (no need to re-enter)
               + 1752 (+ 0) + 25
  Divide by 7 = 316.428571...
  first decimal  =  4  Day of Week = Wed



 (With just 1 modification, Hans' method is adaptable to all Gregorian dates,
 such that it still is easy to do with standard calculators, if not mentally,
 by adding the following Gregorian adjustment:

                 MODIFICATION FOR THE GREGORIAN CALENDAR

                          Integer(YL32 / 16)

 wherein YL is the nominal century of YLLD. Take the integer part of the
 division, store it in the calculator's memory, and include it in Step 2
 as a summand. Examples are likewise left to the Reader as an exercise.)

--

       REFERENCE

gopher://gopherite.org/0/users/retroburrowers/TemporalRetrology/cc/jg