This is a more involved method to calculate the day of the week
 for Gregorian calendar dates from 15.oct.1582 & as far into the
 future as workable for Abacus users via formulas in base 8 that
 require fewer operations than any other method not using tables.


Given:

 XY.EFG.MO.DA as the octal digits of a Date in c.y.m.d format, &
 xy.efg as the digits of the century & year 2 months earlier,
 one can convert the given Date into a day of the week in less
 than two dozen operations by means of the three steps below.

STEP 0. Process components of the Date as follows:

          PQR = efg - Floor(.MO - .03)
          pqr = efg + 44
       VW.bug = xy.pqr + xy.pqr

STEP 1. Apply Lachman's Congruence in base 8

         cow = MM+MM+MOO+O + MM+MM+MOO+O
         min = co + 71

STEP 2. Apply the octal formula for converting the Date

         bu-W + P+Q+R + ~m+i+n + D+A

STEP 3. Likewise add the digits of the result, and repeat for
 each successive result until only one digit remains. This is
 a number as assigned by ISO 8601 to each day of the week:
 Mon=1  Tue=2  Wed=3  Thu=4  Fri=5  Sat=6  Sun=7.


EXAMPLE 0. December 31st, 2099:  XY.EFG.MO.DA = 24.143.14.37

 xy.efg = 24.143 
    PQR = 143 - 0
    pqr = 143 + 44 = 207
 xy.pqr = 24.207
 VW.bug = 50.416
 cow = 11+11+144+4 + same = 172 + 172 = 364
 min = 36 + 71 = 127
 41-0 + 1+4+3 + 0+2+7 + 3+7 = 41+10+11+12 = 74  7+4 = 13
 1+3 = 4    Day of Week = Thursday 


EXAMPLE 1.  January 1st, 2100:  XY.EFG.MO.DA = 25.000.01.01
 
 xy.efg = 24.143
    PQR = 143 - -1 = 144
    pqr = 143 + 44 = 207 
 xy.pqr = 24.207
 VW.bug = 50.416
 cow = 00+00+011+1 + same = 012 + 012 = 024
 min = 02 + 71 = 073
 41-0 + 1+4+4 + 1+7+3 + 01 = 41+11+13+1 = 66  6+6 = 14
 1+4 = 5   Day of Week = Friday 
 
 
EXAMPLE 2.  February 2nd, 2200:  XY.EFG.MO.DA = 26.000.02.02
                
 xy.efg = 25.143
    PQR = 143 - -1 = 144
    pqr = 143 + 44 = 207
 xy.pqr = 25.207
 VW.bug = 52.416
 cow = 00+00+022+2 + same = 024 + 024 = 050
 min = 05 + 71 = 076
 41-2 + 1+4+4 + 1+7+6 + 02 = 37+11+16+2 = 70  7+0 = 7
 Day of Week = Sunday
         
         
EXAMPLE 3.  March 3rd, 2300:  XY.EFG.MO.DA = 27.000.03.03
 
 xy.efg = 27.000
    PQR = 000 - 0
    pqr = 000 + 44
 xy.pqr = 27.044
 VW.bug = 56.110
 cow = 00+00+033+3 + same = 036 + 036 = 074
 min = 07 + 71 = 100
 11-6 + 000 + 0+0+0 + 03 = 3+0+0+3 = 6
 Day of Week = Saturday 
 

EXAMPLE 4.  April 4th, 2400:  XY.EFG.MO.DA = 30.000.04.04
 
 xy.efg = 30.000
    PQR = 000 - 0
    pqr = 000 + 44
 xy.pqr = 30.044
 VW.bug = 60.110
 cow = 00+00+044+4 + same = 050 + 050 = 120
 min = 12 + 71 = 103
 11-0 + 000 + 0+0+3 + 04 = 11+0+3+4 = 20  2+0 = 2
 Day of Week = Tuesday
 

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      REFERENCES

gopher://gopherite.org/0/users/retroburrowers/TemporalRetrology/68k/all
gopher://gopherite.org/0/users/retroburrowers/TemporalRetrology/cc/g4