1600/2000 | 1700/2100 | 1800/2200 | 1900/2300 |
0 | 5 | 3 | 1 |
When we refer to the Century, we are referring to the cardinal representation for the century years (e.g., 1600s for the 17th century). This table repeats itself on four-century cycles into the distant future and to some extent into the past, as shown above for one extra cycle. So what would be the value for the 1500s? And the 2400s?
You do not need to know the following to do the calculation of the Day-of-Week (etc.) but for those purists among our readers, here is some additional information about the Century table.
What is the meaning of the value for the Century? For centuries not evenly divisible by 400 (e.g., 1700, 1800, 1900) where there is no leap year in the turn-of-century year, the Century value means the numerical value of the day-of-week prior to the first day of the new century. For instance, the 1 (which also means Sunday) for the 1900s means that the first day of the century was the day after, a Monday or a 2. (January 1, 1900, was indeed a Monday.) For the turn-of-century years evenly divisible by 400 (e.g., 1600, 2000), the Century value means the value of the first day of the new century. For instance, the value for the 2000 century is 0, or Saturday. The value for January 1, 2000, is 0+1+0+0+0-1 equals 0, or Saturday, and it was indeed a Saturday.
How did we compute the value for the different centuries? We know that in a non-leap calendar year, the calendar moves forward one extra day of the week (365 days is 52 full weeks plus one day), but in leap years it moves forward by still one more day for the extra day in February. So in a century that starts with a leap year (e.g., 1600 and 2000), there are 75 non-leap years (1 extra day) and 25 leap years (2 extra days) for a total of 125 days or 17 full weeks (of 7 days) plus 6 days left over. So, a century starting with a non-leap year has one less day, or 5 left over. So, if we start the whole process with January 1, 1600, which actually fell on a Saturday (a value of 0), the Century value for centuries starting with a leap year means the Day-of-Week on which the Century started. Moving forward 125 days from that 1600s century, or 5 weekly calendar days forward, the value going into the 1700’s is 5 (the zero starting the prior century plus 5 equals 5, which translates to a Thursday, and so if January 1, 1700, (a non-leap year) was a Friday (a value of 6), the century value translates to the day before. The same goes for the next two centuries, both starting with non-leap years. Moving forward into the 1800s, we have the 5 going into the prior century plus another 5 days from the 1700s which equals 10, and 10 minus 7 (take out the full weeks) yields a 3 going into the 1800s. Moving forward into the 1900s, we have the 3 going into the prior century plus 5 more from the 1800s for a total of 8, and 8 minus 7 (a full week) equals 1, the value going into the 1900s. Taking the 1 going into the 1900s and adding 5 for the 1900s, we get a total of 6, which means that a Friday was the day before the first day of the new century. But since we know that 2000 is a leap year turn-of-century year (because it is divisible by 400) and that the meaning of the Century value in such years is the FIRST day of the year, the first day of the week of that new century is the day after Friday which is Saturday, and that means a 0 for that century. Got it? Again, you do not need to know this. Just apply the formula.
How far into the future does this century table (and technique in general) go? Forever, repeating the 0, 5, 3, 1 cycle every four centuries. I understand that another adjustment will have to be made around the year 20,000, but to all intents and purposes we can all safely ignore that.
How far into the past does this table go? Techically the century table goes backwards, too, repeating the 0, 5, 3, 1 cycle every four hundred years. But since Pope Gregory XIII decreed the calendar in 1582, that's a good starting point, at least for in Italy. As for other countries, the "U.S." adopted it only in 1752 when England did, which sparked the calendar riots in England when people lost 11 days of wages but still have to pay full months rent. Read more about the calendar at Wikipedia (click here). Russia adopted it on in 1917 after the Bolsheviks took over. And so on. Some web sites have detailed conversion tables from the Julian calendar to the Gregorian, but unless you need it for your job, why bother? As for dates before 1582, do it for any date you want going back to the year 0001 (and maybe before) because no one will be around who can challenge you.
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