|
|
|
|
|
|
|
Therefore, only six possible numbers of days are between two dates within a quad 365, 366, 730, 731, 1,095, and 1,096. If the number of days is 1,461, you have a complete quad. |
|
|
|
|
|
|
|
|
In conclusion, then, any number of days that satisfies these conditions must include some multiple of 1,461 and one of the six remainders above. That is, your possibilities are limited to numbers expressed by the formula: |
|
|
|
|
|
|
|
|
where rem is one of 0, 365, 366, 730, 731, 1,095, or 1,096. |
|
|
|
|
|
|
|
|
In addition, however, any number of days n must also satisfy the condition that it be evenly divisible by seven, or: |
|
|
|
|
|
|
|
|
You can calculate the numbers that satisfy both of these conditions. Restrict your attention to i in the range of 0 to 24, since i represents the number of complete quads, and you are only considering numbers of days within one century (425 = 100). These numbers are calculated in Table 9.5. |
|
|
|
|
|
|
|
|
This list represents all the numbers of days that can possibly separate two dates within one century and still satisfy the two conditions that the two dates have the same month and day and occur on the same DOW. Note that this list does not describe all of the possible cycle lengths within the Gregorian calendar, some of which can, and do, extend over periods greater than one century. |
|
|
|
|
|
|
|
|
This result also answers the question of why all of the apparent cycles are separated by four-year intervals within the source and target sequences. In order to encounter cycles with periods of fewer than four years, one of the values 365, 366, 730, 731, 1,095, or 1096 would have to be evenly divisible by seven in order to create intervals of 1, 2, or 3 years. But none of them are. Hence, no cycle can occur with an interval of fewer than four years. |
|
|
|
|
|
|
|
|
Looking at the original data, you can finally begin to see the actual patterns emerging. For the 1827/1877 match, 1827 JAN 01 and 1877 JAN 01 are separated by 18,263 days, one of the numbers in the list. This number represents (121,461 + 731) |
|
|
|
|
|
