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Page 254 source and target dates starts with 1 March of the previous years (1826 and 1876) and continues through 28 February of the following years (1828 and 1878). Therefore, for a given quad of 1,461 days, the matching is actually a continuous block of days that extends from 1 March of year (n - 1) and continues until 28 February of year (n + 1). Looking at the quad of 1825 through 1828, you can see where the matching period occurs, and easily count the matching days: 1825 1826 1827 1828 JFMAMJJASOND JFMAMJJASOND JFMAMJJASOND JFMAMJJASOND starts stops +- - - - - - - - - - - - - matching - - - - - - - - - - - - -+ You can total the number of matching and nonmatching days: Matching Nonmatching 1825 0 365 1826 306 59 1827 365 0 1828 60 306 Totals 731 730 You can see, then, that far from being restricted to a calendar year, the period of matching actually occupies slightly more than half of the entire quad (731 of 1,461 days). Second, you should note that the period of matching is strictly determined by the relative positions of leap years in the two sequences. Matching begins when a leap year occurs in the target sequence, and it ends when a leap year occurs in the source sequence. This result suggests several consequences. You have already seen that the number of calendar years between the source and target dates is not the determining factor for DOW matching. Clearly, the relative positions of leap years in the two sequences determine the start and stop points for matching sequences. Now you must consider the nature of the number of intervening days. In the case examined, it was 18,263. Why does this particular ''magic number" work? The answer to this question is simple and instructive. A number of days separating two dates, such that they have both the same DOW and the same month and day date, must fulfill some simple requirements.
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