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In the following year, 1986, J.P. Parisot published an "Additif" to Hatcher's papers, expanding the system to include the French Republican Calendar and two periods early in the history of the Julian calendar. The first period is from 1 January 46 B.C. to 4 January 8 B.C., during which the pontifices erred in the calculation of leap years; the second period is from 5 January 8 B.C. to 31 December 8 A.D., during which Augustus eliminated the insertion of leap years to correct the calendar for the errors created in the first period. These periods are discussed in section 9.1. |
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The $64K question, however, is: Does it work? The definitive answer, of course, is yes and no. The test program DTLT_090 exercises the Hatcher equations as is. The results of this program show that the equations function well for the mobile calendars. The Egyptian, Armenian, and Khwarizmian calendars pass the preliminary test. The Persian calendar, however, shows a recurring offset problem, caused because the epagomenal days do not fall at the end of their year, which causes a difference between the computational and given dates for months 19. This discrepancy is easily addressed by the addition of simple corrective code. |
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The more complex structure of the Alexandrian calendars creates a more complex pattern of discrepancies between the computational and given dates. The Ethiopic and Coptic dates are in disagreement for the epagomena only, so patch code is relatively simple. The Alexandrian calendar itself shows virtually no agreement between the two types of date. The amount and type of code required to correct the discrepancies largely negates the benefit of the simplified Hatcher equations in this case. |
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Among the Julian calendars, the more complex structure creates a pattern of discrepancies which varies by month. These differences are systematic and correctable with additional code. |
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In summary, the Hatcher equations are a laudable attempt to introduce a single general solution in place of a plethora of individual solutions. From the perspective of practical code, however, it is not possible to call a single Hatcher function with a single set of arguments and receive correct given dates in return. In general, adjustments must be made to the computational date in each case. The equations can be used as the basis for calendar solutions by studying their form and using the knowledge to write code that adheres to certain standard forms. |
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In the treatment of the calendars that follow in this section, you will find that the information from the papers by Hatcher and Parisot has been used to implement several solutions. The goal of a generalized set of equations continues to be one worthy of future exploration. |
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The term "mobile" is used to denote calendars that move, in the sense that their dates are not fixed in position with respect to the solar year. This typically occurs because the year contains only 365 days and has no intercalation of a leap day to account for the fractional day. Such a year is normally called a vague year. |
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