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the reign of Darius Hystaspes, as will be seen from the following details.
80. The Parsi year consists of twelve months, each con- sisting of thirty days, with five additional days added at the end of the year, and the total number of 365 days never varies, so that, whenever a leap-year occurs in our calendar, the beginning of the Parsi year retreats one day in the Christian calendar. In this manner, the total number of days which the beginning of the Parsi year has retreated, since the institution of their calendar, records the number of leap-years which would have occurred in the same period of Christian years, if the regular leap-years had existed the whole time; and four times the number of leap-years would be the total number of years. But as leap-years have not been used the whole time, we have to calculate from astronomical data.
81. In the first place, we want to know at what season the Parsi year originally began, and we learn this from Bd. XXV, 7, 20, where we are told that the winter of the rectified year ends with the five extra days, and the spring begins with the first month ; which means that the rectified year begins with the vernal equinox. We also have to observe that, retreating at the rate of one day every four years, the beginning of the year retreats all round the year in 1460 years ; and we know from general history that the period, with which we have to deal, is much more than 1460 years and less than 3930. Then we have to ascertain the exact length of the tropical year, which astronomers say is 365*2422 days, with an infinitesimal decrement, quite inappreciable in the period we have in view.
82. We may calculate back from any vernal equinox which occurs not too far from noon, say that of March 22, 1865, when the beginning of the Parsi year, according to Persian reckoning, had retreated to August 24, 1864, or 210 days, in addition to a previous retreat of a whole year of 365 days, or altogether 575 days since the establishment of the calendar. So that the difference between the Parsi year of 365 days and the correct tropical year of 365.2422 days had then accumulated to a total of 575 days. Divid-
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