  ERRORS OF THE JULIAN CALENDAR. It will be necessary in the first place to understand the difference between the Julian and Gregorian rule of intercalation. If the number of any year be exactly divisible by four it is leap year; if the remainder be 1, it is the first year after leap-year; if 2, the second; if 3, the third; thus:
And so on, every fourth year being leap-year of 366 days. This is the Julian rule of intercalation, which is corrected by the Gregorian by making every centurial year, or the year that completes the century, a common year, if not exactly divisible by 400; so that only every fourth centurial year is leap-year; thus, 1,700, 1,800, and 1,900 are common years, but 2,000, the fourth centurial year, is leap year, and so on.
Multiply the difference between the Julian and the solar year by 100, and we have the error in 100 years. Multiply this product by 4 and we have the error in 400 years. Now, 400 is the tenth of 4,000; therefore, multiply the last product by 10, and we have the error in 4,000 years. Now, as the discrepancy between the Julian and Gregorian year is three days in 400 years, making 3-400 of a day every year, so by dividing 365¼, the number of days in a year, by 3-400, we have the time it would take to make a revolution of the seasons.
(365 d, 6 h.) - (365 d, 5 h, 48 m, 49.62 s.) = (11 m, 10.38 s.) Now, (11 m, 10.38 s.) × 100 = 18 h, 37.3 m, the gain in 100 years. This is, reckoned in round numbers, 18 hours, or three-fourths of a day. Now, (¾ × 4) = (1 × 3) = 3: the Julian rule gaining three days, the Gregorian suppressing three days in 400 years. (3 × 10) = 30, the number of days gained by the Julian rule in 4,000 years. 365¼ ÷ 3 400 = 48,700, so that in this long period of time, this falling back ¾ of a day every century would amount to 365¼ days; therefore, 48,699 Julian years are equal to 48,700 Gregorian years. |
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