From the meeting of the Council of Nice, in 325, to 1582, a period of 1257 years, there was found to be an error in the Julian calendar of ten days. Now, in 1257 years the Earth performs 1257 annual and 459,109 daily revolutions, after which the vernal equinox was found to occur on the 21st of March, true or solar time; thus concurring with the vernal equinox of 325. But the erroneous Julian calendar would make the Earth perform 459,119 daily revolutions to complete the 1257 years, a discrepancy of ten days, making the vernal equinox to fall on the 11th instead of the 21st. It will be seen by the diagram that the ten days were deducted from October, in 1582, making it a short month, consisting of only twenty-one days. The discrepancy between the Julian and Gregorian calendar amounts to thirty days in 4000 years; three months in 12,175 years. Hence, in 12,175 years the equinoxes would take the place of the solstices, and the solstices the place of the equinoxes. In 24,350 years, the vernal equinox would take the place of the autumnal equinox, and the winter solstice the place of the summer solstice. And in 48,700 years, according to the Julian rule of intercalation, there would be gained nearly 365-1/4 days, or one entire revolution of the Earth. So, to restore the concurrence of the Julian and Gregorian years, there would have to be suppressed 365-1/4 days, calling the 1st day of January, 48,699, the 1st day of January, 48,700. Thus would disappear from the Julian calendar twelve months, or one whole year, it having been divided among the thousands of the preceding years. [Illustration: The Julian calendar, reformed by Gregory XIII, Oct. 5th, 1582, by suppressing ten days, calling the 5th of Oct. the 15th, making it a short month of 21 days, and the year to consist of 355 days. The Roman calendar, reformed by Julius Caesar, 46 B. C., by intercalating 90 days, making that year to consist of 445 days, that is, 355 + 23 + 67 = 445 days, and "the last year of confusion."] To make this subject better understood, let us suppose the solar year to consist in round numbers of 365 days, and the civil year 366. It is evident that at the end of the year of 365 days, there would still be wanting one day to complete the civil year of 366 days, so one day must be added to that year, and to every succeeding year, to complete the years of 366 days each, which would be the loss of one year of 365 days in 365 years. Hence, 364 years of 366 days each are equal to 365 years of 365 days each, wanting one day. Again, let us suppose the civil year to consist of 364 days. It is evident that at the end of the supposed solar year of 365 days, there would be an advance or gain of one day in that year and every succeeding year, so that in 365 years there would be a gain of 365 days or one whole year. Hence, 366 years of 364 days each are equal to 365 years of 365 days each, wanting one day. Appendix F. CHAPTER V. PECULIARITIES OF THE ROMAN CALENDAR.