In order to restore the vernal equinox to the 24th of March, the place it occupied in the time of Numa, two months, together consisting of 67 days, were inserted between the last day of November and the first day of December of that year. An intercalary month of 23 days had already been added to February of the same year according to the old method, so that the first Julian year commenced with the first day of January, 45 years before Christ, and 709 from the foundation of Rome, making the year A. U. C. 708 to consist of the prodigious number of 445 days, (i. e. 355 + 23 + 67 = 445). Hence it was called by some the year of confusion; Macrobius said it should be named the last year of confusion. There was also adopted at the same time a more commodious arrangement in the distribution of the days throughout the several months. It was decided to give to January, March, May, July, September and November each thirty-one days; and the other months thirty, excepting February, which in common years should have but twenty-nine days, but every fourth year thirty; so that the average length of the Julian year was 365-1/4 days. Augustus Caesar interrupted this order by taking one day from February, reducing it to twenty-eight and giving it to August, that the month bearing his name should have as many days as July, which was named in honor of his great-uncle, Julius. In order that three months of thirty-one days might not come together, September and November were reduced to thirty days, and thirty-one given to October and December. In the Julian calendar a day was added to February every fourth year, it being the shortest month, which was called the additional or intercalary day, and was inserted in the calendar between the 23d and 24th of that month. In the ancient Roman calendar the first day of every month was invariably called the calends. The 24th of February then was the 6th of the calends of March--Sexto calendas; the preceding, which was the additional or intercalary day, was called bis-sexto calendas (from _bis_, twice, and _sextus_, six), twice the sixth day. Hence the term bis-sextile as applied to every fourth year, commonly called leap-year. Appendix B. CHAPTER IV. HISTORY OF THE REFORMATION OF THE JULIAN CALENDAR BY POPE GREGORY XIII. True enough, the year in which Julius Caesar reformed the ancient Roman calendar was the last year of confusion, and the method adopted by him a commodious one, and answered a very good purpose for a short time; but as the years rolled on and century after century had passed away, astronomers began to discover the discrepancy between the solar and the civil year; that the vernal equinox did not occupy the place it occupied in the time of Caesar, namely, the 24th of March, but was gradually retrograding towards the beginning of the year, so that at the meeting of the Council of Nice in 325 it fell on the 21st. Appendix C.