Between the 23d and 24th of February, 46 years before Christ, there was intercalated a month of 23 days according to an established method, but still the civil year was in advance of the solar year by 67 days; so that when the Earth in her annual revolutions should arrive to that point of the ecliptic marked the 22d of October, it would be the 1st day of January in the Roman year. Caesar and his astronomers, knowing this fact and fixing on the 1st day of January, 45 years before Christ and 709 from the foundation of Rome, for the reformed calendar to take effect, were under the necessity of intercalating two months, together consisting of 67 days. Now, as the civil year would end on the 22d of October, true or solar time, it would be reckoned in the old calendar the 1st day of January; so they let the old calendar come to a stand while the Earth performs 67 diurnal revolutions, and thereby restored the concurrence of the solar and the civil year. As an illustration, let us suppose that in a certain shop where hangs a regulator are two clocks to be regulated. Both are set with the regulator at 8 a. m. to see how they will run for ten consecutive hours. It was found that when it was 6 p. m., by the first clock, it was 5:50 by the regulator, the clock having gained one minute every hour. To rectify this discrepancy we must intercalate 10 minutes by stopping the clock until it is 6 by the regulator. By this means the coincidence is restored, and the time lost in the preceding hours is now reckoned in this last hour, making it to consist of 70 minutes. By this it may be seen how Caesar reformed the Roman calendar. The Roman year was too short, by reason of which the calendar was thrown into confusion, being 90 days in advance of the true time, so that December, January and February took the place in the seasons of September, October and November, and September, October and November the place of June, July and August. To make the correction he must stop the old Roman clock (the calendar) while the Earth performs 90 diurnal revolutions to restore the concurrence of the solar and the civil year, making the year 46 B. C. to consist of 445 days. It was also found that when it was 6 p. m., by the regulator, it was only 5:50 by the second clock, it having lost one minute every hour. To rectify this discrepancy we must suppress 10 minutes, calling it 6 p. m., turning the hands of the clock to coincide with the regulator, making the last hour to consist of only 50 minutes, too much time having been reckoned in the preceding hours. It may be seen by this illustration, how Gregory corrected the Julian calendar, the Julian year was too long, consequently behind true or solar time, so that when the correction was made in 1582, the ten days gained had to be suppressed to restore the coincidence, making the year to consist of only 355 days.