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As the real length of the year had not yet been ascertained, great disorders were occasioned in its constitution, which Julius Cæsar, with the advice and consent of Sosigenes, a celebrated mathematician, undertook to rectify about the year B. C. 46. He found that the months had considerably receded from the seasons, to which they had been adjusted by Numa, and that the dispensation of time in the calendar, could never be properly settled, without having a regard to the annual course of the Sun. To bring forward the months to their proper places, he took an account of the days which had been lost by the former mode of reckoning, and formed a year of 15 months, or 445 days, which on account of its quantity and design, has been called the year of confusion. This year being ended, the Julian year commenced on the first of January, B. C. 46. From this time, the civil year and months, were regulated by the course of the Sun. As the philosopher found the annual course of the Sun to consist of 365 days 6 hours, he made his year to consist of 365 days, for three years successively, and every fourth year of 366 days, in order to comprehend the odd six hours. For this purpose he ordained, that an intercalary day, should be added every fourth year to the 23d of February; that is the 24th day, or the 6th, of the calends of March, which was to be reckoned twice, and hence this year was denominated Bissextile. It is likewise called Leap Year, from the year leaping over a day more of time in that year, than in a common year. Hence the Julian Calendar, so called from Julius Cæsar, is disposed into periods of four years each, of which the first three are called common, and consist of 365 days, and the fourth bissextile, having 366 days.

The Julian year was still imperfect; for as the time in which the sun apparently performs his annual revolution, that is the time in which the earth actually makes his journey round that luminary is 365 days, 5 hours, 45 min. and 49 sec. the civil year of 365 days 6 hours, must have exceeded the solar year by 11 minutes 12 seconds, which in the space of 130 years amounted to a whole day. The imperfections of the Julian Calendar were not observed for several hundred years, and it was not until the year 1582, that the next reformation was effected; the error accumulated by this means, amounted to about ten days of that time, so that the vernal equinox, which had been fixed by Susigenes, in the time of Julius Cæsar, on the 25th of March, was at the time of the Council of Nice, held in the year 325, fixed on the 21st of March, and in the year 1582, it was found to happen on the 11th. This constant anticipation of the equinox, became a matter of serious complaint in the 15th century; and in 1474 Pope Sextus IV. being convinced of the necessity of a reformation, sent for Regiomontanus, a celebrated mathematician, and presented him with the archbishopric of Ratisbon, in order to engage him in the undertaking. But a premature death preventing him from the accomplishment of his design, the project was suspended for a whole century. It was now that pope Gregory XIII. had the honour of executing, what several preceding pontiffs and councils had attempted before in vain. He invited to Rome a considerable number of mathematicians and astronomers, employed ten years in the examination of their several formule, and finally gave the preference to the plan proposed, by Aloisius and Antonius Lilius, two brothers of Verona. He transmitted copies of this plan in 1577, to all the catholic states, and the learned academies at tbat time existing. A council of the most erudite prelates was convened by the pope, and the subject being finally settled, a brief was published in the month of March A. D. 1582, by which the use of the old calendar was entirely abrogated in all countries, over which his holiness had any sway, and the new one instituted in its stead, called from his name the Gregorian Calendar.

The principle adopted was, that the few days which had been gained by the old account should be taken from the month of October, of the year then current, and the equinox brought back to the 21st of March, as it had been settled by the council of Nice; and to prevent the future recurrence of a similar variation, it was ordained, that instead of making every hundredth year bissextile, as was the case before, every four-hundreth year only should be considered as bissextile, and the rest as common years. The length of the solar year, and the time of the vernal equinox, were, by these means, very accurately settled: for as a day was gained, by the former mode of reckoning, in every interval of 130 years, this was nearly equivalent to the gain of three days in every 400 years; and, consequently, by making the years 1 700, 1800, 1900, to be common years, instead of leap-years, the error arising from the odd time would be properly corrected ; so that the new mode of reckoning cannot vary a single day from true time in less than 5000 years.

When the pope had reformed this calendar, he ordered all the ecclesiastics under his jurisdiction to conform to this new mode of reckoning; and exhorted Christian princes every where to adopt it in their dominions. Hence it was immediately introduced into almost all catholic countries. The catholic states in Germany adopted it; but those that were of the reformed faith rejected it. Hence arose a difference of 10 days between the methods of reckoning afterwards used in catholie and protestant countries. In the year 1700, the reforination of the calendar was introduced into the protestant states of Germany, and also into Denmark. In Sweden it did not exist till March 1753. In this country, an act of parliament was passed to cancel eleven days out of the month of September; because, as 170 days had elapsed since the Gregorian alteration had taken place, the old-style had consequently gained more than a day upon the course of the Sun than it had done at a former period. The old style then in Great Britain, and all its dependencies, ceased on the 2d of September, 1752, and the next day, instead of being the 3d, was called the 14th, By the same act the beginning of

the year was changed from the 25th of March to the 1st of January.

A considerable difficulty still remained, which was to make the lunar year agree with the solar one, and in settling the true time for the observance of Easter, and the other moveable feasts. It had been ordered by the council of Nice, that Easter should be celebrated upon the first Sunday after the first Full Moon, following the vernal equinox. And, in order to the due observance of this rule, it became necessary to know when the Full Moons would happen in the course of every year. Now the revolutions of the Sun and Moon are not very obviously commensurate, the solar year containing twelve lunations, and about eleven days; but it had been discovered by Meto 2000 years ago, that nineteen solar years contain exactly 235 lunations; and this determination is so very accurate, that it makes the lunar month only half a minute too long. Hence, it happens, that in every period of nineteen years the Moon's age is the same on the same day of the year. The number of the year in the Metonic circle is called the Golden Number, the calendar of Meto having been ordered, at the celebration of the Olympic games, to be engraved in letters of gold on a pillar of marble. At present, if we add 1 to the number of the year and divide by 19, the remainder will be the golden number: thus, for 1814, 1814 +1 1815

=95, and 10 over as a remainder, which re19

19 mainder 10 is the golden number.

If we subtract 1 from the golden number, then multiply by 11 and divide by 30, the remainder will be the epact, which is the Moon's age on the 1st of January: thus, for

11 99 1914, we have 9 (10-1)

3 and 9 over, which

30 30 9, as a remainder, is the epact. The application of these numbers will be shewn in a future number of this work.

The time of the Sun rising and setting in London during the month of April, is as follows, viz:

1st. Sun rises 34m. past 5. Sun sets 26m. past 6.
11th.
14m. 5.

46m. 6.
21st.
55m. 4.

5m. 7.

Equation of Time.- (See the month of January.]

To obtain true time by the clock.

The following table will shew what is to be added to and what is to be subtracted from the apparent time shewn on the dial, to obtain equal or true time for every 5th day of April. Friday, April 1, to the time on the dial add 4m. 5s.? Wednesday, 6,

2 34 Monday, 11,

1 9 Friday, 15,

0 6 Thursday 21,

subtract 1 17 Tuesday, 26,

2 15 The Moon will be at full at 29m. past 8 in the afternoon of the 4th; it enters its last quarter, on the 12th, at 23m. past 9: the change or new moon, is at 55m. past 7 on the 20th, and it enters its last quarter at 6m. past midnight, on the 26th,

The time of the Moon's rising for the first five days after she is full, as follows, viz.

5th day, 27m. past 7
6th 29

8
7th 39

9 8th 43

10 9th 45

11 Venus will be stationary on the 3d, Mercury on the 15th, and Jupiter on the 27th. The Sun enters the sign Taurus Ilm. past 6 in the evening of the 20th. On the 26th, of this month, the moon will eclipse the star d.o. The immersion will occur at 25m. past 12 at night, and the emersion at 18m. after 1 the next morning, the star passing under the moon's centre. On the 1st, there will be an obscuration of

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