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(at the present time) on the 15th of April, 15th of June, 1st of September, and 24th of December; and it would differ most from the sun about the middle of the intervening periods. The difference, however, between the clock and the sun, would not be the same in each case. The following are the differences in question, between the clock and sun at the time of their greatest departure from each other in the several periods above mentioned ; 11th of February, 144' 36.6''; 15th of May, 3' 55.6" ; 26th of July, 6' 7.3"; 3d of November, 16' 16.8".
The want of equality in the length of the solar days may be thought to imply a want of uniformity in the apparent diurnal motion of the heavens, or in the real motion of the earth on its axis. This is not, however, the case. We have never been able to detect the slightest irregularity in these motions. The day, as measured by the retuin of a star to the meridian, or to the same point of the heavens, is always the same. It will naturally be asked, then, how it happens that the solar day, or period measured by the return of the sun to the meridian, should be different at different times of the year. This arises from two causes. If the sun's centre and a star were on the meridian at the same instant tu-day, to-morrow when the star arrived at the meridian, the sun would be advanced towards the east about one degree, or two of its diameters, which would require, according to the uniform rate of the diurnal motion, about four minutes of time for it to reach the meridian. Thus a solar day is made up of a sidereal day, always the same, and a certain portion more. Now these additional portions are unequal. We have said that the sun will be found to have left the star, upon the return of the latter to the meridian, having departed from it toward the east. But these deparcures will be unequal, since the sun's apparent motion among the stars, produced by the real motion of the earth in her orbit, is alternately accelerated and retarded. This is one cause of the inequality of the solar days. Another is, that the sun's path among the stars is sometimes perpendicular to the meridian, and sometimes oblique. It is manifest, that if the sun, after coinciding with a star should move a degree north or south, instead of easterly, it would return to the meridian at the same time with the star, making a solar and sidereal day the same ; and, according as the path of the sun approaches more and more to a perpendicular to the meridian, is the solar day increased, other things being the same. Now the sun's path is actually sometimes perpendicular to the meridian, and sometimes oblique. Its course among the stars is not exactly east, but is generally inclined, sometimes to the north and sometimes to the south, In this manner it happens that the days, as measured by the sun, alternately increase and decrease, and the time shown by the sun, as upon a dial, for instance, is called apparent time. On the other hand, the time furnished by a good clock, as above described, is called mean time. The difference, amounting, when greatest, to about 16 minutes, is called the equation of time,
Days. The day is made to begin at different times in different countries. With the Italians, for instance, it is consiilered as beginning at sunset; with the modern Greeks, on the other hand, it is supposed to begin at sunrise ; while with us, and many other people, its commencement dates from midnight. According to the two former modes, it is necessary to alter clocks and watches continually for the purpose of making the hours begin with the day. The manner of beginning the day at midnight seems to be decidedly the most convenient for the ordinary business of civil life. In this case, the same piece of work is seldom divided between two days, as must frequently happen when the day is made to begin at sunrise or sunset. With us it is rarely necessary to look at the clock or the sun to know what day of the month or week it is. Astronomers, however, find it most convenient to begin the day at noon, 12 hours after the commencement of the civil day, as the time of noon can be accurately determined by observation. They are accustomed, moreover, to count the hours continuously from 1 to 24, whereas, in civil reckor.ing, the hours being counted from 1 to 12, and then repeated, it is necessary to distinguish the two series by A. M. and P. M. Navigators also begin the day at noon, and count the hours from 1 to 24, after the manner of astronomers; but they begin their computation 12 hours before the commencement of the civil day, and consequently 24 hours before the commencement of the astronomical day.
Weeks. The week approaches pretty nearly to a quarter of a lunation; but it has no very obvious foundation in nature. It appears, notwithstanding, to have prevailed very extensively over the world, and from the earliest times ; and what is still more remarkable is, that the days of the week are so generally named after the sun and planets. This manner of distinguishing the series of seven days, “is found to be the same among the ancient Egyptians, Indians, and Chinese. Still the order is not that of the distances, magnitude, or brightness of the planets. It is an order that is apparently arbitrary, or which is at least founded upon reasons not known to us. Sunday is the Sun's day, Monday is the Moon's day, Tuesday, Wednesday, Thursday, and Friday, are derived from Tuesco, Woden, Thor, and Freya, the Saxon names of Mars, Mercury, Jupiter, and Venus.
Months. The months, with the exception of February, are either of 30 or 31 days ; and the following lines, intended to assist the memory, are as useful as they are trite:
" Thirty days hath September,
April, Juno, and November,
* Bailly's Histoire d'Astronomie.
February hath twenty-eight alone,
February's days are twenty-nine.” Our names of the months have come down to us from the Romans; January is said to be derived from Janus, an ancient king of Italy; February from februo, to purify; March, from Mars; April from aperio, to unfold ; May, from Maia; June, from Juno; July and August were so named in honor of Julius and Augustus Cæsar. Before the time of Julius Cæsar, these months were called Quintilis and Sextilis, being the fifth and sixth months, reckoning, as the Romans did at that time, from March, as the commencement of their year. September, October, November, and December, signify the seventh, eighth, ninth, and tenth months from March, when the year began.
The year is a striking period of time obviously marked by the return of the sun to the same point in its course through the heavens, and its consequent effects in renewing the productions of the earth. The year in civil reckoning, that is, the period of the seasons, is not exactly the time of an apparent revolution of the sun in absolute space; in other words, it is not strictly the time employed by the sun in returning to the same star, since those points of the sun's course (or the ecliptic), on which the seasons depend, shift backward a little (50") while the sun is going round. This is called the precession of the equinoxes. Now the sun is about twenty minutes, according to its ordinary rate of 360° in a year, in moving through this space of 5011. Hence the year of the seasons, technically called the tropical year, is about twenty minutes less than a sídereal year, or a complete period through the heavens. But this precession of the equinoxes, which thus shortens the year of the seasons, and which is caused by the attraction of the sun and moon exerted upon the matter accumulated about the equator, is not always the same. It is sometimes greater, and sometimes less. It is a little more now than it was two thousand years ago, the necessary consequence of which is, that the year is shorter than it was. The difference for the period above mentioned amounts to about 11 seconds.
As the year of the seasons, 365 days, 5 hours, 48 minutes, 50 seconds, does not consist of a certain number of entire days, it has been found diffi. cult to allow for the fraction of a day, and keep the months to the same
It is important, in civil reckoning, to have the year consist of a certain number of entire days; and Julius Cæsar, in framing the Calendar that is still in use under the title of the Julian Calendar, proceeded upon the supposition, that the year was 365 days and a quarter or 6 hours. He accordingly provided, that the civil year should be 365 days for three years in succession, and the fourth 366, thus making the average length 3654. But this was making the year too great by 11 minutes and 10 seconds, which would amount to a day in about 130 years. The error, however, remained uncorrected till the latter part of the 16th century, when Pope Gregory XIII. interested himself in this matter on account of its intimate connexion with the festivals of the church. It appeared from the facts that were submitted to his Holiness, that the vernal equinox at this time happened on the 11th of March, whereas it took place on the 21st of March in the year 325, when the Council of Nice was held. It was proposed to reduce the months to their former places, so that the vernal equinox should still happen on the 21st of March. The variation from this time amounted to about 10 days; and 10 days were accordingly to be suppressed, and actually were suppressed in the month of October, the day following the 4th, being called not the 5th, but the 15th. This correction took place in 1582, and was immediately adopted in all Catholic countries. The Julian intercalation of one day in four years was still retained ; and to prevent the like inconvenience occurring in future, it was provided, that when the error of 11 minutes and 10 seconds, according to the Julian mode of reckoning, aniounted to an entire day, it should be suppressed. Now the error in question, as we have said, amounted to a day in about 130 years. But instead of suppressing a day every 130th year, whether common or leap year, it was thought preferable to make the correction in leap years only, thus leaving always 365 days at least in the year. Moreover, as the centurial years 1600, 1700, &c. would be leap years, and memorable years, it was wisely determined, that the accumulated error of a day should be dropped in those years, by which they would be reduced to common years. Now the error of one day in 130 years is equivalent nearly to three days in 400 years. Thus by dropping a day every centurial year for three cen. turial years in succession, and retaining the 4th centurial year as a leap year, the desired effect would be produced, and the civil year would, by a very simple process, be made nearly equal to the tropical year, or year of the seasons. The very small error that still exists, will scarcely amount to a day in four thousand years.
This modification in the Julian Calendar, so simple in itself, and so obviously required, was reluctantly and tardily adopted by those states that did not acknowledge the authority of the Pope. The Reformation was now in its infancy, and every thing was viewed with jealousy that bore the sanction of the see of Rome. It was at length, however, introduced into the Protestant states of Germany in the year 1700; but it was not till half a century afterward, that it found its way into England. The error now amounted to 11 days, a day being suppressed in Catholic countries in the year 1700, and there was 11 days' difference in dates between those who had, and those who had not, adopted the Gregorian reformation. This is the foundation of what is called old and new style. According to an act of Parliament, the 11 days' excess was suppressed in September, 1752. The day following the 20, instead of being called the 3d, was reckoned the 14th.* By the same act the beginning of the year was transferred from the 25th of March to the beginning of January. A knowledge of this alteration is of great importance to the understanding of dates anterior to 1752, especially if they relate to events occurring between the 1st of January and the 25th of March. Washington, for instance, was born the 11th of February, 1731, according to the mode of reckoning in use at the time, but on the 22d, 1732, according to the present improved Calendar. To prevent mistakes, both modes of dating are sometimes used with regard to events that happened before 1752. Thus Washington was born February 11, 1737.
Before the time of Edward IV. there seems to have been three different modes of reckoning, so far as relates to the beginning of the year. With some it began at the Nativity, 25th of December, with others at the Circumcision, the 1st of January. In Scotland, from time immemorial, it began with the 25th of March. From about the year 1462, the custom of beginning the year at the Annunciation, 25th of March, seems to have been fully settled; and this manner of beginning the year was fixed by civil and ecclesiastical authority in the reign of Henry VIII. The above times refer apparently to epochs in the history of the Christian religion. But Julius Cæsar, at the time of the adoption of his Calendar, transferred the beginning of the year from the 1st of March to the 1st of January, It was thought proper to begin the year as near as possible to the time when the sun begins to return, bringing with it the season of vegetation. It is to be recollected, moreover, that the precise time of our Saviour's birth is not known, and in this uncertainty, it was thought best to consider it as taking place on the 25th of December, for no other reason, than that this is the time when the light of the natural sun begins again to visit us.
It was the practice in England, in dating instruments, to refer to the accession of the reigning monarch, till the time of the Commonwealth, when the Puritans and Republicans made use of the Christian era, although chronologists are not agreed as to the precise year when our Lord was born. This custom, introduced during the time when there was no king in England, was found so convenient, that it has continued ever since,
Solar and Lunar Cycle.
The ordinary civil year being 365 days, or nearly 6 hours less than the time of the sun's complete revolution in the ecliptic, it will be seen that upon the returu of the 1st of January, or any other date, the sun has not
* Russia has not yet adopted the reformed Calendar, and a day having been suppressed in the year 1800, the difference amounts now to 12 days. This is to be borne in mind in all dates that come directly from that country, as those of memorable battles, treaties, &c.