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readily, must be caused by a motion of our earth, for it will be noticed, that the inclination of the ecliptic to the equator remains unchanged. Let A B C, represent the ecliptic, and D B E, the celestial equator, intersecting each other in two opposite points, one of which is shown at B. Let P P' be the poles of the earth, 90° distant from the equator F W G, in every direction, and let the star S, in the direction P' P, be the pole of the heavens, every where 90° distant from the celestial equator, DBE, let the point T, be the pole of the ecliptic A B C. We must be careful and not consider the lines FG, H I, marked on the earth as equator and ecliptic, to be fixed, because this would cause the nodes, or equinoctial points, to revolve, apparently, once in a day, through the heavens, but we may suppose them hoops or bands, stationary, while the earth turns around in them. For a moment suppose the diurnal revolution of the earth to be stopped, and let the position of the intersections of the planes of the celestial ecliptic and equator, meet on the earth at W, and let the poles, of the ecliptic H. W. I thus marked on the earth, be O and R, a spectator at the centre of the earth, would locate the equinoctial point among the stars at B. If, now, the earth should be turned a little, not on its diurnal or equatorial axis PP', but on its ecliptical axis O R, in the direction of the letters C B A, the equinox would appear to shift in the heavens to the star X, and the pole of the heavens S, would appear to have moved partly around the pole of the ecliptic S, and be at Z. This is the fact, whilst the earth is moving around the sun, and all the time turning daily on its equatorial axis, it is making a slow backward revolution around its ecliptical axis, and as the stars are fixed, the equinoctial point continually retrogrades along the ecliptic, thus causing the pole of the heavens continually to shift its place, revolving in a circle whose radius is TS, which is the angular inclination of the axis PP to the axis O R, or of the plane of the ecliptic, to the plane of the equator. The early astronomers, located the places of the equinoxes in the heavens, and gave the name Aries to the constellation where the vernal, or spring equinox, was located, and the name Libra to the constellation where the autumnal equinox was located. Since that


time, the equinoctial point has retrograded 30°, or one sign, the whole circle, 360°, being divided into 12 signs of 300 each; consequently, the vernal equinox is now in what was then the last constellation, Pisces, for the stars have not changed places, only the intersecting point. Astronomers, however, have agreed to call the point where the vernal equinox is situated, the first point of Aries, forever, whatever may be the constellation where this point is located, hence the sign Aries, is now in the constellation Pisces, the sign Pisces, in the constellation Aquarius, &c. The annual amount of precession is small, being but 50.1” in a year, hence the time occupied to make a complete revolution, will be 25,868 years. However, small as it is, it is quite palpable in the course of a century, and has been of signal aid in Chronology as we shall show in our chapter upon that subject. As the place of equinox goes forward each year, to meet the sun, 50.1 seconds of space, it is evident the tropical or equinoctial year will be as much shorter than the siderial year, as it takes the sun to describe this small space, which is 20m 20s, nearly, hence the length of the equinoctial year is 365d, 5h, 48m, 51.6s, and this is the year which most intimately concerns us. In ancient times, the days of the summer and winter solstice were determined by means of the shadow of a gnomon, or upright post, as the sun rose higher and higher each day, at noon, the shadow became shorter and shorter, until, having reached its limit, it began to lengthen, this was the day of the summer solstice. The day of the winter solstice, was the time of the longest shadow. When we look back, and think of the ancient philosophers, with their shadow-sticks, and rude dials, and see them trying, with these rough means, to measure the distances of the heavenly bodies, and the size of the earth, we may wonder that they ever approximated as near as they did. In no Science has the advancement of general learning and civilization been more'apparent, than in Astronomy. Tables of the positions of the sun, moon and planets, in the heavens, are now given for many years to come, with such accuracy, that the unassisted eye cannot detect even their greatest errors, and in some cases, the positions are given with more accuracy than even could be obtained from observation itself. d

The tropical, or equinoctial, or mean solar year, for these different names all mean the same, is, as we have just shown, about 3654 days long. Now if this year was to begin upon the first day of January, at 0h,0m, 0s, the next year must begin January 1st, at 5h, 48m, 51.6s, or about a quarter of a day later. This would be excessively inconvenient, hence it was determined to have the civil year consist of 365 days exactly, and this, for a long period, was the case, but the consequences, after awhile, became very apparent. The vernal equinox, which once was at the commencement of the spring months, gradually began to go back, until the calendar was involved in great confusion. This was especially the case with the Roman Calendar, in which the year was reckoned 12 revolutions of the moon, or 354 days, and Julius Caesar, with the aid of Sosigenes, an astronomer of Alexandria, attempted a reformation. The beginning of the year had formerly been placed in March, by Romulus, in honor of his patron, Mars. Caesar determined to commence the year the 1st of January, at the time of the winter solstice. This seems the most natural time, for now, the sun, having reached his greatest southern declination, begins to return, bringing back the spring and summer. Caesar chose, likewise, to have, for the first year of the new calendar, a year when a new moon happened near the time of the winter solstice. This occurred in the second year of his dictatorship, and the 707th from the founding of Rome, when there was a new moon on the 6th of January. This, accordingly, was made the beginning of a new year, and in order to make the year commence at this period, it was necessary to keep the old year dragging on 90 days, or to consist of 444 days. All these days were unprovided with solemnities, hence the year preceding the commencement of Caesar's calendar is called the year of confusion. To prevent the recurrence of error, which was what he had most in view, and keep the civil and astronomical years together, he determined to add, each fourth year, a day to the calendar, because the solar year being, as was then supposed, 3654 days long, this 3, would, in four years, amount to a day, and could then be added. It was true, the second year would begin 6 hours too soon, the third would begin 12 hours too soon, and the fourth 18 hours too soon, but the


commencement of the fifth would correspond with the fifth astronomical year. In the month of February, the lustrations, and other, piaculums to the infernal deities, ceased on the 23d day, and the worship of the celestial deities commenced on the 24th. Caesar chose, therefore, to insert this intercalary day between the 23d and 24th days of February. The Romans did not number their days of the month as we do now, i.e. 1st, 2d, 3d, &c., but they called the first day the Calends, from which our word calendar is derived, thus the 1st day of March was called the Calends of March, the 28th day of February was called the pridie Calendas Martias, the day before the calends of March, the 27th was called the third day of the Calends of March, and the 24th was the sextus, or sixth day, of the Calends of March, and as Caesar's intercalary day was added just after this day, it was called bissextile, or double sixth day, and the year in which it was added, received, and still bears the name, bissextile. Many years after, when Christianity became the religion of the Roman Empire, Dionysius Exiguus, a French Monk, after much research, came to the conclusion that the 25th day of December, of the 45th year of Caesar's era, was the time of the nativity, commonly called Christmas, and therefore the 1st of January, of the 46th year of Caesar, was adopted as the 1st of the Christian era. As the first year of Caesar was a bissextile, and as every fourth year after the 45th, was a bissextile, consequently the fourth year of the Christian era was a bissextile, and as every fourth year is the one in which the intercalary day is added, we can always determine when this year occurs, by simply dividing the year of the Christian era by 4, if there be no remainder, the year is a bissextile, or leap year; but if a remainder, then that remainder shows how many years it is from the last bissextile. The name leap year is given, because the civil reckoning, which had fallen behind the astronomical, leaps ahead and overtakes it.

The correction introduced into the calendar by Caesar, would have been sufficient to always keep the astronomical and civil reckoning together, if the fraction of a day over 365 had been just 6 hours, or #; instead of this, however, it is but 5h, 48m, 51.6s, and the difference is 11m, 8.4s, which, in 4 years, amounts to 44m, 33.6s, by which amount, the fifth civil year begins later than the astronomical year. In 1582 this difference had accumulated,

until it amounted to over 11 days, of course the equinoxes, and sol

stices, no longer happened on those days which had been appointed to them, and the celebrations of the Church festivals, were conse

quently much deranged. The Council of Nice, which sat A. D.

325, had decreed that the great festival of Easter, should be

celebrated in conformity with the Jewish Passover, which was

regulated by the full moon following the vernal equinox. Now

the decree did not say that this festival, upon which all the others . depend, should be on the first Sunday after the full moon following the vernal equinox, but on the Sunday following the full moon, on or after the 21st of March, this being the day, at that time, of the vernal equinox. Pope Gregory XIII., who occupied the pontificate in 1582, determined to rectify this error, which was thus made known, not from any series of observations for that specific purpose, as at the present day, but by the accumulated error becoming so great as to introduce confusion. At this time the vernal equinox really occurred, according to the civil reckoning, on the 11th of March, ten days earlier than the time decreed by the Nicene Council. To remedy this defect, Gregory directed that the day following the 4th of October, 1582, should be reckoned the 15th, instead of the 5th, thus restoring the vernal equinox to its former position, by omitting altogether ten days. To prevent the accumulation, he directed the intercalary day to be omitted on every centurial year; this would have answered every purpose if the difference, which had caused the error, had amounted to a day in 100 years, but it did not, for it was but a little more than 3 of a day, hence omitting théintercalary day every 100th, or centurial year, omitted 3 of a day too much, which, in the course of 400 years, amounts to 1 day. It was, therefore, further provided, that although the intercalary day was ordinarily omitted each centurial year, it was to be retained every 400th year, thus the centurial years 1600, 2000, and 2400, are bissextile; but the years 1500, 1700, 1800, 1900, 2100, 2200, &c., are common years. This correction is sufficiently accurate for all purposes, the slight remaining error will only amount to a day after an interval of 144 centuries. The time of the vernal equinox now is, and always

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