twelve and twelve; but in France, astronomers, adopting the decimal division, divide the day into ten hours, the hour into one hundred minutes, and the minute into a hundred seconds, because of facility in computation, and in conformity with their system of weights and measures. This subdivision is not used in common life, nor has it been adopted in any other country; and although some scientific writers in France still employ that division of time, the custom is beginning to wear out. The mean length of the day, though accurately determined, is not sufficient for the purposes either of astronomy or civil life. The tropical or civil year of 365.242219 mean solar days, the time elapsed between the consecutive returns of the sun to the mean equinoxes or solstices, including all the changes of the seasons, is a natural cycle peculiarly suited for a measure of duration. It is estimated from the winter solstice, the middle of the long annual night under the pole. But although the length of the civil year is pointed out by nature as a measure of long periods, the incommensurability that exists between the length of the day and the revolution of the sun renders it difficult to adjust the estimation of both in whole numbers. If the revolution of the sun were accomplished in 365 days, all the years would be of precisely the same number of days, and would begin and end with the sun at the same point of the ecliptic; but as the sun's revolution includes the fraction of a day, a civil year and a revolution of the sun have not the same duration. Since the fraction is nearly the fourth of a day, in four years it is nearly equal to a revolution of the sun, so that the addition of a supernumerary day every fourth year nearly compensates the difference; but, in process of time, further correction will

be necessary, because the fraction in less than the fourth of a day. In fact, if a bissextile be suppressed at the end of three out of four centuries, the year so determined will only exceed the true year by an extremely small fraction of a day; and if, in addition to this, a bissextile be suppressed every 4000 years, the length of the year will be nearly equal to that given by observation. Were the fraction neglected, the beginning of the year would precede that of the tropical year, so that it would retrograde through the different seasons in a period of about 1507 years. The Egyptians estimated the year at 365.25 days, by which they lost one year in every 14601-their Sothiac period. The division of the year into months is very old and almost universal; but the period of seven days, by far the most permanent division of time, and the most ancient monument of astronomical knowledge, was used by the Brahmins in India with the same denominations employed by us, and was alike found in the calendars of the Jews, Egyptians, Arabs, and Assyrians; it has survived the fall of empires, and has existed among all successive generations, a proof of their common origin.

The new moon immediately following the winter solstice in the 707th year of Rome was made the 1st of January of the first year of Julius Cæsar; the 25th of December of his forty-fifth year is considered as the date of Christ's nativity; and Cæsar's forty-sixth year is assumed to be the first of our era. The preceding year is called the first year before Christ by chronologists, but by astronomers it is called the year 0. The astronomical year begins on the 31st of December, at noon; and the date of an observation expresses the days and hours which have actually elapsed since that time.

Some remarkable astronomical eras are determined by the position of the major axis of the solar ellipse, which depends upon the direct motion of the perigee and the precession of the equinoxes conjointly, the annual motion of the one being 11".2936, and that of the other 50′′.223; hence the axis, moving at the rate of 61".5166 annually, accomplishes a tropical revolution in 21067 years. It coincided with the line of the equinoxes 4000 or 4022 years before the Christian era, much about the time chronologists assign for the creation of man. In 6512 the major axis will again coincide with the line of the equinoxes, but then the solar perigee will coincide with the equinox of spring, whereas at the creation of man it coincided with the autumnal equinox. In the year 1245, the major axis was perpendicular to the line of the equinoxes, then the solar perigee coincided with the solstice of winter, and the apogee with the solstice of summer. According to La Place, who computed these periods from different data, the last coincidence happened in the year 1250 of our era, which induced him to propose that year as a universal epoch, the vernal equinox of the year 1250 to be the first day of the first year.

The variation in the position of the solar ellipse occasions corresponding changes in the length of the seasons. In its present position, spring is shorter than summer, and autumn longer than winter; and while the solar perigee continues as it now is, between the solstice of winter and the equinox of spring, the period including spring and summer will be longer than that including autumn and winter. In this century the difference is between seven and eight days. The intervals will be equal towards the year 6512, when the perigee coincides with the equinox of spring, but when it passes that point, the spring and sum

mer, taken together, will be shorter than the period including the autumn and winter. These changes will be accomplished in a tropical revolution of the major axis of the earth's orbit, which includes an interval of 21067 years; and as the seasons are opposed to each other in the northern and southern hemispheres, they alternately receive, for a period of 10534 years, a greater portion of light and heat. Were the orbit circular, the seasons would be equal; their difference arises from the eccentricity of the orbit, small as it is; but the changes are so trifling, as to be imperceptible in the short space of human life.

No circumstance in the whole science of astronomy excites a deeper interest than its application to chronology. 'Whole nations,' says La Place, 'have been swept from the earth, with their languages, arts, and sciences, leaving but confused masses of ruins to mark the place where mighty cities stood; their history, with the exception of a few doubtful traditions, has perished; but the perfection of their astronomical observations marks their high antiquity, fixes the periods of their existence, and proves that, even at that early time, they must have made considerable progress in science.' The ancient state of the heavens may now be computed with great accuracy; and by comparing the results of computation with ancient observations, the exact period at which they were made may be verified if true, or, if false, their error may be detected. If the date be accurate, and the observation good, it will verify the accuracy of modern tables, and will show to how many centuries they may be extended, without the fear of error. A few examples will show the importance of the subject.

At the solstices the sun is at his greatest distance from

era.

the equator, consequently his declination at these times is equal to the obliquity of the ecliptic, which, in former times, was determined from the meridian length of the shadow of the stile of a dial on the day of the solstice. The lengths of the meridian shadow at the summer and winter solstice are recorded to have been observed at the city of Layang, in China, 1100 years before the Christian From these, the distances of the sun from the zenith of the city of Layang are known. Half the sum of these zenith distances terminates the latitude, and half their difference gives the obliquity of the ecliptic at the period of the observation; and as the law of the variation of the obliquity is known, both the time and place of the observations have been verified by computations from modern tables. Thus the Chinese had made some advances in the science of astronomy at that early period; their chronology is founded on the observation of eclipses, which prove the existence of that empire for more than 4700 years. The epoch of the lunar tables of the Indians, supposed by Baily to be 3000 years before the Christian era, was proved by La Place, from the acceleration of the moon, not to be more ancient than the time of Ptolemy, who lived in the second century after it. The great inequality of Jupiter and Saturn, whose cycle embraces 929 years, is peculiarly fitted for marking the civilization of a people. The Indians had determined the mean motions of these two planets in that part of their periods when the apparent mean motion of Saturn was at the slowest, and that of Jupiter the most rapid. The periods in which that happened was 3102 years before the Christian era, and the year 1491 after it. The returns of comets to their perihelia may possibly mark the present state of astronomy to future ages.