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 calculation 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 the equator; consequently his declination at these times is equal to the obliquity of the ecliptic (N. 152), which was formerly determined from the meridian length of the shadow of the stile of a dial on the day of a solstice. The lengths of the meridian shadow at the summer and winter solstices are recorded to have been observed at the city of Layang, in China, 1100 years before the Christian era. From these the distances of the sun from the zenith (N. 153) of the city of Layang are known. Half the sum of these zenith distances determines 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 whole chronology is founded on the observations 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 Bailly 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 918 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 were 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.