omical calculations. A consideration of the Chaldaean and Egyptian systems, in connection with that of the Chinese, leads to the conclusion of the greater antiquity of the latter as a primitive and very simple equation of lunar and solar years. The Egyptian periods, called Trikontæteridæ, or festivals held every thirty years, are thought to be explainable by the cycle of 60 years, which is supposed to have been divided into two parts in order to give each king the opportunity of having them celebrated in his reign. In his work on Isis and Osiris (c. 75), Plutarch unquestionably alludes to this cycle, when he says that the sixty eggs of the crocodile and the sixty years that it lived were admitted by persons skilled in astronomy to be symbolical, to be the first measure or lowest unit of the equation of time. At the end of every . 60 years there was a difference of half a month between the fixed tropical and the vague civil year. When Martini asserts that the Egyptians computed by the Era of 60 years of Hoangho? he doubtless ment Hoang-Ti. We find the Indians to have commenced their cycles with the rude equation of five years; but it is supposed they made use of one of 12X5 or 60 years as a corrective formula. But there is no proof of their being acquainted with the Chaldee cycle of 600 years, which evidently belongs to a date posterior to that people's having made a remarkable advancement in science. But, in regard to the Chinese, Ideler (p. 214) has fully established that they used a lunar year, which they regulated by the solar year of 365 days. It is, also, satisfactorily proven that they used a sexagesinal cycle for days, months (of 5 years, 5X12=60) and years. The cycle for days implies a year of 6×60=360 days, as well as a fixed lunar year. Their Metonic cycle of 19 years, equaling 235 synodic months (that is, 19×12=228+7 intercallary months), only occurs after the time of Han, whose dynasty embraced the beginning of the Christian era. Still they must have used, prior to that time, a cycle for the same purpose of equation, and everything tends to the conclusion that it was one of 60 years; for the cycle of 60 days can be explained by it; and the cycle of 60 years must have been so arranged that after a certain period the annual cycle was again coincident with the first daily cycle. There appears, it is true, no direct mention of it in the Shuking; and the * That is, 60 years=60X12=720+22 [intercallary months]=742 months. notation of the Annals by means of it after the time of Yao, as appears in their present arrangement, may have been afterwards introduced by calculation. Yet, even if not in use therein, it is universally admitted that this system is well adapted to the old chronology. One circumstance is seen by Ideler to be explained by it, which he fails to perceive is explainable in any other way; this is, that the year so arranged by Yu gradually got into such disorder, that, instead of beginning at the sign of Aquarius, it receded into the sign of Sagittarius. In the idea of Freret it must have been computed as follows: 60 solar years=742 months- 2 days and 20 hours. Therefore, in 600 years=7420 months-28 days=1 small lunar month of 29 days with far less error than the Julian intercallary period, which is 1 day in excess every 125 years. Now, as made out from Ideler (78 seq.) the following divisions of time were in use among the Chaldaeans: 1. The year of 12 years, the Annus Chaldaeaus of Censorinus, for the fertility of the years. Scaliger found that the 12 yearly zodiacal cycle, which is in use among the Tartars, Mongols, Mandschus, Igurians, the Thibetans, Japanese and Siamese, dated from the earliest times. Among some of the Tartaric peoples, however, this is a cycle of 60 years (12×5). 2. The cycles of 60 years-600 years-3600 years. When we find, in connection with this system, that 600 years give an excess of one lunar month with much greater accuracy than the Julian year, we conclude it probable that this cycle must have been in use among the Chinese, it being indispensable where that of 60 years was in use; or it must have been in use with those from whom they borrowed the latter. The Saros cycle of 6X600-3600 years does not pertain to the equation of the year of 365 days with the lunations. Wherever the lunar year was the one in general use it was only necessary to intercallate months not years as was the case with the Egyptians. The Chinese Cosmic year of 129,600 years mentioned by Shao Kang-tsi and Tshu-hi (Neuman, p. 59), also implies the periods of 60 and 600 years: For 129,600-6X6X6=216×600 =2160X60: Then 2160-6×360, a multiple which hardly can be accidental. It is generally admitted that the year of 360 days has in it so much astronomical significance that it must have been a good deal recognized in the ancient calculations. For, first, 360=12×30; and, secondly, the three decades into which the month is divided imply a reference to 30, the number of days in a month as being the standard for the year. In the "little" month the decade consists of only nine days. Now, it being admitted that the Chinese, from the earliest times, made use of a sexagesimal cycle for the division of the year=6×60 days, and that they marked the years by a cycle of 60 years, running concurrently with the cycle of days, what, it may be asked, have we to learn from this? 1st. We conclude that this cycle must have been instituted originally at a time when the first day of the daily cycle coincided with the first year of the annual cycle, that is, when they commenced on the same day. To find out when this was some think impossible, owing to the irregularity of the old calendar; but it might, possibly, by the patient collection and collation of the ancient data be ultimately ascertained. In regard to astronomical observations, for example, Laplace found that the notice about the size of the sun's shadow, as observed by the viceroy Tsheu-Kung, about 1100 B. C., was singularly correct. By this prince, the brother of Wuwang, the founder of the Tsheu dynasty, was the shadow measured at the solstice. Of the most ancient astronomical entry in the Shuking (chap. Y hiün) the date, according to Gaubil (in his Lettres Edifiantes, pp. 322; comp. 272) is the first year of Tai-Kia, the second ruler of the Shang. But the most important entry is in the first chapter of that record. The signs of the four cardinal points of the year are there noted in the reign of Yao. By inspection and calculation Ideler found that they were exactly correct for a period of about 4000 years before 1837 A. D., that is, to about 2163 B. C.; and this, according to the most trusted authorities, as seen above, is near the time set down for Yao's reign. But, according to the chronology of the celestial empire now in use, which has been framed on no sufficiently limited basis, it is placed in the year 2300 B. C. If after sufficient research and accumulation an attempt should be made to fix the ancient chronology care should be taken that the data be properly understood. It is easy, for instance, to calcu late backwards eclipses of the sun as the Romans, Greeks and Egyptians have done. But phenomena of rare occurrences, which are difficult to calculate, such as the conjunctions of the planets, must be either contemporary notices of some extraordinary phenomena or sheer inventions. One instance that may be mentioned is the observation of a conjunction of five planets (among which the sun and moon are spoken of) on the first day of Leitshin in the reign of Tsheuen-hiu, the second successor of Hoang-Ti. Suppose this were the conjunction of the three upper planets, to which Kepler first directed his attention in reference to the date of Christ's birth, and which occurs every 794 years and four months; then it occurred in the following years: This last date might answer to the conjunction in the time of Tscheuen-hiu; for, according to the official Chinese Tables, as given in Ideler's work, he reigned from 2513 to 2436; but the dates vary to the extent of more than 200 years and the year 2375 comes within the limits of these fluctuations. AS TO THE PRIMITIVE DIVISIONS OF THE YEAR AMONG THE CHINESE: On this most of our information is derived from Gaubil and is as follows: 1. In the s nd dynasty the day commenced at mid-day. The founder of the third dynasty, Wee-wang, fixed it at midnight. 2. The week of seven days (Zi = 7) is proved by the 28 lunar stations to be of great antiquity among the Chinese, but it was by them only for astrological purposes. It plainly depended, originally upon the four lunar phases, but in China, as elsewhere, it was connected with a certain succession of the planets. Gaubil says Confucius mentions the Zi-week as being in use in the time of Tsheu, the third dynasty: 3. Their solar year of 365 days the Chinese began to reckon from the day of the winter solstice, which they fixed by observation of the longest shadow on the ground at midday. 4. Their civil year commenced at the lunar month in which the sun entered Pisces. This is determined by the conjunction in Aquarius. The beginning of the first moon is the new moon in Aquarius, consequently the vernal equinox is the full moon of the second moon, the Autumnal equinox the full moon of the eighth. With the full moon of the fifth and tenth months the solstice coincides. The Chinese have four seasons of three months each, being the first, second and third moons of each season. They are divided into six sections (zi tshi) of 15 to 16 days. Hence they divide the ecliptic into 24 equal parts, each containing half a sign. 4. 66 = 1. Zi tshi. Winter Solstice, Dec. 21 = beginning of Capricorn. Beginning of Spring, Feb. 5 middle of Capricorn 45 days before the vernal equinox. Sidsuen the first new moon of the year. = = Vernal equinox = March 22 = beginning of Aries. = The beginning of their civil year, as above is seen in the month nearest to the middle of Aquarius, is said to have been instituted by Tshuen-hiü (2513-2436 B. C.), that is, one of the kings prior to Yu, the first historical dynast, so called. The great Yu farther ordained that the first month of Spring, that is, the month in which the sun entered into Pisces (Gaubil, |