FIG. circumstances in respect to thei 1247. The series y=A+ Br.. area. Let the intervals of x=0, 1, 2, 3, 4, &c. from the equation y ordinates AP, BQ,: ordinates AP, BQ, following cases. CASE I. For t Here =1, a + 1 b. CASE II. He the time of this prince, that the Greeks had rs of Egypt. It is therefore no wonder that impose upon them fictitious accounts of their the creation according to the account of MOSES. rd Year very well promoted their views; which, Sually signified the apparent annual revolution of the eant a revolution in general, and was used for that of RCH says, "the Egyptian year was a month;" he adds is it consisted of four months." And CENSORINUS says, quidem, antiquissimum ferunt annum bimestrem fuisse; post Rege quadrimestrem factum, novissimè ARMINON ad tredecim quinque perduxisse." At what distinct times these several e length of the year were made, would be an enquiry not to our pose; the Egyptians however, to impose upon the Greeks, would y take the shortest time for the year, that of a month. And this render the heathen chronology subject to great uncertainty. The Egyptians appear to have studied Astronomy very early; but the re of their year being for a considerable time subject to very different hs, caused great confusion in their chronology. The Thebans, who passinto Egypt, are supposed to have been the first who cultivated Astronomy ere. They established a year of 360 days; but it was soon found necessary add five days more. They seem to have founded their observations upon the heliacal rising of Sirius; for observing the interval between two days in which Sirius thus rose, they determined the length of the year. But it was afterwards discovered that by making the year to consist of 365 days, Sirius rose later every year by six hours. They then made the year to consist of 365 days. The year however, so far as regarded their religious ceremonies, still consisted of 365 days. Making therefore these two years to begin together, they would not coincide again till after four times 365 years, or 1460 years. This was called the Sothiacal period. Mr. E. BARNARD says, that the Egyptians discovered that the stars had an annual motion of 50". 9". 45" in a year (Phil. Trans. No. 158). According to MACROBIUS, the Egyptians made the planets revolve about the sun in the same order as we do; but it does not appear at what time the planets were discovered. He also says, that they divided the zodiac in the same manner as the Chaldeans did; and fixed the commencement at the first degree of Aries. DIODORUS SICULUS says, that the Egyptians discovered that the planets had sometimes a direct and sometimes a retrograde motion, and that they were sometimes stationary. He also asserts, that they made the sun move in a circle inclined to the equator, and in a direction contrary to the diurnal motion. The idea of dedicating the seven days of the week to the planets is also ascribed to them. DIOGENES LAERTIUS, from MANETHO, says, that the Egyptians believed the earth to be spherical, and that the moon was eclipsed by falling into the earth's shadow. They attempted to measure the diameter of the sun, by observing the motion of the shadow of the gnomon in the time the body of the sun was ascending above the horizon. The discovery of the planets and their motions we may consider as a proof of the early arrangement of the stars into constellations; as it must be by comparing the places of the planets with the fixed stars, that their motions could be discovered. 1252. When ALEXANDER took Babylon, CALLISTHENES found that the most ancient observations made by the Chaldeans were not above 1903 years before that time, which carries them to about the time of the dispersion of mankind by the confusion of tongues. These observations are supposed to have been made in the temple of JUPITER BELUS at Babylon. M. GOUET however thinks this account is not to be depended upon, as it was first published by SIMPLICIUS in the sixth century, who took it from PORPHYRY; and HIPPARCHUS and ProLEMY, who lived long before, knew nothing of them, though they made a very diligent search after the writings of the ancient Astronomers. They met with no observations made at Babylon before the time of NABONASSAR, who began to reign in the year 747 A. C. EPIGENES speaks of Babylonian observations for the space of 720 years. BEROSUS allows them to have been made 480 years before his time, which carries them back to 746 A. C. and this is in some measure confirmed by the oldest eclipses which are recorded by PTOLEMY, one of which is mentioned to have happened 721 years A. C. and two, 720 A. C. About this time, the Babylonians sent to HEZEKIAH to enquire about the shadow's going back on the dial of АHAZ. The period of 223 lunar months, comprehending 6585 days according to the Chaldeans, make the periodic time of the moon to be 27d. 7h. 43'. 13", and its synodic time to be 29d. 12h. 44. 7′′. They moreover determined its motion not to be uniform, but to be something more than 11° in a day and less than 12° when it moves slowest, and something more than 15° and less than 16° when it moves quickest; and the mean daily motion they fixed at 13°. 10'. 35". It does not appear by what methods they determined these matters; but it is probable that it was from observing the path of the moon by the fixed stars; for there are stars called by the Arabs, Minázil Al-Kamar, or Mansions of the Moon, by which is meant, such stars as the moon approaches at night in the course of its revolution. They were twenty-eight in number, the latitudes and longitudes of which are given by ULUGH BEIGH. It is also asserted by PTOLEMY, that they were acquainted with the motion of the nodes and apogee of the moon; and they supposed the former made a revolution in 18y. 15d. 8h. which period, containing 223 complete lunations, is usually called the Chaldean Saros. The 223 lunations they reckoned to contain 6585d. 8h. And if we take the period of the moon as now determined, they would make 6585d. 7h. 43', which shows how very nearly This pe the Chaldeans had determined the synodic revolution of the moon. riod completes the revolution in respect to the node and apogee. The knowledge of this might probably enable them to foretel eclipses, at least those of the moon. ARISTOTLE informs us, that the Chaldeans made observations on the occultations of the fixed stars and planets by the moon; from which they were led to conclude, that an eclipse of the sun was caused by the moon. And DIODORUS SICULUS speaks of their having observed comets, which they held to be lasting bodies, having revolutions like the planets, but in more extensive orbits. The same author also says, that "the southern parts of Arabia are made up of sandy plains of a prodigious extent; the travellers through which direct their course by the Bears, in the same manner as is done at sea." It appears therefore that the inhabitants were acquainted with some of the constellations. The Phoenicians were probably the first people who sailed by the stars. He further observes, that the Chaldeans made the annual motion of the sun oblique to the ecliptic, and contrary to the daily motion. Dialling was also first known amongst them, and long before any thing upon that subject is related by the Greeks. HERODOTUS says, that the Greeks borrowed the use of the Pole and Gnomon, and the method of dividing the day into twelve parts, from the Babylonians. The gnomon seems to have been the most ancient astronomical instrument. The Chaldeans made thirty-six constellations; twelve in the zodiac, and twenty-four without. They also made an observation on Saturn in the year 228 A. C. which is preserved by PTOLEMY, and it appears to be the only one which they made on the planets. The distance was measured by digits, of which 24 made a degree. They observed that the sun, moon and planets passed through the twelve signs; the sun in a year, the moon in a month, and that the planets had their particular periods. They placed the moon below all the stars and planets; made it the least of all; placed it nearest to the earth, and made the time of its revolution the least, according to DIODORUS SICULUS. Their civil year consisted of 365 days; and ALBATEGNIUS relates, that the Chaldeans made the sidereal year 365d. 6h. 11'. They formed some idea of the magnitude of the earth; for they discovered, it is said, that a man, walking a good rate, might follow the sun round the earth, that is, he might make the tour of the earth, in a year. Now if we allow a good rate to mean three miles in an hour, then there being 8760 hours in a year of 365 days, the circumference of the earth would be 26280 miles, which. does not differ a great deal from the truth. Respecting the Chaldean Astronomers, history gives us but a very little information. BEROSUs is supposed to be the oldest, from a very absurd opinion of his respecting the phases of the moon and its eclipses. According to him, the moon is a globe having one side luminous, and the other side a sky blue. At what time he lived is uncertain. On the Astronomy of the Chinese and Indians. 1253. M. BAILLY states, that the first king of the Indies lived about 3553 years before our æra; this is a little more than 400 years before their astronomical epoch, which is supposed by M. le GENTIL to be 3101 A.C. Their zodiac had two different divisions, one of twenty-eight, and another of twelve; and they divided their zodiac into twenty-seven constellations; they also had a moveable zodiac, to explain the precession of the equinoxes, the motion of which they stated at 54" in a year, and the entire revolution in 24000 years. This discovery they appear to have made about the year 2250 A.C. They regulated their chronology by periods of 60 years; but in their astronomical calculations, they employed the period of 3600 years, which is six times the lunisolar period. The Brahmins were acquainted with the obliquity of the ecliptic; and they constructed Tables showing the increase of the days arising from the change of the sun's declination, for different latitudes. M. le GENTIL found that according to these Tables, the obliquity of the ecliptic must have been more than 25°. They have a Table of the time which the sun employs to move through each sign of the ecliptic. The sign in which it moves slowest they make Gemini, and that in which it moves quickest is Sagittarius. The apogee of the sun was therefore less advanced by a sign when these Tables were constructed than it is now; this carries their construction back to the year 78 of our æra; at which time died SALIVAGENA, one of their kings, who was a great encourager of Astronomy. They applied also to the sun a correction which answers to our equation of the center, being subtractive in the first six signs of anomaly, and additive in the last six; the greatest subtractive is 25′, and answers to 20° of Gemini; and the greatest additive is 11', and answers to 20° of Sagittarius; this seems to have been the joint effect of two different corrections. The Brahmins also made use of the gnomon; and got a meridian by describing concentric circles, in the manner we do. By this they also found the latitude of the place from the length of its shadow at the day of the equinox. In the reign of d'HOANG-TI, 2697 years A. C. the Chinese had invented and constructed a sphere, with the various circles belonging to it. In a book written in the reign of YAO, about 2332 years A.C. we collect the following circumstances: 1st. Hi and Ho (two Astronomers, who were charged with composing a calendar for the people to regulate their husbandry) observed the places of the sun, moon and stars, and instructed the people with respect to the seasons. 2dly. The equality of days and nights, and the star Niao, determined the spring equinox. 3dly. The quality of days and nights, and the star Hiu, marked the autumnal equinox. 4thly. On the longest day, the star Ho marked the summer solstice, 5thly. On the shortest day, the star Mao mark |