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transmitted to us, and by some correct notions which the Chaldeans and Egyptians entertained of the system of the World. The practical astronomy of these early ages seems to have been confined to the observations of the risings and the settings of the principal stars, their occultations by the moon and planets, and to the eclipses of the sun and moon. The most ancient observations of a definite character which have been transmitted to us, are those of three eclipses of the moon made in the years 719 and 720 B. C. These are cited by Ptolemy in the Almagest, and employed by him in determining the elements of the lunar motions.

Laplace says that astronomy is not less ancient in Egypt than in Chaldea. Long before the Christian era the Egyptians were acquainted with the excess of the year of one-fourth of a day above three hundred and sixty-five days; and a knowledge of this fact enabled them to construct the sothic period of 1460 years. It is probable, also, that they had methods of calculating eclipses.

Grecian astronomy also dates back several centuries before the Christian era. Thales, born in Miletus about 640 B. C., went to Egypt for instruction; and on his return he founded the celebrated Ionian school, in which he taught the sphericity of the earth, the obliquity of the ecliptic, and the true cause of the eclipses of the sun and moon; and he even predicted them. Anaximander, Anaximenes, and Anaxagoras were the successors of Thales; the first of whom invented the gnomon and geographical charts. Anaxagoras was persecuted by the Athenians for teaching that nature is governed by immutable laws.

From the Ionian school came Pythagoras, born at Samos, 590 B. c. He was at first a disciple of Thales; but this philosopher advised him to travel in Egypt, where he obtained a knowledge of the doctrines of the priests. He finally left his own country and retired to Italy, where he established his school. Here Pythagoras taught the doctrines of the Ionian school on a more extended scale. What particularly distinguishes the Pythagorean system of astronomy is the doctrine of the two motions of the earth, the annual and diurnal. The discoveries of this great man in the pure science of geometry are nearly equal to those in astronomy. The invention of the multiplication table and the discovery of the fortyseventh proposition of Euclid are due to Pythagoras.

After the death of Alexander, science seemed to decline in Greece, owing, perhaps, to the unsettled state of affairs

there. The establishment of the Alexandrine school by the second Ptolemy, however, gave a new impetus to the progress of astronomical science. The men of science who had been attracted thither were established in a vast edifice, which contained both an observatory and the celebrated Alexandrine library. Here they were supplied with whatever books and instruments were necessary to carry on their scientific labours. We see here, for the first time, a connected series of observations. Singular instruments were here employed, and trigonometrical methods were used in calculations. Here the celebrated Euclid, author of the Elements of Geometry, studied and taught.

Arystillus and Thimocares were the first observers of this rising school; they flourished about the year 300 B. C. Their observations of the principal stars of the zodiac enabled Hipparchus to discover the precession of the equinoxes; and Ptolemy founded his theory of the planets on their observations of those bodies. Here flourished the great astronomer Aristarchus, of Samos. "The most delicate elements of astronomy were the subjects of his investigations." He observed the summer solstice 281 B. C.; he measured the apparent magnitude of the sun, and the relative distances of the sun and moon, by a method which reflects great honour on the genius of that astronomer. His method was to observe the angular distance between the sun and moon, when the disk of the latter was just half enlightened, which makes known the three angles of a rightangled triangle, and this enabled him to find the ratio of the sun's distance to the moon's. In this way he found the distance of the sun about nineteen times as great as that of the moon. He also received the Pythagorean notion of the motion of the earth.

The successor of Aristarchus, Eratosthenes, is celebrated for his determination of the obliquity of the ecliptic, and for his measurement of the magnitude of the earth. He made the circumference of the earth equal to 250,000 stadia, but the length of this stadium is uncertain, so that we are unable to judge of the accuracy of the determination. Such then was the science of astronomy when Hipparchus began his researches.

Hipparchus was born at Nicæa, in Bithynia, about 200 B. C., but it is related by both Theon and Ptolemy that he made many celestial observations at Rhodes, and it is probable that the most of his works were composed at that place. It is also said that he made observations at Alexandria; but this is a point that cannot easily be

settled. "This great man," says Grant, "was at once a mathematician, an observer, and a theorist; and in all these capacities he exhibited powers of genius of the highest order: only two or three individuals can rank with him in the history of physical science."* "Not content with what had already been done, he determined to recommence every thing, and not to admit any results but those founded on a new examination of former observations, or on new observations, more exact than those of his predecessors."+

Hipparchus was probably the inventor and certainly the first to employ trigonometry in astronomical researches, by which the facility of fixing with precision the places of the celestial bodies, and of exhibiting the variations in their movements, was, in an important degree, augmented. He first distinguished himself by writing a commentary on the astronomical poem of Aratus. In this work he solved a problem of considerable intricacy, and of great practical utility in astronomical science in his day. He supposed a given star to be situated in the horizon, its right ascension and declination, and also the latitude of the place of observation to be known; and from these data he deduces the value of the diurnal arc described by the star, the longitude, right ascension of the point of the ecliptic which is in the horizon, the right ascension of the mid-heaven, and the culminating point of the ecliptic at the time when the star is in the horizon. A work which Hipparchus wrote on the simultaneous risings and settings of the stars, and one in twelve books on the calculation of a table of chord lines inscribed in a circle, are lost. The latter was probably to be used in computations in plane and spherical trigonometry similarly to that of a table of sines at the present day.

Much of the labour in a fixed observatory of the present day, is to observe the positions of the fixed stars, for they are the basis upon which the science of astronomy rests. They are a sort of landmarks to which reference is continually being made in determining the positions of a moving celestial body. Hipparchus conferred a great benefit on the science of the stars by forming a catalogue of 1080 of those which were called fixed. We are uncertain whether the positions of the stars were given by their right ascensions and declinations, or latitudes and longitudes. It is said that he was induced to form his

* His. Phys. Ast., p. ii. † Laplace, Syst. of the World, vol. ii., p. 267.

catalogue by the appearance of a temporary star which was visible in the day-time, so that posterity might tell whether new stars had made their appearance, or old ones passed away.

The ancient method of determining the situation of a star or planet, with respect to the equinox, was to obtain the distance of it in right ascension, or longitude, from the sun by the intervention of the moon. Because the sun and star could not be seen at the same time, the distance of the latter from the moon was measured, and from the known synodical motion of the moon her distance from the sun was found, and thence that of the star; and as the distance of the sun from the equinoctial points was known, the longitude of the star was thus ascertained.* But the errors in the solar and lunar tables in those times necessarily precluded all idea of accuracy in such determinations. Many centuries elapsed before the lunar movements were sufficiently well known to give the moon's place in the heavens with accuracy.

Another important discovery made by Hipparchus, is that of the precession of the equinoxes. Aristyllus and Thimocares, in observing the longitude of the star Spica Virginis, found it equal to 172°, and Hipparchus, one hundred and seventy years afterwards, found it equal to 174°, showing a change of 2° in the interval, or about 42" annually. As there was no change in the latitude of the star, the change in the longitude could easily be accounted for by supposing a retrograde movement of the equinoctial points. Modern astronomers, by comparing the position of Eta Canis Major, as given by Hipparchus, with its position in our day, find the annual precession equal to about 50' 8" greater than that astronomer's determination.

The length of the solar day, or the interval of two_successive arrivals of the sun to the meridian of any place, was found by Hipparchus, from his observations of the daily motion of the sun, to be variable in different seasons; and in order to reduce this to its mean value, he is said to have applied a correction similar to our equation of time. Another source of inconvenience then existing was the practice of beginning the day at sunrise. To remedy this Hipparchus changed the beginning of the day from sunrise to midnight. The modern astronomer makes the astronomical day begin at noon,

* Narrion's Origin and Prog. of Ast., p. 222.

and considers it as consisting of twenty-four hours, and not of twice twelve. The method of Hipparchus is still followed in reckoning time for civil purposes. "It is Worthy of observation, that in or before the time of Hipparchus, the hour of the night at which any phenomenon occurred, was determined, as we are informed by Ptolemy, by observing what star was on the meridian at the time; for the right ascension of the sun being known, the dif ference between this and the right ascension of the star is the time required."*

One of the principal objects of the astronomer is to determine the laws by which the movements of the sun, moon, and planets are regulated. As soon as Hipparchus had determined the positions of the principal fixed stars, he applied himself to the difficult task of investigating the theory of the motions of the sun and moon. Here he displayed the resources of his great genius, and we find him comparable in that respect to the greatest astronomers of modern times. The length of the tropical year is the first thing in the solar theory that must be determined with exactness; not only for the regulation of the calendar, but because the elements of the apparent orbit of the sun are dependent upon it. Astronomers before the time of Hipparchus had found this element by comparing the observations of the Chaldeans and Egyptians with those in their own day; but Hipparchus was not satisfied with those ancient observations, because they were not sufficiently exact, and he sought for some of a later date that would answer his purpose better. Sometimes the great length of time between two observations will more than compensate for the want of accuracy of one of them, but we cannot allow too great a margin of this kind. Aristarchus observed the time when the sun was at the summer solstice in the year 281 B. C., and 145 years afterwards Hipparchus made a similar observation of the same solstice and he found it to happen twelve hours, or half a day, later than it ought if the year had consisted exactly of 3651 days, a circumstance which shows that this latter period is in excess a little of the true length of the year, for exactly 145 years had elapsed; but by assuming the year to consist of 365 days, the time lacked half a day of making 145 years. If we divide 0-5 of a day by 145 we find 0-00345, which, being taken from 365 25, we have

*Narrion, p. 226.

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