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goras, studied science in his travels in Egypt and elsewhere. He was held in so great reverence by all learned men that a problem which he set to the astronomers was the keynote to all astronomical investigation from this date till the time of Kepler in the sixteenth century. He proposed to astronomers the problem of representing the courses of the planets by circular and

Systematic observation among the Greeks began with the rise of the Alexandrian school. Aristillus and Timocharis set up instruments and fixed the positions of the zodiacal stars, near to which all the planets in their orbits pass, thus facilitating the determination of planetary motions. Aristarchus (320–250 B.C.) showed that the sun must be at least nineteen times as far off as the moon, which is far short of the mark. He also found the sun's diameter, correctly, to be half a degree. Eratosthenes (276–196 B.C.) measured the inclination to the equator of the sun's apparent path in the heavens i.e., he measured the obliquity of the ecliptic, making it 23° 5'1', confirming our knowledge of its continuous diminution during historical times. He measured an arc of meridian, from Alexandria to Syene (Assuan), and found the difference of latitude by the length of a shadow at noon, summer solstice. He deduced the diameter of the earth, 2.5o,ooo stadia. Unfortunately, we do not know the length of the stadium he used. Hipparchus (190–120 B.C.) may be regarded as the founder of observational astronomy. He measured the obliquity of the ecliptic, and agreed with Eratosthenes. He altered the length of the tropical year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes — still four minutes too much. He measured the equation of time and the irregular motion of the sun; and allowed for this in his calculations by supposing that the centre, about which the sun moves uniformly, is situated a little distance from the fixed earth. He called this point the excentric. The line from the earth to the “excentric’’ was called the line of apses. A circle having this centre was called the equant, and he supposed that a radius drawn to the sun from the excentric passes over equal arcs on the equant in equal times. He then computed tables for predicting the place of the sun. He proceeded in the same way to compute Lunar tables. Making use of Chaldaean eclipses, he was able to get an accurate value of the moon's mean motion. [Halley, in 1693, compared this value with his own measurements, and so discovered the acceleration of the moon's mean motion. This was conclusively established, but could not be explained by the Newtonian theory for quite a long time.] He determined the plane of the moon's orbit and its inclination to the ecliptic. The motion of this plane round the pole of the ecliptic once in eighteen years complicated the problem. He located the moon's excentric as he had done the sun's. He also discovered some of the minor irregularities of the moon's motion, due, as Newton's theory proves, to the disturbing action of the sun's attraction. In the year 134 B.C. Hipparchus observed a new star. This upset every notion about the permanence of the fixed stars. He then set to work to catalogue all the principal stars so as to know if any others appeared or disappeared. Here his experiences resembled those of several later astronomers, who, when in search of some special object, have been rewarded by a discovery in a totally different direction. On comparing his star positions with those of Timocharis and Aristillus he found no stars that had appeared or disappeared in the interval of 150 years; but he found that all the stars seemed to have changed their places with reference to that point in the heavens where the ecliptic is 90° from the poles of the earth — i.e., the equinox. He found that this could be explained by a motion of the equinox in the direction of the apparent diurnal motion of the stars. This discovery of precession of the equinoxes, which takes place at the rate of 52". I every year, was necessary for the progress of accurate astronomical observations. It is due to a steady revolution of the earth's pole round the pole of the ecliptic once in 26, ooo years in the opposite direction to the planetary revolutions. Hipparchus was also the inventor of trigonometry, both plane and spherical. He explained the method of using eclipses for determining the longitude. In connection with Hipparchus's great discovery it may be mentioned that modern astronomers have often attempted to fix dates in history by the effects of precession of the equinoxes. (1) At about the date when the Great Pyramid may have been built r Draconis was near to the pole, and must have been used as the pole-star. In the north face of the Great Pyramid is the entrance to an inclined passage, and six of the nine pyramids at Gizeh possess the same feature; all the passages being inclined at an angle between 26° and 27° to the horizon and in the plane of the meridian. It also appears that 4,000 years ago i.e., about 2 Ioo B.C. — an observer at the lower end of the passage would be able to see rDraconis, the then polestar, at its lower culmination." It has been suggested that the passage was made for this purpose. On other grounds the date assigned to the Great Pyramid is 2 123 B.c.

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(2) The Chaldaeans gave names to constellations now invisible from Babylon which would have been visible in 2000 B.C., at which date it is claimed that these people were studying astronomy.

(3) In the Odyssey, Calypso directs Odysseus, in accordance with Phoenician rules for navigating the Mediterranean, to keep the Great Bear “ever on the left as he traversed the deep " when sailing from the pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now would land the traveller in Africa. Odysseus is said in his voyage in springtime to have seen the Pleiades and Arcturus setting late, which seemed to early commentators a proof of Homer's inaccuracy. Likewise Homer, both in the Odyssey" (v. 272-5) and in the Iliad (xviii. 489), asserts that the Great Bear never set in those latitudes. Now it has been found that the precession of the equinoxes explains all these puzzles; shows that in springtime on the Mediterranean the Bear was just above the horizon, near the sea but not touching it, between 750 B.C. and I ooo B.c.; and fixes the

1 IIAmúðas r'éoopóvre kai ble Sisovra Boćrmy "Apktov 8", inv kai &uašav čmixAmaruv kaxeovoruv, "H r" auroi, or rpédérat kai T' 'Qptova Šokevet, Otm 6' du Mopos éatu Aoetpøv 'Qxeavoto. “The Pleiades and Boötes that setteth late, and the Bear, which they likewise call the Wain, which turneth ever in one place, and keepeth watch upon Orion, and alone hath no part in the baths of the ocean.” o

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