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° 51’, 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, 250,000 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 Chaldæan 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.