With all this attention to astronomical matters it is not surprising that every great city boasted of an observatory, erected on the summit of a lofty tower. Astronomers were appointed by the state to take charge of these observatories, and to send in fortnightly reports to the king. Here are specimens of them, the first of which is dated B.C. 649:—'To the king, my lord, thy servant Istar-iddin-pal, one of the chief astronomers of Arbela. May there be peace to the king, my lord, may Nebo, Merodach, and Istar of Arbela, be favourable to the king, my lord. On the twenty-ninth day we kept a watch. The observatory was covered with cloud: the moon we did not see. (Dated) the month Sebat, the first day, the eponymy of Bel-kharran-Sadua.' 'To the king, my lord, thy servant Abil-Istar. May there be peace to the king, my lord. May Nebo and Merodach be propitious to the king, my lord. May the great gods grant unto the king, my lord, long days, soundness of body, and joy of heart. On the twenty-seventh day (of the month) the moon disappeared. On the twenty-eighth, twenty-ninth, and thirtieth days, we kept a watch for the eclipse of the sun. But the sun did not pass into eclipse. On the first day the moon was seen during the day. During the month Tammuz (June) it was above the planet Mercury, as I have already reported to the king. During the period when the moon is called Anu (_i.e._, from the first to the fifth days of the lunar month), it was seen declining in the orbit of Arcturus. Owing to the rain the horn was not visible. Such is my report. During the period when the moon was Anu, I sent to the king, my lord, the following account of its conjunction:—It was stationary and visible below the star of the chariot. During the period when the moon is called Bel (_i.e._, from the tenth to the fifteenth day), it became full; to the star of the chariot it approached. Its conjunction (with the star) was prevented; but its conjunction with Mercury, during the period when it was Anu, of which I have already sent a report to the king, my lord, was not prevented. May the king, my lord, have peace!' Astronomical observations imply a knowledge of mathematics, and in this the Babylonians and Assyrians seem to have excelled. Tables of squares and cubes have been found at Senkereh, the ancient Larsa, and a series of geometrical figures used for augural purposes presupposes a sort of Babylonian Euclid. The mathematical unit was 60, which was understood as a multiple when high numbers had to be expressed, IV, for example, standing for (4 × 60 =) 240. Similarly, 60 was the unwritten denominator of fractional numbers. The plan of an estate outside the gate of Zamama at Babylon, and belonging to the time of Nebuchadnezzar, has been discovered, while the famous Hanging Gardens of that city were watered by means of a screw.