American and Egyptian archaeologists have discovered a rare structure called a nilometer in the ruins of the ancient city of Thmuis in Egypt’s Delta region. Likely constructed during the third century B.C., the nilometer was used for roughly a thousand years to calculate the water level of the river during the annual flooding of the Nile. Fewer than two dozen of the devices are known to exist. Before the completion of the Aswan High Dam in 1970, the Nile flooded the surrounding plains each year in late July or August. As the waters receded in September and October, they left...