The geraniums grew in an oblong stone vessel, and no one ever thought much about it. But when Luke Irwin, a rug designer in the county of Wiltshire, England, hired workmen to lay electric cables under his yard, so that his son could have light in a barn when the family played table tennis, they uncovered an intricate mosaic floor of red, blue and white tiles only 18 inches down. Mr. Irwin called the local council, which sent archaeologists who discovered the remains of a lavish Roman villa under his extensive yard, and told him that the flowers were growing...