THE tradition of dropping a ball in Times Square began more than a century ago when Adolph S. Ochs, the publisher of The New York Times, hired the sign maker Artkraft Strauss to build — then lower — a 700-pound wood-and-iron ball, five feet in diameter and illuminated by 100 25-watt bulbs, to mark the passage from 1907 to 1908. The ball descended slowly from a flagpole atop One Times Square, at the intersection of Broadway, Seventh Avenue and 42nd Street, where thousands witness it live — and millions more on television — each New Year’s Eve. The ritual echoes one that has taken place since 1833 at the Royal Observatory in Greenwich, England, where a ball is lowered daily at 1 p.m., originally to help ship captains nearby synchronize their chronometers. Beginning in 1845, there was also a ball dropped each noon at the United States Naval Observatory in Washington so inhabitants could reset their timepieces; it was eventually replaced by more advanced methods including today’s master clock system, which automatically resets using an atomic clock....