NEW YORK CITY: Police and city officials in New York are cheering an impressive, but somewhat uncomfortable crime statistic. For the first time since 1968, the number of murders committed in the city will drop below 1,000. As of Tuesday morning, the total stood at 978 deaths, fewer than half 1990's grisly record 2,245 killings. The symbolic importance of the 1,000-murder mark has not been lost on the Police Department or the press. In the days before New Yearĺs, the New York Post ran the tally each day on what looked like a big odometer. Meanwhile, police spent the holidays rounding up wanted wife-batterers and walking the beat outside nightclubs known for violence. Mayor Rudolph Giuliani and police chief Howard Safir (along with former chief William Bratton) are eagerly taking credit for the decline. Though previous Mayor David Dinkins deserves some credit for putting more cops on the beat, Giuliani allowed Bratton to do something Dinkins would never have approved: use those cops to crack down on minor offenders. This quality of life campaign tested a principle that Giuliani and Bratton had believed for years: the "Broken Windows" theory, first put forth in 1982 by criminologists James Q. Wilson and George L. Kelling, who argued that a city that tolerates minor violations creates a disorderly environment encouraging graver crimes. Sure enough, as arrests for small offenses rocketed, New York's streets became notably safer. It was these small arrests for such crimes as aggressive panhandling and minor theft, police believe, that have lowered New York to 63rd in homicides per 100,000 people. One reason: the greater vigilance raises everyoneĺs awareness that police are on the lookout for lawbreakers. But New York officials see another benefit: when people are arrested for relatively minor offenses, police often discover concealed weapons. Police say that this encourages criminals to leave guns at home, and as a result, shootings are down more than 50 percent in the past three years.