During the last half of the 18th century, my estimate is that there were 222 inhabitants per police personnel in Paris. In American cities of 1,000,000 inhabitants or more, the 2009 number is roughly the same: 232 inhabitants per police employee. And don’t forget that ID papers and technology now make them much more efficient at tracking individuals. Some progress!
Sources: For Paris: Marc Chassaigne (1906), La Lieutenance générale de police (Genève: Slatkine_Megariotis, 1975); for the US: http://www2.fbi.gov/ucr/cius2009/data/table_74.html.