"The Sword of Damocles: A Story of New York Life" is not a specific literary work or known title in the public domain up to my last knowledge update in January 2022. However, the phrase "Sword of Damocles" is a well-known metaphorical expression that originated from a moral anecdote by the ancient Greek philosopher Cicero.

The story revolves around Damocles, a courtier of the tyrant Dionysius II of Syracuse. Damocles expressed envy for Dionysius's luxurious life and power. In response, Dionysius offered to switch places with Damocles for a day, placing him on the throne surrounded by opulence. However, above Damocles' head hung a sword suspended by a single hair of a horse's tail, symbolizing the constant and imminent peril that comes with great power.

If "The Sword of Damocles: A Story of New York Life" is a specific work, it might be a book, article, or other media created after my last update in 2022. I recommend checking contemporary sources or specific databases for the latest information on this title.