Hildegarde Withers is a third-grade teacher at Manhattan's Jefferson Elementary School. Miss Withers' class is on a field trip to the New York Aquarium, which, by the way, is the oldest continuously operating aquarium in the US. It was in Manhattan in the 1930s when Miss Withers' class visited; it is now in Coney Island.
Miss Withers uses her umbrella to trip up a fleeing pickpocket and in the melee she loses her hat pin. As the class searches for the pin, Miss Withers witnesses a body being tossed into the penguin pool. She raises the alarm and Inspector Oscar Piper arrives to investigate what turns out to have been a murder. And the murder weapon was Miss Withers' hat pin.
In The Penguin Pool Murder by Stuart Palmer, published in 1932, we are forcibly reminded of the costumes and customs of the era. Another important clue, in addition to the hat pin, is a bowler hat, or rather, a missing bowler hat. The murderer's hat fell into the penguin pool and he couldn't leave his hiding place without it. His hatlessness would stand out and the police would nab him immediately: autres temps, autres moeurs.